Vorticity Fluctuations in Plane Couette Flow
Ortiz de Zarate, Jose; Sengers, Jan V.
2010-11-01
In this presentation we evaluate the flow-induced amplification of the thermal noise in plane Couette configuration. The physical origin of the noise is the random nature of molecular collisions, that contribute with a stochastic component to the stress tensor (Landau's fluctuating hydrodynamics). This intrinsic stochastic forcing is then amplified by the mode- coupling mechanisms associated to shear flow. In a linear approximation, noise amplification can be studied by solving stochastic Orr-Sommerfeld and Squire equations. We compare the efficiency of the different mechanisms, being the most important the direct coupling between Squire and Orr-Sommerfed equations. The main effect is to amplify wall-normal vorticity fluctuations with an spanwise modulation at wave number around 1.5, a configuration that resembles the streaks that have been proposed as precursors of the flow instability.
Homotopy between plane Couette flow and Pipe flow
Nagata, Masato; Deguchi, Kengo
2014-11-01
In order to investigate symmetry connections between two canonical shear flows, i.e. plane Couette (PCF) and pipe flow (PF), which are linearly stable for all Reynolds numbers and therefore undergo subcritical transition, we take annular Poiseuille-Couette flow (APCF) as an intermediary Although PCF and PF are very different geometrically, APCF recovers PCF by taking the narrow gap limit, and also PF by taking the limit of vanishing inner cylinder where a homotopy of the basis functions from no-slip to regular conditions at the centre is considered. We show that the double-layered mirror-symmetric solutions in sliding Couette flow (APCF without axial pressure gradient) found by Deguchi & Nagata (2011) can be traced back to the mirror-symmetric solutions in PCF. Also we show that only the double-layered solution successfully reaches the PF limit, reproducing the mirror-symmetric solution in PF classified as M1 by Pringle & Kerswell (2007).
Linear Instability of the Plane Couette and Plane Poiseuille Flows
Chefranov, Sergey G
2015-01-01
We show possibility of the Plane Couette (PC) flow instability for Reynolds number Re>Reth=140. This new result of the linear hydrodynamic stability theory is obtained on the base of refusal from the traditionally used assumption on longitudinal periodicity of the disturbances along the direction of the fluid flow. We found that earlier existing understanding on the linear stability of this flow for any arbitrary large Reynolds number is directly related with an assumption on the separation of the variables of the spatial variability for the disturbance field and their periodicity in linear theory of stability. By the refusal from the pointed assumptions also for the Plane Poiseuille (PP) flow, we get a new threshold Reynolds value Reth=1040 that with 4% accuracy agrees with the experiment contrary to more than 500% discrepancy for the earlier known estimate Reth=5772 obtained in the frame of the linear theory but when using the "normal" disturbance form (S. A. Orszag, 1971).
Linear stability of plane creeping Couette flow for Burgers fluid
Hu, Kai-Xin; Peng, Jie; Zhu, Ke-Qin
2013-02-01
It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simplified perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.
Emergence of stochastic dynamics in plane Couette flow
Gvalani, Rishabh
2016-01-01
Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between laminar and turbulent flows, little is known of their dynamics. We investigate here the temporal dynamics of such steady spatially localized solutions in the context of plane Couette flow. These solutions exist on oscillating branches in parameter space. We consider the saddle-nodes of these branches as initial conditions of simulations run with offset Reynolds numbers. We observe a relaminarization regime mostly characterized by deterministic dynamics and identify within this regime the existence of parameter intervals in which the results are stochastic and long-lived chaotic transients are observed. These results are obtained below the threshold for transition, shed light on the emergence of stochasticity in transitional plane Couette flow and will likely inform a ra...
Snakes and ladders: localized solutions of plane Couette flow
Schneider, Tobias M; Burke, John
2009-01-01
We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in space. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming PDE systems. These new solutions are a step towards extending the dynamical systems view of transitional turbulence to spatially extended flows.
Direct numerical simulation of turbulent plane Couette flow
Lee, Moon Joo
1991-01-01
Turbulent plane Couette flow was numerically simulated at a Reynolds number (U(sub w)h/nu) of 6000, where U(sub w) is the relative wall speed and h is half the channel-height. Unlike in Poiseuille flow, where the mean shear rate changes its sign at the centerline, the sign of mean shear rate in plane Couette flow remains the same across the whole channel. This difference is expected to yield several differences between the two flows, especially in the core region. The most significant and dramatic difference observed was the existence of large-scale structures in the core region of the plane Couette flow. The large eddies are extremely long in the flow direction and fill the entire channel (i.e., their vertical extent is 2h). The large-scale structures have the largest contribution from the wavenumber (k(sub x)h,k(sub z)h) = (0, plus or minus 1.5), corresponding to a wavelength lambda(sub z)/h is approximately equal to 4. The secondary motion associated with the k(sub x)h = 0 mode consists of the large-scale vortices. The large eddies contribute about 30 percent of turbulent kinetic energy.
Traveling hairpin-shaped fluid vortices in plane Couette flow.
Deguchi, K; Nagata, M
2010-11-01
Traveling-wave solutions are discovered in plane Couette flow. They are obtained when the so-called steady hairpin vortex state found recently by Gibson [J. Fluid Mech. 638, 243 (2009)] and Itano and Generalis [Phys. Rev. Lett. 102, 114501 (2009)] is continued to sliding Couette flow geometry between two concentric cylinders by using the radius ratio as a homotopy parameter. It turns out that in the plane Couette flow geometry two traveling waves having the phase velocities with opposite signs are associated with their appearance from the steady hairpin vortex state, where the amplitude of the phase velocities increases gradually from zero as the Reynolds number is increased. The solutions obviously inherit the streaky structure of the hairpin vortex state, but shape preserving flow patterns propagate in the streamwise direction. Other striking features of the solution are asymmetric mean flow profiles and strong quasistreamwise vortices which occupy the vicinity of only the top or bottom moving boundary, depending on the sign of the phase velocity. Furthermore, we find that the pitchfork bifurcation associated with the appearance of the solution becomes imperfect when the flow is perturbed by a Poiseuille flow component.
Linear stability of plane creeping Couette flow for Burgers fluid
Institute of Scientific and Technical Information of China (English)
Kai-Xin Hu; Jie Peng; Ke-Qin Zhu
2013-01-01
It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable.However,for Burges fluid,which includes UCM and Oldroyd-B fluids as special cases,unstable modes are detected in the present work.The wave speed,critical parameters and perturbation mode are studied for neutral waves.Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different.At low Reynolds number limit,analytical solutions are obtained for simplified perturbation equations.The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.
2006-03-01
COUETTE & POISEUILLE FLOWS OF NEMATIC POLYMERS IN VISCOUS SOLVENTS: MORPHOLOGY IN MOLECULAR ORIENTATION, STRESS & FLOW Hong Zhou...viscoelastic stresses, and flow feedback. Pre- vious studies in plane Couette & Poiseuille flow (with the exception of [7]) have focused on the coupling between...with Plane Couette & Poiseuille Flows of Nematic Polymers in Viscous Solvents: Morphology in Molecular Orientation, Stress & Flow 5a. CONTRACT
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
A streamwise constant model of turbulence in plane Couette flow
Gayme, D. F.; McKeon, B. J.; Papachristodoulou, A.; Bamieh, B; Doyle, J. C.
2010-01-01
Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier–Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity p...
How does turbulence spread in plane Couette flows?
Couliou, Marie
2015-01-01
We investigate the growth in the spanwise direction of turbulent spots invading a laminar flow in a plane Couette flow. Direct Numerical Simulation is used to track the nucleation of streaks during the spot growth. Experiment and direct numerical simulation allow us to study the velocity of the spot fronts and of the vortices observed at the spots' edges. All these results show that two mechanisms are involved when turbulent spots grow: a formerly proposed local growth occurring at the spot spanwise tips but also in comparable proportion a global growth induced by large-scale advection identified in the present work.
Geometry of state space in plane Couette flow
Cvitanović, P.; Gibson, J. F.
A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear flows (such as pipes and plane Couette flow) result from close passes to weakly unstable invariant solutions of the Navier-Stokes equations. These 3D, fully nonlinear solutions (equilibria, traveling waves, and periodic orbits) structure the state space of turbulent flows and provide a skeleton for analyzing their dynamics. We calculate a hierarchy of invariant solutions for plane Couette, a canonical wall-bounded shear flow. These solutions reveal organization in the flow's turbulent dynamics and can be used to predict directly from the fundamental equations physical quantities such as bulk flow rate and mean wall drag. All results and the code that generates them are disseminated through through our group's open-source CFD software and solution database Channelflow.org and the collaborative e-book ChaosBook.org.
Linear instability of plane Couette and Poiseuille flows
Chefranov, S. G.; Chefranov, A. G.
2016-05-01
It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Reth ≈ 139, which agrees with the experimental value of Reth ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicity in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Reth ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Reth ≈ 5772 obtained in the framework of the linear theory under assumption of the "normal" shape of disturbances [2].
Low-order invariant solutions in plane Couette flow
Ahmed, Muhammad; Sharma, Ati
2016-11-01
Ten new equilibrium solutions of the Navier-Stokes equations in plane Couette flow are presented. The new solutions add to the inventory of known equilibria in plane Couette flow found by Nagata JFM 1990, Gibson JFM 2008, 2009, and Halcrow JFM 2008, who together found 13. These new solutions elucidate the low-dimensional nature of exact coherent structures, which are essential to defining simplified mechanisms that explain the self-sustaining nature of wall-bounded flows. In particular, one of the solutions found has a one-dimensional unstable manifold in the symmetry-invariant subspace and otherwise, like the lower branch equilibrium solution found by Nagata JFM 1990. A new method for generating initial guesses for Newton-Krylov-hookstep (NKH) searches is also presented. This method allows the NKH algorithm to find equilibrium solutions that are derived from previous solutions. Air Force Office of Scientific Research (European Office of Aerospace Research and Development) under award FA9550-14-1-0042.
On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles
2006-01-01
SIAM J. APPL. MATH. c© 2006 Society for Industrial and Applied Mathematics Vol. 66, No. 4, pp. 1227–1260 ON WEAK PLANE COUETTE AND POISEUILLE FLOWS ...anisotropic elasticity; to compare Couette versus Poiseuille flow ; and to consider dynamics and stability of these steady states within the asymptotic model...On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6
Particle Tracking Velocimetry in Transitional Plane Couette Flow
Lüthi, B.; Holzner, B.; Kinzel, M.; Liberzon, A.; Tsinober, A.
Plane Couette flow has the peculiar property that transition to turbulence occurs despite the fact that its laminar profile is linearly stable. For high enough Reynolds numbers small amplitude perturbations are enough to initiate the growth of turbulent spots. Such spots have been subject to investigation for a few decades, see e.g. [1, 2]. In addition, it has been observed that around transitional Reynolds numbers laminar and turbulent regions can co-exist if this Reynolds number is approached from the turbulent side, e.g., [3, 4]. For both cases, distinct interfaces divide the regimes between turbulent and non turbulent flow. It is our main interest to study the evolution of such interfaces similar to the work of [5] where the shear free case with inhomogeneous forcing by an oscillating grid has been investigated in detail.
Enhancement of thermal fluctuations in Plane Couette Flow
Ortiz de Zarate, Jose M.; Sengers, Jan V.
2011-11-01
Mode-coupling phenomena in systems outside equilibrium generically cause an enhancement of thermal fluctuations. These enhancements can be studied by Landau's fluctuating hydrodynamics. Here we present a detailed study for the case of plane Couette flow based on stochastically forced Orr-Sommerfeld and Squire equations. The forcing arises from random contributions to the stress tensor due to the stochastic nature of molecular collisions. This intrinsic stochastic forcing is then amplified by mode- coupling mechanisms associated with the shear flow. We discuss the different coupling mechanisms, the most important one being the direct coupling between fluctuations of the wall-normal velocity and vorticity. The most pronounced effect is amplification of wall-normal vorticity fluctuations with a spanwise modulation at dimensionless wave numbers q∥ around 1.5. Financial support: MICINN FIS2008/03801.
Symmetry Broken Exact Coherent Structures in Plane Couette Flow
Gopalaswamy, Varchas; Borrero-Echeverry, Daniel
2015-11-01
Invariant solutions of the fully resolved Navier-Stokes equation, known as exact coherent structures (ECS) are an exciting and potentially revolutionary method for understanding turbulent dynamics. The geometry of plane Couette flow leads to the existence of ECS with a high degree of symmetry. However, turbulent flows do not display a high degree of symmetry, so it is unclear whether these symmetric ECS can truly capture the turbulent dynamics. We report the discovery of four new periodic orbits - P85 and P60 which are fully symmetric, and P32 and P8, which have partially broken symmetry. Projections of these periodic orbits in the dissipation-energy input plane reveal that P32, P60 and P85 lie in the turbulent region of the state space, whereas P8 lies very far away from this region. Parametric continuation in the spanwise periodic cell length Lz suggests that P8 undergoes two bifurcations, which are verified by analysis of various properties of P8 in the dissipation-energy input plane, and by observations of changes in the stability of eigenvectors that are consistent with bifurcations.
Amplification and Nonlinear Mechanisms in Plane Couette Flow
Gayme, Dennice F; Bamieh, Bassam; Papachristodoulou, Antonis; Doyle, John C
2010-01-01
We study the input-output response of a streamwise constant projection of the Navier-Stokes equations for plane Couette flow, the so-called 2D/3C model. Study of a streamwise constant model is motivated by numerical and experimental observations that suggest the prevalence and importance of streamwise and quasi-streamwise elongated structures. Periodic spanwise/wall-normal (z-y) plane stream functions are used as input to develop a forced 2D/3C streamwise velocity field that is qualitatively similar to a fully turbulent spatial field of DNS data. The input-output response associated with the 2D/3C nonlinear coupling is used to estimate the energy optimal spanwise wavelength over a range of Reynolds numbers. The results of the input-output analysis agree with previous studies of the linearized Navier-Stokes equations. The optimal energy corresponds to minimal nonlinear coupling. On the other hand, the nature of the forced 2D/3C streamwise velocity field provides evidence that the nonlinear coupling in the 2D/3...
A Streamwise Constant Model of Turbulence in Plane Couette Flow
Gayme, D F; Papachristodoulou, A; Bamieh, B; Doyle, J C
2010-01-01
There is a consensus that turbulent flow is characterized by coherent structures. In particular, streamwise and quasi-streamwise elongated structures have been observed in both numerical simulations and experiments. Using this idea the mean behavior of fully turbulent plane Couette flow is modeled using a streamwise constant projection of the Navier Stokes equations. This assumption results in a two dimensional, three velocity component (2D/3C) model. We first use a steady state version of this 2D/3C model to demonstrate that the nonlinear coupling in the equations provides the mathematical mechanisms associated with the shape of the turbulent velocity profile. In simulating the full model we borrow some ideas from robust control and represent uncertainty as well as modeling errors using small amplitude noise forcing. Simulations of the 2D/3C model under small amplitude Gaussian forcing of the cross stream components is compared to DNS data. The results indicate that a streamwise constant projection of the Na...
Plane Couette-Poiseuille flow past a homogeneous poroelastic layer
Alexiou, Terpsichori S.; Kapellos, George E.
2013-07-01
An analytical solution is presented for the problem of fully developed plane Couette-Poiseuille flow past a homogeneous, permeable poroelastic layer. Main novel feature of this work is that the compressibility, which is related to the action of the free-fluid pressure on the poroelastic layer, is taken into account. Therefore, the solid stress problem is two-dimensional, although the fluid flow problem remains one-dimensional in the limit of infinitesimal strain. The pressure-related compressibility affects strongly the distribution of the von Mises stress in the poroelastic layer by shifting the local maximum towards the high-pressure region of the channel. Furthermore, the established analytical solution is used to investigate some aspects of the mechanotransducing role of the endothelial surface layer. A compressible surface layer might serve as a "bumper'' by reducing the magnitude of the overall shearing force (viscous and elastic) acting on endothelial cells, as compared to the magnitude of the fluid shear force that would be exerted in its absence.
Study of shear-thinning/thickening effects on plane Couette-Poiseuille flow with uniform crossflow
Institute of Scientific and Technical Information of China (English)
刘玉泉; 朱克勤
2014-01-01
The shear-thinning/thickening effects on the plane Couette-Poiseuille flow with a uniform crossflow are studied. The detailed solution procedures for both theo-retical and numerical purposes are given. In order to clarify the difference between the Newtonian flow and the power-law flow, all cases of the plane Couette-Poiseuille flows with uniform crossflows for different power indexes are assigned to the phase diagram in the parameter plane corresponding to the Couette number and the crossflow Reynolds number. The effects of shear-thinning/thickening on the phase diagram are discussed. An important feature of the shear-thinning circumstance distinguished from the shear-thickening circumstance is discovered.
Large scale flows in transitional plane Couette flow: a key ingredient of the spot growth mechanism
Couliou, M
2015-01-01
Using Particle Image Velocimetry (PIV) in a new experimental plane Couette flow, we investigate the dynamics of turbulent patches invading formerly laminar flows. We evidence experimentally for the first time in this geometry the existence of large scale flows. These flows appear as soon as laminar and turbulent domains coexist. Spectral analysis is used to study the dynamical evolution of these large scales as well as that of the small scales associated with turbulence. We show that large-scale flows grow before turbulent spots develop and we point out the crucial role they play in the growth mechanism and possibly also in the emergence of organised patterns.
Homoclinic snaking in plane Couette flow: bending, skewing, and finite-size effects
Gibson, John F
2015-01-01
Invariant solutions of shear flows have recently been extended from spatially periodic solutions in minimal flow units to spatially localized solutions on extended domains. One set of spanwise-localized solutions of plane Couette flow exhibits homoclinic snaking, a process by which steady-state solutions grow additional structure smoothly at their fronts when continued parametrically. Homoclinic snaking is well understood mathematically in the context of the one-dimensional Swift-Hohenberg equation. Consequently, the snaking solutions of plane Couette flow form a promising connection between the largely phenomenological study of laminar-turbulent patterns in viscous shear flows and the mathematically well-developed field of pattern-formation theory. In this paper we present a numerical study of the snaking solutions, generalizing beyond the fixed streamwise wavelength of previous studies. We find a number of new solution features, including bending, skewing, and finite-size effects. We show that the finite-si...
Kawata, Takuya; Alfredsson, P. Henrik
2016-07-01
Plane Couette flow under spanwise, anticyclonic system rotation [rotating plane Couette flow (RPCF)] is studied experimentally using stereoscopic particle image velocimetry for different Reynolds and rotation numbers in the fully turbulent regime. Similar to the laminar regime, the turbulent flow in RPCF is characterized by roll cells, however both instantaneous snapshots of the velocity field and space correlations show that the roll cell structure varies with the rotation number. All three velocity components are measured and both the mean flow and all four nonzero Reynolds stresses are obtained across the central parts of the channel. This also allows us to determine the wall shear stress from the viscous stress and the Reynolds stress in the center of the channel, and for low rotation rates the wall shear stress increases with increasing rotation rate as expected. The results show that zero absolute vorticity is established in the central parts of the channel of turbulent RPCF for high enough rotation rates, but also that the mean velocity profile for certain parameter ranges shows an S shape giving rise to a negative velocity gradient in the center of the channel. We find that from an analysis of the Reynolds stress transport equation using the present data there is a transport of the Reynolds shear stress towards the center of the channel, which may then result in a negative mean velocity gradient there.
Mean flow of turbulent-laminar patterns in plane Couette flow
Barkley, D; Barkley, Dwight; Tuckerman, Laurette S.
2007-01-01
A turbulent-laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x,y,z) = U_0(y) + U_c(y) cos(kz) + U_s(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic compu...
On the stability of plane Couette-Poiseuille flow with uniform cross-flow
Guha, Anirban
2010-01-01
We present a detailed study of the linear stability of plane Couette-Poiseuille flow in the presence of a cross-flow. The base flow is characterised by the cross flow Reynolds number, $R_{inj}$ and the dimensionless wall velocity, $k$. Squire's transformation may be applied to the linear stability equations and we therefore consider 2D (spanwise-independent) perturbations. Corresponding to each dimensionless wall velocity, $k\\in[0,1]$, two ranges of $R_{inj}$ exist where unconditional stability is observed. In the lower range of $R_{inj}$, for modest $k$ we have a stabilisation of long wavelengths leading to a cut-off $R_{inj}$. This lower cut-off results from skewing of the velocity profile away from a Poiseuille profile, shifting of the critical layers and the gradual decrease of energy production. Cross-flow stabilisation and Couette stabilisation appear to act via very similar mechanisms in this range, leading to the potential for robust compensatory design of flow stabilisation using either mechanism. As...
Turbulent statistics and flow structures in spanwise-rotating turbulent plane Couette flows
Gai, Jie; Xia, Zhenhua; Cai, Qingdong; Chen, Shiyi
2016-09-01
A series of direct numerical simulations of spanwise-rotating turbulent plane Couette flows at a Reynolds number of 1300 with rotation numbers Ro between 0 and 0.9 is carried out to investigate the effects of anticyclonic rotation on turbulent statistics and flow structures. Several typical turbulent statistics are presented, including the mean shear rate at the centerline, the wall-friction Reynolds number, and volume-averaged kinetic energies with respect to the secondary flow field, turbulent field, and total fluctuation field. Our results show that the rotation changes these quantities in different manners. Volume-averaged balance equations for kinetic energy are analyzed and it turns out that the interaction term acts as a kinetic energy bridge that transfers energy from the secondary flow to the turbulent fluctuations. Several typical flow regimes are identified based on the correlation functions across the whole channel and flow visualizations. The two-dimensional roll cells are observed at weak rotation Ro=0.01 , where alternant clustering of vortices appears. Three-dimensional roll cells emerge around Ro≈0.02 , where the clustering of vortices shows the meandering and bifurcating behavior. For moderate rotation 0.07 ≲Ro≲0.36 , well-organized structures are observed, where the herringbonelike vortices are clustered between streaks from the top view of three-dimensional flow visualization and form annuluses. More importantly, the vortices are rather confined to one side of the walls when Ro≤0.02 and are inclined from the bottom to upper walls when Ro≥0.07 .
Heat transfer effects on the stability of low speed plane Couette-Poiseuille flow
Energy Technology Data Exchange (ETDEWEB)
Oezgen, Serkan [Middle East Technical University, Department of Aerospace Engineering, Ankara (Turkey); Dursunkaya, Zafer [Middle East Technical University, Department of Mechanical Engineering, Ankara (Turkey); Ebrinc, Ali A. [FORD Otosan, Kocaeli (Turkey)
2007-10-15
The stability problem of low-speed plane Couette-Poiseuille flow of air under heat transfer effects is solved numerically using the linear stability theory. Stability equations obtained from two-dimensional equations of motion and their boundary conditions result in an eigenvalue problem that is solved using an efficient shoot-search technique. Variable fluid properties are accounted for both in the basic flow and the perturbation (stability) equations. A parametric study is performed in order to assess the roles of moving wall velocity and heat transfer. It is found that the moving wall velocity and the location of the critical layers play decisive roles in the instability mechanism. The flow becomes unconditionally stable whenever the moving wall velocity exceeds half of the maximum velocity in the channel. With wall heating and Mach number effects included, the flow is stabilized. (orig.)
Stochastic analysis of the time evolution of Laminar-Turbulent bands of plane Couette flow
Rolland, Joran
2015-01-01
This article is concerned with the time evolution of the oblique laminar-turbulent bands of transitional plane Couette flow under the influence of turbulent noise. Our study is focused on the amplitude of modulation of turbulence. In order to guide the numerical study of the flow, we first perform an analytical and numerical analysis of a Stochastic Ginzburg-Landau equation for a complex order parameter. The modulus of this order parameter models the amplitude of modulation of turbulence. Firstly, we compute the autocorrelation function of said modulus once the band is established. Secondly, we perform a calculation of average and fluctuations around the exponential growth of the order parameter. This type of analysis is similar to the Stochastic Structural Stability Theory. We then perform numerical simulations of the Navier-Stokes equations in order to confront these predictions with the actual behaviour of the bands. Computation of the autocorrelation function of the modulation of turbulence shows quantita...
Manneville, Paul
2014-01-01
The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re_g, the upper bound for unconditional return to the base flow, and the linear instability threshold Re_c characterized by unconditional departure from the base flow. The transitional range around Re_g is first discussed from an empirical viewpoint ({\\S}1). The recent determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re_t beyo...
Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow
Energy Technology Data Exchange (ETDEWEB)
Thomas, Vaughan L.; Gayme, Dennice F. [Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland, 21218 (United States); Lieu, Binh K.; Jovanović, Mihailo R. [Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota, 55455 (United States); Farrell, Brian F. [School of Engineering and Applied Science, Harvard University, Cambridge, Massachusetts, 02138 (United States); Ioannou, Petros J. [Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens, 15784 (Greece)
2014-10-15
This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier-Stokes equations and permits higher resolution studies of the dynamical system associated with the stochastic structural stability theory (S3T) model, which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented by reducing a DNS code so that it retains only the RNL dynamics. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivate use of the RNL/S3T framework for further study of wall-turbulence.
Zero absolute vorticity: insight from experiments in rotating laminar plane Couette flow.
Suryadi, Alexandre; Segalini, Antonio; Alfredsson, P Henrik
2014-03-01
For pressure-driven turbulent channel flows undergoing spanwise system rotation, it has been observed that the absolute vorticity, i.e., the sum of the averaged spanwise flow vorticity and system rotation, tends to zero in the central region of the channel. This observation has so far eluded a convincing theoretical explanation, despite experimental and numerical evidence reported in the literature. Here we show experimentally that three-dimensional laminar structures in plane Couette flow, which appear under anticyclonic system rotation, give the same effect, namely, that the absolute vorticity tends to zero if the rotation rate is high enough. It is shown that this is equivalent to a local Richardson number of approximately zero, which would indicate a stable condition. We also offer an explanation based on Kelvin's circulation theorem to demonstrate that the absolute vorticity should remain constant and approximately equal to zero in the central region of the channel when going from the nonrotating fully turbulent state to any state with sufficiently high rotation.
Chefranov, Sergey; Chefranov, Alexander
2016-04-01
Linear hydrodynamic stability theory for the Hagen-Poiseuille (HP) flow yields a conclusion of infinitely large threshold Reynolds number, Re, value. This contradiction to the observation data is bypassed using assumption of the HP flow instability having hard type and possible for sufficiently high-amplitude disturbances. HP flow disturbance evolution is considered by nonlinear hydrodynamic stability theory. Similar is the case of the plane Couette (PC) flow. For the plane Poiseuille (PP) flow, linear theory just quantitatively does not agree with experimental data defining the threshold Reynolds number Re= 5772 ( S. A. Orszag, 1971), more than five-fold exceeding however the value observed, Re=1080 (S. J. Davies, C. M. White, 1928). In the present work, we show that the linear stability theory conclusions for the HP and PC on stability for any Reynolds number and evidently too high threshold Reynolds number estimate for the PP flow are related with the traditional use of the disturbance representation assuming the possibility of separation of the longitudinal (along the flow direction) variable from the other spatial variables. We show that if to refuse from this traditional form, conclusions on the linear instability for the HP and PC flows may be obtained for finite Reynolds numbers (for the HP flow, for Re>704, and for the PC flow, for Re>139). Also, we fit the linear stability theory conclusion on the PP flow to the experimental data by getting an estimate of the minimal threshold Reynolds number as Re=1040. We also get agreement of the minimal threshold Reynolds number estimate for PC with the experimental data of S. Bottin, et.al., 1997, where the laminar PC flow stability threshold is Re = 150. Rogue waves excitation mechanism in oppositely directed currents due to the PC flow linear instability is discussed. Results of the new linear hydrodynamic stability theory for the HP, PP, and PC flows are published in the following papers: 1. S.G. Chefranov, A
On the growth of laminar-turbulent patterns in plane Couette flow
Manneville, Paul
2012-01-01
The growth of laminar-turbulent band patterns in plane Couette flow is studied in the vicinity of the global stability threshold R_g below which laminar flow ultimately prevails. Appropriately tailored direct numerical simulations are performed to manage systems extended enough to accommodate several bands. The initial state or germ is an oblique turbulent patch of limited extent. The growth is seen to result from several competing processes: (i) nucleation of turbulent patches close to or at the extremities of already formed band segments, with the same obliquity as the germ or the opposite one, and (ii) turbulence collapse similar to gap formation for band decay. Growth into a labyrinthine pattern is observed as soon as spanwise expansion is effective. An ideally aligned pattern is usually obtained at the end of a long and gradual regularisation stage when R is large enough. Stable isolated bands can be observed slightly above R_g. When growth rates are not large enough, the germ decays at the end of a long...
Mechanical and statistical study of the laminar hole formation in transitional plane Couette flow
Rolland, Joran
2015-01-01
This article is concerned with the numerical study and modelling of two aspects the formation of laminar holes in transitional turbulence of plane Couette flow (PCF). On the one hand, we consider quenches: sudden decreases of the Reynolds number R which force the formation of holes. The Reynolds number is decreased from featureless turbulence to the range of existence of the oblique laminar-turbulent bands [Rg;Rt]. The successive stages of the quench are studied by means of visualisations and measurements of kinetic energy and turbulent fraction. The behaviour of the kinetic energy is explained using a kinetic energy budget: it shows that viscosity causes quasi modal decay until lift-up equals it and creates a new balance. Moreover, the budget confirms that the physical mechanisms at play are independent of the way the quench is performed. On the other hand we consider the natural formation of laminar holes in the bands, near Rg. The Direct Numerical simulations (DNS) show that holes in the turbulent bands pr...
Turbulent plane Poiseuille-Couette flow as a model for fluid slip over superhydrophobic surfaces
Nguyen, Quoc T.; Papavassiliou, Dimitrios V.
2013-12-01
In this study, plane Poiseuille-Couette flow is simulated as a model for specified streamwise slip on one of the channel walls. The relative velocity between the two walls is set to be 1, 2, and 4 in viscous wall units. This is equivalent to the presence of a superhydrophobic surface at one of the channel walls that causes fluid to slip on the boundary. The results show that the streamwise slip forces turbulence in the near-wall region to tend towards a limiting one-component state. This leads to the suppression of small scale turbulence and laminarization close to the wall and then to drag reduction. The selective weakening of the streamwise vorticity close the wall and the observed decrease of turbulence kinetic energy production can then be considered as a consequence of this effect. Changes in the coherent structures, including a decrease of sweep events and increase of ejection events close to the wall where slip occurs, are also observed.
Stochastic analysis of the time evolution of laminar-turbulent bands of plane Couette flow.
Rolland, Joran
2015-11-01
This article is concerned with the time evolution of the oblique laminar-turbulent bands of transitional plane Couette flow under the influence of turbulent noise. Our study is focused on the amplitude of modulation of turbulence (the bands). In order to guide the numerical study of the flow, we first perform an analytical and numerical analysis of a Stochastic Ginzburg-Landau (GL) equation for a complex order parameter. The modulus of this order parameter models the amplitude of modulation of turbulence. Firstly, we compute the autocorrelation function of said modulus once the band is established. Secondly, we perform a calculation of average and fluctuations around the exponential growth of the order parameter. This type of analysis is similar to the Stochastic Structural Stability Theory (S3T). We then perform numerical simulations of the Navier-Stokes equations in order to confront these predictions with the actual behaviour of the bands. Computation of the autocorrelation function of the modulation of turbulence shows quantitative agreement with the model: in the established band regime, the amplitude of modulation follows an Ornstein-Uhlenbeck process. In order to test the S3T predictions, we perform quench experiments, sudden decreases of the Reynolds number from uniform turbulence, in which modulation appears. We compute the average evolution of the amplitude of modulation and the fluctuations around it. We find good agreement between numerics and modeling. The average trajectory grows exponentially, at a rate clearly smaller than that of the formation of laminar holes. Meanwhile, the actual time evolution remains in a flaring envelope, centered on the average, and expanding at the same rate. These results provide further validation of the stochastic modeling for the time evolution of the bands for further studies. Besides, they stress on the difference between the oblique band formation and the formation of laminar holes.
Rolland, Joran
2014-01-01
This article investigates the formation of spanwise vorticity in the velocity streaks of the oblique laminar- turbulent bands of plane Couette flow (PCF) by mean of Direct Numerical Simulations (DNS). The spanwise vorticity is created by a roll-up type development of the streamwise-wall normal shear layer of the velocity streaks. It is advected by the large scale flow along the bands. We propose a criterion on spanwise vorticity which detects these events in order to perform systematic measurements. Beside of the streamwise and spanwise correlation lengths of the rolls, their advection velocity is measured and shown to match the large scale flow along the band near the turbulent region. Eventually, we discuss the possible relation between ejection of vorticity away from the bands near the laminar region and the size of said laminar region.
Rolland, Joran
2016-01-01
This article presents a modelling of the formation of spanwise vorticity in the turbulent streaks of the oblique bands and spots of transitional plane Couette flow. A functional model is designed to mimic the coherent flow in the streaks. The control parameters of the model are extracted from Direct Numerical Simulations (DNS) statistical data. A Reynolds stress is proposed to study the effect on the instability of this additional force maintaining the baseflow. Local (quasi-parallel) temporal stability analysis is performed on that model to investigate the linear development of the spanwise vorticity. Results show that average profiles, even if they have an inflection, are stable: the shear layers inside the velocity streaks are responsible for the vorticity formation. Emphasis is put on the convective or absolute nature of the instability, depending on the location in the band. This shows that a transition from a convective to an absolute instability occurs in the zone in between fully turbulent and laminar...
Pantokratoras, A
2007-01-01
In the above paper by Bechtel, Cai, Rooney and Wang, Physics of Fluids, 2004, 16, 3955-3974 six different theories of a Newtonian viscous fluid are investigated and compared, namely, the theory of a compressible Newtonian fluid, and five constitutive limits of this theory: the incompressible theory, the limit where density changes only due to changes in temperature, the limit where density changes only with changes in entropy, the limit where pressure is a function only of temperature, and the limit of pressure a function only of entropy. The six theories are compared through their ability to model two test problems: (i) steady flow between moving parallel isothermal planes separated by a fixed distance with no pressure gradient in the flow direction (Couette flow), and (ii) steady flow between stationary isothermal parallel planes with a pressure gradient (Poiseuille flow). The authors found, among other, that the incompressible theory admits solutions to these problems of the plane Couette/Poiseuille flow f...
Dubrulle, B; Daviaud, F; Longaretti, P-Y; Richard, D; Zahn, J-P
2011-01-01
This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in several studies of the transition to turbulence and turbulent transport in Taylor-Couette flow. We first introduce a new set of control parameters, based on dynamical rather than geometrical considerations, so that the analysis applies more naturally to rotating shear flows in general and not only to Taylor-Couette flow. We then investigate the transition thresholds in the supercritical and the subcritical regime in order to extract their general dependencies on the control parameters. The inspection of the mean profiles provides us with some general hints on the mean to laminar shear ratio. Then the examination of the torque data allows us to propose a decomposition of the torque dependence on the control parameters in two terms, one completely given by measurements in the ca...
Investigation of Turbulent Laminar Patterns in Poiseuille-Couette flow
Nguyen, Quoc; Papavassiliou, Dimitrios
2014-11-01
Laminar-turbulent intermittency has recently been observed in the transitional regime of pipe ... and plane Couette flow .... While many works focus on behavior of these patterns in plane Couette flow, little attention has been paid to Poiseuille flow and transition from Couette to Poiseuille flow. In this study, we investigate behavior of turbulent laminar patterns in Poiseuille-Couette flow, including pure Poiseuille and Couette flows at two limits. Direct Numerical Simulation (DNS) is used to simulate a Poiseuille-Couette channel at a size of 16 πh × 2h × 2 πh (corresponding to a resolution of 512 × 129 × 128 in x, y and z directions), with periodic boundary condition applied in the x and z directions (h is half of the channel height). The Reynolds number is 300, and the flow is at transitional regime in all simulations. Behavior of laminar turbulent patterns as the flow goes from Couette to Poiseuille flow will be presented in details. This would shed some light on the effect of different types of flow on these patterns, as well as how these patterns vary from fully Poiseuille flow to fully Couette flow.
Oscillatory Couette flow of rotating Sisko fluid
Institute of Scientific and Technical Information of China (English)
T.HAYAT; S.ABELMAN; M.HAMESE
2014-01-01
The oscillatory Couette flow of a magnetohydrodynamic (MHD) Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.
Garaud, Pascale; Gagnier, Damien; Verhoeven, Jan
2017-03-01
Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn. In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent viscosity and the turbulent diffusivity of a passive tracer as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn, namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values {(J\\Pr )}c for instability, adequately accounts for the transition to turbulence in the flow, with {(J\\Pr )}c≃ 0.007. This result recovers and confirms the prior findings of Prat et al. Zahn’s model for the turbulent diffusivity and viscosity, namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfactorily match our numerical data. It fails (as expected) in the limit of large stratification where the Richardson number exceeds the aforementioned threshold for instability, but it also fails in the limit of low stratification where the turbulent eddy scale becomes limited by the computational domain size. We propose a revised model for turbulent mixing by diffusive stratified shear instabilities that properly accounts for both limits, fits our data satisfactorily, and recovers Zahn’s model in the limit of large Reynolds numbers.
Garaud, P; Verhoeven, J
2016-01-01
Shear-induced turbulence could play a significant role in mixing momentum and chemical species in stellar radiation zones, as discussed by Zahn (1974). In this paper we analyze the results of direct numerical simulations of stratified plane Couette flows, in the limit of rapid thermal diffusion, to measure the turbulent diffusivity and turbulent viscosity as a function of the local shear and the local stratification. We find that the stability criterion proposed by Zahn (1974), namely that the product of the gradient Richardson number and the Prandtl number must be smaller than a critical values $(J\\Pr)_c$ for instability, adequately accounts for the transition to turbulence in the flow, with $(J\\Pr)_c \\simeq 0.007$. This result recovers and confirms the prior findings of Prat et al. (2016). Zahn's model for the turbulent diffusivity and viscosity (Zahn 1992), namely that the mixing coefficient should be proportional to the ratio of the thermal diffusivity to the gradient Richardson number, does not satisfact...
Couette Flow of Unmagnetized Plasma
Collins, C; Cooper, C M; Flanagan, K; Khalzov, I V; Nornberg, M D; Seidlitz, B; Wallace, J; Forest, C B
2014-01-01
Differentially rotating flows of unmagnetized, highly conducting plasmas have been created in the Plasma Couette Experiment. Previously, hot-cathodes have been used to control plasma rotation by a stirring technique [C. Collins et al., Phys. Rev. Lett. 108, 115001(2012)] on the outer cylindrical boundary---these plasmas were nearly rigid rotors, modified only by the presence of a neutral particle drag. Experiments have now been extended to include stirring from an inner boundary, allowing for generalized Couette flow and opening a path for both hydrodynamic and magnetohydrodynamic experiments, as well as fundamental studies of plasma viscosity. Plasma is confined in a cylindrical, axisymmetric, multicusp magnetic field, with $T_e< 10$ eV, $T_i<1$ eV, and $n_e<10^{11}$ cm$^{-3}$. Azimuthal flows (up to 12 km/s, $M=V/c_s\\sim 0.7$) are driven by edge ${\\bf J \\times B}$ torques in helium, neon, argon, and xenon plasmas. We present measurements of a self-consistent, rotation-induced, species-dependent rad...
Transient Growth of Ekman-Couette Flow
Shi, Liang; Tilgner, Andreas
2013-01-01
Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We here report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to the shear direction. External rotation causes linear instability. At small rotation rates, the onset of linear instability scales inversely with the rotation rate and the optimal transient growth in the linearly stable region is slightly enhanced, ~Re^2. The corresponding optimal initial perturbations are characterized by roll structures inclined in the streamwise direction and are twisted under external rotation. At large rotation rates, the transient growth is significantly inhibited and hence linear stability analysis is a reliable indicator for instability.
Instability of Taylor-Couette Flow between Concentric Rotating Cylinders
Dou, H S; Phan-Thien, N; Yeo, K S; Dou, Hua-Shu; Khoo, Boo Cheong; Phan-Thien, Nhan; Yeo, Koon Seng
2005-01-01
The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. In our previous studies, the energy gradient theory was demonstrated to be applicable for wall bounded parallel flows. It was found that the critical value of the energy gradient parameter K at subcritical transition is about 370-389 for wall bounded parallel flows (which include plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow) below which no turbulence occurs. In this paper, the detailed derivation for the calculation of the energy gradient parameter in the flow between concentric rotating cylinders is provided. The theoretical results for the critical condition of primary instability obtained are in very good agreement with the experiments found in literature. The mechanism of spiral vortices generation for counter-rotating of two cylinders is also explained using the energy gradient theory. The energy gradient theory can also serve to relate the condition of flow tran...
Stability of the Couette-Poiseuille flow by the Reynolds-Orr energy equation
Lam, F
2012-01-01
The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization problem for the Couette-Poiseuille flow. The minimum Reynolds number for every Couette-Poiseuille velocity profile has been computed and compared with those available in the literature. For fully three-dimensional disturbances, it is shown that the minimum Reynolds number is in general smaller than the corresponding two-dimensional counterpart for all the Couette-Poiseuille profiles except plane Couette flow.
Localized spirals in Taylor-Couette flow.
Heise, M; Abshagen, J; Küter, D; Hochstrate, K; Pfister, G; Hoffmann, Ch
2008-02-01
We present a type of spiral vortex state that appears from a supercritical Hopf bifurcation below the linear instability of circular Couette flow in a Taylor-Couette system with rigid end plates. These spirals have been found experimentally as well as numerically as "pure" states but also coexist with "classical" spirals (or axially standing waves for smaller systems) which typically appear from linear instability in counterrotating Taylor-Couette flow. These spiral states have an axial distribution of the strongly localized amplitude in the vicinity of the rigid end plates that confine the system in the axial direction. Furthermore, they show significantly different oscillation frequencies compared to the critical spiral frequencies. Despite the localization of the amplitude near the ends, the states appear as global states with spirals that propagate either toward the middle from each end of the system or vice versa. In contrast to classical spirals, these states exhibit a spatial or a spatiotemporal reflection symmetry.
Farrell, Brian F
2016-01-01
This paper describes a study of the self-sustaining process (SSP) that maintains turbulence in wall-bounded shear flow. The study uses Couette flow and is based on a statistical state dynamics (SSD) model closed at second order with state variables the streamwise mean (first cumulant) and the covariance of perturbations (second cumulant). The SSD is closed by either neglecting or stochastically parameterizing the perturbation--perturbation nonlinearity in the perturbation covariance equation. This class of quasi-linear SSD models, which are referred to as RNL models, are a second order SSD systems that includes the stochastic structural stability theory (S3T or equivalently RNL$_\\infty$) model which is used in this study. Comparisons of turbulence maintained in DNS and RNL simulations have demonstrated that RNL systems self-sustain turbulence with a mean flow and perturbation structure consistent with DNS. The current results isolate the dynamical components sustaining turbulence in the S3T system concentrati...
Turbulent Poiseuille & Couette flows at high Re
Lee, Myoungkyu; Moser, Robert D.
2016-11-01
We present the results of direct numerical simulation (DNS) of high Re turbulent Poiseuille and Couette flows. Couette flow has been simulated with a streamwise (x) domain that is 100 πδ long at Reynolds number up to Reτ 500 . In addition Poiseuille flow simulations up to Reτ 5200 were performed. In Couette flow, extremely large scale motions, which are approximately 50 πδ long in the x-direction with very strong intensity, have been observed. In this presentation we will focus on a comparison between these two flows in terms of the vorticity-velocity co-spectra, which are interesting because of the relationship between the Reynolds stress and the velocity-vorticity correlation (∂y = - ). Also considered will be the spectra of the turbulent transport term in the evolution equation for the turbulent kinetic energy. In both (co)-spectra it is shown that the difference between the two flows at high Re are primarily at large scales. This work was supported by NSF (OCI-0749223 and PRAC Grant 0832634), and computation resources were provided by the Argonne Leadership Computing Facility through the Early Science, INCITE 2013 and Directors Discretionary Programs.
Destabilizing Taylor-Couette flow with suction
Gallet, Basile; Spiegel, Edward A
2009-01-01
We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.
A Nonlinear Stability Theory for Plane Boundary-Layer Flows
1980-07-01
flows , Poiseuille flows and Couette flows . For example, 3 for plane Polseutlle flow with...published results for plane Poiseuille flow and the Orr-Sonunerfeld solutions for ~lasius flow and a numerical solution of Navier-Stokes flow along a flat...TWO-POINT BOUNDARY-VALUE PROBLEM .......... 21 4. NUMERICAL RESULTS ............................................. 44 4.1 Plane Poiseuille Flow
Finite length Taylor Couette flow
Streett, C. L.; Hussaini, M. Y.
1987-01-01
Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cylinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments.
Moser, K W; Raguin, L G; Harris, A; Morris, H D; Georgiadis, J; Shannon, M; Philpott, M
2000-02-01
A new magnetic resonance imaging technique was applied to the Taylor-Couette and spiral Poiseuille (Taylor-Couette with superposed mean axial flux) flows for the first time. The experimental technique is a combination of spatial tagging methods and a snapshot FLASH imaging sequence, which allows the full-field visualization of 2-D slices of the flow field, with image acquisition times approximately half a second. By acquiring images every few seconds, direct visualization of flow patterns can be obtained in the form of cinematography. Tagged images of the Taylor-Couette flow were acquired in both the axial and transverse planes and confirmed previously reported numerical predictions of Taylor cell size. Tagged images of the spiral Poiseuille flows verified that the cells in this flow propagate at a higher velocity than the mean axial flow. In addition, intermittent cell formation was observed as the axial flow was increased.
Ultimate Turbulent Taylor-Couette Flow
Huisman, Sander G; Grossmann, Siegfried; Sun, Chao; Lohse, Detlef
2011-01-01
The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re_i = 2*10^6 of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV). The wind Reynolds numbers Re_w of the turbulent Taylor-vortex flow is found to scale as Re_w ~ Ta^(1/2), exactly as predicted for the ultimate turbulence regime, in which the boundary layers are turbulent. The dimensionless angular velocity flux has an effective scaling of Nu_{\\omega} ~ Ta^0.38, also in correspondence with turbulence in the ultimate regime. The scaling of Nu_{\\omega} is confirmed by local angular velocity flux measurements extracted from high-speed PIV measurements: though the flux shows huge fluctuations, its spatial and temporal average nicely agrees with the result from the global torque measurements.
Subcritical Transition to Turbulence in Couette-Poiseuille flow
Wesfreid, Jose Eduardo; Klotz, Lukasz
2016-11-01
We study the subcritical transition to turbulence in the plane Couette-Poiseuille shear flow with zero mean advection velocity. Our experimental configuration consists on one moving wall of the test section (the second one remains stationary), which acts like a driving force for the flow, imposing linear streamwise velocity profile (Couette) and adverse pressure gradient in the streamwise direction (Poiseuille) at the same time. This flow, which had only been studied theoretically up to now, is always linearly stable. The transition to turbulence is forced by a very well controlled finite-size perturbation by injection, into the test section, of a water jet during a very short time. Using PIV technique, we characterized quantitatively the initial development of the triggered turbulent spot and compared its energy evolution with the theoretical predictions of the transient growth theory. In addition, we show results concerning the importance of nonlinearities, when waviness of streaks in streamwise direction induced self-sustained process in the turbulent spot. We also measured precisely the large-scale flow which is generated around the turbulent spot and studied its strength as a function of the Reynolds number.
Model Polyelectrolytes in Turbulent Couette Flow
Price, Brian; Hoagland, David A.
1997-03-01
Isolated polymer chains in strong flow are deformed significantly from their equilibrium conformations, imparting a pronounced change in the local velocity field. Turbulent drag reduction by dilute polymer solutions is an important example. The onset of drag reduction appears dependent on a characteristic shear stress at the wall τw for a given polymer. (Virk, P.S. AIChE Journal 21 1975) Length and time scales formed from τw and solvent kinematic viscosity provide different scalings of the onset with chain length. It is likely that length polydispersity could be responsible for the disparity among the previously reported results concerning the correct onset condition. We have employed preparative gel electrophoresis to produce samples of very low polydispersity to determine the onset scaling of drag reduction in turbulent couette flow. The same technique provides information about chain scission in turburlence, yielding an indirect indication of chain conformation.
Solitary vortex couples in viscoelastic Couette flow
Groisman, A; Groisman, Alexander; Steinberg, Victor
1996-01-01
We report experimental observation of a localized structure, which is of a new type for dissipative systems. It appears as a solitary vortex couple ("diwhirl") in Couette flow with highly elastic polymer solutions. A unique property of the diwhirls is that they are stationary, in contrast to the usual localized wave structures in both Hamiltonian and dissipative systems which are stabilized by wave dispersion. It is also a new object in fluid dynamics - a couple of vortices that build a single entity somewhat similar to a magnetic dipole. The diwhirls arise as a result of a purely elastic instability through a hysteretic transition at negligible Reynolds numbers. It is suggested that the vortex flow is driven by the same forces that cause the Weissenberg effect. The diwhirls have a striking asymmetry between the inflow and outflow, which is also an essential feature of the suggested elastic instability mechanism.
Magnetorotational Instability in Liquid Metal Couette Flow
Noguchi, K; Colgate, S A; Nordhaus, J; Beckley, H F
2002-01-01
Despite the importance of the magnetorotational instability (MRI) as a fundamental mechanism for angular momentum transport in magnetized accretion disks, it has yet to be demonstrated in the laboratory. A liquid sodium alpha-omega dynamo experiment at the New Mexico Institute of Mining and Technology provides an ideal environment to study the MRI in a rotating metal annulus (Couette flow). A local stability analysis is performed as a function of shear, magnetic field strength, magnetic Reynolds number, and turbulent Prandtl number. The later takes into account the minimum turbulence induced by the formation of an Ekman layer against the rigidly rotating end walls of a cylindrical vessel. Stability conditions are presented and unstable conditions for the sodium experiment are compared with another proposed MRI experiment with liquid gallium. Due to the relatively large magnetic Reynolds number achievable in the sodium experiment, it should be possible to observe the excitation of the MRI for a wide range of w...
Momentum transport in Taylor-Couette flow with vanishing curvature
Brauckmann, Hannes J; Eckhardt, Bruno
2015-01-01
We numerically study turbulent Taylor-Couette flow (TCF) between two independently rotating cylinders and the transition to rotating plane Couette flow (RPCF) in the limit of infinite radii. By using the shear Reynolds number $Re_S$ and rotation number $R_\\Omega$ as dimensionless parameters, the transition from TCF to RPCF can be studied continuously without singularities. Already for radius ratios $\\eta\\geq0.9$ we find that the simulation results for various radius ratios and for RPCF collapse as a function of $R_\\Omega$, indicating a turbulent behaviour common to both systems. We observe this agreement in the torque, mean momentum transport, mean profiles, and turbulent fluctuations. Moreover, the central profiles in TCF and RPCF for $R_\\Omega>0$ are found to conform with inviscid neutral stability. Intermittent bursts that have been observed in the outer boundary layer and have been linked to the formation of a torque maximum for counter-rotation are shown to disappear as $\\eta \\rightarrow 1$. The correspo...
Energy Technology Data Exchange (ETDEWEB)
Nakabayashi, K.; Kito, O.; Kato, Y. [Nagoya Institute of Technology, Nagoya (Japan)
1998-10-25
Turbulence intensities in Couette Poiseuille flow, developed between stationary and moving walls, have been measured by I- and X-type hot wires. The intensities in the wall region are affected by non-dimensional shear stress gradient parameter {mu} ({identical_to} u*{sup 3}/{alpha}{nu}), but not by Reynolds number Re* ({identical_to} hu*/{nu}). As |{mu}| decreases, distributions of streamwise and wall-normal turbulence intensities shift upward or downward from those of plane-Couette flow depending on the sign of {mu}. In the turbulent core region, turbulence intensities of Poiseuille-type flow distribute quite differently from that of Couette-type flow. The effective parameter in this region is 13, but the effect of 13 on the turbulence intensities is obscured by the low Reynolds number effect. 13 refs., 12 figs., 2 tabs.
Particle rotation in a Couette flow
Ye, J.; Roco, M. C.
1992-02-01
The rotational velocity of neutrally buoyant particles was measured in a planar Couette flow. The flow cross section is rectangular with a 4-to-1 (200 mm/50 mm) aspect ratio. The mixtures consist of uniform polystyrene spheres and a glycerol-water solution of specific density 1.052. Four sphere sizes have been tested: 3, 4.76, 6.35, and 7.94 mm. Particle motion in turbulent flow was recorded with a high-speed SP-2000 motion analysis system. The characteristics of particle motion, including particle spin, were measured as a function of the distance from the wall, at three shear rates corresponding to Re=4.6, 6.8, and 9.2×104. It was found that the particle angular velocity normalized by shear rate is a function of the normalized distance to the moving and stationary walls. The flow conditions are defined with measurements on mean velocities, particle velocity fluctuations, kinetic energy, inertial stresses, and diffusion coefficients.
Turbulent Taylor–Couette flow with stationary inner cylinder
Ostilla-Monico, R.; Verzicco, Roberto; Lohse, Detlef
2016-01-01
A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\\times 10^{4}$Reo=5.5×104
Rubber Bands as Model Polymers in Couette Flow
Dunstan, Dave E.
2008-01-01
We present a simple device for demonstrating the essential aspects of polymers in flow in the classroom. Rubber bands are used as a macroscopic model of polymers to allow direct visual observation of the flow-induced changes in orientation and conformation. A transparent Perspex Couette cell, constructed from two sections of a tube, is used to…
Turbulent Taylor–Couette flow with stationary inner cylinder
Ostilla-Monico, R.; Verzicco, R.; Lohse, D.
2016-01-01
A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\\times 10^{4}$Reo=5.5×104
Dynamics near the subcritical transition of the 3D Couette flow I: Below threshold case
Bedrossian, Jacob; Masmoudi, Nader
2015-01-01
We study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number $\\textbf{Re}$. We prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\textbf{Re}^{-1}$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty$. For times $t \\gtrsim \\textbf{Re}^{1/3}$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of "2.5 dimensional" streamwise-independent solutions referred to as streaks. Our analysis contains perturbations that experience a transient growth of kinetic energy from $O(\\textbf{Re}^{-1})$ to $O(c_0)$ due to the algebraic linear instability known as the lift-up effect. Furthermore, solutions can exhibit a direct cascade of energy to small scales. The behavior is very different from the 2D Couette flow, in which stability is independ...
Continuum model for Couette-Poiseuille flow in a drag molecular pump
Skovorodko, P A
2004-01-01
A continuum one-dimensional model of the plane Couette-Poiseuille flow is developed to describe the pressure distribution in a drag stage of molecular pump of either the Gaede or Holweck type. In spite of its simplicity and approximate nature the model provides a good qualitative representation of the drag pump operation in the whole range of the regimes from the continuum to free molecular ones.
Velocity profiles in strongly turbulent Taylor-Couette flow
Grossmann, S.; Lohse, D.; Sun, C.
2014-01-01
We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as funct
Steady hydromagnetic Couette flow in a rotating system with non ...
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energy equation and numerical values of rate of heat transfer at both plates are ... It may be noted that MHD Couette flow may be generated into two ways and .... Equations (5), (6), (10) and (11) with the use of (12), in non-dimensional form, ...
Smooth and rough boundaries in turbulent Taylor-Couette flow
Berg, van den Thomas H.; Doering, Charles R.; Lohse, Detlef; Lathrop, Daniel P.
2003-01-01
We examine the torque required to drive the smooth or rough cylinders in turbulent Taylor-Couette flow. With rough inner and outer walls the scaling of the dimensionless torque G is found to be consistent with pure Kolmogorov scaling G~Re2. The results are interpreted within the Grossmann-Lohse theo
Intrinsic Viscosity of Flexible Polymers in Couette and Poiseuille Flows
van Vliet, Johannes; Brinke, G. ten
1992-01-01
The zero-shear-rate intrinsic viscosity of a flexible polymer confined in a slit in Couette and Poiseuille flow is investigated by Monte Carlo simulations of self-avoiding random walks on a simple cubic lattice and by analytical calculations in the free-draining limit. In the simulations an equilibr
Extension to nonlinear stability theory of the circular Couette flow
Yau, Pun Wong; Wang, Shixiao; Rusak, Zvi
2016-11-01
A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function Ard of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of ΔArd depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of ΔArd leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph & Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades.
Structure parameters in rotating Couette-Poiseuille channel flow
Knightly, George H.; Sather, D.
1986-01-01
It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.
Structures and scaling laws of turbulent Couette flow
Oberlack, Martin; Avsarkisov, Victor; Hoyas, Sergio; Rosteck, Andreas; Garcia-Galache, Jose P.; Frank, Andy
2014-11-01
We conducted a set of large scale DNS of turbulent Couette flow with the two key objectives: (i) to better understand large scale coherent structures and (ii) to validate new Lie symmetry based turbulent scaling laws for the mean velocity and higher order moments. Though frequently reported in the literature large scale structures pose a serious constraint on our ability to conduct DNS of turbulent Couette flow as the largest structures grow with increasing Re#, while at the same time Kolmogorov scale decreases. Other than for the turbulent Poiseuille flow a too small box is immediately visible in low order statistics such as the mean and limited our DNS to Reτ = 550 . At the same time we observed that scaling of the mean is peculiar as it involves a certain statistical symmetry which has never been observed for any other parallel wall-bounded turbulent shear flow. Symmetries such as Galilean group lie at the heart of fluid dynamics, while for turbulence statistics due to the multi-point correlation equations (MPCE) additional statistical symmetries are admitted. Most important, symmetries are the essential to construct exact solutions to the MPCE, which with the new above-mentioned special statistical symmetry led to a new turbulent scaling law for the Couette flow. DFG Grant No; KH 257/2-1.
Transitions in a magnetized quasi-laminar spherical Couette Flow
Kaprzyk, C; Seilmayer, M; Stefani, F
2016-01-01
First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations.
Particle interaction in oscillatory Couette and Poiseuille flows
Fathi, Nima; Ingber, Marc; Vorobieff, Peter
2013-11-01
In oscillating Poiseuille flows of relatively dense suspensions, the direction of particle migration changes with the amplitude of oscillation. High amplitudes produce migration toward low shear rate regions of the flow, and vice versa, low oscillation amplitude results in particle migration toward the high shear rate region. We demonstrate that a similar behavior can be observed in a two-particle system, where it can be physically interpreted more easily, and discuss numerical modeling and experimental studies of oscillatory Poiseuille and Couette flows. This research is supported by the National Science Foundation and (in part) by a gift from the Procter & Gamble Company.
Patterns of the turbulent Taylor-Couette flow
Prigent, Arnaud; Talioua, Abdessamad; Mutabazi, Innocent
2016-11-01
We are interested in the study of the transition to turbulence in the Taylor-Couette flow, the flow between two independently rotating coaxial cylinders. Once the geometry is fixed, the flow is controlled by the inner and outer Reynolds numbers and present a large variety of flow regimes. In counter-rotation, the transition is characterized by a succession of more or less turbulent flow regimes: intermittency with turbulent spots, spiral turbulence, featureless turbulence. For larger values of the inner Reynolds number, turbulent Taylor roll re-emerge from the featureless turbulence and remain for very large values of the Reynolds numbers. Bifurcations between different turbulent rolls states are even observed in the ultimate turbulence regime. Nevertheless the transition from the featureless turbulence to the turbulent rolls still requires a detailed study and the mechanism which causes and sustains turbulent spots or turbulent spirals remains unknown. In this study we present new experimental information on the organization of the flow for the different regimes with turbulence. The experiments are conducted in a Taylor-Couette flow with η = 0 . 8 . Stereo-Particle Image Velocimetry measurements and visualizations of the different flow regimes are realized and discussed. This work was supported by the ANR TRANSFLOW - ANR-13-BS09-0025.
Hydrodynamic modeling of granular flows in a modified Couette cell.
Jop, Pierre
2008-03-01
We present simulations of granular flows in a modified Couette cell, using a continuum model recently proposed for dense granular flows. Based on a friction coefficient, which depends on an inertial number, the model captures the positions of the wide shear bands. We show that a smooth transition in velocity-profile shape occurs when the height of the granular material is increased, leading to a differential rotation of the central part close to the surface. The numerical predictions are in qualitative agreement with previous experimental results. The model provides predictions for the increase of the shear band width when the rotation rate is increased.
Following analytically stages of transition in Couette flow
Karp, Michael; Cohen, Jacob
2013-11-01
A possible explanation for transition in Couette flow is the mechanism of transient growth (TG). Accordingly, a small disturbance can achieve a significant non-modal TG and trigger nonlinear mechanisms before its eventual decay owing to viscosity. The linear optimal disturbance achieving the maximal growth consists of a pair of streamwise independent counter-rotating vortices (CVPs) which create spanwise-varying streamwise streaks. These may become unstable with respect to infinitesimal disturbances. It is shown that four decaying normal modes, obtained analytically, are sufficient to follow the linear TG mechanism. A secondary linear stability analysis of the modified base-flow (Couette flow with streaks) is conducted using Floquet theory for the spanwise periodic base-flow. The predictions of the stability analysis are compared with direct numerical simulations using the ``Channelflow'' code. It is shown analytically that the inclusion of nonlinear interactions between the base-flow and the CVPs is required in order to predict instability. Furthermore, it is demonstrated that the generation of a `strong' inflectional point is more important than obtaining maximal growth. The minimal number of modes enables us to follow analytically several key stages of the transition process.
Instability of Taylor-Couette Flow of Electrorheological Fluid
Institute of Scientific and Technical Information of China (English)
PENG Jie; ZHU Ke-Qin
2004-01-01
A linearized instability analysis of Taylor-Couette flow between two rotating concentric cylinders of an electrorheological (ER) fluid is carried out. The ER fluid exhibits a yield stress in addition to the plastic viscosity when an extra electric-field is applied. It can be found that the yield stress plays a dual role in the flow instability.The possibility of the yield surface falling between the cylinders is analysed. Although small waves appeared on the yielded surface is considered, the yielded surface, which has been treated as a free surface, has little effect on the flow instability. The effects of axisymmetric perturbation on the flow instability are presented due to the axisymmetric of the basic flow. The parameterβ in the yield stress formula of the ER fluid is shown to have distinct effects on the flow instability characteristics.
Large-scale structures in turbulent Couette flow
Kim, Jung Hoon; Lee, Jae Hwa
2016-11-01
Direct numerical simulation of fully developed turbulent Couette flow is performed with a large computational domain in the streamwise and spanwise directions (40 πh and 6 πh) to investigate streamwise-scale growth mechanism of the streamwise velocity fluctuating structures in the core region, where h is the channel half height. It is shown that long streamwise-scale structures (> 3 h) are highly energetic and they contribute to more than 80% of the turbulent kinetic energy and Reynolds shear stress, compared to previous studies in canonical Poiseuille flows. Instantaneous and statistical analysis show that negative-u' structures on the bottom wall in the Couette flow continuously grow in the streamwise direction due to mean shear, and they penetrate to the opposite moving wall. The geometric center of the log layer is observed in the centerline with a dominant outer peak in streamwise spectrum, and the maximum streamwise extent for structure is found in the centerline, similar to previous observation in turbulent Poiseuille flows at high Reynolds number. Further inspection of time-evolving instantaneous fields clearly exhibits that adjacent long structures combine to form a longer structure in the centerline. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2057031).
Taylor-Couette flow with radial fluid injection
Wilkinson, Nikolas; Dutcher, Cari S.
2017-08-01
Taylor-Couette cells have been shown to improve a number of industrial processes due to the wide variety of hydrodynamic flow states accessible. Traditional designs, however, limit the ability to introduce new fluids into the annulus during device operation due to geometric confinement and complexity. In this paper, a co- and counter-rotating Taylor-Couette cell with radial fluid injection has been constructed. The incorporation of 16 ports in the inner cylinder enables radial fluid injection during rotation of both cylinders. The design is also capable of continuous axial flow, enabling large injection volumes. The new inner cylinder design does not modify the critical Re for flow instabilities and can precisely inject a desired mass at a desired flow rate. A range of injection rates and masses were explored to quantify the effect of radial injection on the stability of the turbulent Taylor vortex structure. Only the highest injection rate and total mass studied (5.9 g/s, 100 g) modified the turbulent Taylor vortex structure after injection for a sustained period. The post-injection vortices remained larger than the pre-injection vortices, whereas at lower injection rates or masses, the vortex structure quickly returned to the pre-injection structure. This new system allows for in situ study of hydrodynamic effects on fluid-fluid (gas and liquid) mixing and multiphase complexation, growth, and structure. We demonstrated this new design's potential for studying the flocculation of bentonite using cationic polyacrylamide for enhancing water treatment operations.
Oblique Laminar-Turbulent Interfaces in Plane Shear Flows
Duguet, Yohann; Schlatter, Philipp
2013-01-01
Localized structures such as turbulent stripes and turbulent spots are typical features of transitional wall-bounded flows in the subcritical regime. Based on an assumption for scale separation between large and small scales, we show analytically that the corresponding laminar-turbulent interfaces are always oblique with respect to the mean direction of the flow. In the case of plane Couette flow, the mismatch between the streamwise flow rates near the boundaries of the turbulence patch generates a large-scale flow with a nonzero spanwise component. Advection of the small-scale turbulent fluctuations (streaks) by the corresponding large-scale flow distorts the shape of the turbulence patch and is responsible for its oblique growth. This mechanism can be easily extended to other subcritical flows such as plane Poiseuille flow or Taylor-Couette flow.
Optimal Taylor-Couette flow: direct numerical simulations
Mónico, Rodolfo Ostilla; Grossman, Siegfried; Verzicco, Roberto; Lohse, Detlef
2013-01-01
We numerically simulate turbulent Taylor-Couette flow for independently rotating inner and outer cylinders, focusing on the analogy with turbulent Rayleigh-B\\'enard flow. Reynolds numbers of Re_i = 8\\times10^3 and Re_o =\\pm4\\times10^3 of the inner and outer cylinders, respectively, are reached, corresponding to Taylor numbers Ta up to 10^8 . Effective scaling laws for the torque and other system responses are found. Recent experiments with the Twente turbulent Taylor-Couette (T^3C) setup at very high Reynolds numbers have vealed an optimum transport at a certain non-zero rotation rate ratio a = -{\\omega}_o/{\\omega}_i that depends on Ta. For large enough Ta in the numerically accessible range we find such an optimum at non-zero counter-rotation also in the numerics. We furthermore numerically calculate the corresponding angular velocity profiles and visualize the different flow structures for the various regimes. By writing the equations in a frame co-rotating with the outer cylinder a link is found between th...
Multiple states in highly turbulent Taylor-Couette flow
Huisman, Sander G; Sun, Chao; Lohse, Detlef
2016-01-01
The ubiquity of turbulent flows in nature and technology makes it of utmost importance to fundamentally understand turbulence. Kolmogorov's 1941 paradigm suggests that for strongly turbulent flows with many degrees of freedom and its large fluctuations, there would only be \\emph{one} turbulent state as the large fluctuations would explore the entire higher-dimensional phase space. Here we report the first conclusive evidence of multiple turbulent states for large Reynolds number $\\text{Re}=\\mathcal{O}(10^6)$ (Taylor number $\\text{Ta}=\\mathcal{O}(10^{12})$) Taylor-Couette flow in the regime of ultimate turbulence, by probing the phase space spanned by the rotation rates of the inner and outer cylinder. The manifestation of multiple turbulent states is exemplified by providing combined global torque and local velocity measurements. This result verifies the notion that bifurcations can occur in high-dimensional flows i.e. very large $\\text{Re}$) and questions Kolmogorov's paradigm.
DSMC Simulation of High Mach Number Taylor-Couette Flow
Pradhan, Sahadev, , Dr.
2017-01-01
The main focus of this work is to characterise the Taylor-Couette flow of an ideal gas between two coaxial cylinders at Mach number Ma = (U_w /√{ kbT_w / m }) in the range 0.01 Boltzmann constant. The cylindrical surfaces are specified as being diffusely reflecting with the thermal accommodation coefficient equal to one. In the present analysis of high Mach number compressible Taylor-Couette flow using DSMC method, wall slip in the temperature and the velocities are found to be significant. Slip occurs because the temperature/velocity of the molecules incident on the wall could be very different from that of the wall, even though the temperature/velocity of the reflected molecules is equal to that of the wall. Due to the high surface speed of the inner cylinder, significant heating of the gas is taking place. The gas temperature increases until the heat transfer to the surface equals the work done in moving the surface. The highest temperature is obtained near the moving surface of the inner cylinder at a radius of about (1.26 r_1).
Optimal Taylor-Couette flow: Radius ratio dependence
Monico, Rodolfo Ostilla; Jannink, Tim J G; van Gils, Dennis P M; Verzicco, Roberto; Grossmann, Siegfried; Sun, Chao; Lohse, Detlef
2013-01-01
Taylor-Couette flow with independently rotating inner (i) and outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio {\\eta} on the system response. Numerical simulations reach Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to Taylor numbers of up to Ta=10^8 for four different radius ratios {\\eta}=r_i/r_o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for {\\eta}=0.714-0.909. Effective scaling laws for the torque J^{\\omega}(Ta) are found, which for sufficiently large driving Ta are independent of the radius ratio {\\eta}. As previously reported for {\\eta}=0.714, optimum transport at a non-zero Rossby number Ro=r_i|{\\omega}_i-{\\omega}_o|/[2(r_o-r_i){\\omega}_o] is found in both experiments and numerics. Ro_opt is found to depend on the radius ratio and the driving of the system. At a drivi...
Logarithmic boundary layers in highly turbulent Taylor-Couette flow
Huisman, Sander G; Cierpka, Christian; Kahler, Christian J; Lohse, Detlef; Sun, Chao
2013-01-01
We provide direct measurements of the boundary layer properties in highly turbulent Taylor-Couette flow up to $\\text{Ta}=6.2 \\times 10^{12}$ using high-resolution particle image velocimetry (PIV). We find that the mean azimuthal velocity profile at the inner and outer cylinder can be fitted by the von K\\'arm\\'an log law $u^+ = \\frac 1\\kappa \\ln y^+ +B$. The von K\\'arm\\'an constant $\\kappa$ is found to depend on the driving strength $\\text{Ta}$ and for large $\\text{Ta}$ asymptotically approaches $\\kappa \\approx 0.40$. The variance profiles of the local azimuthal velocity have a universal peak around $y^+ \\approx 12$ and collapse when rescaled with the driving velocity (and not with the friction velocity), displaying a log-dependence of $y^+$ as also found for channel and pipe flows [1,2].
The effect of Taylor rolls on Taylor-Couette flow
Monico, Rodolfo Ostilla; Grossmann, Siegfried; Lohse, Detlef
2015-01-01
Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders have been performed. Reynolds numbers of up to $3\\cdot 10^5$, corresponding to frictional Reynolds numbers $Re_\\tau \\approx 4000$ were reached. The gap between the cylinders was kept small by fixing the radius ratio to $\\eta=r_i/r_o=0.909$. Small gap TC was found to be dominated by large scale structures, which are permanent in time and known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e they transport angular velocity through Reynolds stresses. Evidence for the existence of logarithmic velocity fluctuations, and of an overlap layer where the velocity fluctuations collapse in outer units was also found. An externally imposed axial flow of comparable strength as the wind of the TRs was found to convect them without any weakening effect.
DNS of turbulent Couette flow with transpiration - spectra and symmetry induced scaling laws
Hoyas, Sergio; Kraheberger, Stefanie; Oberlack, Martin
2016-11-01
We present DNS results of turbulent plane Couette flow with constant wall-normal transpiration for Reynolds numbers of Reτ = 250 , 500 , 1000 and several transpiration Reynolds numbers Retr =V0 /Uw . To obtain the DNS data, a pseudo-spectral code, which originally was developed at UP Madrid, see (Hoyas and Jiménez 2006), is used for the simulations. Due to the lack of experimental and DNS data, the convergence of every simulation has been validated using the total shear stress equation and the relation between the friction velocities at the lower and upper wall. Examining the spectra we found that the large and wide structures, which appear in pure Couette flow, see (Avsarkisov et al. 2014), are destroyed as soon as transpiration velocity is different from zero. This and the presence of anomalous spectra near the blowing wall indicates the strong influence of suction on the whole flow, which was observed in (Antonia et al. 1988) as well. As classical scaling laws are not valid due to transpiration, new scaling laws of the mean velocity are derived using Lie symmetry methods. Additionally, suction creates a comparably larger uτ which, in turn, causes a flat and long region in the indicator function for the largest transpiration rate. SH was partially funded by ENE2015-71333-R. SK was funded by DFG under Grant No. OB96/39-1. Computer resources have been provided by LRZ Munich under Grant pr92la.
Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow
Child, Adam; Hollerbach, Rainer
2015-01-01
We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself, and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types, and modes with a...
Magneto--Coriolis waves in a spherical Couette flow experiment
Schmitt, Denys; La Rizza, Patrick; Nataf, Henri-Claude
2016-01-01
The dynamics of fluctuations in a fast rotating spherical Couette flow experiment in the presence of a strong dipolar magnetic field is investigated in detail, through a thorough analysis of the experimental data as well as a numerical study. Fluctuations within the conducting fluid (liquid sodium) are characterized by the presence of several oscillation modes, identified as magneto-Coriolis (MC) modes, with definite symmetry and azimuthal number. A numerical simulation provides eigensolutions which exhibit oscillation frequencies and magnetic signature comparable to the observation. The main characteristics of these hydromagnetic modes is that the magnetic contribution has a fundamental influence on the dynamical properties through the Lorentz forces, although its importance remains weak in an energetical point of view. Another specificity is that the Lorentz forces are confined near the inner sphere where the dipolar magnetic field is the strongest, while the Coriolis forces are concentrated in the outer fl...
Magnetorotational Instability in a Couette Flow of Plasma
Noguchi, K; Noguchi, Koichi; Pariev, Vladimir I.
2003-01-01
All experiments, which have been proposed so far to model the magnetorotational instability (MRI) in the laboratory, involve a Couette flow of liquid metals in a rotating annulus. All liquid metals have small magnetic Prandtl numbers, Pm, of about 10^{-6} (the ratio of kinematic viscosity to magnetic diffusivity). With plasmas both large and small Pm are achievable by varying the temperature and the density of plasma. Compressibility and fast rotation of the plasma result in radial stratification of the equilibrium plasma density. Evolution of perturbations in radially stratified viscous and resistive plasma permeated by an axial uniform magnetic field is considered. The differential rotation of the plasma is induced by the ExB drift in applied radial electric field. Global unstable eigenmodes are calculated by our newly developed matrix code. The plasma is shown to be MRI unstable for parameters easily achievable in experimental setup.
Velocity profiles in strongly turbulent Taylor-Couette flow
Grossmann, Siegfried; Sun, Chao
2013-01-01
We derive the velocity profiles in strongly turbulent Taylor-Couette flow for the general case of independently rotating cylinders. The theory is based on the Navier-Stokes equations in the appropriate (cylinder) geometry. In particular, we derive the axial and the angular velocity profiles as functions of distance from the cylinder walls and find that both follow a logarithmic profile, with downwards-bending curvature corrections, which are more pronounced for the angular velocity profile as compared to the axial velocity profile, and which strongly increase with decreasing ratio $\\eta$ between inner and outer cylinder radius. In contrast, the azimuthal velocity does not follow a log-law. We then compare the angular and azimuthal velocity profiles with the recently measured profiles in the ultimate state of (very) large Taylor numbers. Though the {\\em qualitative} trends are the same -- down-bending for large wall distances and (properly shifted and non-dimensionalized) angular velocity profile $\\omega^+(r)$...
Cell exclusion in couette flow: evaluation through flow visualization and mechanical forces.
Leslie, Laura J; Marshall, Lindsay J; Devitt, Andrew; Hilton, Andrew; Tansley, Geoff D
2013-03-01
Cell exclusion is the phenomenon whereby the hematocrit and viscosity of blood decrease in areas of high stress. While this is well known in naturally occurring Poiseuille flow in the human body, it has never previously been shown in Couette flow, which occurs in implantable devices including blood pumps. The high-shear stresses that occur in the gap between the boundaries in Couette flow are known to cause hemolysis in erythrocytes. We propose to mitigate this damage by initiating cell exclusion through the use of a spiral-groove bearing (SGB) that will provide escape routes by which the cells may separate themselves from the plasma and the high stresses in the gap. The force between two bearings (one being the SGB) in Couette flow was measured. Stained erythrocytes, along with silver spheres of similar diameter to erythrocytes, were visualized across a transparent SGB at various gap heights. A reduction in the force across the bearing for human blood, compared with fluids of comparable viscosity, was found. This indicates a reduction in the viscosity of the fluid across the bearing due to a lowered hematocrit because of cell exclusion. The corresponding images clearly show both cells and spheres being excluded from the gap by entering the grooves. This is the first time the phenomenon of cell exclusion has been shown in Couette flow. It not only furthers our understanding of how blood responds to different flows but could also lead to improvements in the future design of medical devices.
Perturbation Enstrophy Decay in Poiseuille and Couette Flows according to Synge's Method
Domenicale, Loris; Fraternale, Federico; Staffilani, Gigliola; Tordella, Daniela
2015-11-01
In this work we derive the conditions for no enstrophy growth for bidimensional perturbations in the plane Couette and Poiseuille flows. We follow the method of vorticity proposed by Synge in 1938 (see the Semi-Centennial Puplication of the Amer. Math. Soc., equation 12.13, and the more detailed version in the Proc. of the Fifth Inter. Congress of Applied Mechanics, pages 326-332), which is actually based on the analysis of the spatially averaged enstrophy. We find that the limit curve in the perturbation wavenumber-Reynolds number map differs from the limit for no energy growth (see e.g. Reddy 1993). In particular, the absolute stability region for the enstrophy is wider than that of the kinetic energy, and the maximum Reynolds number giving the monotonic enstrophy decay, at all wavenumbers, is 155 and 80 for the Poiseuille and Couette flows, respectively. It should be noted that in past literature the energy-based analysis was preferred to Synge's enstrophy analysis. This, possibly, for two reasons: the low diffusivity of the 1938 Vth ICAM proceedings and the objectively very complicated analytical treatment required. Nevertheless, the potentiality of this method seems high and therefore it is interesting nowadays to exploit it by means of the symbolic calculus. MITOR-MISTI SEEDS GRANT http://web.mit.edu/mitor/recipients/faculty.html
3D couette flow of dusty fluid with transpiration cooling
Institute of Scientific and Technical Information of China (English)
GOVINDARAJAN A.; RAMAMURTHY V.; SUNDARAMMAL K.
2007-01-01
The couette dusty flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the dusty fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion was analyzed. Due to this type of injection velocity the dusty flow becomes 3D. Perturbation method is used to obtain the expressions for the velocity and temperature fields of both the fluid and dust. It was found that the velocity profiles of both the fluid and dust in the main flow direction decrease with the increase of the mass concentration of the dust panicles, and those in cross flow direction increase with an increase in the mass concentration of the dust particles up to the middle of the channel and thereafter decrease with increase in mass concentration of the dust particles. The skin friction components Tx and Tz in the main flow and transverse directions respectively increase with an increase in the mass concentration of the dust particles (or) injection parameter. The heat transfer coefficient decreases with the increase of the injection parameter and increases with the increase in the mass concentration of the dust particles.
Turbulent Taylor-Couette flow with stationary inner cylinder
Ostilla-Monico, Rodolfo; Lohse, Detlef
2016-01-01
A series of direct numerical simulations of Taylor-Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed, were performed. Three cases, with outer cylinder Reynolds numbers $Re_o$ of $Re_o=5.5\\cdot10^4$, $Re_o=1.1\\cdot10^5$ and $Re_o=2.2\\cdot10^5$ were considered. The radius ratio $\\eta=r_i/r_o$ was fixed to $\\eta=0.909$ to mitigate the effects of curvature. The vertical aspect ratio $\\Gamma$ was fixed to $\\Gamma=2.09$. Being linearly stable, outer cylinder rotation TC flow is known to have very different behavior than pure inner cylinder rotation TC flow. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The ...
Population splitting of rodlike swimmers in Couette flow
Nili, Hossein; Kheyri, Masoud; Abazari, Javad; Fahimniya, Ali; Naji, Ali
We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of swimming direction for a finite fraction of swimmers from down- to upstream or vice versa, depending on swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsion-dominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Peclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.
Taylor-Couette flow instabilities in neutrally-buoyant suspensions
Majji, Madhu; Banerjee, Sanjoy; Morris, Jeffrey F.
2016-11-01
Experimentally-determined instabilities and flow states of a neutrally-buoyant suspension are described. The flow is studied in a concentric-cylinder device with inner-to-outer cylinder ratio of 0.877 with inner cylinder rotating and outer stationary. The cylinder length to annular gap ratio is 20, while the gap to particle size ratio is approximately 30, for spherical particles of 250 μm diameter. Using a slowly increasing or decreasing Re ramp, the flow agrees with all expectations for the pure fluid, while a slowly decreasing (quasi-static) ramp is used for the suspension flow, which is found to be unstable at lower Reynolds number Re (based on the effective viscosity) than pure fluid, and exhibits spiraling and ribbon states not found for a pure fluid with only inner cylinder rotating. Strikingly, the suspension at solid fraction ϕ >= 0 . 05 goes unstable first to a nonaxisymetric state rather than axisymmetric Taylor vortices. At 0 . 1 states during quais-static ramping of Re , while for ϕ = 0 . 3 , the base state Couette flow gives way to wavy spirals (WS) at Re 80 and exhibits only the WS state up to Re = 150 . Transient behavior on sudden change of Re and particle tracking will also be presented.
Experimental Studies of Acoustics in a Spherical Couette Flow
Gowen, Savannah; Adams, Matthew; Stone, Douglas; Lathrop, Daniel
2016-11-01
The Earth, like many other astrophysical bodies, contains turbulent flows of conducting fluid which are able to sustain magnetic field. To investigate the hydromagnetic flow in the Earth's outer core, we have created an experiment which generates flows in liquid sodium. However, measuring these flows remains a challenge because liquid sodium is opaque. One possible solution is the use of acoustic waves. Our group has previously used acoustic wave measurements in air to infer azimuthal velocity profiles, but measurements attempted in liquid sodium remain challenging. In the current experiments we measure acoustic modes and their mode splittings in both air and water in a spherical Couette device. The device is comprised of a hollow 30-cm outer sphere which contains a smaller 10-cm rotating inner sphere to drive flow in the fluid in between. We use water because it has material properties that are similar to those of sodium, but is more convenient and less hazardous. Modes are excited and measured using a speaker and microphones. Measured acoustic modes and their mode splittings correspond well with the predicted frequencies in air. However, water modes are more challenging. Further investigation is needed to understand acoustic measurements in the higher density media.
Asymptotic theory of neutral stability curve of the Couette flow of vibrationally excited gas
Grigor'ev, Yu N.; Ershov, I. V.
2016-06-01
The asymptotic theory of neutral stability curve of the supersonic plane Couette flow of vibrationally excited gas is constructed. The system of two-temperature viscous gas dynamics equations was used as original mathematical model. Spectral problem for an eighth order linear system of ordinary differential equations was obtained from the system within framework of classical theory of linear stability. Transformations of the spectral problem universal for all shear flows were carried along the classical Dunn — Lin scheme. As a result the problem was reduced to secular algebraic equation with a characteristic division on “inviscid” and “viscous” parts which was solved numerically. The calculated neutral stability curves coincide in limits of 10% with corresponding results of direct numerical solution of original spectral problem.
Krygier, Michael; Grigoriev, Roman
2015-11-01
A direct transition from laminar to turbulent flow has recently been discovered experimentally in the small-gap Taylor-Couette flow with counter-rotating cylinders. The subcritical nature of this transition is a result of relatively small aspect ratio, Γ = 5 . 26 for large Γ the transition is supercritical and involves an intermediate stable state (Coughlin & Marcus, 1996) - interpenetrating spirals (IPS). We investigate this transition numerically to probe the dynamics in regimes inaccessible to experiments for a fixed Reo = - 1000 by varying Rei . The numerics reproduce all the experimentally observed features and confirm the hysteretic nature of the transition. As Rei is increased, the laminar flow transitions to turbulence, with an unstable IPS state mediating the transition, similar to the Tollmien-Schlichting waves in plane Poiseuille flow. As Rei is decreased, turbulent flow transitions to a stable, temporally chaotic IPS state. This IPS state further transitions to either laminar or turbulent flow as Rei is decreased or increased. The stable IPS state is reminiscent of the pre-turbulent chaotic states found numerically in plane Poiseuille flow (Zammert & Eckhardt, 2015), but previously never observed experimentally.
A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow
Moser, R. D.; Moin, P.; Leonard, A.
1983-01-01
A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.
Numerical Simulations of Dynamos Generated in Spherical Couette Flows
Guervilly, Céline; 10.1080/03091920903550955
2010-01-01
We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculi...
Polymer solutions in co-rotating Taylor-Couette flow without vorticity
Zell, A.; Wagner, C.
2012-02-01
We present experimental results of the flow of dilute and semi-dilute polymer solutions in co-rotating Taylor-Couette cylinders. The experimental set-up consists of a modified Mars II rheometer (Thermo Scientific) with two drive units that are mounted opposite each other. The rotational velocities of the inner and outer cylinders are chosen in a way such that the angular velocity has a 1/r profile and the flow is free of vorticity, but the direction of elongation is not constant, but rotates with the flow. Our particle image velocimetry (PIV) measurements show that for polymer solutions without shear thinning the flow is indeed free of vorticity and is equal to a stagnation point flow at a given position and a given instant in time. In contrast, torque measurements reveal that the stresses are identical to the stresses that are present in a plane shear flow. Thus, we find that for polymer solutions a flow with vorticity and a constant direction of elongation is equal to a flow without vorticity in which the direction of elongation is rotating. Finally, we show that for shear thinning solutions the flow velocity becomes non-monotonic through the gap and resembles a pluglike profile which is known from the Poiseuille flow.
Stability of Couette flow past a viscoelastic solid
Hess, Andrew; Gao, Tong
2016-11-01
Soft materials such as polymer gels have been widely used in engineering applications such as microfluidics, micro-optics, and active surfaces. It is important to obtain fundamental understandings of the dynamics of various soft materials when interacting with fluid. Here we investigate the material behavior of a viscoelastic solid film immersed in a simple Newtonian Couette flow. An Eulerian formulation of the Zener model is used to model the solid phase with the surface tension effect. A linear stability analysis is first performed to predict the material instabilities induced by the shear flow field, and provide an analytical basis to the numerical results. The nonlinear fluid/elastic structure interactions are further explored by using the direct numerical simulations. Phase tracking is accomplished through the use of a generalized Cahn-Hilliard model for the surface tension between the gel-like material and the ambient fluid. The coupled Cahn-Hilliard/Navier-Stokes/Zener equations are then solved on a staggered grid through a finite difference method. The results are compared with previous studies for both the hyperelastic and viscoelastic materials.
Heat transfer in laminar Couette flow laden with rigid spherical particles
Ardekani, Mehdi Niazi; Picano, Francesco; Brandt, Luca
2016-01-01
We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations using a direct-forcing immersed boundary method to account for the dispersed phase. A volume of fluid approach is employed to solve the temperature field inside and outside of the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed. In addition, an average composite diffusivity can be used to predict the effective diffusivity of the suspension the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger...
Stability of the Couette-Poiseuille flow by the Reynolds-Orr energy equation
Lam, F
2012-01-01
The normal-mode analysis of the Reynolds-Orr energy equation governing the stability of viscous motion for general three-dimensional disturbances has been revisited. The energy equation has been solved as an unconstrained minimization problem for the Couette-Poiseuille flow. The minimum Reynolds number for every Couette-Poiseuille velocity profile has been computed and compared with those available in the literature. For fully three-dimensional disturbances, it is shown that the minimum Reyno...
Rigid spherical particles in highly turbulent Taylor-Couette flow
Bakhuis, Dennis; Verschoof, Ruben A.; Mathai, Varghese; Huisman, Sander G.; Lohse, Detlef; Sun, Chao
2016-11-01
Many industrial and maritime processes are subject to enormous frictional losses. Reducing these losses even slightly will already lead to large financial and environmental benefits. The understanding of the underlying physical mechanism of frictional drag reduction is still limited, for example, in bubbly drag reduction there is an ongoing debate whether deformability and bubble size are the key parameters. In this experimental study we report high precision torque measurements using rigid non-deformable spherical particles in highly turbulent Taylor-Couette flow with Reynolds numbers up to 2 ×106 . The particles are made of polystyrene with an average density of 1.036 g cm-3 and three different diameters: 8mm, 4mm, and 1.5mm. Particle volume fractions of up to 6% were used. By varying the particle diameter, density ratio of the particles and the working fluid, and volume fraction of the particles, the effect on the torque is compared to the single phase case. These systematic measurements show that adding rigid spherical particles only results in very minor drag reduction. This work is financially supported by Netherlands Organisation for Scientific Research (NWO) by VIDI Grant Number 13477.
Nonaxisymmetric linear instability of cylindrical magnetohydrodynamic Taylor-Couette flow.
Child, Adam; Kersalé, Evy; Hollerbach, Rainer
2015-09-01
We consider the nonaxisymmetric modes of instability present in Taylor-Couette flow under the application of helical magnetic fields, mainly for magnetic Prandtl numbers close to the inductionless limit, and conduct a full examination of marginal stability in the resulting parameter space. We allow for the azimuthal magnetic field to be generated by a combination of currents in the inner cylinder and fluid itself and introduce a parameter governing the relation between the strength of these currents. A set of governing eigenvalue equations for the nonaxisymmetric modes of instability are derived and solved by spectral collocation with Chebyshev polynomials over the relevant parameter space, with the resulting instabilities examined in detail. We find that by altering the azimuthal magnetic field profiles the azimuthal magnetorotational instability, nonaxisymmetric helical magnetorotational instability, and Tayler instability yield interesting dynamics, such as different preferred mode types and modes with azimuthal wave number m>1. Finally, a comparison is given to the recent WKB analysis performed by Kirillov et al. [Kirillov, Stefani, and Fukumoto, J. Fluid Mech. 760, 591 (2014)JFLSA70022-112010.1017/jfm.2014.614] and its validity in the linear regime.
Linear stability of the Couette flow of a vibrationally excited gas. 2. viscous problem
Grigor'ev, Yu. N.; Ershov, I. V.
2016-03-01
Based on the linear theory, stability of viscous disturbances in a supersonic plane Couette flow of a vibrationally excited gas described by a system of linearized equations of two-temperature gas dynamics including shear and bulk viscosity is studied. It is demonstrated that two sets are identified in the spectrum of the problem of stability of plane waves, similar to the case of a perfect gas. One set consists of viscous acoustic modes, which asymptotically converge to even and odd inviscid acoustic modes at high Reynolds numbers. The eigenvalues from the other set have no asymptotic relationship with the inviscid problem and are characterized by large damping decrements. Two most unstable viscous acoustic modes (I and II) are identified; the limits of these modes were considered previously in the inviscid approximation. It is shown that there are domains in the space of parameters for both modes, where the presence of viscosity induces appreciable destabilization of the flow. Moreover, the growth rates of disturbances are appreciably greater than the corresponding values for the inviscid flow, while thermal excitation in the entire considered range of parameters increases the stability of the viscous flow. For a vibrationally excited gas, the critical Reynolds number as a function of the thermal nonequilibrium degree is found to be greater by 12% than for a perfect gas.
Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field
Institute of Scientific and Technical Information of China (English)
G.S.SETH; S.M.HUSSAIN; S.SARKAR
2014-01-01
This paper presents a study of hydromagnetic Couette flow of an incompress-ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp-totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.
Zhu, X.; Ostilla-Monico, Rodolfo; Verzicco, R.; Lohse, D.
2016-01-01
We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\\it\\eta}=r_{i}/r_{o}=0.714$η=ri/ro=0.714 with inner cylinder Reynolds number up to $Re_{i}=3.76\\times 10^{4}$Rei=3.76×104, corresponding to Taylor number up to $Ta=2.15\\times 10^{9}$Ta=2.15×10
Borrero-Echeverrry, Daniel; Morrison, Benjamin; Peairs, Evan
2015-11-01
Despite centuries of study, fluid dynamicists are still unable to explain why a large class of flows, including pipe flow and plane Couette flow, become turbulent. Hydrodynamic stability theory predicts these flows should be stable to infinitesimal perturbations, which means finite-amplitude perturbations need to be applied to destabilize them. We present the results of a series of experiments studying such subcritical transitions to turbulence in linearly-stable configurations of Taylor-Couette flow. In particular, we discuss how the stability of these flows depends on the size and duration of the applied perturbation as the aspect ratio of the experimental apparatus is varied. We show that for experimental configurations where the end caps rotate with the outer cylinder, the stability of the flow is enhanced at small aspect ratios. We find that at sufficiently high Reynolds numbers, perturbations must exceed a critical amplitude before the transition to turbulence can be triggered. The scaling of this threshold with Re appears to be different than that which has been reported for other linearly-stable shear flows. This work was supported by Reed College's Summer Scholarship Fund, the James Borders Physics Student Fellowship, and the Reed College Science Research Fellowship. We also thank H.L. Swinney, who kindly donated the apparatus used in these experiments.
Three-Dimensional Modes of Fiber Suspensions in the Taylor-Couette Flow
Institute of Scientific and Technical Information of China (English)
WAN Zhan-hong; LIN Jian-zhong; YOU Zhen-jiang
2007-01-01
The linear stability analysis of the fiber suspension Taylor-Couette flow against axisymmetric and non-axisymmetric disturbances is investigated. A generalized complex eigenvalue problem generated from the linearized set of the three-dimensional governing system equations around the basic Couette azimuthal solution are solved numerically with the Chebyshev spectral method. In a wide range of radius ratios and the magnitudes of counter rotating, critical bifurcation thresholds from the axisymmetric Couette flow to the flow with different azimuthal wave numbers are obtained. The complex dispersion relations of the linearized stability equation system for vortex patterns with different azimuthal wave number are calculated for real axial wave numbers for axially extended vortex structures.
Navier-Stokes-Fourier analytic solutions for non-isothermal Couette slip gas flow
Directory of Open Access Journals (Sweden)
Milićev Snežana S.
2016-01-01
Full Text Available The explicit and reliable analytical solutions for steady plane compressible non-isothermal Couette gas flow are presented. These solutions for velocity and temperature are developed by macroscopic approach from Navier-Stokes-Fourier system of continuum equations and the velocity slip and the temperature jump first order boundary conditions. Variability of the viscosity and thermal conductivity with temperature is involved in the model. The known result for the gas flow with constant and equal temperatures of the walls (isothermal walls is verified and a new solution for the case of different temperature of the walls is obtained. Evan though the solution for isothermal walls correspond to the gas flow of the Knudsen number Kn≤0.1, i.e. to the slip and continuum flow, it is shown that the gas velocity and related shear stress are also valid for the whole range of the Knudsen number. The deviation from numerical results for the same system is less than 1%. The reliability of the solution is confirmed by comparing with results of other authors which are obtained numerically by microscopic approach. The advantage of the presented solution compared to previous is in a very simple applicability along with high accuracy. [Projekat Ministarstva nauke Republike Srbije, br. 35046 i 174014
Exploring the phase diagram of fully turbulent Taylor–Couette flow
Ostilla Monico, Rodolfo; Poel, van der Erwin P.; Verzicco, Roberto; Grossmann, Siegfried; Lohse, Detlef
2014-01-01
Direct numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to 3×10 5 , corresponding to Taylor numbers of Ta=4.6×10 10 , were reached. Effective scaling laws for the torque are presented.
Experimental techniques for turbulent Taylor–Couette flow and Rayleigh–Bénard convection
Sun, Chao; Zhou, Quan
2014-01-01
Taylor–Couette (TC) flow and Rayleigh–B´enard (RB) convection are two systems in hydrodynamics, which have been widely used to investigate the primary instabilities, pattern formation, and transitions from laminar to turbulent flow. These two systems are known to have an elegant mathematical similar
Energy Technology Data Exchange (ETDEWEB)
Siewert, C.E. [North Carolina State Univ., Dept. Mathematics, Raleigh, NC (United States)
2002-10-01
A synthetic-kernel model (CES model) of the linearized Boltzmann equation is used along with an analytical discrete-ordinates method (ADO) to solve three fundamental problems concerning flow of a rarefied gas in a plane channel. More specifically, the problems of Couette flow, Poiseuille flow and thermal-creep flow are solved in terms of the CES model equation for an arbitrary mixture of specular and diffuse reflection at the walls confining the flow, and numerical results for the basic quantities of interest are reported. The comparisons made with results derived from solutions based on computationally intensive methods applied to the linearized Boltzmann equation are used to conclude that the CES model can be employed with confidence to improve the accuracy of results available from simpler approximations such as the BGK model or the S model. (author)
Quantitative investigation of the transition process in Taylor-Couette flow
Energy Technology Data Exchange (ETDEWEB)
Tu, Xin Cheng; Kim, Hyoung Bum Kim [Gyeongsang National University, Jinju (Korea, Republic of); Liu, Dong [Jiangsu University, Zhenjiang (China)
2013-02-15
The transition process from circular Couette flow to Taylor vortex flow regime was experimentally investigated by measuring the instantaneous velocity vector fields at the annular gap flow region between two concentric cylinders. The proper orthogonal decomposition method, vorticity calculation, and frequency analysis were applied in order to analyze the instantaneous velocity fields to identify the flow characteristics during the transition process. From the results, the kinetic energy and corresponding reconstructed velocity fields were able to detect the onset of the transition process and the alternation of the flow structure. The intermittency and oscillation of the vortex flows during the transition process were also revealed from the analysis of the instantaneous velocity fields. The results can be a measure of identifying the critical Reynolds number of the Taylor-Couette flow from a velocity measurement method.
Exact near-wall traveling waves of plane Poiseuille flow
Gibson, John; Brand, Evan
2013-11-01
We present several spatially-localized equilibrium and traveling-wave solutions of plane Couette and plane Poiseuille flow. The solutions consist of highly concentrated and spanwise-localized alternating streamwise rolls, centered over low-speed streamwise streaks and flanked on either side by high-speed streaks. For large Reynolds numbers the solutions develop critical layers that are concentrated at isolated points on the critical surface u = c . For several traveling-wave solutions of plane Poiseuille flow, the rolls are concentrated near one wall, producing streaks near the wall and larger reduction of the bulk flow in the core. These solutions form particularly isolated and elemental versions of near-wall coherent structures in shear flows and capture, as precise time-independent solutions of Navier-Stokes, the process by which near-wall rolls exchange momentum between the wall and core regions and thereby increase drag.
Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas
Grigor'ev, Yu. N.; Ershov, I. V.
2017-01-01
An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.
Energy Technology Data Exchange (ETDEWEB)
Aydin, Orhan; Avci, Mete [Karadeniz Technical University, Trabzon (Turkey). Department of Mechanical Engineering
2006-08-15
In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette-Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement. (author)
Intermittent boundary layers and torque maxima in Taylor-Couette flow
Brauckmann, H.J.; Eckhardt, B.E.
2013-01-01
Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios η=0.5 and 0.71 and propose a theoretical model for the critical value
Torque scaling in turbulent Taylor–Couette flow between independently rotating cylinders
Eckhardt, Bruno; Grossmann, Siegfried; Lohse, Detlef
2007-01-01
Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, c
Taylor–Couette turbulence at radius ratio η=0.5: scaling, flow structures and plumes
Veen, van der R.C.A.; Huisman, S.G.; Merbold, S.; Harlander, U.; Egbers, C.; Lohse, D.; Sun, C.
2016-01-01
Using high-resolution particle image velocimetry, we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor–Couette flow for a radius ratio of 0.5 and Taylor number of up to 6:2 109. The extracted angular velocity profiles follow a log law more closely
Drag reduction by surface treatment in turbulent Taylor-Couette flow
Greidanus, A.J.; Delfos, R.; Westerweel, J.
2011-01-01
We use a Taylor-Couette facility to study the drag reducing effects of commercial surface products at high shear Reynolds numbers (Res) under perfect couter-rotating conditions (riwi=rowo). The correlation between torque contribution of the von Karman flow and shear Reynolds number is investigated.
Torque scaling in turbulent Taylor-Couette flow between independentely rotating cylinders
Eckhardt, Bruno; Grossmann, Siegfried; Lohse, Detlef
2007-01-01
Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, c
Zhu, Xiaojue; Verzicco, Roberto; Lohse, Detlef
2015-01-01
We present direct numerical simulations of Taylor-Couette flow with grooved walls at a fixed radius ratio $\\eta=r_i/r_o=0.714$ with inner cylinder Reynolds number up to $Re_i=3.76\\times10^4$, corresponding to Taylor number up to $Ta=2.15\\times10^9$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of $90^\\circ$. Results are compared with the smooth wall case in order to investigate the effects of grooves on Taylor-Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from tips of the grooves and a secondary circulation between the latter is formed. This is associated to a sharp increase of the torque and thus the effective scaling law for the torque vs. $Ta$ becomes much ...
Klotz, Lukasz; Lemoult, Gregoire; Wesfreid, Jose Eduardo
2015-11-01
We describe a new experimental set-up which allows us to study the sub-critical transition to turbulence in a two dimensional shear flow (including plane Couette, plane Couette-Poiseuille and plane Poiseuille flows). Our facility is an extension of a classical plane Couette experiment, in which one uses a single closed loop of plastic belt to generate the opposite sign velocity at each wall of the test section. However, in our case, we use two independent closed loops of plastic belt, one at each wall of the test section. The speed of these belts may be controlled separately. That enables to set two different velocities (in value and direction) as a boundary conditions at each of two test section's walls. In addition the pressure gradient in streamwise direction can be controlled. In particular, the plane Poiseuille flow with zero mean advection velocity can be created. We characterize by PIV the basic flow for different configurations. For a plane Poiseuille flows as base flow, we were able to observe for the first time the nearly stationary turbulent spots in this flow, with structures of characteristic wavelength ~ the distance between the two plates.
Subcritical transition to turbulence in plane channel flows
Orszag, S. A.; Patera, A. T.
1980-01-01
A linear three dimensional mechanism for the transition of plane Poiseuille flows to turbulence is presented which provides good agreement with experimental observations. The mechanism is based on the evolution of states within a band of quasi-equilibria which slowly approach the stable upper branch solutions for the evolution of flow energy but which are strongly unstable to infinitesimal three-dimensional disturbances. Numerical simulation has shown that if two-dimensional flow persists long enough for the three-dimensional perturbations to attain finite amplitude, the resulting three dimensional flow quickly develops a turbulent character with nonperiodic behavior, and thus transition can be predicted from knowledge of the initial two- and three-dimensional energies and time scales. The mechanism predicts transition to turbulence at Reynolds numbers greater than 1000, as observed in experiments, and implies higher threshold three-dimensional energies in plane Couette flow.
On sufficient stability conditions of the Couette — Poiseuille flow of monodisperse mixture
Popov, D. I.; Sagalakov, A. M.; Nikitenko, N. G.
2011-06-01
The stability of the Couette — Poiseuille flow of a monodisperse mixture is considered. Sufficient stability conditions are derived. Results of the computation of the spectrum are presented. A considerable stabilization of the flow with particles admixture to small disturbances is observed. It is found that the regions of instability generation may have complex geometry. The influence of the main velocity profile and admixture parameters on the stability conditions is considered.
Transition to two-dimensionality in magnetohydrodynamic turbulent Taylor-Couette flow.
Zhao, Yurong; Tao, Jianjun; Zikanov, Oleg
2014-03-01
Transition from a Taylor-Couette turbulent flow to a completely two-dimensional axisymmetric turbulent state is realized numerically by increasing gradually the strength of the azimuthal magnetic field produced by electric current flowing through the axial rod. With the increase of the Hartmann number, the Taylor-vortex-like structures shrink, move closer to the inner cylinder, and turn into unsteady but perfect tori at sufficiently high Hartmann numbers.
Directory of Open Access Journals (Sweden)
Damala Ch Kesavaiah
2013-04-01
Full Text Available The present study the free convection in unsteady Couette flow of a viscous incompressible fluid confined between two vertical parallel plates in the presence of thermal radiation with heat source in the presence of uniform magnetic field is presented. The flow is induced by means of Couette motion and free convection currents occurring as a result of application of constant heat flux on the wall with a uniform vertical motion in its own plane while constant temperature on the stationary wall. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The dimensionless governing partial differential equations are solved by using regular perturbation technique. The results for the velocity, temperature and the skin-friction are shown graphically. The effects of different parameters are discussed.
Exploring the phase space of multiple states in highly turbulent Taylor-Couette flow
van der Veen, Roeland C. A.; Huisman, Sander G.; Dung, On-Yu; Tang, Ho L.; Sun, Chao; Lohse, Detlef
2016-06-01
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of Ta =1011 to 9 ×1012 by measuring the global torques and the local velocities while probing the phase space spanned by the rotation rates of the inner and outer cylinders. The multiple states are found to be very robust and are expected to persist beyond Ta =1013 . The rotation ratio is the parameter that most strongly controls the transitions between the flow states; the transitional values only weakly depend on the Taylor number. However, complex paths in the phase space are necessary to unlock the full region of multiple states. By mapping the flow structures for various rotation ratios in a Taylor-Couette setup with an equal radius ratio but a larger aspect ratio than before, multiple states are again observed. Here they are characterized by even richer roll structure phenomena, including an antisymmetrical roll state.
The numerical simulation of Taylor-Couette flow with radial temperature gradient
Tuliszka-Sznitko, E.; Kiełczewski, K.
2016-10-01
The Taylor-Couette flow with radial temperature gradient is a canonical problem for the study of heat transfer in engineering issues. However, gaining insight into the transitional Taylor-Couette flow with temperature gradient still requires detailed experimental and numerical investigations. In the present paper we have performed computations for the cavity of aspect ratio Γ= 3.76 and radii ratios η= 0.82 and 0.375 with the heated rotating bottom disk and stationary outer cylinder. We analyse the influence of the end-wall boundary conditions and the thermal conditions on the flow structure, and on the distributions of the Nusselt number and torque along the inner and outer cylinders. The averaged values along the inner cylinder of the Nusselt number and torque obtained for different Re are analysed in the light of the results published in [2, 16, 17].
Mutabazi, Innocent; Bai, Yang; Crumeyrolle, Olivier
2015-11-01
The analogy between viscoelastic instability in the Taylor-Couette flow and the magnetorotational instability (MRI) has been found by Ogilvie & Potter. It relies on the similarity between the governing equations of viscoelastic flows of constant viscosity (Oldroyd-B model equations)and those of Magnetohydrodynamics (MHD). We have performed linear stability analysis of the Taylor-Couette flow with a polymer solution obeying the Oldroyd-B model. A diagram of critical states shows the existence of stationary and helicoidal modes depending on the elasticity of the polymer solution. A generalized Rayleigh criterion determines the potentially unstable zone to pure elasticity-driven perturbations. Experimental results yield four type of modes : one pure elasticity mode and three elastorotational modes that are the MRI-analog modes. Anti-Keplerian case has also been investigated. There is a good agreement between experimental and theoretical results. Work supported by the CPER and ANR-LABEX EMC3.
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow
Vastano, John A.; Moser, Robert D.
1991-01-01
The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.
Magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
Guseva, A; Hollerbach, R; Avila, M
2015-01-01
The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor--Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in agree...
Short-time Lyapunov exponent analysis and the transition to chaos in Taylor-Couette flow
Vastano, John A.; Moser, Robert D.
1991-01-01
The physical mechanism driving the weakly chaotic Taylor-Couette flow is investigated using the short-time Liapunov exponent analysis. In this procedure, the transition from quasi-periodicity to chaos is studied using direct numerical 3D simulations of axially periodic Taylor-Couette flow, and a partial Liapunov exponent spectrum for the flow is computed by simultaneously advancing the full solution and a set of perturbations. It is shown that the short-time Liapunov exponent analysis yields more information on the exponents and dimension than that obtained from the common Liapunov exponent calculations. Results show that the chaotic state studied here is caused by a Kelvin-Helmholtz-type instability of the outflow boundary jet of Taylor vortices.
Deguchi, K.; Altmeyer, S.
2013-04-01
Interactions between nearly bicritical modes in Taylor-Couette flow, which have been concerned with the framework of weakly nonlinear theory, are extended to fully nonlinear Navier-Stokes computation. For this purpose, a standard Newton solver for axially periodic flows is generalized to compute any mixed solutions having up to two phases, which typically arise from interactions of two spiral or Taylor vortex modes. Also, a simple theory is developed in order to classify the mixed solutions. With these methods, we elucidate pattern formation phenomena, which have been observed in a Taylor-Couette flow experiment. Focusing on the counter-rotating parameter range, all possible classes of interaction of various solutions with different azimuthal and axial wave numbers are considered within our computational restriction, and we observe numerous connection branches, e.g., footbridge solutions. Some of the mixed solutions result in a three-dimensional wavy spiral solution with axial relative periodicity or an axially doubly periodic toroidally closed vortex solution. The possible connection of the former solution family to spiral turbulence, which has been observed in highly counter-rotating Taylor-Couette flow, is discussed.
Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers
Abramov, Rafail V
2016-01-01
In the current work we propose a diffusive modification of the Boltzmann equation. This naturally leads to the corresponding diffusive fluid dynamics equations, which we numerically investigate in a simple Couette flow setting. This diffusive modification is based on the assumption of the "imperfect" model collision term, which is unable to track all collisions in the corresponding real gas particle system. The effect of missed collisions is then modeled by an appropriately scaled long-term homogenization process of the particle dynamics. The corresponding diffusive fluid dynamics equations are produced in a standard way by closing the hierarchy of the moment equations using either the Euler or the Grad closure. In the numerical experiments with the Couette flow, we discover that the diffusive Euler equations behave similarly to the conventional Navier-Stokes equations, while the diffusive Grad equations additionally exhibit Knudsen-like velocity boundary layers. We compare the simulations with the correspond...
Chinyoka, T.; Makinde, O. D.
2013-01-01
The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively. PMID:23956691
Influence of nonlinear chemical reactions on the transport coefficients in oscillatory Couette flow
Barik, Swarup; Dalal, D. C.
2016-10-01
A multiple-scale method of averaging is applied to the study of transport of a chemical species in oscillatory Couette flow where the species may undergoes a reversible phase exchange with the boundary wall and nonlinear chemical reactions both within the fluid and at the boundary wall. Analytical expressions are obtained for transport coefficients. The results shows how the transport coefficients are influenced by the reversible phase exchange reaction kinetics and the rate and degree of the nonlinear decay chemical reaction.
Drag reduction by surface treatment in turbulent Taylor-Couette flow
Greidanus, A. J.; Delfos, R.; Westerweel, J.
2011-12-01
We use a Taylor-Couette facility to study the drag reducing effects of commercial surface products at high shear Reynolds numbers (Res) under perfect couter-rotating conditions (riwi = -rowo). The correlation between torque contribution of the von Kármán flow and shear Reynolds number is investigated. At this moment no significant drag changes are found for the commercial products. However, further research is needed to exclude uncertainties and errors from the torque measurements.
Reynolds Number Effects on Turbulent Characteristics of Taylor-Couette Flow
Park, Joonhwi; Fukushima, Naoya; Shimura, Masayasu; Tanahashi, Mamoru; Miyauchi, Toshio
2012-11-01
Laminar and turbulent Taylor-Couette flow is of great importance in a wide range of engineering applications, such as viscosity measurement devices, rotating machineries and reactors. In this study, we focus on turbulent Taylor-Couette flow with a fixed outer cylinder and a rotating inner cylinder. Direct numerical simulation (DNS) of turbulent Taylor-Couette flow has been conducted to investigate turbulent characteristics including Reynolds stress budget at Reynolds number from 8000 to 20000. Reynolds number, Re, is defined by gap width and rotating speed of inner cylinder. In this range of Re, turbulent characteristics are expected to change around Re=10000, referring to Wendt's empirical formula. Averaged torque from DNS agrees well with Wendt's empirical formula and torque transition is confirmed around Re=10000. Averaged azimuthal velocity normalized by friction velocity on inner/outer wall increases in logarithmic region with increase in Re. All components of Reynolds stress tensor also increase in all domain. The minute movement of center of Taylor vortices is observed spatially and temporally when Re is over 12000. Finally, Reynolds stress budgets are investigated to figure out Reynolds number effects on turbulent statistics in detail.
A kinetic theory treatment of heat transfer in plane Poiseuille flow with uniform pressure
Bahrami, Parviz A.
1992-01-01
Plane compressible Poiseuille flow with uniform pressure (Couette flow with stationary boundaries) is revisited where the Lees two-steam method with the Enskog equation of change is applied. Single particle velocity distribution functions are chosen, which preserve the essential physical features of this flow with arbitrary but uniform plate temperatures and gas pressure. Lower moments are shown to lead to expressions for the parameter functions, molecular number densities, and temperatures which are entirely in agreement with those obtained in the analysis of Lees for compressible plane Couette flow in the limit of low Mach number and vanishing mean gas velocity. Important simplifications result, which are helpful in gaining insight into the power of kinetic theory in fluid mechanics. The temperature distribution, heat flux, as well as density, are completely determined for the whole range of Knudson numbers from free molecular flow to the continuum regime, when the pressure level is specified.
The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow
Clark, S E
2016-01-01
We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor-Couette flow. This is a multiscale perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor-Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg-Landau equation (GLE), while the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.
ASYMPTOTIC ANALYSIS OF DOWNSTREAM EIGENVALUES FOR STATIONARY PERTURBATION OF COUETTE-POISEUILLE FLOW
Institute of Scientific and Technical Information of China (English)
Song Jin-bao; Wei En-bo; Tian Ji-wei
2003-01-01
Two-dimensional viscous flow in a straight channel was studied. The steady Navier-Stokes equations were linearized on the assumption of small disurbance from the Couette-Poiseuille flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation. The eigenvalues determine the rate of decay for the stationary perturbation. Asymptotic forms of the downstream eigenvalues were derived in the limiting cases of small and large Reynolds number, for the flow with a general mass flux per unit width, and thus the work of Wilson (1969) and Stocker and Duck (1995) was generalized. The asymptotic results are in agreement with numerical ones presented by Song and Chen (1995).
Second Law Analysis for a Variable Viscosity Reactive Couette Flow under Arrhenius Kinetics
Directory of Open Access Journals (Sweden)
N. S. Kobo
2010-01-01
Full Text Available This study investigates the inherent irreversibility associated with the Couette flow of a reacting variable viscosity combustible material under Arrhenius kinetics. The nonlinear equations of momentum and energy governing the flow system are solved both analytically using a perturbation method and numerically using the standard Newton Raphson shooting method along with a fourth-order Runge Kutta integration algorithm to obtain the velocity and temperature distributions which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field.
New exact coherent states in plane Poiseuille flow
Nagata, Masato; Deguchi, Kengo
2012-11-01
Two new classes of traveling wave solution are found in plane Poiseuille flow by continuing the stationary and traveling hairpin vortex states in plane Couette flow. One of them, referred to as MS hereafter, arises from a saddle-node bifurcation, characterized by two planes of mirror-symmetry perpendicular to the span-wise direction. The second new class solution, referred to as AS hereafter, bifurcates by breaking the mid-plane symmetry of the first class. Both MS and AS are characterized by two quasi-stream-wise low-speed streaks within one span-wise period. The low-speed streaks are aligned with the vertical planes of mirror symmetry, with their width varying in a varicose fashion in the stream-wise direction. These streaks appear close to both top and bottom channel walls for MS, and to only one of the channel walls for AS. We find that the Reynolds numbers at the saddle-node bifurcation for MS and AS are smaller than that of the exact coherent state in plane Poiseuille flow known to date found by Waleffe (2003).
Bypass transition and subcritical turbulence in plane Poiseuille flow
Zammert, Stefan
2015-01-01
Plane Poiseuille flow shows turbulence at a Reynolds number that is lower than the critical one for the onset of Tollmien-Schlichting waves. The transition to turbulence follows the same route as the by-pass transition in boundary layers, i.e. finite amplitude perturbations are required and the flow is dominated by downstream vortices and streaks in the transitional regime. In order to relate the phenomenology in plane Poiseuille flow to our previous studies of plane Couette flow (Kreilos & Eckhardt, 2012), we study a symmetric subspace of plane Poiseuille flow in which the bifurcation cascade stands out clearly. By tracing the edge state, which in this system is a travelling wave, and its bifurcations, we can trace the formation of a chaotic attractor, the interior crisis that increase the phase space volume affected by the flow, and the ultimate transition into a chaotic saddle in a crisis bifurcation. After the boundary crisis we can observe transient chaos with exponentially distributed lifetimes.
Institute of Scientific and Technical Information of China (English)
Bhupendra.Kumar Sharma; Mamta Agarwal; R.C.Chaudhary
2007-01-01
A theoretical analysis of three-dimensional Couette flow with radiation effect on temperature distribution has been analysed, when the injection of the fluid at the lower stationary plate is a transverse sinusoidal one and its corresponding removal by constant suction through the upper porous plate is in uniform motion. Due to this type of injection velocity, the flow becomes three-dimensional. The effect of Prandtl number,radiation parameter and injection parameter on rate of heat transfer has been examined by the help of graphs. The Prandtl number has a much greater effect on the temperature distribution than the injection or radiation parameter.
Unsteady hydromagnetic Couette flow through a porous medium in a rotating system
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper investigates the unsteady hydromagnetic Couette fluid flow through a porous medium between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system using boundary layer approximation.The fluid is assumed to be Newtonian and incompressible.Laplace transform technique is adopted to obtain a unified solution of the velocity fields.Such a flow model is of great interest,not only for its theoretical significance,but also for its wide applicatio...
The stratorotational instability of Taylor-Couette flows of moderate Reynolds numbers
Rüdiger, G; Schultz, M; Gellert, M; Harlander, U; Egbers, Chr
2016-01-01
The instability against nonaxisymmetric perturbations of a Taylor-Couette flow with an axial density stratification is considered. The potential flow (driven by cylinders rotating according to the Rayleigh limit) becomes unstable if the Froude number Fr (= rotation frequency/buoyancy frequency) fulfills ${\\rm Fr}_{\\rm min} 1$ so that measurements for too high Reynolds numbers are excluded for axially bounded containers. The instability pattern migrates azimuthally with $\\dot{\\phi} / \\Omega_{\\rm out} \\simeq 1$ so that the SRI pattern always drifts (slightly) faster than the outer cylinder rotates. The measurements confirm this prediction with high accuracy.
Suppression of turbulent resistivity in turbulent Couette flow
Energy Technology Data Exchange (ETDEWEB)
Si, Jiahe, E-mail: jsi@nmt.edu; Sonnenfeld, Richard G.; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe [New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801 (United States); Colgate, Stirling A.; Li, Hui [Los Alamos National Laboratory, Los Alamos, New Mexico 87544 (United States); Nornberg, Mark D. [University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)
2015-07-15
Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations.
Computational modeling of flow and combustion in a couette channel simulating microgravity
Hamdan, Ghaleb
Theoretically a Couette flow in a narrow channel can be utilized to simulate microgravity conditions experienced by a surface flame due to the linear velocity profile. Hence, the Couette channel is a potential apparatus for the study of flame spread in an environment that recreated microgravity flow conditions. Simulated microgravity conditions were achieved by limiting the vertical extent over and under the flame to suppress buoyancy. This numerical study was done for a 2-D channel using Fire Dynamics Simulator (FDS). This thesis is divided into two sections; the first is the study of Couette flow with a non-reacting cold flow in a finite length channel, a subject with surprisingly little past research, despite the ubiquity of "infinite" Couette channels in text books. The channel was placed in a room to allow for a better representation of a realistic channel and allow the flow and pressure field to develop without forcing them at the inlet and outlet. The plate's velocities, channel's gap and the channel's length were varied and the results of the u-velocity profile, w-velocity profile and pressure were investigated. The entrance length relationship with Reynolds number for a finite Couette Channel was determined for the first time - as far as the author knows - in order to ensure the flame occurs in a fully developed flow. In contrast to an infinite channel, the u-velocity was found to be nonlinear due to an adverse pressure differential created along the channel attributed to the pull force along the entrance of the channel created by the top plate a well as the pressure differential created by the flow exiting the channel. The linearity constant was derived for the one moving plate case. The domain consisted of a rectangular region with the top plate moving and the bottom plate fixed except for a few cases in which the bottom plate also moved and were compared with only one moving plate. The second section describes the combustion of a thin cellulose sample
Optimal separation times for electrical field flow fractionation with Couette flows.
Pascal, Jennifer; O'Hara, Ryan; Oyanader, Mario; Arce, Pedro E
2008-11-01
The prediction of optimal times of separation as a function of the applied electrical field and cation valence have been studied for the case of field flow fractionation [Martin M., Giddings J. C., J. Phys. Chem. 1981, 85, 727] with charged solutes. These predictions can be very useful to a priori design or identify optimal operating conditions for a Couette-based device for field flow fractionation when the orthogonal field is an electrical field. Mathematically friendly relationships are obtained by applying the method of spatial averaging to the solute species continuity equation; this is accomplished after the role of the capillary geometrical dimensions on the applied electrical field equations has been assessed [Oyanader M. A., Arce P., Electrophoresis 2005; 26, 2857]. Moreover, explicit analytical expressions are derived for the effective parameters, i.e. diffusivity and convective velocity as functions of the applied (orthogonal) electrical field. These effective transport parameters are used to study the effect of the cation valence of the solutes and of the magnitude of the applied orthogonal electrical field on the values of the optimal time of separation. These parameters play a significant role in controlling the optimal separation time, leading to a family of minimum values, for particular magnitudes of the applied orthogonal electrical field.
Massive separation of turbulent Couette flow in a one-sided expansion channel
Energy Technology Data Exchange (ETDEWEB)
El Khoury, George K. [Department of Marine Technology, Norwegian University of Science and Technology, Trondheim NO-7491 (Norway); Andersson, Helge I.; Barri, Mustafa [Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim NO-7491 (Norway); Pettersen, Bjornar, E-mail: bjornar.pettersen@ntnu.n [Department of Marine Technology, Norwegian University of Science and Technology, Trondheim NO-7491 (Norway)
2010-06-15
Direct numerical simulation has been performed to study wall-driven flow over a backward-facing step at Reynolds number Re=5200 based on the step height h and the upper-wall velocity U{sub w}. The flow configuration consisted of a step with height equal to that of the upstream channel yielding an expansion ratio 2:1. Instantaneous enstrophy contours revealed the formation of Kelvin-Helmholtz instabilities downstream of the step. Intense velocity and vorticity fluctuations were generated in the shear-layer formed between the bulk flow and the massive recirculation zone in the lee of the step. Extraordinarily high turbulence levels persisted in the center region even 7.5h downstream of the step, i.e. where the separated shear-layer reattached to the wall. A fully redeveloped Couette flow cannot be reached in the downstream part of the channel due to the principle of mass conservation. The local wall pressure coefficient gave evidence of an adverse pressure gradient in the recovery region, where a Couette-Poiseuille flow type prevailed.
Effect of intermolecular potential on compressible Couette flow in slip and transitional regimes
Weaver, Andrew B.; Venkattraman, A.; Alexeenko, Alina A.
2014-10-01
The effect of intermolecular potentials on compressible, planar flow in slip and transitional regimes is investigated using the direct simulation Monte Carlo method. Two intermolecular interaction models, the variable hard sphere (VHS) and the Lennard-Jones (LJ) models, are first compared for subsonic and supersonic Couette flows of argon at temperatures of 40, 273, and 1,000 K, and then for Couette flows in the transitional regime ranging from Knudsen numbers (Kn) of 0.0051 to 1. The binary scattering model for elastic scattering using the Lennard-Jones (LJ) intermolecular potential proposed recently [A. Venkattraman and A. Alexeenko, "Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations," Phys. Fluids 24, 027101 (2012)] is shown to accurately reproduce both the theoretical collision frequency in an equilibrium gas as well as the theoretical viscosity variation with temperature. The use of a repulsive-attractive instead of a purely repulsive potential is found to be most important in the continuum and slip regimes as well as in flows with large temperature variations. Differences in shear stress of up to 28% between the VHS and LJ models is observed at Kn=0.0051 and is attributed to differences in collision frequencies, ultimately affecting velocity gradients at the wall. For Kn=1 where the Knudsen layer expands the entire domain, the effect of the larger collision frequency in the LJ model relative to VHS diminishes, and a 7% difference in shear stress is observed.
Unsteady hydromagnetic Couette flow within a porous channel with ...
African Journals Online (AJOL)
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It may be noted that the study of hydromagnetic flow within a porous channel may find application in designing of cooling systems with liquid metals, geothermal reservoirs, ... The paper is organized as follows: In Section 2, formulation of the problem and its ...... Combined effect of free and forced convection on MHD flow in a.
The friction control of magnetic fluid in the Couette flow
Labkovich, O. N.; Reks, A. G.; Chernobai, V. A.
2017-06-01
In the work characteristic areas of magnetic fluid flow are experimentally determined in the gap between the cylinders: the area of strong dipole-dipole interaction between magnetite particles 041,2. For areas with high flow losses in viscous friction is shown the possibility of reducing the introduction of magnetic fluid of carbon nanotubes and creating a rotating magnetic field.
Ellahi, Rahmat; Wang, Xinil; Hameed, Muhammad
2014-02-01
This article is concerned with the study of heat transfer and nonlinear slip effects on the Couette flow of a third-grade fluid. Numerical solutions are obtained by solving nonlinear differential equations using the higher-order Chebyshev spectral method. The results for no slip and no thermal slip become special cases of this study. Moreover, the results for Poiseuille flow can be obtained as a special case from the generalized Couette flow analysis by setting the plate velocity to zero. Graphical results for involved pertinent parameters are sketched and examined.
Bi-stability in turbulent, rotating spherical Couette flow
Zimmerman, Daniel S; Lathrop, Daniel P; 10.1063/1.3593465
2011-01-01
Flow between concentric spheres of radius ratio $\\eta = r_\\mathrm{i}/r_\\mathrm{o} = 0.35$ is studied in a 3 m outer diameter experiment. We have measured the torques required to maintain constant boundary speeds as well as localized wall shear stress, velocity, and pressure. At low Ekman number $E = 2.1\\times10^{-7}$ and modest Rossby number $0.07 < Ro < 3.4$, the resulting flow is highly turbulent, with a Reynolds number ($Re=Ro/E$) exceeding fifteen million. Several turbulent flow regimes are evident as $Ro$ is varied for fixed $E$. We focus our attention on one flow transition in particular, between $Ro = 1.8$ and $Ro = 2.6$, where the flow shows bistable behavior. For $Ro$ within this range, the flow undergoes intermittent transitions between the states observed alone at adjacent $Ro$ outside the switching range. The two states are clearly distinguished in all measured flow quantities, including a striking reduction in torque demanded from the inner sphere by the state lying at higher $Ro$. The redu...
Two-Fluid Couette Flow between Concentric Cylinders.
1984-01-01
CONCENTRIC CYLINDERS Yuriko Renardy and Daniel D. Joseph* Technical Summary Report #2622 January 1984 ABSTRACT -1W considers,he flow of two immiscible...CYLINDERS Yuriko Renardy and Daniel D. Joseph* Introduction We consider linear stability of the flow of two immiscible fluids separated by an interface...AUTiOR(,) 8. CONTRACT OR GRANT NUMBER(@) Yuriko Renardy and Daniel D. Joseph DAAGZ9-80-C-0041 11. PERFORMING ORGANIZATION NAME AND ADDRESS 10
Exploring the phase space of multiple states in highly turbulent Taylor-Couette flow
van der Veen, Roeland C A; Dung, On-Yu; Tang, Ho L; Sun, Chao; Lohse, Detlef
2016-01-01
We investigate the existence of multiple turbulent states in highly turbulent Taylor-Couette flow in the range of $\\mathrm{Ta}=10^{11}$ to $9\\cdot10^{12}$, by measuring the global torques and the local velocities while probing the phase space spanned by the rotation rates of the inner and outer cylinder. The multiple states are found to be very robust and are expected to persist beyond $\\mathrm{Ta}=10^{13}$. The rotation ratio is the parameter that most strongly controls the transitions between the flow states; the transitional values only weakly depend on the Taylor number. However, complex paths in the phase space are necessary to unlock the full region of multiple states. Lastly, by mapping the flow structures for various rotation ratios in a Taylor-Couette setup with an equal radius ratio but a larger aspect ratio than before, multiple states were again observed. Here, they are characterized by even richer roll structure phenomena, including, for the first time observed in highly turbulent TC flow, an ant...
Stability of two-layer Couette flow with application to drag reduction
Mohammadi, Alireza; Smits, Alexander J.
2016-11-01
We consider the linear stability of flows composed of two superposed fluids in Couette flow in order to improve our understanding of the longevity and performance of superhydrophobic surfaces (SHS) or liquid-infused surfaces (LIS) which are important for drag reduction. Here, we assume that the fluids are immiscible, incompressible, and Newtonian with constant properties. Single-fluid Couette flow is known to be linearly stable for any Reynolds number. However, inclusion of the second layer of fluid enriches the problem and introduces five new parameters: viscosity ratio, density ratio, thickness ratio, Froude number and Weber number. Two kinds of instability can appear: an unstable interfacial mode, and a Tollmein-Schlichting mode. In this work we parametrically study the flow stability with specific emphasis on the effects of viscosity ratio, interfacial tension, and thickness ratio. Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Office of Naval Research (ONR) through MURI Grants N00014-12-1-0875 and N00014-12-1-0962 (Program Manager Dr. Ki-Han Kim).
Non-Newtonian Couette-Poiseuille flow of a dilute gas
Tij, Mohamed; Santos, Andrés
2010-01-01
The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the...
Indian Academy of Sciences (India)
M H Mkwizu; O D Makinde; Yaw Nkansah-Gyekye
2015-10-01
This work investigates the effects of convective cooling on entropy generation in a transient generalized Couette flow of water-based nanofluids containing Copper (Cu) and Alumina (Al2O3) as nanoparticles. Both First and Second Laws of thermodynamics are utilised to analyse the problem. The model partial differential equations for momentum and energy balance are tackled numerically using a semidiscretization finite difference method together with Runge–Kutta Fehlberg integration scheme. Graphical results on the effects of parameter variation on velocity, temperature, skin friction, Nusselt number, entropy generation rate, irreversibility ratio and Bejan number are presented and discussed.
An exact solution of unsteady Couette flow of generalized second grade fluid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The fractional calculus approach is introduced into the rheological constitutive model of a generalized second grade fluid. A constitutive model with fractional derivative is developed for the generalized second grade fluid. Unsteady Couette flow of the generalized second grade fluid is studied by using the method of the discrete inverse Laplace transform and generalized Mittag-Leffler function. And then an exact solution is obtained for this problem with arbitrary fractional derivative. This provides a new analytical tool for the study of viscoelastic fluid mechanics.
Directory of Open Access Journals (Sweden)
Ahmada Omar Ali
2015-01-01
Full Text Available This paper investigates numerically the effects of variable viscosity on unsteady generalized Couette flow of a water base nanofluid with convective cooling at the moving surface. The Buongiorno model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The nonlinear governing equations of continuity, momentum, energy and nanoparticles concentration are tackled numerically using a semi discretization finite difference method together with Runge-Kutta Fehlberg integration scheme. Numerical results for velocity, temperature, and nanoparticles concentration profiles together with skin friction and Nusselt number are obtained graphically and discussed quantitatively.
Three dimensional free convection couette flow with transpiration cooling
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Free convection flow between two vertical parallel plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by constant suction through the plate in uniform motion has been analyzed. Due to this type of injection velocity, the flow becomes three-dimensional. Analytical expressions for the velocity, temperature, skin friction and rate of heat transfer were obtained. The important characteristics of the problem, namely the skin friction and the rate of heat transfer are discussed in detail with the help of graphs.
Spherical Couette flow in a dipolar magnetic field
Hollerbach, R; Fournier, A; Hollerbach, Rainer; Canet, Elisabeth; Fournier, Alexandre
2007-01-01
We consider numerically the flow of an electrically conducting fluid in a differentially rotating spherical shell, in a dipolar magnetic field. For infinitesimal differential rotation the flow consists of a super-rotating region, concentrated on the particular field line C just touching the outer sphere, in agreement with previous results. Finite differential rotation suppresses this super-rotation, and pushes it inward, toward the equator of the inner sphere. For sufficiently strong differential rotation the outer boundary layer becomes unstable, yielding time-dependent solutions. Adding an overall rotation suppresses these instabilities again. The results are in qualitative agreement with the DTS liquid sodium experiment.
Nonlinear dynamics in eccentric Taylor-Couette-Poiseuille flow
Pier, Benoît; Caulfield, C. P.
2015-11-01
The flow in the gap between two parallel but eccentric cylinders and driven by an axial pressure gradient and inner cylinder rotation is characterized by two geometrical parameters (radius ratio and eccentricity) and two dynamic parameters (axial and azimuthal Reynolds numbers). Such a theoretical configuration is a model for the flow between drill string and wellbore in the hydrocarbon drilling industry. The linear convective and absolute instability properties have been systematically derived in a recent study [Leclercq, Pier & Scott, J. Fluid Mech. 2013 and 2014]. Here we address the nonlinear dynamics resulting after saturation of exponentially growing small-amplitude perturbations. By using direct numerical simulations, a range of finite-amplitude states are found and characterized: nonlinear traveling waves (an eccentric counterpart of Taylor vortices, associated with constant hydrodynamic loading on the inner cylinder), modulated nonlinear waves (with time-periodic torque and flow rate) and more irregular states. In the nonlinear regime, the hydrodynamic forces are found to depart significantly from those prevailing for the base flow, even in situations of weak linear instability.
Riblet drag reduction and the effect of bulk fluid rotation in a fully turbulent Taylor-Couette flow
Greidanus, A.J.; Delfos, R.; Tokgoez, S.; Westerweel, J.
2015-01-01
Low drag surfaces are often desired in many industries with applications in open and closed channel flows, such as ship hulls and pipe flows. Drag reduction is a phenomenon that can have substantial energy savings, resulting in ecological and economical benefits. We use a Taylor-Couette facility as
Electrically driven convection in a thin annular film undergoing Couette flow
Daya, Z A; Morris, S W; Daya, Zahir A.; Morris, Stephen W.
1998-01-01
We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio $\\alpha$ and Reynolds number ${R e}$ of the shear flow, and obtain the critical control parameter $R_c (\\alpha, {R e})$ and the critical azimuthal mode number ...
Characteristic-Based Split Meshless Solution for Couette Flow
Directory of Open Access Journals (Sweden)
Mužík Juraj
2014-05-01
Full Text Available The paper deals with use of the meshless method for incompressible fluid flow analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG - local weak formulation of the Navier-Stokes equations. The shape function construction is the crucial part of the meshless numerical analysis in the construction of shape functions. The article presents the radial point interpolation method (RPIM for the shape functions construction
Linear Inviscid Damping for Couette Flow in Stratified Fluid
Yang, Jincheng
2016-01-01
We study the inviscid damping of Coutte flow with an exponentially stratified density. The optimal decay rates of the velocity field and density are obtained for general perturbations with minimal regularity. For Boussinesq approximation model, the decay rates we get are consistent with the previous results in the literature. We also study the decay rates for the full equations of stratified fluids, which were not studied before. For both models, the decay rates depend on the Richardson number in a very similar way. Besides, we also study the inviscid damping of perturbations due to the exponential stratification when there is no shear.
Strange attractors in weakly turbulent Couette-Taylor flow
Brandstater, A.; Swinney, Harry L.
1987-01-01
An experiment is conducted on the transition from quasi-periodic to weakly turbulent flow of a fluid contained between concentric cylinders with the inner cylinder rotating and the outer cylinder at rest. Power spectra, phase-space portraits, and circle maps obtained from velocity time-series data indicate that the nonperiodic behavior observed is deterministic, that is, it is described by strange attractors. Various problems that arise in computing the dimension of strange attractors constructed from experimental data are discussed and it is shown that these problems impose severe requirements on the quantity and accuracy of data necessary for determining dimensions greater than about 5. In the present experiment the attractor dimension increases from 2 at the onset of turbulence to about 4 at a Reynolds number 50-percent above the onset of turbulence.
Leclercq, Colin; Kerswell, Rich R
2016-01-01
The `Rayleigh line' mu=eta^2, where mu=Omega_o/Omega_i and eta=r_i/r_o are respectively the rotation and radius ratios between inner (subscript `i') and outer (subscript `o') cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor--Couette flow, for both axisymmetric [1] and non-axisymmetric [2] modes. Non-axisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e. eta^2<\\mu<1 for axially stably-stratified Taylor--Couette flow [3,4], but the competition between CI and SRI in the range mu
Turbulent Taylor-Couette flow over riblets: drag reduction and the effect of bulk fluid rotation
Greidanus, A. J.; Delfos, R.; Tokgoz, S.; Westerweel, J.
2015-05-01
A Taylor-Couette facility was used to measure the drag reduction of a riblet surface on the inner cylinder. The drag on the surfaces of the inner and outer cylinders is determined from the measured torque when the cylinders are in exact counter-rotation. The three velocity components in the instantaneous flow field were obtained by tomographic PIV and indicate that the friction coefficients are strongly influenced by the flow regimes and structures. The riblet surface changes the friction at the inner-cylinder wall, which generates an average bulk fluid rotation. A simple model is proposed to distinguish drag changes due to the rotation effect and the riblet effect, as a function of the measured drag change and shear Reynolds number . An uncorrected maximum drag reduction of 5.3 % was found at that corresponds to riblet spacing Reynolds number . For these conditions, the model predicts an azimuthal bulk velocity shift of 1.4 %, which is confirmed by PIV measurements. This shift indicates a drag change due to a rotation effect of -1.9 %, resulting in a net maximum drag reduction of 3.4 %. The results correspond well with earlier reported results and demonstrate that the Taylor-Couette facility is a suitable and accurate measurement tool to characterize the drag performance of surfaces.
Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio
Altmeyer, Sebastian; Do, Younghae; Lai, Ying-Cheng
2017-01-01
We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.
Instabilities of Shercliff and Stewartson layers in spherical Couette flow
Wei, Xing
2010-01-01
We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The non-axisymmetric instabilities of both types of layer separately have been studied before; here we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and t...
Directory of Open Access Journals (Sweden)
Chigozie Israel-Cookey
2010-09-01
Full Text Available This paper investigates effects of thermal radiation and magnetic field on hydromagnetic Couette flow of a highly viscous fluid with temperature-dependent viscosity and thermal conductivity at constant pressure through a porous channel. The influence of the channel permeability is also assessed. The relevant governing partial differential equations have been transformed to non-linear coupled ordinary differential equations by virtue of the steady nature of the flow and are solved numerically using a marching finite difference scheme to give approximate solutions for the velocity and temperature profiles. We highlight the effects of Nahme numbers, magnetic field, radiation and permeability parameters on both profiles. The results obtained are used to give graphical illustrations of the distribution of the flow variables and are discussed.
Directory of Open Access Journals (Sweden)
Oluwole D. Makinde
2015-11-01
Full Text Available In this paper, we employed both first and second laws of thermodynamics to analyze the flow and thermal decomposition in a variable viscosity Couette flow of a conducting fluid in a rotating system under the combined influence of magnetic field and Hall current. The non-linear governing differential equations are obtained and solved numerically using shooting method coupled with fourth order Runge–Kutta–Fehlberg integration technique. Numerical results obtained for velocities and temperature profiles are utilized to determine the entropy generation rate, skin fictions, Nusselt number and the Bejan number. By plotting the graphs of various values of thermophysical parameters, the features of the flow characteristics are analyzed in detail. It is found that fluid rotation increases the dominant effect of heat transfer irreversibility at the upper moving plate region while the entropy production is more at the lower fixed plate region.
Thermal influence of the Couette flow in a hydrostatic spindle on the machining precision
Chen, Dongju; Fan, Jinwei; Li, Haiyong; Wang, Xiaofeng; Zhang, Feihu
2013-05-01
Hydrostatic spindles are increasingly used in precision machine tools. Thermal error is the key factor affecting the machining accuracy of the spindle, and research has focused on spindle thermal errors through examination of the influence of the temperature distribution, thermal deformation and spindle mode. However, seldom has any research investigated the thermal effects of the associated Couette flow. To study the heat transfer mechanism in spindle systems, the criterion of the heat transfer direction according to the temperature distribution of the Couette flow at different temperatures is deduced. The method is able to deal accurately with the significant phenomena occurring at every place where thermal energy flowed in such a spindle system. The variation of the motion error induced by thermal effects on a machine work-table during machining is predicated by establishing the thermo-mechanical error model of the hydrostatic spindle for a high precision machine tool. The flow state and thermal behavior of a hydrostatic spindle is analyzed with the evaluated heat power and the coefficients of the convective heat transfer over outer surface of the spindle are calculated, and the thermal influence on the oil film stiffness is evaluated. Thermal drift of the spindle nose is measured with an inductance micrometer, the thermal deformation data 1.35 μm after running for 4 h is consistent with the value predicted by the finite element analysis's simulated result 1.28 μm, and this demonstrates that the simulation method is feasible. The thermal effects on the processing accuracy from the flow characteristics of the fluid inside the spindle are analyzed for the first time.
Intermittent boundary layers and torque maxima in Taylor-Couette flow
Brauckmann, Hannes J
2012-01-01
Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios \\eta=0.5 and 0.71 and propose a theoretical model for the critical value in the rotation ratio. Numerical results as well as experiments show that the onset of this intermittency coincides with the maximum in torque. The variations in torque correlate with the variations in mean Taylor vortex flow which is first enhanced for weak counter-rotation, and then reduced as intermittency sets in. To support the model, we compare to numerical results, experiments at higher Reynolds numbers, and to Wendt's data.
Transient hydromagnetic reactive Couette flow and heat transfer in a rotating frame of reference
Directory of Open Access Journals (Sweden)
S. Das
2016-03-01
Full Text Available This paper is concerned with the study of a transient hydromagnetic Couette flow and heat transfer of a reactive viscous incompressible electrically conducting fluid between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The transient momentum equations are solved analytically using the Laplace transform technique and the velocity field and shear stresses are obtained in a unified closed form. The energy equation is tackled numerically using MATLAB. The effects of the pertinent parameters on the fluid velocity, temperature, the shear stress and the rate of heat transfer at the plates are presented in graphical form and discussed in detail. Our results reveal that the combined effects of magnetic field, rotation, exothermic reaction and variable thermal conductivity have significant impact on the hydromagnetic flow and heat transfer.
Development of a Couette-Taylor flow device with active minimization of secondary circulation
Energy Technology Data Exchange (ETDEWEB)
Ethan Schartman
2009-01-27
A novel Taylor-Couette experiment has been developed to produce rotating shear ows for the study of hydrodynamic and magnetohydrodynamic instabilities which are believed to drive angular momentum transport in astrophysical accretion disks. High speed, concentric, corotating cylinders generate the flow where the height of the cylinders is twice the radial gap width. Ekman pumping is controlled and minimized by splitting the vertical boundaries into pairs of nested, differentially rotating rings. The end rings and cylinders comprise four independently driven rotating components which provide exibility in developing flow profiles. The working fluids of the experiment are water, a water-glycerol mix, or a liquid gallium alloy. The mechanical complexity of the apparatus and large dynamic pressures generated by high speed operation with the gallium alloy presented unique challenges. The mechanical implementation of the experiment and some representative results obtained with Laser Doppler Velocimetry in water are discussed.
Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer formation
Leclercq, Colin; Augier, Pierre; Caulfield, Colm-Cille P; Dalziel, Stuart B; Linden, Paul F
2016-01-01
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex density interface patterns, seemingly appearing and disappearing periodically as the coherent structure slowly rotates around the annulus. These coherent structures seem to be responsible for the formation of layers reported in a recent experiment by Oglethorpe et al. (2013). We distinguish `dynamic layering', instantaneous, localized and caused by the vortical motions, from `static layering' corresponding to the formation of...
Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow
Priede, JÄnis
2008-01-01
We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field (HMRI) using the inductionless approximation defined by a zero magnetic Prandtl number (Pm=0). The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically-modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the t...
Dynamic Domains of DTS: Simulations of a Spherical Magnetized Couette Flow
Kaplan, Elliot; Schaeffer, Nathanaël
2016-01-01
The Derviche Tourneur Sodium experiment, a spherical Couette magnetohydrodynamics experi- ment with liquid sodium as the medium and a dipole magnetic field imposed from the inner sphere, recently underwent upgrades to its diagnostics to better characterize the flow and induced magnetic fields with global rotation. In tandem with the upgrades, a set of direct numerical simulations were run with the xshells code [1] to give a more complete view of the fluid and magnetic dynamics at various rotation rates of the inner and outer spheres. These simulations reveal several dynamic regimes, determined by the Rossby number. At positive differential rotation there is a regime of quasigeostrophic flow, with low levels of fluctuations near the outer sphere. Negative differential rotation shows a regime of what appear to be saturated hydrodynamic instabilities at low negative differential rotation, followed by a regime where filamentary structures develop at low latitudes and persist over five to ten differential rotation...
Intermittent boundary layers and torque maxima in Taylor-Couette flow
Brauckmann, Hannes J.; Eckhardt, Bruno
2013-03-01
Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios η=0.5 and 0.71 and propose a theoretical model for the critical value in the rotation ratio. Numerical results as well as experiments show that the onset of this intermittency coincides with the maximum in torque. The variations in torque correlate with the variations in mean Taylor vortex flow, which is first enhanced for weak counter-rotation and then is reduced as intermittency sets in. To support the model, we compare it to numerical results, to experiments at higher Reynolds numbers, and to Wendt's data.
Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
Liu, Wei
2007-01-01
In this paper we present axisymmetric nonlinear simulations about magnetized Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a centrifugally stable angular-momemtum profile. The magnetic field is found to inhibit the Ekman suction. The width of the Ekman layer is reduced with increased magnetic field normal to the end plate. A uniformly-rotating region forms near the outer cylinder. A strong magnetic field leads to a steady Stewartson layer emanating from the junction between differentially rotating rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds number and penetrates deeper into the bulk flow with stronger magnetic field and larger Reynolds number. However, at Reynolds number larger than a critical value $\\sim 600$, axisymmetric, and perhaps also nonaxisymmetric, instabilities occur and result in a less prominent Stewartson layer that extends less far from the boundary.
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
Computational Modelling of Couette Flow of Nanofluids with Viscous Heating and Convective Cooling
Directory of Open Access Journals (Sweden)
Oluwole Daniel Makinde
2014-01-01
Full Text Available The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO and Alumina (Al2O3 as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively.
Danish, Mohammad; Kumar, Shashi; Kumar, Surendra
2012-03-01
Exact analytical solutions for the velocity profiles and flow rates have been obtained in explicit forms for the Poiseuille and Couette-Poiseuille flow of a third grade fluid between two parallel plates. These exact solutions match well with their numerical counter parts and are better than the recently developed approximate analytical solutions. Besides, effects of various parameters on the velocity profile and flow rate have been studied.
Energy Technology Data Exchange (ETDEWEB)
Nakabayashi, K.; Kito, O.; Kato, Y. [Nagoya Institute of Technology, Nagoya (Japan)
1998-10-25
Turbulence statistics in Couette Poiseuille flow are obtained by measurements. These include correlation coefficient, skewness and flatness factors and four-quadrant analysis of Reynolds shear stress -{rho}uv. In the region of y{sup +} {<=}30-40, the distributions of all these quantities are only affected by non-dimensional parameter {mu}({identical_to}u*{sup 3}/{alpha}{nu}), as the mean velocity and the turbulence intensities profiles are. The four-quadrant analysis shows that the fractional contribution from 4th-quadrant is affected largely by parameter {mu} whereas that from 2nd-quadrant remains unaffected. In the case of 0<{mu}{<=}94, the fractional contribution from 4th-quadrant is greater than that from 2nd-quadrant, unlike the conventional wall turbulent flow. 8 refs., 17 figs., 2 tabs.
Colgate, Stirling A; Pariev, Vladimir; Finn, John; Beckley, Howard; Si, Jiahe; Martinic, Joe; Westpfahl, David; Slutz, James; Westrom, Cebastian; Klein, Brianna; Schendel, Paul; Scharle, Cletus; McKinney, Travis; Ginanni, Rocky; Bentley, Ian; Mickey, Timothy
2010-01-01
The $\\Omega$-phase of the liquid sodium $\\alpha$-$\\Omega$ dynamo experiment at NMIMT in cooperation with LANL has successfully demonstrated the production of a high toroidal field, $B_{\\phi} \\simeq 8\\times B_r$ from the radial component of an applied poloidal magnetic field, $B_r$. This enhanced toroidal field is produced by rotational shear in stable Couette flow within liquid sodium at $Rm \\simeq 120$. The small turbulence in stable Taylor-Couette flow is caused by Ekman flow where $ (\\delta v/v)^2 \\sim 10^{-3} $. This high $\\Omega$-gain in low turbulence flow contrasts with a smaller $\\Omega$-gain in higher turbulence, Helmholtz-unstable shear flows. This result supports the ansatz that large scale astrophysical magnetic fields are created within semi-coherent large scale motions in which turbulence plays only a smaller diffusive role that enables magnetic flux linkage.
Couette-Taylor-Poiseuille流的数值模拟%Numerical Simulation of Couette-Taylor-Poiseuille Flow
Institute of Scientific and Technical Information of China (English)
袁艳平; 吉洪湖; 杜雁霞; 徐亮
2006-01-01
对中等半径比同心旋转圆柱间Couette-Taylor-Poiseuille流进行了数值计算, 并与已有的实验数据进行比较以获得流场的更多信息.结果表明,数值计算与实验结果吻合较好,依次再现了层流涡、波动涡、非波动螺旋涡以及波动螺旋涡;轴流可以起到稳定流场的作用,轴流存在时,流场转捩的临界泰勒数Ta值会变大,涡胞变小,涡心不再位于轴间隙的中间,从左向右的轴流比较明显,交替指向内轴和外轴,并缠绕在涡胞的周围;除去平均轴流速度后,速度矢量场显示出不同的涡形,形状与相同Ta时的涡胞基本相同;在不同的泰勒数Ta和雷诺数Re下,涡心的轴向传播速度约为平均轴向流速的1.17倍, 相传播速度约为内筒转速的0.42倍.
Mapping the omega-effect in the DTS magnetized spherical Couette flow experiment
Nataf, Henri-Claude
2012-01-01
The DTS experiment is a spherical Couette flow experiment with an imposed dipolar magnetic field. Liquid sodium is used as a working fluid. In a series of measurement campaigns, we have obtained data on the mean axisymmetric velocity, the mean induced magnetic field and electric potentials. All these quantities are coupled through the induction equation. In particular, a strong omega-effect is produced by differential rotation within the fluid shell, inducing a significant azimuthal magnetic field. Taking advantage of the simple spherical geometry of the experiment, I expand the azimuthal and meridional fields into Legendre polynomials and derive the expressions that permit to relate all measurements to the radial functions of the velocity field for each harmonic degree. For small magnetic Reynolds numbers Rm the relations are linear, and the toroidal and poloidal equations decouple. Selecting a set of measurements for a given rotation frequency of the inner sphere (Rm = 9.4), I invert simultaneously the velo...
Noise-sustained convective instability in a magnetized Taylor-Couette flow
Energy Technology Data Exchange (ETDEWEB)
Liu, Wei [Los Alamos National Laboratory
2008-01-01
The helical magnetorotational instability of the magnetized Taylor-Couette flow is studied numerically in a finite cylinder. A distant upstream insulating boundary is shown to stabilize the convective instability entirely while reducing the growth rate of the absolute instability. The reduction is less severe with larger height. After modeling the boundary conditions properly, the wave patterns observed in the experiment turn out to be a noise-sustained convective instability. After the source of the noise resulted from unstable Ekman and Stewartson layers is switched off, a slowly-decaying inertial oscillation is observed in the simulation. We reach the conclusion that the experiments completed to date have not yet reached the regime of absolute instability.
Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
Liu, Wei
2008-01-01
The helical magnetorotational instability of the magnetized Taylor-Couette flow is studied numerically in a finite cylinder. A distant upstream insulating boundary is shown to stabilize the convective instability entirely while reducing the growth rate of the absolute instability. The reduction is less severe with larger height. After modeling the boundary conditions properly, the wave patterns observed in the experiment turn out to be a noise-sustained convective instability. After the source of the noise resulted from unstable Ekman and Stewartson layers is switched off, a slowly-decaying inertial oscillation is observed in the simulation. We reach the conclusion that the experiments completed to date have not yet reached the regime of absolute instability.
Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation
Directory of Open Access Journals (Sweden)
Basant K. Jha
2015-10-01
Full Text Available This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.
Makinde, O. D.
2014-12-01
In this paper, the steady generalized axial Couette flow of Ostwald-de Waele power law reactive fluids between concentric cylindrical pipes is investigated. It is assumed that the outer cylinder is stationary and exchanges heat with the ambient surrounding following Newton's law of cooling, while the inner cylinder with isothermal surface is set in motion in the axial direction. The model nonlinear differential equations for the momentum and energy balance are obtained and tackled numerically using the shooting method coupled with the Runge-Kutta-Fehlberg integration technique. The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal criticality conditions are presented graphically and discussed quantitatively.
Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
Energy Technology Data Exchange (ETDEWEB)
W. Liu
2009-02-20
The helical magnetorotational instability of the magnetized Taylor-Couette flow is studied numerically in a finite cylinder. A distant upstream insulating boundary is shown to stabilize the convective instability entirely while reducing the growth rate of the absolute instability. The reduction is less severe with larger height. After modeling the boundary conditions properly, the wave patterns observed in the experiment turn out to be a noise-sustained convective instability. After the source of the noise resulted from unstable Ekman and Stewartson layers is switched off, a slowly-decaying inertial oscillation is observed in the simulation. We reach the conclusion that the experiments completed to date have not yet reached the regime of absolute instability.
Families of subcritical spirals in highly counter-rotating Taylor-Couette flow.
Meseguer, Alvaro; Mellibovsky, Fernando; Avila, Marc; Marques, Francisco
2009-03-01
A comprehensive numerical exploration of secondary finite-amplitude solutions in small-gap Taylor-Couette flow for high counter-rotating Reynolds numbers is provided, using Newton-Krylov methods embedded within arclength continuation schemes. Two different families of rotating waves have been identified: short axial wavelength subcritical spirals ascribed to centrifugal mechanisms and large axial scale supercritical spirals and ribbons associated with shear dynamics in the outer linearly stable radial region. This study is a first step taken in order to provide the inner structure of the skeleton of equilibria that may be responsible for the intermittent regime usually termed as spiral turbulence that has been reported by many experimentalists in the past.
Vortices and Particle-banding in Granular Taylor-Couette Flow
Mahajan, Achal; Alam, Meheboob
2016-11-01
A collection of smooth inelastic hard spheres is simulated between two rotating concentric cylinders, dubbed granular Taylor-Couette flow (gTCF), using event-driven molecular dynamics simulations. The inner cylinder is rotating with rotational speed ωi and the outer cylinder is kept stationary in the absence of gravity. The onset of Taylor-like vortices is studied as functions of the inner rotation ωi, the restitution coefficient (en) and the aspect ratio of the cylinder. The strength of vortices is found to decrease with increasing dissipation. A novel banding-pattern of particle-rich and particle-depleted regions along the axial direction is found - the density-contrast between the dense and dilute regions increases with decreasing restitution coefficient. The combined effect of inelastic dissipation and compressibility seems to be responsible for the genesis of Taylor-like vortices with axial-banding of particles.
Log law of the wall revisited in Taylor-Couette flows at intermediate Reynolds numbers
Singh, Harminder; Suazo, Claudio Alberto Torres; Liné, Alain
2016-11-01
We provide Reynolds averaged azimuthal velocity profiles, measured in a Taylor-Couette system in turbulent flow, at medium Reynolds (7800 image velocimetry technique. We find that in the wall regions, close to the inner and outer cylinders, the azimuthal velocity profile reveals a significant deviation from classical logarithmic law. In order to propose a new law of the wall, the profile of turbulent mixing length was estimated from data processing; it was shown to behave nonlinearly with the radial wall distance. Based on this turbulent mixing length expression, a law of the wall was proposed for the Reynolds averaged azimuthal velocity, derived from momentum balance and validated by comparison to different data. In addition, the profile of viscous dissipation rate was investigated and compared to the global power needed to maintain the inner cylinder in rotation.
A Molecular Dynamics Simulation of the Turbulent Couette Minimal Flow Unit
Smith, E R
2015-01-01
A molecular dynamics (MD) simulation of planar Couette flow is presented for the minimal channel in which turbulence structures can be sustained. Evolution over a single breakdown and regeneration cycle is compared to computational fluid dynamics (CFD) simulations. Qualitative similar structures are observed and turbulent statistics show excellent quantitative agreement. The molecular scale law of the wall is presented in which stick-slip molecular wall-fluid interactions replace the no-slip conditions. The impact of grid resolution is explored and the observed structures are seen to be dependant on averaging time and length scales. The kinetic energy spectra show a range of scales are present in the molecular system and that spectral content is dependent on the grid resolution employed. The subgrid velocity of the molecules is compared to spatial averaged velocity using joint probability density functions. Molecular trajectories, diffusions and Lagrangian statistics are presented. The importance of sub-grid ...
Numerical modeling of fluid flow and heat transfer in a narrow Taylor-Couette-Poiseuille system
Energy Technology Data Exchange (ETDEWEB)
Poncet, Sebastien, E-mail: poncet@l3m.univ-mrs.f [Laboratoire M2P2, UMR 6181 CNRS, Universite d' Aix-Marseille, Ecole Centrale Marseille, IMT la Jetee, 38 rue Joliot-Curie, 13451 Marseille (France); Haddadi, Sofia, E-mail: sofia.haddadi@gmail.co [Laboratoire M2P2, UMR 6181 CNRS, Universite d' Aix-Marseille, Ecole Centrale Marseille, IMT la Jetee, 38 rue Joliot-Curie, 13451 Marseille (France); Viazzo, Stephane, E-mail: stephane.viazzo@l3m.univ-mrs.f [Laboratoire M2P2, UMR 6181 CNRS, Universite d' Aix-Marseille, Ecole Centrale Marseille, IMT la Jetee, 38 rue Joliot-Curie, 13451 Marseille (France)
2011-02-15
Research highlights: {yields} Turbulence modeling of opened Taylor-Couette flows. {yields} Parametric study of the flow parameters on the hydrodynamic and thermal fields. {yields} The RSM as an adequate level of closure for rotating flows. - Abstract: We consider turbulent flows in a differentially heated Taylor-Couette system with an axial Poiseuille flow. The numerical approach is based on the Reynolds Stress Modeling (RSM) of widely validated in various rotor-stator cavities with throughflow () and heat transfer (). To show the capability of the present code, our numerical predictions are compared very favorably to the velocity measurements of in the isothermal case, for both the mean and turbulent fields. The RSM model improves, in particular, the predictions of the k-{epsilon} model of . Then, the second order model is applied for a large range of rotational Reynolds (3744 {<=} Re{sub i} {<=} 37,443) and Prandtl numbers (0.01 {<=} Pr {<=} 12), flow rate coefficient (0 {<=} C{sub w} {<=} 30,000) in a very narrow cavity of radius ratio s = R{sub i}/R{sub o} = 0.961 and aspect ratio L = (R{sub o} - R{sub i})/h = 0.013, where R{sub i} and R{sub o} are the radii of the inner and outer cylinders respectively and h is the cavity height. Temperature gradients are imposed between the incoming fluid and the inner and outer cylinders. The mean hydrodynamic and thermal fields reveal three distinct regions across the radial gap with a central region of almost constant axial and tangential mean velocities and constant mean temperature. Turbulence, which is weakly anisotropic, is mainly concentrated in that region and vanishes towards the cylinders. The mean velocity distributions are not clearly affected by the rotational Reynolds number and the flow rate coefficient. The effects of the flow parameters on the thermal field are more noticeable and considered in details. Correlations for the averaged Nusselt numbers along both cylinders are finally provided according to the
Pattern Selection, Wave Formation, Turbulence and Vortex Breakdown in Spiral Flows
1990-01-01
problems in rotating plane Couette - Poiseuille flow " (joint work with George H. Knightly), Contemporary Math., 108 (1990), to appear. The following...continuum of periodic waves in rotating plane Couette flow , and an analytic description of a mechanism to generate the turbulent-like flows observed in...during the period of the report: (1) "Waves in rotating plane Couette flow " (joint work with George H. Knightly, University of Massachusetts), Geometry
Experimental Study on Momentum Transfer of Surface Texture in Taylor-Couette Flow
Xue, Yabo; Yao, Zhenqiang; Cheng, De
2017-05-01
The behavior of Taylor-Couette (TC) flow has been extensively studied. However, no suitable torque prediction models exist for high-capacity fluid machinery. The Eckhardt-Grossmann-Lohse (EGL) theory, derived based on the Navier-Stokes equations, is proposed to model torque behavior. This theory suggests that surfaces are the significant energy transfer interfaces between cylinders and annular flow. This study mainly focuses on the effects of surface texture on momentum transfer behavior through global torque measurement. First, a power-law torque behavior model is built to reveal the relationship between dimensionless torque and the Taylor number based on the EGL theory. Second, TC flow apparatus is designed and built based on the CNC machine tool to verify the torque behavior model. Third, four surface texture films are tested to check the effects of surface texture on momentum transfer. A stereo microscope and three-dimensional topography instrument are employed to analyze surface morphology. Global torque behavior is measured by rotating a multi component dynamometer, and the effects of surface texture on the annular flow behavior are observed via images obtained using a high-speed camera. Finally, torque behaviors under four different surface conditions are fitted and compared. The experimental results indicate that surface textures have a remarkable influence on torque behavior, and that the peak roughness of surface texture enhances the momentum transfer by strengthening the fluctuation in the TC flow.
Colgate, Stirling A; Beckley, Howard; Si, Jiahe; Martinic, Joe; Westpfahl, David; Slutz, James; Westrom, Cebastian; Klein, Brianna; Schendel, Paul; Scharle, Cletus; McKinney, Travis; Ginanni, Rocky; Bentley, Ian; Mickey, Timothy; Ferrel, Regnar; Li, Hui; Pariev, Vladimir; Finn, John
2011-04-29
The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(ϕ) that is ≃8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm≃120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)(2)∼10(-3).
An analogy of Taylor's instability criterion in Couette and rotating-magnetic-field-driven flows
Ungarish, Marius
2012-01-01
The classical stability solution of Taylor for the Couette flow between a rotating inner cylinder and a stationary outer cylinder is used to model the "critical magnetic Taylor number," Tacr, in a flow of a liquid metal driven by a rotating magnetic field (RMF) in a cylindrical cavity characterized by the parameter H = height/radius. (The magnetic Taylor number is defined as Ta =σωBo2Ro4/(2ρν2), where σ ,ν, and ρ are the electrical conductivity, kinematic viscosity, and density of the liquid; ω and Bo are the magnetic field frequency and induction; Ro is the radius of the cavity; the cr superscript means "critical") In typical conditions, the RMF flow develops a solid-body-rotating core analogous to the inner rotating cylinder, embedded in a layer in which the swirl decays to zero at the outer wall. Using small-Ekman-number approximations for the core and gap flow, the analogy yields an insightful expression for Tacr. In particular, the model indicates that Tacr depends strongly on the parameter H. Comparisons of the present theoretical results with available realistic data show a good qualitative agreement and plausible quantitative agreement. The model was improved by an empirical adjustment of a coefficient and can be used as simple approximate prediction tool for Tacr in a quite wide range of cylindrical cavity configurations.
Shiels, C.; Butler, S. L.
2015-09-01
Mantle convection models with a low viscosity asthenosphere and high viscosity surface plates have been shown to produce very large aspect ratio convection cells like those inferred to exist in Earth's mantle and to exhibit two asthenospheric flow regimes. When the surface plate is highly mobile, the plate velocity exceeds the flow velocities in the asthenosphere and the plate drives a Couette-type flow in the asthenospheric channel. For sluggish plates, the flow velocities in the asthenosphere exceed the plate velocity and the asthenospheric flow is more Poiseuille-like. It has been shown that under certain circumstances, flows become increasingly Couette-like as the aspect ratio of the plate is increased in numerical simulations. These models also show an increase in the average surface heat flux with aspect ratio which is counterintuitive, as one would expect that large aspect ratio models would result in older and colder oceanic lithosphere. Previous investigations have used single internal heating rates and Rayleigh numbers and a plate formulation that did not preclude significant deformation within the plate. In this paper, we investigate the conditions necessary for Couette and Poiseuille asthenospheric flows and for surface heat flux to increase with plate aspect ratio by varying the internal heating rate, the Rayleigh number and the representation of surface plates in 2D mantle convection models Plates are represented as a high viscosity layer with (1) a free-slip top surface boundary condition and (2) a force-balance boundary condition that imposes a constant surface velocity within the plate. We find that for models with a free-slip surface boundary condition, the internal heating rate and Rayleigh number do not strongly affect the dominance of Couette or Poiseuille flows in the asthenosphere but the increase in surface heat flux with model aspect ratio in the Poiseuille asthenospheric flow regime increases with internal heating rate. For models using
Energy Technology Data Exchange (ETDEWEB)
Scurtu, Nicoleta; Egbers, Christoph [Brandenburgische Technische Universitaet (BTU), Cottbus (Germany); Stuecke, Peter [Westsaechsische Hochschule (WHZ), Zwickau (Germany)], E-mail: scurtu@tu-cottbus.de
2008-11-01
The eccentric small gap Taylor-Couette system with rotating inner cylinder and fixed outer cylinder is investigated numerically. The main flow fields were examined and the transition region from the laminar Couette-flow to the Taylor-vortex-flow in different eccentric arrangements of the cylinders. The effect of the eccentricity on flow patterns was studied for different values of the eccentricity between 0 and 0.75 in relation to the mean gap. This flow was further disturbed by the superimposed cross flow entering into the gap through the feed hole with a cross flow rate of 0.1 of the circumferential flow rate. Hence, more complex three dimensional flow structures evolved in the cylinders' gap, especially in the vicinity of the feed hole.
Dynamically dominant exact coherent structures in turbulent Taylor-Couette flow
Krygier, Michael; Grigoriev, Roman
2016-11-01
Unstable Exact Coherent Structures (ECS), which are solutions to the Navier-Stokes equation, provide a connection between turbulence and dynamical systems and offer a method for exploiting the low dimensionality of weakly turbulent flows. We investigate ECS in an intermittent Taylor-Couette flow (TCF) found in a small-aspect-ratio geometry with counter-rotating cylinders (η = 0 . 5 , Γ = 1 , Rei = - 1200 , Reo = 1200). The presence of end-caps breaks the axial translational symmetry of TCF, but continuous rotational symmetry remains, which suggest that typical ECS should be the relative versions of equilibria and time-periodic orbits. Indeed, previous studies (Meseguer et al., 2009 and Deguchi, Meseguer & Mellibovsky, 2014) found several unstable traveling wave solutions (relative equilibria). We have shown that the dynamically dominant ECS for weakly turbulent TCF in the small-aspect-ratio geometry are relative periodic orbits (not relative equilibria), as evidenced by the frequent visits of their neighborhoods by the turbulent flow. This work is supported by a Grant from the Army Research Office (Contract # W911NF-15-1-0471).
COUETTE FLOW PROBLEM FOR AN UNSTEADY MHD THIRD-GRADE FLUID WITH HALL CURRENTS
Directory of Open Access Journals (Sweden)
Muhammad Azram
2014-12-01
Full Text Available ABSTRACT: In this work, we analyze Coutte flow problem for an unsteady mangneto-hydrodynamic (MHD third-grade fluid in the presence of a pressure gradient and Hall currnts. Existing literature on the topic shows that the effecs of Hall current on Coutte flow of an unsteady MHD third-grade fluid with a prssure gradient has not yet been investigated. The arising non-linear problem is solved by the homotopy analysis method (HAM and the convergence of the obtained complex series solution is carefully analyzed. The effects of pressure number, Hartmann number and Hall parameter on unsteady velocity are discussed via analysis of plots. ABSTRAK: Kajian dijalan untuk menganalisa masalah aliran Coutte bagi bendalir MHD gred ketiga dan arus Hall. Bagi topik ini kesan arus Hall terhadap aliran Couette dalam bendalir MHD gred ketiga tak mantap dengan kecerunan tekanan, belum pernah dikaji selidik. Masalah tak linear berbangkit diselesaikan dengan kaedah analisis homotopi (HAM dan ketumpuan solusi rangkaian kompleks dianalisa dengan teliti. Kesan nilai tekanan, nombor Hartmann dan parameter Hall terhadap halaju tak mantap diperbincangkan melalui plot yang dianalisis.KEYWORDS: Cuette; flow; hall currents; unsteady; third-grade fluid; HAM
Indian Academy of Sciences (India)
Hazem A Attia; W Abbas; Mostafa A M Abdeen; Ahmed A M Said
2015-02-01
The aim of the present paper is to study the unsteady magneto-hydrodynamic viscous Couette flow with heat transfer in a Darcy porous medium between two infinite parallel porous plates considering Hall effect, and temperature dependent physical properties under constant pressure gradient. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is flowing through a porous medium that is assumed to obey Darcy’s law. A numerical solution for the governing nonlinear partial differential equations coupled with set of momentum equations and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions are investigated. It is found that the porosity numberMhas a marked effect on decreasing the velocity distribution (owing to a simultaneous increase in Darcy porous drag). Also the temperature T is decreased considerably with increasing porosity number.With increasing Hall current parameter m, the velocity component u (x-direction) is considerably increased, whereas velocity component w (z-direction) is reduced. Temperatures are decreased in the early stages of flow but effectively increased in the steady state with increasing m.
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Colgate, Stirling [Los Alamos National Laboratory; Li, Jui [Los Alamos National Laboratory; Finn, John [Los Alamos National Laboratory; Pariev, Vladimir [Los Alamos National Laboratory; Beckley, Howard [NM INSTIT. OF MINING AND TECH; Si, Jiahe [NM INSTIT. OF MINING AND TECH.; Martinic, Joe [NM INSTIT. OF MINING AND TECH.; Westpfahl, David [NM INSTIT. OF TECH.; Slutz, James [NM INSTIT. OF MINING AND TECH.; Westrom, Zeb [NM INSTIT. OF TECH.; Klein, Brianna [NM INSTIT. OF MINING AND TECH.
2010-11-08
The {Omega}-phase of the liquid sodium {alpha}-{Omega} dynamo experiment at NMIMT in cooperation with LANL has successfully demonstrated the production of a high toroidal field, B{sub {phi}} {approx_equal} 8 x B{sub r} from the radial component of an applied poloidal magnetic field, B{sub r}. This enhanced toroidal field is produced by rotational shear in stable Couette Row within liquid sodium at Rm {approx_equal} 120. The small turbulence in stable Taylor-Couette Row is caused by Ekman Row where ({delta}v/v){sup 2} {approx} 10{sup -3}. This high {Omega}-gain in low turbulence flow contrasts with a smaller {Omega}-gain in higher turbulence, Helmholtz-unstable shear flows. This result supports the ansatz that large scale astrophysical magnetic fields are created within semi-coherent large scale motions in which turbulence plays a diffusive role that enables magnetic flux linkage.
Turbulence decay towards the linearly-stable regime of Taylor-Couette flow
Mónico, Rodolfo Ostilla; Grossmann, Siegfried; Lohse, Detlef
2013-01-01
Taylor-Couette (TC) flow is used to probe the hydrodynamical stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC are in conflict about the existence of turbulence (cf. Ji et al. Nature, 444, 343-346 (2006) and Paoletti et al., A$\\&$A, 547, A64 (2012)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of sub-critical transitions to turbulence when no end-plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \\sim10^5$ and the radius ratio is $\\eta=0.714$. The stabilization causes the system to behave as a damped oscillator and correspondingly the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and th...
Effect of the number of vortices on the torque scaling in Taylor-Couette flow
Martínez-Arias, B; Crumeyrolle, O; Mutabazi, I
2014-01-01
Torque measurements in Taylor-Couette flow, with large radius ratio and large aspect ratio, over a range of velocities up to a Reynolds number of 24 000 are presented. Following a specific procedure, nine states with distinct number of vortices along the axis were found and the aspect ratio of the vortices were measured. The relationship between the speed and the torque for a given number of vortices is reported. In the turbulent Taylor vortex flow regime, at relatively high Reynolds number, a change in behaviour is observed corresponding to intersections of the torque-speed curves for different states. Before each intersection, the torque for a state with larger number of vortices is higher. After each intersection, the torque for a state with larger number of vortices is lower. The exponent, from the scaling laws of the torque, always depends on the aspect ratio of the vortices. When the Reynolds number is rescaled using the mean aspect ratio of the vortices, only a partial collapse of the exponent data is ...
On the self-sustained nature of large-scale motions in turbulent Couette flow
Rawat, Subhandu; Hwang, Yongyun; Rincon, François
2015-01-01
Large-scale motions in wall-bounded turbulent flows are frequently interpreted as resulting from an aggregation process of smaller-scale structures. Here, we explore the alternative possibility that such large-scale motions are themselves self-sustained and do not draw their energy from smaller-scale turbulent motions activated in buffer layers. To this end, it is first shown that large-scale motions in turbulent Couette flow at Re=2150 self-sustain even when active processes at smaller scales are artificially quenched by increasing the Smagorinsky constant Cs in large eddy simulations. These results are in agreement with earlier results on pressure driven turbulent channels. We further investigate the nature of the large-scale coherent motions by computing upper and lower-branch nonlinear steady solutions of the filtered (LES) equations with a Newton-Krylov solver,and find that they are connected by a saddle-node bifurcation at large values of Cs. Upper branch solutions for the filtered large scale motions a...
Roll/streak Structure Instability Induced by Free-stream Turbulence in Couette Flow
Farrell, Brian; Ioannou, Petros; Nikolaidis, Marios
2016-11-01
Statistical state dynamics (SSD) provides a new perspective for studying mechanisms underlying turbulence in shear flow including instabilities which arise intrinsically from interaction between coherent and incoherent components of the turbulence. Implementations of SSD in the form of a closure at second order is used in this work to analyze the instability emergent from the statistical interaction between coherent perturbations of roll/streak form and the incoherent free-stream turbulence in a minimal channel configuration of Couette flow. By perturbing the nonlinear SSD dynamics a new manifold of stable modes with roll/streak structure is shown to exist in the presence of small amplitude free-stream turbulence. With increase in a parameter controlling the free-stream turbulence energy, a member of this set of stable roll/streak structures is destabilized at a bifurcation and the associated roll/streak eigenmode is found to equilibrate at finite amplitude. The bifurcation structure predicted by the SSD roll/streak instability is reflected in both a closely related quasi-linear dynamical system, referred to as the restricted non-linear (RNL) system, and in DNS. This correspondence is further verified using ensemble implementations of the RNL and DNS systems.
Turbulent transitions in the stable boundary layer: Couette and Poiseuille flow
Holdsworth, Amber M.; Monahan, Adam H.
2016-11-01
The stable boundary layer (SBL) can be classified into two distinct regimes. The weakly stable regime (WSBL) which occurs in the presence of moderate to strong pressure gradients or cloudy skies and is characterized by continuous turbulent mixing, and the very stable regime (VSBL) which occurs in the presence of weak pressure gradients or clear skies and turbulence weakens to the point of collapse. Modelling and observational results indicate that transitions from the WSBL to the VSBL occur when the maximum sustainable heat flux (MSHF), or shear capacity, is exceeded. The collapse of turbulence in the SBL is investigated using a one dimensional model of Couette flow with a constant heat flux. We show that the MSHF framework for predicting turbulent collapse is qualitatively robust to the choice of turbulence parameterization and extend these earlier stability analyses by numerically determining the unstable modes along the unstable branch. To explore transitions between the VSBL and the WSBL we extend the model to include a horizontal pressure gradient and a surface radiation scheme. Analysis of the Poiseuille flow demonstrates how the idealized energy/momentum budget model with parameterized turbulence can reproduce the regime transitions present in atmospheric data. We acknowledge support from NSERC and the computing facilities of Westgrid and Compute Canada.
Normal Solutions of the Boltzmann Equation for Fourier and Couette Flow
Torczynski, J. R.
2005-11-01
Bird's Direct Simulation Monte Carlo (DSMC) method is used to simulate Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) for highly nonequilibrium conditions. The gas is confined between two parallel, fully-accommodating walls at unequal temperatures with opposite tangential velocities. For small system Knudsen numbers, the solution is normal in the central region of the domain (outside the Knudsen layers). For small heat-flux Knudsen numbers, the normal solution exhibits Chapman-Enskog (CE) behavior. More specifically, excellent agreement is observed between the DSMC and CE thermal conductivity, viscosity, and Sonine-polynomial coefficients of the molecular velocity distribution function. At larger heat-flux Knudsen numbers, the normal solution systematically departs from the CE solution. Under these conditions, the DSMC results for Maxwell molecules are in excellent agreement with the exact solution of Santos and co-workers, and the DSMC results for hard-sphere molecules exhibit similar trends. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Nonlinear waves in stratified Taylor--Couette flow. Part 2. Buoyancy flux
Leclercq, Colin; Caulfield, Colm-Cille P; Dalziel, Stuart B; Linden, Paul F
2016-01-01
This paper is the second part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. In a first paper, we showed that the dynamics of the flow was dominated by coherent structures made of a superposition of nonlinear waves. (Mixed)-ribbons and (mixed)-cross-spirals are generated by interactions between a pair of linearly unstable helical modes of opposite `handedness', and appear to be responsible for the formation of well-mixed layers and sharp density interfaces. In this paper, we show that these structures are also fully accountable for the upwards buoyancy flux in the simulations. The mechanism by which this occurs is a positive coupling between the density and vertical velocity components of the most energetic waves. This coupling is primarily caused by diffusion of density at low Schmidt number Sc, but can also be a nonlinear effect at larger Sc. Turbulence was found to contribute negatively to the buo...
Axisymmetry vs. nonaxisymmetry of hydromagnetic Taylor-Couette flows with axial electric currents
Gellert, M; Rüdiger, G
2013-01-01
The stability of a Taylor-Couette flow with resting outer cylinder under the influence of a homogeneous axial electric current is investigated. In the linear theory the critical Reynolds number for axisymmetric perturbations Re=68 is not influenced by the current-induced magnetic field but all the axisymmetric magnetic perturbations decay. The nonaxisymmetric perturbations with |m|=1 are excited even without rotation for large enough Hartmann numbers ('Tayler Instability') but the growth rate increases with Reynolds number. In the nonlinear regime shear energy is pumped into the neighboring modes m=0 and |m|=2. The ratio q of the energy of the magnetic |m|=1 modes and the toroidal background field is very small for the pure (non-rotating) Tayler instability and grows strongly if differential rotation is present. For super-Alfv\\'enic rotation the energy in the |m|=1 modes of flow and field are in equipartition, with about 1% of the centrifugal energy of the inner cylinder. If the electric current is strong eno...
Direct numerical simulation of Taylor-Couette flow subjected to a radial temperature gradient
Energy Technology Data Exchange (ETDEWEB)
Teng, Hao; Liu, Nansheng, E-mail: lns@ustc.edu.cn; Lu, Xiyun [Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Khomami, Bamin, E-mail: bkhomami@utk.edu [Department of Chemical and Biomolecular Engineering, The University of Tennessee, Knoxville, Tennessee 37996 (United States)
2015-12-15
Direct numerical simulations have been performed to study the Taylor-Couette (TC) flow between two rotating, coaxial cylinders in the presence of a radial temperature gradient. Specifically, the influence of the buoyant force and the outer cylinder rotation on the turbulent TC flow system with the radius ratio η = 0.912 was examined. For the co-rotating TC flows with Re{sub i} (inner cylinder) =1000 and Re{sub o} (outer cylinder) =100, a transition pathway to highly turbulent flows is realized by increasing σ, a parameter signifying the ratio of buoyant to inertial force. This nonlinear flow transition involves four intriguing states that emerge in sequence as chaotic wavy vortex flow for σ = 0, wavy interpenetrating spiral flows for σ = 0.02 and 0.05, intermittent turbulent spirals for σ = 0.1 and 0.2, and turbulent spirals for σ = 0.4. Overall, the fluid motion changes from a centrifugally driven flow regime characterized by large-scale wavy Taylor vortices (TVs) to a buoyancy-dominated flow regime characterized by small-scale turbulent vortices. Commensurate changes in turbulence statistics and heat transfer are seen as a result of the weakening of large-scale TV circulations and enhancement of turbulent motions. Additionally, the influence of variation of the outer cylinder rotation, −500 < Re{sub o} < 500 in presence of buoyancy (σ = 0.1) with Re{sub i} = 1000, has been considered. Specifically, it is demonstrated that this variation strongly influences the azimuthal and axial mean flows with a weaker influence on the fluctuating fluid motions. Of special interest, here are the turbulent dynamics near the outer wall where a marked decrease of turbulence intensity and a sign inversion of the Reynolds stress R{sub rz} are observed for the strongly counter-rotating regimes (Re{sub o} = − 300 and −500). To this end, it has been shown that the underlying flow physics for this drastic modification are associated with the modification of the correlation
Marginally stable and turbulent boundary layers in low-curvature Taylor-Couette flow
Brauckmann, Hannes J
2016-01-01
Marginal stability arguments are used to describe the rotation-number dependence of torque in Taylor-Couette (TC) flow for radius ratios $\\eta \\geq 0.9$ and shear Reynolds number $Re_S=2\\times 10^4$. With an approximate representation of the mean profile by piecewise linear functions, characterized by the boundary-layer thicknesses at the inner and outer cylinder and the angular momentum in the center, profiles and torques are extracted from the requirement that the boundary layers represent marginally stable TC subsystems and that the torque at the inner and outer cylinder coincide. This model then explains the broad shoulder in the torque as a function of rotation number near $R_\\Omega\\approx 0.2$. For rotation numbers $R_\\Omega < 0.07$ the TC stability conditions predict boundary layers in which shear Reynolds numbers are very large. Assuming that the TC instability is bypassed by some shear instability, a second maximum in torque appears, in very good agreement with numerical simulations. The results s...
Turbulent magnetic Prandtl numbers obtained with MHD Taylor-Couette flow experiments
Gellert, M
2008-01-01
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\\_in = B\\_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The...
Taylor-Couette turbulence at radius ratio $\\eta=0.5$: scaling, flow structures and plumes
van der Veen, Roeland C A; Merbold, Sebastian; Harlander, Uwe; Egbers, Christoph; Lohse, Detlef; Sun, Chao
2015-01-01
Using high-resolution particle image velocimetry we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor-Couette flow for a radius ratio of 0.5 and Taylor number of up to $6.2\\cdot10^9$. The extracted angular velocity profiles follow a log-law more closely than the azimuthal velocity profiles due to the strong curvature of this $\\eta=0.5$ setup. The scaling of the wind Reynolds number with the Taylor number agrees with the theoretically predicted 3/7-scaling for the classical turbulent regime, which is much more pronounced than for the well-explored $\\eta=0.71$ case, for which the ultimate regime sets in at much lower Ta. By measuring at varying axial positions, roll structures are found for counter-rotation while no clear coherent structures are seen for pure inner cylinder rotation. In addition, turbulent plumes coming from the inner and outer cylinder are investigated. For pure inner cylinder rotation, the plumes in the radial velocity move away from the inn...
Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models
Papageorgiou, Demetrios; Cimpeanu, Radu; Kalogirou, Anna; Keaveny, Eric
2016-11-01
The nonlinear stability of two-fluid Couette flows is studied using a novel evolution equation whose dynamics are validated by direct numerical simulations (DNS). The evolution equation incorporates inertial effects at arbitrary Reynolds numbers through a nonlocal term arising from the coupling between the two fluid regions, and is valid when one of the layers is thin. The equation predicts asymmetric solutions and exhibits bistability as seen in experiments. Related low-inertia models have been used in qualitative predictions using ad hoc modifications rather than the direct comparisons carried out here. Comparisons between model solutions and DNS show excellent agreement at Reynolds numbers of O (103) found in experiments. Direct comparisons are also made with the available experimental results of Barthelet et al. (1995) when the thin layer occupies 1 / 5 of the channel height. Pointwise comparisons of the travelling wave shapes are carried out and once again the agreement is very good. EPSRC Grant Numbers EP/K041134 and EP/L020564.
Effect of roll number on the statistics of turbulent Taylor-Couette flow
Ostilla-Mónico, Rodolfo; Lohse, Detlef; Verzicco, Roberto
2016-09-01
A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette flow. The latter is the flow between two coaxial independently rotating cylinders of radius ri and ro, respectively. Large axial aspect ratios Γ =7 -8 [with Γ =L /(ro-ri) , and L the axial length of the domain] and a simulation with Γ =14 were used in order to allow the system to select the most unstable wave number and to possibly develop multiple states. The radius ratio was taken as η =ri/ro=0.909 , the inner cylinder Reynolds number was fixed to Rei=3.4 ×104 , and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of Reτ≈500 , except for the Γ =14 simulation where Rei=1.5 ×104 and Reτ≈240 . The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls nr and roll wavelength λz were found for Γ =7 . The effect of λz and nr on the statistics was quantified. The torque and mean flow statistics were found to be independent of both λz and nr, while the velocity fluctuations and energy spectra showed some box-size dependence. Finally, the axial velocity spectra were found to have a very sharp dropoff for wavelengths larger than λz, while for the small wavelengths they collapse.
Paule, A; Lauga, B; Ten-Hage, L; Morchain, J; Duran, R; Paul, E; Rols, J L
2011-11-15
In their natural environment, the structure and functioning of microbial communities from river phototrophic biofilms are driven by biotic and abiotic factors. An understanding of the mechanisms that mediate the community structure, its dynamics and the biological succession processes during phototrophic biofilm development can be gained using laboratory-scale systems operating with controlled parameters. For this purpose, we present the design and description of a new prototype of a rotating annular bioreactor (RAB) (Taylor-Couette type flow, liquid working volume of 5.04 L) specifically adapted for the cultivation and investigation of phototrophic biofilms. The innovation lies in the presence of a modular source of light inside of the system, with the biofilm colonization and development taking place on the stationary outer cylinder (onto 32 removable polyethylene plates). The biofilm cultures were investigated under controlled turbulent flowing conditions and nutrients were provided using a synthetic medium (tap water supplemented with nitrate, phosphate and silica) to favour the biofilm growth. The hydrodynamic features of the water flow were characterized using a tracer method, showing behaviour corresponding to a completely mixed reactor. Shear stress forces on the surface of plates were also quantified by computer simulations and correlated with the rotational speed of the inner cylinder. Two phototrophic biofilm development experiments were performed for periods of 6.7 and 7 weeks with different inoculation procedures and illumination intensities. For both experiments, biofilm biomasses exhibited linear growth kinetics and produced 4.2 and 2.4 mg cm(-)² of ash-free dry matter. Algal and bacterial community structures were assessed by microscopy and T-RFLP, respectively, and the two experiments were different but revealed similar temporal dynamics. Our study confirmed the performance and multipurpose nature of such an innovative photosynthetic bioreactor
Brauckmann, Hannes J.; Eckhardt, Bruno; Schumacher, Jörg
2017-03-01
Rayleigh-Bénard convection and Taylor-Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh-Bénard convection in air at Rayleigh number Ra=107 and Taylor-Couette flow at shear Reynolds number ReS=2×104 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport.
Brauckmann, Hannes; Schumacher, Joerg
2016-01-01
Rayleigh-Benard convection and Taylor-Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh-Benard convection in air at Rayleigh number Ra=1e7 and Taylor-Couette flow at shear Reynolds number Re_S=2e4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angula...
Experimental investigation of geometry on torque hysteresis behaviour of Taylor-Couette flow
Gul, M.; Elsinga, G.E.; Westerweel, J.
2015-01-01
This study investigates the effect of the Taylor-Couette geometry, namely the aspect ratio, Γ, and the gap width ratio, ƞ, on the torque hysteresis reported by [1]. Measurements were taken at two shear Reynolds numbers, Re s, of 5.5x10⁴ and 9x10⁴.The torque was recorded while decreasing or increasin
Farrell, Brian F.; Ioannou, Petros J.; Nikolaidis, Marios-Andreas
2017-03-01
Although the roll-streak structure is ubiquitous in both observations and simulations of pretransitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the roll-streak structure has been invoked to explain its appearance as resulting from chance occurrence in the background turbulence of perturbations configured to optimally excite it. However, there is an alternative interpretation for the role of free-stream turbulence in the genesis of the roll-streak structure, which is that the background turbulence interacts with the roll-streak structure to destabilize it. Statistical state dynamics (SSD) provides analysis methods for studying instabilities of this type that arise from interaction between the coherent and incoherent components of turbulence. SSD in the form of a closure at second order is used in this work to analyze the cooperative eigenmodes arising from interaction between the coherent streamwise invariant component and the incoherent background component of turbulence. In pretransitional Couette flow a manifold of stable modes with roll-streak form is found to exist in the presence of low-intensity background turbulence. The least stable mode of this manifold is destabilized at a critical value of a parameter controlling the background turbulence intensity and a finite-amplitude roll-streak structure arises from this instability through a bifurcation in this parameter. Although this bifurcation has analytical expression only in the infinite ensemble formulation of second order SSD, referred in this work as the S3T system, it is closely reflected in numerical simulations of both the dynamically similar quasilinear system, referred to as the restricted nonlinear (RNL) system, as well as in the full Navier-Stokes equations. This correspondence is verified using ensemble implementations of the RNL system and the Navier-Stokes equations. The S3T
Hemolysis in a laminar flow-through Couette shearing device: an experimental study.
Boehning, Fiete; Mejia, Tzahiry; Schmitz-Rode, Thomas; Steinseifer, Ulrich
2014-09-01
Reducing hemolysis has been one of the major goals of rotary blood pump development and in the investigational phase, the capability of hemolysis estimation for areas of elevated shear stresses is valuable. The degree of hemolysis is determined by the amplitude of shear stress and the exposure time, but to date, the exact hemolytic behavior at elevated shear stresses and potential thresholds for subcritical shear exposure remain vague. This study provides experimental hemolysis data for a set of shear stresses and exposure times to allow better estimations of hemolysis for blood exposed to elevated shearing. Heparinized porcine blood with a hematocrit of 40% was mechanically damaged in a flow-through laminar Couette shear flow at a temperature of 23°C. Four levels of shear stress, 24, 592, 702, and 842 Pa, were replicated at two exposure times, 54 and 873 ms. For the calculation of the shear stresses, an apparent viscosity of 5 mPas was used, which was verified in an additional measurement of the blood viscosity. The hemolysis measurements were repeated four times, whereby all conditions were measured once within the same day and with blood from the same source. Samples were taken at the inlet and outlet of the shear region and an increase in plasma-free hemoglobin was measured. An index of hemolysis (IH) was thereby calculated giving the ratio of free to total hemoglobin. The results are compared with data from previously published studies using a similar shearing device. Hemolysis was found to increase exponentially with shear stress, but high standard deviations existed at measurements with elevated IH. At short exposure times, the IH remained low at under 0.5% for all shear stress levels. For high exposure times, the IH increased from 0.84% at 592 Pa up to 3.57% at the highest shear stress level. Hemolysis was significant for shear stresses above ∼600 Pa at the high exposure time of 873 ms. Copyright © 2014 International Center for Artificial
Large eddy simulations of Taylor-Couette-Poiseuille flows in a narrow-gap system
Poncet, Sébastien; Viazzo, Stéphane; Oguic, Romain
2014-10-01
The present paper concerns Large-Eddy Simulations (LES) of turbulent Taylor-Couette-Poiseuille flows in a narrow-gap cavity for six different combinations of rotational and axial Reynolds numbers. The in-house numerical code has been first validated in a middle-gap cavity. Two sets of refined LES results, using the Wall-Adapting Local Eddy Viscosity (WALE) and the Dynamic Smagorinsky subgrid-scale models available within an in-house code based on high-order compact schemes, have been then compared with no noticeable difference on the mean flow field and the turbulent statistics. The WALE model enabling a saving of about 12% of computational effort has been finally used to investigate the influence on the hydrodynamics of the swirl parameter N within the range [1.49 - 6.71]. The swirl parameter N, which compares the effects of rotation of the inner cylinder and the axial flowrate, does not influence significantly the mean velocity profiles. Turbulence intensities are enhanced with increasing values of N with remarkably high peak values within the boundary layers. The inner rotating cylinder has a destabilizing effect inducing asymmetric profiles of the Reynolds stress tensor components. The rotor and stator boundary layers exhibit the main characteristics of two-dimensional boundary layers. Turbulence is also mainly at two-component there. Thin coherent structures appearing as negative (resp. positive) spiral rolls are observed along the rotor (resp. stator) side. Their inclination angle depends strongly on the value of the swirl parameter, which fixes the intensity of the crossflow. On the other hand, the intensity and the size of the coherent structures observed within the boundary layers are governed by the effective Reynolds number. For its highest value, they penetrate the whole gap. Finally, the results have been extended to the non-isothermal case in the forced convection regime. A correlation for the Nusselt number along the rotor has been provided showing a
Influence of fluid thermal sensitivity on the thermo-mechanical stability of the Taylor-Couette flow
Thomas, D. G.; Sureshkumar, R.; Khomami, B.
2003-11-01
Recent theoretical [Al-Mubaiyedh et al., Phys. Fluids 11, 3217 (1999); J. Fluid Mech. 462, 111 (2002)] and experimental [White and Muller, Phys. Rev. Lett. 84, 5130 (2000); J. Fluid Mech. 462, 133 (2002)] studies have revealed that viscous heating causes significant destabilization of the Taylor-Couette flow of highly viscous and thermally sensitive fluids. In this work, the roles of thermal sensitivity of fluid properties and co-rotation on the thermo-mechanical stability of Taylor-Couette flow are investigated theoretically. In turn, our theoretical findings are compared with the recent experimental ones by White and Muller [Phys. Fluids 14, 3880 (2002)]. It is shown that a finite gap temperature is necessary to predict the time-dependent transitions observed in the experiments. A universal scaling between the critical Reynolds number and the Nahme number is obtained for intermediate values of Nahme number ranging from 0.01 to 1.0. Studies are also performed to determine the influence of co-rotation of the outer cylinder relative to the inner one on the thermo-mechanical stability. Overall, a very favorable comparison between theoretical and experimental results is obtained.
Nordsiek, Freja; van der Veen, Roeland C A; Sun, Chao; Lohse, Detlef; Lathrop, Daniel P
2014-01-01
Azimuthal velocity profiles were measured in a Taylor-Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of $\\eta = 0.7158$, an aspect-ratio of $\\Gamma = 11.74$, and axial boundaries attached to the outer cylinder --- known to have significant Ekman pumping. We investigated angular momentum transport and Ekman pumping in the Rayleigh-stable regime. The regime is linearly stable and is characterized by radially increasing specific angular momentum. We measured several Rayleigh-stable profiles for shear Reynolds numbers $Re_S \\sim O\\left(10^5\\right) \\,$, both for $\\Omega_i > \\Omega_o > 0$ (quasi-Keplerian regime) and $\\Omega_o > \\Omega_i > 0$ (sub-rotating regime) where $\\Omega_{i,o}$ is the inner/outer cylinder rotation rate. None of the velocity profiles matched the non-vortical laminar Taylor-Couette profile. The deviation from that profile increased as solid-body rotation was approached at fixed $Re_S$. Flow super-rotation, a...
Numerical study of bifurcation solutions of spherical Taylor-Couette flow
Institute of Scientific and Technical Information of China (English)
袁礼; 傅德薰; 马延文
1996-01-01
The steady bifurcation flows in a spherical gap (gap ratio =0.18) with rotating inner and stationary outer spheres are simulated numerically for Reci
McDonald, K. R.; Czarnocki, C. J.; Burin, M. J.
2010-11-01
We have experimentally investigated the momentum distribution and transition to turbulence within a high curvature (radii ratio of 0.55), low aspect ratio (height/gap of 6.3) Taylor-Couette flow using three different horizontal boundary conditions. End-caps between the two cylinders were wholly coupled to either the inner or outer cylinder, or otherwise split in half. By rotating only the outer cylinder we have obtained velocity data from fully cyclonic regimes using Laser Doppler Velocimetry (LDV). The subcritical transition to turbulence is clearly affected by the horizontal boundaries: end-caps that move with either cylinder yield a transition Reynolds number that is higher than when split. These results help clarify the role of secondary flows in the turbulent transition of this system, and also add to the early torque-based work of Wendt (1933) & Taylor (1936).
Intermittency at Fine Scales and Complex Singularities of Turbulent Couette Flow
Souza, Andre
2015-01-01
Fine scales of turbulent velocity fields, beyond the inertial range and well into the dissipative range, are highly intermittent. It has been hypothesized that complex plane singularities are the principal mechanism behind fine scale intermittency. In this article, we view the velocity field of a turbulent flow as an analytic function of time. Although the function is only available for real values of time, we present a numerical technique to analytically continue the function to complex values of time, and with sufficient fidelity to locate and visualize the singularity closest to the real axis. Using this technique, we demonstrate a robust connection between temporal intermittency and the location of singularities in the complex plane.
STABLE AND UNSTABLE IDEAL PLANE FLOWS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.
Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates
Energy Technology Data Exchange (ETDEWEB)
Siddiqui, A.M. [Pennsylvania State University, York Campus, York, PA 17403 (United States); Zeb, A. [COMSATS Institute of Information Technology, 30 H-8/1, Islamabad (Pakistan)], E-mail: amtaz56@yahoo.co.uk; Ghori, Q.K. [COMSATS Institute of Information Technology, 30 H-8/1, Islamabad (Pakistan); Benharbit, A.M. [Pennsylvania State University, York Campus, York, PA 17403 (United States)
2008-04-15
The present paper studies the heat transfer flow of a third grade fluid between two heated parallel plates for the constant viscosity model. Three flow problems, namely plane Couette flow, plane Poiseuille flow and plane Couette-Poiseuille flow have been considered. In each case the non-linear momentum equation and the energy equation have been solved using the homotopy perturbation method. Explicit analytical expressions for the velocity field and the temperature distribution have been derived.
Crisis bifurcations in plane Poiseuille flow
Zammert, Stefan
2015-01-01
Direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace reveal several interior and exterior crisis bifurcations. They appear in the upper branch that emerges in a saddle-node bifurcation near $Re_{SN}=641$ and then undergoes several bifurcations into a chaotic attractor. Near $Re_{XC}=785.95$ the attractor collides with the lower-branch state and turns into a chaotic saddle in a exterior crisis, with a characteristic $(Re-Re_{XC})^{-\\delta}$ variation in lifetimes. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. They contribute to increasing the complexity of the dynamics and to a more dense coverage of state space. The exterior crisis marks the onset of transient turbulence in this subspace of plane Poiseuille flow.
Saikia, Bijaylakshmi; Ramachandran, Ashwin; Sinha, Krishnendu; Govindarajan, Rama
2017-02-01
Accurate prediction of laminar to turbulent transition in compressible flows is a challenging task, as it can be affected by a combination of factors. Compressibility causes large variations in thermodynamic as well as transport properties of a gas, which in turn are known to affect flow stability. We study the stratification of individual transport properties and their combined behavior. We also examine the effect of a change in the magnitude of viscosity and conductivity on flow stability. The Couette flow of a perfect gas is our model problem and both modal and non-modal analyses are carried out. We notice a large destabilizing role of the increase in the conductivity value and a dramatic stabilizing effect of mean viscosity stratification, over a range of free-stream Mach number, Reynolds number, Prandtl number, and disturbance wavenumber. In the combined case, viscosity stratification plays a dominant role. We find this to be the case for finite-time transient growth in the parameter regime below linear instability as well as asymptotically at large time. A budget of the transient growth energy amplification is also shown to identify the effects of transport properties on the constituents of perturbation energy. The extensive results presented in this paper, we believe should motivate those studying more realistic flows to examine how these contrasting effects of stratification come together.
A Molecular Dynamics Simulation of the Turbulent Couette Minimal Flow Unit
Smith, Edward
2016-11-01
What happens to turbulent motions below the Kolmogorov length scale? In order to explore this question, a 300 million molecule Molecular Dynamics (MD) simulation is presented for the minimal Couette channel in which turbulence can be sustained. The regeneration cycle and turbulent statistics show excellent agreement to continuum based computational fluid dynamics (CFD) at Re=400. As MD requires only Newton's laws and a form of inter-molecular potential, it captures a much greater range of phenomena without requiring the assumptions of Newton's law of viscosity, thermodynamic equilibrium, fluid isotropy or the limitation of grid resolution. The fundamental nature of MD means it is uniquely placed to explore the nature of turbulent transport. A number of unique insights from MD are presented, including energy budgets, sub-grid turbulent energy spectra, probability density functions, Lagrangian statistics and fluid wall interactions. EPSRC Post Doctoral Prize Fellowship.
Special-relativistic model flows of viscous fluid
Rogava, A D
1996-01-01
Two, the most simple cases of special-relativistic flows of a viscous, incompressible fluid are considered: plane Couette flow and plane Poiseuille flow. Considering only the regular motion of the fluid we found the distribution of velocity in the fluid (velocity profiles) and the friction force, acting on immovable wall. The results are expressed through simple analytical functions for the Couette flow, while for the Poiseiulle flow they are expressed by higher transcendental functions (Jacobi's elliptic functions).
Monico, Rodolfo Ostilla; Verzicco, Roberto; Grossmann, Siegfried; Lohse, Detlef
2014-01-01
DNS of Taylor-Couette flow (TC), i.e. the flow between two coaxial and independently rotating cylinders were performed. Shear Reynolds numbers of up to $3\\cdot10^5$, corresponding to Taylor numbers of $Ta=4.6\\cdot10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect- and rotation- ratios, but depends significantly on the radius-ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime ...
Farzad, Reza; Puttinger, Stefan; Pirker, Stefan; Schneiderbauer, Simon
2016-11-01
Liquid-liquid systems are widely used in the several industries such as food, pharmaceutical, cosmetic, chemical and petroleum. Drop size distribution (DSD) plays a key role as it strongly affects the overall mass and heat transfer in the liquid-liquid systems. To understand the underlying mechanisms single drop breakup experiments have been done by several researchers in the Taylor-Couette flow; however, most of those studies concentrate on the laminar flow regime and therefore, there is no sufficient amount of data in the case of in turbulent flows. The well-defined pattern of the Taylor-Couette flow enables the possibility to investigate DSD as a function of the local fluid dynamic properties, such as shear rate, which is in contrast to more complex devices such as stirred tank reactors. This paper deals with the experimental investigation of liquid-liquid DSD in Taylor-Couette flow. From high speed camera images we found a simple correlation for the Sauter mean diameter as a function of the local shear employing image processing. It is shown that this correlation holds for different oil-in-water emulsions. Finally, this empirical correlation for the DSD is used as an input data for a CFD simulation to compute the local breakup of individual droplets in a stirred tank reactor.
Spandan, Vamsi; Lohse, Detlef
2016-01-01
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\\hat \\mu$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of def...
Role of viscoelasticity in instability in plane shear flow over a deformable solid
Indian Academy of Sciences (India)
Paresh Chokshi
2015-05-01
The stability of the flow of a viscoelastic fluid over a deformable elastic solid medium is reviewed focusing on the role played by the fluid elasticity on the earlier known instability modes for the Newtonian fluids. In particular, two classes of modes are emphasized: the viscous mode for the creeping flow, and the wall mode for high Reynolds number flow. The flow geometry is restricted to plane Couette flow of fluid supported on elastic substrate of finite thickness. The viscoelastic fluid is described using the Oldroyd-B model and the dynamics of the deformable solid continuum is described by either Hookean or neo-Hookean elastic model. In the limit of $Re \\to 0$, the introduction of fluid elasticity delays the onset of instability and for sufficiently viscoelastic fluid with dilute polymer concentration, the instability is suppressed rendering the flow stable. For concentrated solution and polymer melt, the instability persists, but with higher value of critical shear rate than for the Newtonian fluid, indicating stabilizing role of fluid elasticity in creeping flow regime. However, for high Reynolds number flow of dilute polymer solution, the polymer addition plays a destabilizing role for wall modes, indicated by reduction in critical Reynolds number by an order of magnitude.
Heifetz, H Vitoshkin E; Harnik, N
2012-01-01
The three dimensional optimal energy growth mechanism, in plane parallel shear flows, is reexamined in terms of the role of vortex stretching and the interplay between the span-wise vorticity and the planar divergent components. For high Reynolds numbers the structure of the optimal perturbations in Couette, Poiseuille, and mixing layer shear profiles is robust and resembles localized plane-waves in regions where the background shear is large. The waves are tilted with the shear when the span-wise vorticity and the planar divergence fields are in (out of) phase when the background shear is positive (negative). A minimal model is derived to explain how this configuration enables simultaneous growth of the two fields, and how this mutual amplification reflects on the optimal energy growth. This perspective provides an understanding of the three dimensional growth solely from the two dimensional dynamics on the shear plane.
Crisis bifurcations in plane Poiseuille flow.
Zammert, Stefan; Eckhardt, Bruno
2015-04-01
Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.
Ostilla-Mónico, Rodolfo; Verzicco, Roberto
2016-01-01
A series of direct numerical simulations in large computational domains has been performed in order to probe the spatial feature robustness of the Taylor rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two coaxial independently rotating cylinders of radius $r_i$ and $r_o$, respectivel. Large axial aspect ratios $\\Gamma = 7$-$8$ (with $\\Gamma = L/(r_o-r_i)$, and $L$ the axial length of the domain) were used in order to allow the system to select the most unstable wavenumber and to possibly develop multiple states. The radius ratio was taken as $\\eta=r_i/r_o=0.909$, the inner cylinder Reynolds number was fixed to $Re_i=3.4\\cdot10^4$, and the outer cylinder was kept stationary, resulting in a frictional Reynolds number of $Re_\\tau\\approx500$. The large-scale rolls were found to remain axially pinned for all simulations. Depending on the initial conditions, stable solutions with different number of rolls $n_r$ and roll wavelength $\\lambda_z$ were found for $\\Gamma=7$. The effect of $\\l...
Direct Numerical Simulations of Local and Global Torque in Taylor-Couette Flow up to Re=30.000
Brauckmann, Hannes
2015-01-01
The torque in turbulent Taylor-Couette flows for shear Reynolds numbers Re_S up to 3x10^4 at various mean rotations is studied by means of direct numerical simulations for a radius ratio of \\eta=0.71. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of \\Gamma=2, close to the torque maximum. The connection between the torque and the transverse current J^\\omega of azimuthal motion which can be computed from the velocity field enables us to investigate the local transport resulting in the torque. The typical spatial distribution of the individual convective and viscous contributions to the local current is analysed for a turbulent flow case. To characterise the turbulent statistics of the transport, PDF's of local current fluctuatio...
ARBITRARY INTERACTION OF PLANE SUPERSONIC FLOWS
Directory of Open Access Journals (Sweden)
P. V. Bulat
2015-11-01
Full Text Available Subject of study.We consider the Riemann problem for parameters at collision of two plane flows at a certain angle. The problem is solved in the exact statement. Most cases of interference, both stationary and non-stationary gas-dynamic discontinuities, followed by supersonic flows can be reduced to the problem of random interaction of two supersonic flows. Depending on the ratio of the parameters in the flows, outgoing discontinuities turn out to be shock waves, or rarefactionwaves. In some cases, there is no solution at all. It is important to know how to find the domain of existence for the relevant decisions, as the type of shock-wave structures in these domains is known in advance. The Riemann problem is used in numerical methods such as the method of Godunov. As a rule, approximate solution is used, known as the Osher solution, but for a number of problems with a high precision required, solution of this problem needs to be in the exact statement. Main results.Domains of existence for solutions with different types of shock-wave structure have been considered. Boundaries of existence for solutions with two outgoing shock waves are analytically defined, as well as with the outgoing shock wave and rarefaction wave. We identify the area of Mach numbers and angles at which the flows interact and there is no solution. Specific flows with two outgoing rarefaction waves are not considered. Practical significance. The results supplement interference theory of stationary gas-dynamic discontinuities and can be used to develop new methods of numerical calculation with extraction of discontinuities.
Subcritical transition in plane Poiseuille flow as a linear instability process
Roizner, Federico; Karp, Michael; Cohen, Jacob
2016-05-01
In this work, a transition scenario is demonstrated, in which most of the stages are followed analytically. The transition is initiated by the linear transient growth mechanism in plane Poiseuille flow subjected to an infinitesimally small secondary disturbance. A novel analytical approximation of the linear transient growth mechanism enables us to perform a secondary linear stability analysis of the modified base-flow. Two possible routes to transition are highlighted here, both correspond to a small secondary disturbance superimposed on a linear transient growth. The first scenario is initiated by four decaying odd normal modes which form a counter-rotating vortex pair; the second is initiated by five even decaying modes which form a pair of counter-rotating pairs. The approximation of the linear transient growth stage by a combination of minimal number of modes allows us to follow the transition stages analytically by employing the multiple time scale method. In particular, the secondary instability stage is followed analytically using linear tools, and is verified by obtaining transition in a direct numerical simulation initiated by conditions dictated by the transient growth analytical expressions. Very good agreement is observed, verifying the theoretical model. The similarities between the two transition routes are discussed and the results are compared with similar results obtained for plane Couette flow.
Spandan, Vamsi; Lohse, Detlef; Verzicco, Roberto
2016-12-01
The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\\hat \\mu$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number $Ca$, the major-axis of the ellipsoids tends to align with the stream-wise direction and the extensional strain rate eigen direction in the boundary layer region while the distribution is highly isotropic in the bulk. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.
Farrell, Brian F.; Ioannou, Petros J.
2017-08-01
This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium
Bedrossian, Jacob; Masmoudi, Nader; Vicol, Vlad
2014-01-01
In this work we study the long time, inviscid limit of the 2D Navier-Stokes equations near the periodic Couette flow, and in particular, we confirm at the nonlinear level the qualitative behavior predicted by Kelvin's 1887 linear analysis. At high Reynolds number Re, we prove that the solution behaves qualitatively like 2D Euler for times t \\lesssim Re^(1/3), and in particular exhibits inviscid damping (e.g. the vorticity weakly approaches a shear flow). For times t \\gtrsim Re^(1/3), which is...
Plane Stratified Flow in a Room Ventilated by Displacement Ventilation
DEFF Research Database (Denmark)
Nielsen, Peter Vilhelm; Nickel, J.; Baron, D. J. G.
2004-01-01
The air movement in the occupied zone of a room ventilated by displacement ventilation exists as a stratified flow along the floor. This flow can be radial or plane according to the number of wall-mounted diffusers and the room geometry. The paper addresses the situations where plane flow...
Moser, K W; Raguin, L G; Georgiadis, J G
2001-07-01
The quantitative visualization of flow in a wide-gap annulus (radius ratio 0.5) between concentric cylinders with the inner cylinder rotating and a superimposed axial flow reveals a novel mixed-mode state at relatively high flow rates. A fast magnetic resonance imaging sequence allows the cinematographic dissection and three-dimensional reconstruction of supercritical nonaxisymmetric modes in a regime where stationary helical and propagating toroidal vortices coexist. The findings shed light on symmetry-breaking instabilities, flow pattern selection, and their consequences for hydrodynamic mixing in a complex laminar flow that constitutes a celebrated prototype of many mixing or fractionation processes.
Transient growth in Rayleigh-B\\'enard-Poiseuille/Couette convection
Jerome, J John Soundar; Huerre, Patrick
2016-01-01
An investigation of the effect of a destabilizing cross-stream temperature gradient on the transient growth phenomenon of plane Poiseuille flow and plane Couette flow is presented. Only the streamwise-uniform and nearly streamwise-uniform disturbances are highly influenced by the Rayleigh number Ra and Prandtl number Pr. The maximum optimal transient growth G max of streamwise-uniform disturbances increases slowly with increasing Ra and decreasing Pr. For all Ra and Pr, at moderately large Reynolds numbersRe, the supremum of G max is always attained for streamwise-uniform perturbations (or nearly streamwise-uniform perturbations, in the case of plane Couette flow) which produce large streamwise streaks and Rayleigh-B\\'enard convection rolls (RB). The optimal growth curves retain the same large-Reynolds-number scaling as in pure shear flow. A 3D vector model of the governing equations demonstrates that the short-time behavior is governed by the classical lift-up mechanism and that the influence of Ra on this m...
Measurements of Vorticity Vectors in Couette Flow with the Vorticity Optical Probe
1991-05-01
measurements, Frish (1981) invented a method of encasing microscopic plane mirrors carbonate crystal platelets ) in 20 to 30 Am clear plastic spheres having...sufficient size to give acceptably small diver iBasic lead carbonate, 3PbCO3 ŖPb(OH)2, in the form of hexagonal crystal platelets of 15 um diameter and...discussion of Buchhave, George and Lumley (1979) is recounted % some modifications. If the Lagrangian velocity field is represented by Fourier components
Stability of Flow around a Cylinder in Plane Poiseuille Flow
Dou, Hua-Shu; Ben, An-Qing; Fluid Mechanics Research Team
2013-11-01
Simulation of Navier-Stokes equations is carried out to study the stability of flow around a cylinder in plane Poiseuille flow. The energy gradient method is employed to analyze the mechanism of instability of cylinder wake. The ratio of the channel width to the cylinder diameter is 30, and the Reynolds number based on the cylinder diameter and incoming centerline velocity is 26 and 100, respectively. The incoming flow is given as being laminar. It is found that the instability of the cylinder wake, starting near the front stagnation point upstream. The recirculation zone behind the cylinder has no effect on the stability of the wake. In the wake behind the recirculation zone, the flow stability is controlled by the energy gradient in the shear layer along the two sides of the wake. At high Re, the energy gradient of averaged flow in the channel interacts with the wake vortex, strengthening the wake vortex structure. Due to the large ratio of the channel width to the cylinder diameter, the disturbance caused by the cylinder mainly occurs in the vicinity of the centerline and has little effect on the flow near the wall. The velocity profile on the two sides of the cylinder wake in the downstream channel remains laminar (parabolic profile). Professor in Fluid Mechanics; AIAA Associate Fellow.
Three dimensional Couette flow and heat transfer through a porous medium with variable permeability
Institute of Scientific and Technical Information of China (English)
CHAUDHARYR.C.; SHARMAPawanKumar
2003-01-01
This paper reports research on the effects of variations in injection velocity and permeability on the heat transfer and flow through a highly porous medium between two horizontal parallel plates situated at constant distance with constant suction by the upper plate.Due to this type of variation in injection velocity and in permeability the flow becomes three dimensional.The governing equstions are solved by adopting complex variable notations to obtain the expressions for the velocity and temperature field.The skin-friction along the main flow direction and rate of heat transfer are discussed with the help of graphs.
Nordsiek, F.; Huisman, S.G.; Veen, van der R.C.A.; Sun, C.; Lohse, D.; Lathrop, D.P.
2015-01-01
We present azimuthal velocity profiles measured in a Taylor–Couette apparatus, which has been used as a model of stellar and planetary accretion disks. The apparatus has a cylinder radius ratio of ${\\it\\eta}=0.716$η=0.716, an aspect ratio of ${\\it\\Gamma}=11.74$Γ=11.74, and the plates closing the cyl
Gils, Dennis P.M.; Bruggert, Gert-Wim; Lathrop, Daniel P.; Sun, Chao; Lohse, Detlef
2011-01-01
A new turbulent Taylor–Couette system consisting of two independently rotating cylinders has been constructed. The gap between the cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and o
Experimental Investigation of the Free Surface Effect on the Conical Taylor-Couette Flow System
Directory of Open Access Journals (Sweden)
F. Yahi
2016-01-01
Full Text Available The aim of this work is to highlight the critical thresholds corresponding to the onset of different instabilities considered in the flow between two vertical coaxial cones with and without free surface. The inner cone is rotating and the outer one is maintained at rest. Both cones have the same apex angle Φ =12° giving a constant annular gap δ =d/R1max. The height of the fluid column is H=155mm and It can be progressively decreased for each studied case of the flow system. Two kinds of configurations are studied, small and large gap. The working fluid is assumed as Newtonian and having constant properties like density and viscosity within the range of the required experimental conditions. By means of visualization technique of the flow we have been able to show the different transition modes occurring in the conical flow system according to the aspect ratio and then the induced action of the free surface which introduces a delay in the onset of different instability modes. The obtained results in term of features and stability of the flow are compared to those of Wimmer and Noui-Mehidi.
Worst-case amplification of disturbances in inertialess Couette flow of viscoelastic fluids
Lieu, Binh K; Kumar, Satish
2013-01-01
Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations. In strongly elastic flows, we show that disturbances with large streamwise length scales may be significantly amplified even in the absence of inertia. For fluctuations without streamwise variations, we derive explicit analytical expressions for the dependence of the worst-case amplification (from different forcing to different velocity and polymer stress components) on the Weissenberg number ($We$), the maximum extensibility of the polymer chains ($L$), the viscosity ratio, and the spanwise wavenumber. For the Oldroyd-B model, the amplification of the most energetic components of velocity and polymer stress fields scales as $We^2$ and $We^4$. On the other hand, finite extensibility of polymer molecules limits the largest achievable amplification even in flows with infinite...
ON INSTABILITY OF DILUTE FIBER SUSPENSIONS IN AN AXISYMMETRIC TAYLOR-COUETTE FLOW
Institute of Scientific and Technical Information of China (English)
WAN Zhan-hong; LIN Jian-zhong; LI Bing-ru
2005-01-01
A stability analysis of flow between two coaxial rotating cylinders in the presence of fibers was performed. Based on the axisymmetric normal mode for the disturbances, a modified stability equation was derived. Then the numerical solution of the eigenvalue problem about the equation was obtained using the fourth order finite difference scheme. The marginal curves that determine the instability property were drawn. The results show that the flow instability of the dilute fiber suspensions is governed by the aspect ratio of fiber H, the increment of H causes an increase of critical inner Reynolds number. The fiber additives effectively attenuate the instability of the flow, which is in agreement with those of related experiments.
The Three-Dimensional Velocity Distribution of Wide Gap Taylor-Couette Flow Modelled by CFD
Directory of Open Access Journals (Sweden)
David Shina Adebayo
2016-01-01
Full Text Available A numerical investigation is conducted for the flow between two concentric cylinders with a wide gap, relevant to bearing chamber applications. This wide gap configuration has received comparatively less attention than narrow gap journal bearing type geometries. The flow in the gap between an inner rotating cylinder and an outer stationary cylinder has been modelled as an incompressible flow using an implicit finite volume RANS scheme with the realisable k-ε model. The model flow is above the critical Taylor number at which axisymmetric counterrotating Taylor vortices are formed. The tangential velocity profiles at all axial locations are different from typical journal bearing applications, where the velocity profiles are quasilinear. The predicted results led to two significant findings of impact in rotating machinery operations. Firstly, the axial variation of the tangential velocity gradient induces an axially varying shear stress, resulting in local bands of enhanced work input to the working fluid. This is likely to cause unwanted heat transfer on the surface in high torque turbomachinery applications. Secondly, the radial inflow at the axial end-wall boundaries is likely to promote the transport of debris to the junction between the end-collar and the rotating cylinder, causing the build-up of fouling in the seal.
Taylor-Couette flow control by amplitude variation of the inner cylinder cross-section oscillation
Oualli, Hamid; Mekadem, Mahmoud; Lebbi, Mohamed; Bouabdallah, Ahcene
2015-07-01
The hydrodynamic stability of a viscous fluid flow evolving in an annular space between a rotating inner cylinder with a periodically variable radius and an outer fixed cylinder is considered. The basic flow is axis-symmetric with two counter-rotating vortices each wavelength along the whole filled system length. The numerical simulations are implemented on the commercial Fluent software package, a finite-volume CFD code. It is aimed to make investigation of the early flow transition with assessment of the flow response to radial pulsatile motion superimposed to the inner cylinder cross-section as an extension of a previous developed work in Oualli et al. [H. Oualli, A. Lalaoua, S. Hanchi, A. Bouabdallah, Eur. Phys. J. Appl. Phys. 61, 11102 (2013)] where a comparative controlling strategy is applied to the outer cylinder. The same basic system is considered with similar calculating parameters and procedure. In Oualli et al. [H. Oualli, A. Lalaoua, S. Hanchi, A. Bouabdallah, Eur. Phys. J. Appl. Phys. 61, 11102 (2013)], it is concluded that for the actuated outer cylinder and relatively to the non-controlled case, the critical Taylor number, Tac1, characterizing the first instability onset illustrated by the piled Taylor vortices along the gap, increases substantially to reach a growing rate of 70% when the deforming amplitude is ɛ = 15%. Interestingly, when this controlling strategy is applied to the inner cylinder cross-section with a slight modification of the actuating law, this tendency completely inverts and the critical Taylor number decreases sharply from Tac1 = 41.33 to Tac1 = 17.66 for ɛ = 5%, corresponding to a reduction rate of 57%. Fundamentally, this result is interesting and can be interpreted by prematurely triggering instabilities resulting in rapid development of flow turbulence. Practically, important applicative aspects can be met in several industry areas where substantial intensification of transport phenomena (mass, momentum and heat) is
Toroidal field instability and eddy viscosity in Taylor-Couette flows
Gellert, M
2008-01-01
Toroidal magnetic fields subject to the Tayler instability can transport angular momentum. We show that the Maxwell and Reynolds stress of the nonaxisymmetric field pattern depend linearly on the shear in the cylindrical gap geometry. Resulting angular momentum transport also scales linear with shear. It is directed outwards for astrophysical relevant flows and directed inwards for superrotating flows with dOmega/dR>0. We define an eddy viscosity based on the linear relation between shear and angular momentum transport and show that its maximum for given Prandtl and Hartmann number depends linear on the magnetic Reynolds number Rm. For Rm=1000 the eddy viscosity is of the size of 30 in units of the microscopic value.
Savenkov, I. V.
2015-02-01
For the pressure-driven flow in an annular channel with a wall moving in the axial direction, its linear instability with respect to axisymmetric perturbations at high Reynolds numbers is investigated within the framework of the triple-deck theory. When the gap between the cylinders is sufficiently small (as compared to the radii of the cylinders), it is shown that the perturbations can split into two wave packets, the first of which grows faster and moves at a higher velocity.
Direct Numerical Simulation of Turbulent Couette-Poiseuille Flow With Zero Skin Friction
Coleman, Gary N.; Spalart, Philippe R.
2015-01-01
The near-wall scaling of mean velocity U(yw) is addressed for the case of zero skin friction on one wall of a fully turbulent channel flow. The present DNS results can be added to the evidence in support of the conjecture that U is proportional to the square root of yw in the region just above the wall at which the mean shear dU=dy = 0.
Axisymmetric pulse train solutions in narrow-gap spherical Couette flow
Child, Adam; Kersalé, Evy
2016-01-01
We numerically compute the flow induced in a spherical shell by fixing the outer sphere and rotating the inner one. The aspect ratio $\\epsilon=(r_o-r_i)/r_i$ is set at 0.04 and 0.02, and in each case the Reynolds number measuring the inner sphere's rotation rate is increased to $\\sim10\\%$ beyond the first bifurcation from the basic state flow. For $\\epsilon =0.04$ the initial bifurcations are the same as in previous numerical work at $\\epsilon=0.154$, and result in steady one- and two-vortex states. Further bifurcations yield travelling wave solutions similar to previous analytic results valid in the $\\epsilon\\to0$ limit. For $\\epsilon=0.02$ the steady one-vortex state no longer exists, and the first bifurcation is directly to these travelling wave solutions, consisting of pulse trains of Taylor vortices travelling toward the equator from both hemispheres, and annihilating there in distinct phase-slip events. We explore these time-dependent solutions in detail, and find that they can be both equatorially symm...
Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus
Directory of Open Access Journals (Sweden)
Basant K. Jha
2011-12-01
Full Text Available The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving outer cylinder. The problem is solved using a combination of the Laplace transform technique, D’Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases.
The weakly nonlinear magnetorotational instability in a thin-gap Taylor-Couette flow
Clark, S E
2016-01-01
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a thin-gap, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We extend these results by performing a detailed force balance for the saturated azimuthal velocity and vertical magnetic field, demonstrating that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demons...
Finite-amplitude steady waves in plane viscous shear flows
Milinazzo, F. A.; Saffman, P. G.
1985-01-01
Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.
2007-01-01
6ErN) (1 + s0 − 2s20 −B1 Er)ErD 2 , C1 = B3 − 2C3 sinh(Er 1/2D) 2 sinh(Er1/2F ) . This result for Poiseuille flow is qualitatively similar to Couette ...nematic flows ,” Physical Review A 34 (4), 3393-3404 (1986). [3] Cui, Z., Forest, M.G., Wang, Q., and Zhou, H., “On weak plane Couette and Poiseuille ...Zhou, H. and Forest, M. G., “Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: morphology
On circulation-preserving plane MFD flows
Energy Technology Data Exchange (ETDEWEB)
Choubey, K.R.; Singh, S.N.; Singh, B.P.
1985-11-11
A theoretical analysis based on the equations of magnetofluid dynamics is undertaken in order to completely classify the flow geometries admitted by these equations. It is shown that the only possible flows with steady vorticity are, 1. motions having constant vorticity magnitude, 2. motions whose stream lines are concentric circles. Conditions are derived for which the results hold also for the unsteady case. (orig.).
Plane wave fast color flow mode imaging
DEFF Research Database (Denmark)
Bolic, Ibrahim; Udesen, Jesper; Gran, Fredrik
2006-01-01
degrees and 75 degrees. Compared to the conventional ultrasound imaging the frame rate is similar to 30 - 60 times higher. The bias, B-est of the velocity profile estimate, based on 8 pulse-echo emissions, is between 3.3% and 6.1% for beam to flow angles between 45 degrees and 75 degrees, and the standard...... deviation, sigma(est) of the velocity profile estimate is around 2% for beam to flow angles between 45 degrees and 75 degrees relative to the peak velocity, when the flow angle is known in advance. A study is performed to investigate how different parameters influence the blood velocity estimation....... The results confirmed expectations for beam to flow angles between 45 degrees and 75 degrees. The parameter study shows that the PWM using Directional velocity estimation gives the best results using spatial sampling interval = 10A, and number of directional signals >= 6...
2008-01-01
v Yi Statistical analysis dependent variable Greek Symbols 13 Contact angle of sessile drop a Concentration thickness A Evaporated vapor penetration...31 5 FIGURES 1. Configuration of Three Sessile Drops ............................................. 10 2. Sketch of...Droplet Geometry ............................................................. 11 3. Shape Factor as a Function of Contact Angle
Solution of the Problem of the Couette Flow for a Fermi Gas with Almost Specular Boundary Conditions
Bedrikova, E. A.; Latyshev, A. V.
2016-06-01
A solution of the Couette problem for a Fermi gas is constructed. The kinetic Bhatnagar-Gross-Krook (BGK) equation is used. Almost specular boundary conditions are considered. Formulas for the mass flux and the heat flux of the gas are obtained. These fluxes are proportional to the difference of the tangential momentum accommodation coefficients of the molecules. An expression for the viscous drag force acting on the walls of the channel is also found. An analysis of the macroparameters of the gas is performed. The limit to classical gases is taken. The obtained results are found to go over to the known results in this limit.
Energy Technology Data Exchange (ETDEWEB)
Sankar, D. S. [Universiti Teknologi Brunei, Bandar Seri Begawan (Brunei Darussalam); Lee, U Sik [Inha University, Incheon (Korea, Republic of)
2016-07-15
This theoretical study investigates three types of basic flows of viscous incompressible Herschel-Bulkley fluid such as (i) plane Couette flow, (ii) Poiseuille flow and (iii) generalized Couette flow with slip velocity at the boundary. The analytic solutions to the nonlinear boundary value problems have been obtained. The effects of various physical parameters on the velocity, flow rate, wall shear stress and frictional resistance to flow are analyzed through appropriate graphs. It is observed that in plane Poiseuille flow and generalized Couette flow, the velocity and flow rate of the fluid increase considerably with the increase of the slip parameter, power law index, pressure gradient. The fluid velocity is significantly higher in plane Poiseuille flow than in plane Couette flow. The wall shear stress and frictional resistance to flow decrease considerably with the increase of the power law index and increase significantly with the increase of the yield stress of the fluid. The wall shear stress and frictional resistance to flow are considerably higher in plane Poiseuille flow than in generalized Couette flow.
Integral representation in the hodograph plane of compressible flow
DEFF Research Database (Denmark)
Hansen, Erik Bent; Hsiao, G.C.
2003-01-01
Compressible flow is considered in the hodograph plane. The linearity of the equation determining the stream function is exploited to derive a representation formula involving boundary data only, and a fundamental solution to the adjoint equation. For subsonic flow, an efficient algorithm for com...
STOKES FLOW DUE TO FUNDAMENTAL SINGULARITIES BEFORE A PLANE BOUNDARY
Institute of Scientific and Technical Information of China (English)
N.Aktar; F. Rahman; S.K. Sen
2004-01-01
A representation for the velocity and pressure fields in three-dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B. This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary.Collins' s theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the theorem. A few illustrative examples are given to show its usefulness.
Reddy, G. J.; Raju, R. S.; Rao, J. A.; Gorla, R. S. R.
2017-02-01
An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.
Directory of Open Access Journals (Sweden)
Reddy G.J.
2017-02-01
Full Text Available An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40 in a rotating system has been considered. A Finite Element Method (FEM was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid size and the present numerical solutions through the Finite Element Method (FEM are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT. These are shown in tabular and graphical forms.
Energy Technology Data Exchange (ETDEWEB)
Atkhen, K
1998-10-19
This thesis characterized a mixer hydrodynamic, using the Couette-Taylor properties in the case of one-phase, two-phase (air-liquid) and three-phase (air-liquid-liquid). An ideal configuration has been defined. This study brings a contribution to the fuels processing processes.
Transient growth in Rayleigh-Bénard-Poiseuille/Couette convection
John Soundar Jerome, J.; Chomaz, Jean-Marc; Huerre, Patrick
2012-04-01
An investigation of the effect of a destabilizing cross-stream temperature gradient on the transient growth phenomenon of plane Poiseuille flow and plane Couette flow is presented. Only the streamwise-uniform and nearly streamwise-uniform disturbances are highly influenced by the Rayleigh number Ra and Prandtl number Pr. The maximum optimal transient growth Gmax of streamwise-uniform disturbances increases slowly with increasing Ra and decreasing Pr. For all Ra and Pr, at moderately large Reynolds numbers Re, the supremum of Gmax is always attained for streamwise-uniform perturbations (or nearly streamwise-uniform perturbations, in the case of plane Couette flow) which produce large streamwise streaks and Rayleigh-Bénard convection rolls (RB). The optimal growth curves retain the same large-Reynolds-number scaling as in pure shear flow. A 3D vector model of the governing equations demonstrates that the short-time behavior is governed by the classical lift-up mechanism and that the influence of Ra on this mechanism is secondary and negligible. The optimal input for the largest long-time response is given by the adjoint of the dominant eigenmode with respect to the energy scalar product: the RB eigenmode without its streamwise velocity component. These short-time and long-time responses depict, to leading order, the optimal transient growth G(t). At moderately large Ra (or small Pr at a fixed Ra), the dominant adjoint mode is a good approximation to the optimal initial condition for all time. Over a general class of norms that can be considered as growth functions, the results remain qualitatively similar, for example, the dominant adjoint eigenmode still approximates the maximum optimal response.
Huisman, Sander G; Bruggert, Gert-Wim H; Lohse, Detlef; Sun, Chao
2016-01-01
A new Taylor-Couette system has been designed and constructed with precise temperature control. Two concentric independently rotating cylinders are able to rotate at maximum rates of $f_i = \\pm20$ Hz for the inner cylinder and $f_o = \\pm10$ Hz for the outer cylinder. The inner cylinder has an outside radius of $r_i = 75$ mm, and the outer cylinder has an inside radius of $r_o = 105$ mm, resulting in a gap of $d=30$ mm. The height of the gap $L =549$ mm, giving a volume of $V=9.3$l. The geometric parameters are $\\eta = r_i/r_o = 0.714$ and $\\Gamma = L/d = 18.3$. With water as working fluid at room temperature the Reynolds numbers that can be achieved are $\\text{Re}_i = \\omega_i r_i (r_o-r_i)/\
Energy Technology Data Exchange (ETDEWEB)
Colgate, S. A. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Beckley, H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Si, J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Martinic, J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Westpfahl, D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Slutz, J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Westrom, C. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Klein, B. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Schendel, P. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Scharle, C. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); McKinney, T. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ginanni, R. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Bentley, I. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mickey, T. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ferrel, R. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Li, H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Pariev, V. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Finn, J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2011-04-28
The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B_{Φ} that is ≃8×B_{r}, where B_{r} is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodium at a magnetic Reynolds number Rm≃120. Small turbulence in stable Taylor-Couette flow is caused by Ekman flow at the end walls, which causes an estimated turbulence energy fraction of (δv/v)^{2}~10^{-3}.
Intermittency in spherical Couette dynamos
Raynaud, Raphaël; 10.1103/PhysRevE.87.033011
2013-01-01
We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
Narsimhan, Vivek; Zhao, Hong; Shaqfeh, Eric S. G.
2013-06-01
We develop a coarse-grained theory to predict the concentration distribution of a suspension of vesicles or red blood cells in a wall-bound Couette flow. This model balances the wall-induced hydrodynamic lift on deformable particles with the flux due to binary collisions, which we represent via a second-order kinetic master equation. Our theory predicts a depletion of particles near the channel wall (i.e., the Fahraeus-Lindqvist effect), followed by a near-wall formation of particle layers. We quantify the effect of channel height, viscosity ratio, and shear-rate on the cell-free layer thickness (i.e., the Fahraeus-Lindqvist effect). The results agree with in vitro experiments as well as boundary integral simulations of suspension flows. Lastly, we examine a new type of collective particle motion for red blood cells induced by hydrodynamic interactions near the wall. These "swapping trajectories," coined by Zurita-Gotor et al. [J. Fluid Mech. 592, 447-469 (2007), 10.1017/S0022112007008701], could explain the origin of particle layering near the wall. The theory we describe represents a significant improvement in terms of time savings and predictive power over current large-scale numerical simulations of suspension flows.
Tohidi, Masoumeh; Toghraie, Davood
2017-08-01
The effect of geometrical parameters, roughness and the number of nanoparticles on self-diffusion in Couette flow in a nanochannel is investigated by using of molecular dynamics simulation. Gold nanoparticles (50, 100 and 200) were also distributed randomly between the nanochannel upper and lower walls. The effect of geometrical parameters of rectangular roughness in a nanochannel and the number of Gold nanoparticles on global self-diffusion and local self-diffusion as well as the average amounts were investigated in Couette flow. The results show that by increasing the roughness height, the particles are entrapped within the roughness and hence reduce the local self-diffusion coefficient in the vicinity of the upper wall. Also, by increasing the roughness height, the roughness length has less effect on the local diffusion coefficient.
Geometric structure of pseudo-plane quadratic flows
Sun, Che
2017-03-01
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.
Douglass, Eric; Zhao, Yunjie; Hill, Lucas; Brenman, David; Olsen, Thomas; Wiener, Richard
2008-11-01
Chaos has been observed in the formation of Taylor Vortex pairs in Modified Taylor Couette flow with hourglass geometry. Control of chaos has been demonstrated in this system employing the RPF algorithm. Seeking alternative algorithms, we are implementing the OGY algorithm in a numerical model of a damped driven mechanical pendulum and a physical apparatus. We report on both and future plans for the Modified Taylor-Couette system. Wiener et al, Phys. Rev. E 55, 5489 (1997). Rollins et al, Phys. Rev. E 47, R780 (1993). Wiener et al, Phys. Rev. Lett. 83, 2340 (1999). E. Ott, C. Grebogi, & J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990). G. L. Baker, Am. J. Phys. 63, 832 (1995). J. A. Blackburn et al, Rev. Sci. Instr. 60, 422 (1989).
Numerical simulations of heat transfer in plane channel flow
Gharbi, Najla El; Benzaoui, Ahmed
2010-01-01
Reynolds-averaged Navier-Stokes (RANS) turbulence models (such as k-{\\epsilon} models) are still widely used for engineering applications because of their relatively simplicity and robustness. In fully developed plane channel flow (i.e. the flow between two infinitely large plates), even if available models and near-wall treatments provide adequate mean flow velocities, they fail to predict suitable turbulent kinetic energy "TKE" profiles near walls. TKE is involved in determination of eddy viscosity/diffusivity and could therefore provide inaccurate concentrations and temperatures. In order to improve TKE a User Define Function "UDF" based on an analytical profile for TKE was developed and implemented in Fluent. Mean streamwise velocity and turbulent kinetic energy "TKE" profiles were compared to DNS data for friction Reynolds number $Re_{\\tau}$ = 150. Simulation results for TKE show accurate profiles. Simulation results for horizontal heated channel flows obtained with Fluent are presented. Numerical result...
Boundary layers interactions in the plane parallel incompressible flows
Nguyen, Toan
2011-01-01
We study the inviscid limit problem of the incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighborhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane parallel flows introduced by Di Perna and Majda in \\cite{DM}.
Experimental study of collisional granular flows down an inclined plane
Azanza, Emmanuel; Chevoir, François; Moucheront, Pascal
1999-12-01
The collisional flow of a slightly inelastic granular material down a rough inclined plane is usually described by kinetic theories. We present an experimental study aimed at analysing the assumptions and the quantitative predictions of such theories. A two-dimensional channel coupled to a model granular material and image analysis allow detailed and complete measurement of the kinematics and structure of the flows. We determine the range of inclination and particle flux for which the flow is stationary and uniform. The characteristic profiles of solid fraction, mean velocity and granular temperature are systematically measured. Both the true collisional and the dilute kinetic regimes are examined. We show that a quasi-hydrodynamic description of these regimes seems relevant, and that the pressure and the viscosity terms are in good qualitative agreement with the prediction of the kinetic theory. The profiles are well described by the kinetic theory near the top of the flow, at low solid fraction. Conversely there are large discrepancies near the rough plane, where the material is structured in layers.
Circulation-preserving plane flows of incompressible viscous fluids
Yin, W.-L.
1983-06-01
The present investigation is concerned with a systematic use of the method of complex variables in a study of (generally unsteady) plane solutions of the Navier-Stokes equation. Circulation-preserving flows are considered in the investigation. However, the employed method can also be applied to more general cases. A circulation-preserving plane solution of the Navier-Stokes equation possesses a biharmonic stream function. The stream function may, therefore, be expressed in terms of two complex analytic functions, taking into account Goursat's representation. Attention is given to differential equations in the complex form, the case of steady vorticity, the case of unsteady vorticity with a spatially constant vorticity gradient, solutions with logarithmic vorticity fields, and a proof of completeness.
Circulation in a Short Cylindrical Couette System
Energy Technology Data Exchange (ETDEWEB)
Akira Kageyama; Hantao Ji; Jeremy Goodman
2003-07-08
In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. The flow is very different from that of an ideal, infinitely long Couette system. Simulations show that endcaps co-rotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted toroidal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at Re less than or equal to 3200 agrees remarkably well with experiment at Re approximately equal to 106. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings.
Energy Technology Data Exchange (ETDEWEB)
Jeng, Tzer-Ming [Air Force Institute of Technology, Gangshan (Taiwan). Department of Mechanical Engineering; Tzeng, Sheng-Chung; Lin, Chao-Hsien [ChienKuo Technology University, Changhua (Taiwan). Department of Mechanical Engineering
2007-01-15
This work experimentally investigates the heat transfer characteristics of Taylor-Couette-Poiseuille flow in an annular channel by mounting longitudinal ribs on the rotating inner cylinder. The ranges of the axial Reynolds number (Re) and the rotational Reynolds number (Re{sub {omega}}) are Re=30-1200 and Re{sub {omega}}=0-2922, respectively. Three modes of the inner cylinder without/with longitudinal ribs are considered. A special entry and exit design for the axial coolant flow reveals some interesting findings. The value of Nusselt number (Nu) is almost minimal at the inlet of the annular channel, and then sharply rises in the axial direction. The average Nusselt number (Nu|) increases with Re. Nu increases rapidly with Re{sub {omega}} at low Re (such as at Re=30 and 60) but that the effect of Re{sub {omega}} decreases as the value increases (such as at Re=300-1200). The ratio Nu|/Nu|{sub 0} increases with Re{sub {omega}} and exceed two at all Re and in the test modes. The heat transfer is typically promoted by mounting longitudinal ribs on the rotating inner cylinder, especially at Re=300 and 600. When Re=300 or 600 and Re{sub {omega}}>2000, the Nu| of the system with ribs reaches around 1.4 times that of Nu|{sub A} (Nu| in mode A). Under a given pumping power constraint (PRe{sup 3}), the Nu| of the system with ribs (modes B and C) generally exceeds that without ribs (mode A), while the difference between the values of Nu| in modes B and A slowly falls as PRe{sup 3} increases. Additionally, mode B (with ribs) is preferred for high heat transfer when PRe{sup 3}<4.5x10{sup 13} but mode C (with cavities on ribs) is optimal for high heat transfer when PRe{sup 3}>4.5x10{sup 13}. (author)
PREFACE: The 15th International Couette-Taylor Worskhop
Mutabazi, Innocent; Crumeyrolle, Olivier
2008-07-01
The 15th International Couette-Taylor Worskhop (ICTW15) was held in Le Havre, France from 9-12 July 2007. This regular international conference started in 1979 in Leeds, UK when the research interest in simple models of fluid flows was revitalized by systematic investigation of Rayleigh-Bénard convection and the Couette-Taylor flow. These two flow systems are good prototypes for the study of the transition to chaos and turbulence in closed flows. The workshop themes have been expanded from the original Couette-Taylor flow to include other centrifugal instabilities (Dean, Görtler, Taylor-Dean), spherical Couette flows, thermal convection instabilities, MHD, nonlinear dynamics and chaos, transition to turbulence, development of numerical and experimental techniques. The impressive longevity of the ICTW is due to the close interaction and fertile exchanges between international research groups from different disciplines: Physics and Astrophysics, Applied Mathematics, Mechanical Engineering, Chemical Engineering. The present workshop was attended by 100 participants, the program included over 83 contributions with 4 plenary lectures, 68 oral communications and 17 posters. The topics include, besides the classical Couette-Taylor flows, the centrifugal flows with longitudinal vortices, the shear flows, the thermal convection in curved geometries, the spherical Couette-Taylor flow, the geophysical flows, the magneto-hydrodynamic effects including the dynamo effect, the complex flows (viscoelasticity, immiscible fluids, bubbles and migration). Selected papers have been processed through the peer review system and are published in this issue of the Journal of Physics: Conference Series. The Workshop has been sponsored by Le Havre University, the Region Council of Haute-Normandie, Le Havre City Council, CNRS (ST2I, GdR-DYCOEC), and the European Space Agency through GEOFLOW program. The French Ministry of Defense (DGA), the Ministry of Foreign Affairs, the Ministry of
Fardin, M A; Perge, C; Taberlet, N
2014-05-28
The flow between concentric cylinders is routinely used in soft matter studies. In many cases, the purpose of the setup is rheometric: the idea is to relate macroscopic changes in material properties to microscopic changes in the structure of the material. The correspondence between the modifications of the microscopic structure and the macroscopic flow often relies on viscometric assumptions, which require the flow to be at least laminar. Flow instabilities are usually neglected because the viscosities of the materials are high and the geometries are small, such that the creeping flow approximation can be used. Nonetheless, the phenomenology of viscoelastic instabilities that emerged in the last twenty years warns us that flows can become turbulent without inertia, in particular flows between concentric cylinders. Given the strong similarities between inertial hydrodynamic instabilities and viscoelastic instabilities, a general knowledge of the former is advised for any researcher working on complex fluids. In this tutorial review, we focus on the inertial instability of isothermal and incompressible Newtonian fluids flowing between concentric cylinders. We highlight important aspects that can guide the study and control of instabilities in complex fluids in general.
Hinvi, L A; Orou, J B Chabi
2013-01-01
This paper analyses the effects of small injection/suction Reynolds number, Hartmann number, permeability parameter and wave number on a viscous incompressilbe electrically conduction fluid flow in a parallel porous channel. The plates of the channel with small constant injection/suction, have constant temperature. The upper plate is allowed to mouve in flow direction and the lower plate is kept at rest. A magnetic field of uniform strength is also applied normally to the plates what are parallel. The originality of the paper is to study the effect of the above parameter in temporal linear stabilty analysis of the flow throught the modified Orr-Sommerfeld equation.
Numerical Calculation of Interaction Between Plane Jet and Subsonic Flow
Directory of Open Access Journals (Sweden)
V. O. Moskalenko
2016-01-01
Full Text Available The paper makes numerical calculation of interaction between plane jet and subsonic flow. Its aim is to determine the jet trajectory, velocity profiles, distribution of pressure coefficient on the plate surface at different jet angles, namely ωj=45°; 90°; 105° and at low blowing strengths ( ≤1.5 as well as a to make comparison with the experimental data of other authors.To simulate a two-dimensional jet in the subsonic flow the software package “CAD SolidWorks Flow Simulation” has been used. Initially, the test task was solved with its calculation results compared with experimental ones [6.8] in order to improve the convergence; the size of the computational domain and a computational grid within the k-ε turbulence model were selected. As a result of the calculation, were identified and analysed the pressure values, jet trajectories, and velocity profiles. In the graphs the solid lines show calculation results, and dots represent experimental data.From the calculation results it is seen that, with increasing intensity of the reduced mass flow ¯q in the above range, the change of the jet pressure coefficient p¯ distribution behind a slotted nozzle is almost linear and significant. Before the nozzle, with increasing ¯q the pressure coefficient increases slightly.Analysis of results has shown that blowing of jets with ωj>90ω, provides a greater perturbation of the subsonic flow. Thus, the jet penetrates into the flow deeper, forms a dead region of the greater length, and more significantly redistributes the pressure coefficient on the surface of the plate.The calculation results are in good compliance with the experimental data both for the jet axis and for the pressure coefficient distribution on the plate surface. The research results can be used in the designing the jet control of aircrafts.
Turbulent-laminar patterns in plane Poiseuille flow
Tuckerman, Laurette S; Schrobsdorff, Hecke; Schneider, Tobias M; Gibson, John F
2014-01-01
Turbulent-laminar banded patterns in plane Poiseuille flow are studied via direct numerical simulations in a tilted and translating computational domain using a parallel version of the pseudospectral code Channelflow. 3D visualizations via the streamwise vorticity of an instantaneous and a time-averaged pattern are presented, as well as 2D visualizations of the average velocity field and the turbulent kinetic energy. Simulations for Reynolds numbers descending from 2300 to 700 show the gradual development from uniform turbulence to a pattern with wavelength 20 half-gaps near Re=1900, to a pattern with wavelength 40 near Re=1300 and finally to laminar flow near Re=800. These transitions are tracked quantitatively via diagnostics using the amplitude and phase of the Fourier transform and its probability distribution. The propagation velocity of the pattern is approximately that of the mean flux and is a decreasing function of Reynolds number. Examination of the time-averaged flow shows that a turbulent band is ...
Periodically bursting edge states in plane Poiseuille flow
Zammert, Stefan
2013-01-01
We investigate the laminar-turbulent boundary in plane Poiseuille flow by the method of edge tracking. In short and narrow computational domains we find for a wide range in Reynolds number that all states in the boundary converge to a period orbit with a period of the order of $10^{3}$ time units. The attracting states in these small domains are periodically extended in the spanwise and streamwise direction, but always localized to one side of the channel in the normal direction. In short and wide domains the edge states are localized in the spanwise direction. The periodic motion found in the small domains then induces a large variety of dynamical activity. The findings are very similar to the ones in the asymptotic suction boundary layer.
Nasibullayev, I Sh; Tarasov, O S; Krekhov, A P; Kramer, L
2005-11-01
We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.
Local Reynolds number and thresholds of transition in shear flows
Tao, JianJun; Chen, ShiYi; Su, WeiDong
2013-02-01
Recent experimental and numerical investigations reveal that the onset of turbulence in plane-Poiseuille flow and plane-Couette flow has some similar stages separated with different threshold Reynolds numbers. Based on these observations and the energy equation of a disturbed fluid element, a local Reynolds number Re L is derived to represent the maximum ratio of the energy supplement to the energy dissipation in a cross section. It is shown that along the sequence of transition stages, which include transient localized turbulence, "equilibrium" localized turbulence, spatially intermittent but temporally persistent turbulence and uniform turbulence, the corresponding thresholds of Re L for plane-Couette flow, Hagen-Poiseuille flow and plane-Poiseuille flow are consistent, indicating that the critical (threshold) states during the laminar-turbulent transition are determined by the local properties of the base flow and are independent of global features, such as flow geometries (pipe or channel) and types of driving forces (shear driving or pressure driving).
Farrell, Brian F; Nikolaidis, Marios-Andreas
2016-01-01
Although the roll/streak structure is ubiquitous in pre-transitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the roll/streak structure has been invoked to explain its appearance as resulting from chance occurrence in the free-stream turbulence (FST) of perturbations configured to optimally excite it. However, there is an alternative interpretation which is that FST interacts with the roll/streak structure to destabilize it. Statistical state dynamics (SSD) provides analysis methods for studying instabilities of this type which arise from interaction between the coherent and incoherent components of turbulence. Stochastic structural stability theory (S3T), which implements SSD in the form of a closure at second order, is used to analyze the SSD modes arising from interaction between the coherent streamwise invariant component and the incoherent FST component of turbulence. The least stable S3T ...
Firouznia, Mohammadhossein; Metzger, Bloen; Ovarlez, Guillaume; Hormozi, Sarah
2016-11-01
The flows of non-Newtonian slurries, often suspensions of noncolloidal particles in yield stress fluids, are ubiquitous in many natural phenomena and industrial processes. Investigating the microstructure is essential allowing the refinement of macroscopic equations for complex suspensions. One important constraint on the dynamics of a Stokesian suspension is reversibility, which is not necessarily valid for complex fluids. The interaction of two particles in a reversing shear flow of complex fluids is a guide to understand the behavior of complex suspensions. We study the hydrodynamic interaction of two small freely-moving spheres in a linear flow field of yield stress fluids. An important point is that non-Newtonian fluid effects can be varied and unusual. Depending on the shear rate, even a yield stress fluid might show hysteresis, shear banding and elasticity at the local scales that need to be taken into account. We study these effects with the aid of conventional rheometry, Particle Image Velocimetry and Particle Tracking Velocimetry in an original apparatus. We show our preliminary experimental results. NSF.
Symmetry plane model for turbulent flows with vortex generators
Arnaud, Gilles L.; Russell, David A.
1991-01-01
An approximate procedure is proposed for predicting the performance of counterrotating vortex-generator installations in incompressible flow. An inviscid calculation that includes the motion of the vortices is used to obtain crossflow velocities at the boundary-layer edge as a function of initial position, spacing, and strength of the vortices, and local values of the spanwise gradient are then folded into an integral turbulent-boundary layer procedure applied in the plane of symmetry. Special attention is paid to the consistency of the approximations and equations used. The two-dimensional aerodynamics of vortex generator installations on a NACA 0016 airfoil at angle-of-attack are estimated in this manner, and the results compared with experiments carried out with a 30-cm chord wing mounted in a 2.4 x 3.6-m cross-section wind tunnel and tested at chord Reynolds numbers of 0.7 and 1.4 x 10 to the 6th. Agreement in the separation location is found for these complex flows for a range of conditions.
HYPERBOLIC MEAN CURVATURE FLOW:EVOLUTION OF PLANE CURVES
Institute of Scientific and Technical Information of China (English)
Kong Dexing; Liu Kefeng; Wang Zenggui
2009-01-01
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves.More precisely, we consider a family of closed curves F: S1×[0,T)→R2 which satisfies the following evolution equationε2F/εt2(u,t)=k(u,t)-▽p(u,t),▽(u,t)∈ S1X[0,T) with the initial data F(u,0)=Fo(u) and εF/εt(u,0)=F(u)No,Where k is the mean curvature and N is the unit inner normal vector of the plane curve F(u,t)f(u) and No are the initial velocity and the unit inner normal vector of the initial convex closed curve Fo,respectively,and ▽p is given by ▽p≧(ε2F/εsε和/εF/ε和)T,in which T stands for the unit tangent vector.The above problem is an initial value problem for a system of partial differential equations for F,it can be completely reduced to an initial value problem for a single partial differential equation for its support function.The latter equation is a hyperbolic Monge-Ampere equation.Based on this,we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at the a finite time interval[0,Tmax)and when t goes to Tmax,either the solution converges to a point or shocks and other propagating discontinuities are generated.Furthermore,we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support function adn the curvature of the curve.In the end,we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-timeR1,1.
High-Reynolds Number Taylor-Couette Turbulence
Grossmann, Siegfried; Lohse, Detlef; Sun, Chao
2016-01-01
Taylor-Couette flow, the flow between two coaxial co- or counter-rotating cylinders, is one of the paradigmatic systems in the physics of fluids. The (dimensionless) control parameters are the Reynolds numbers of the inner and outer cylinders, the ratio of the cylinder radii, and the aspect ratio. O
Lattice Boltzmann mo deling of microscale oscillating Couette flow%微尺度振荡Couette流的格子Boltzmann模拟
Institute of Scientific and Technical Information of China (English)
陶实; 王亮; 郭照立
2014-01-01
采用有效多松弛时间-格子Boltzmann 方法(Effective MRT-LBM)数值模拟了微尺度条件下的振荡 Couette 和Poiseuille 流动。在微流动LBM 中引入Knudsen 边界层模型,对松弛时间进行修正。模拟时平板或外力以正弦周期振动, Couette 流中考虑了单平板振动、上下板同相振动这两类情况。研究结果表明,修正后的MRT-LBM 模型能有效用于这类非平衡的微尺度流动模拟；对于Couette 流,随着Kn 数的增大,壁面滑移效应变得越明显。 St 越大,板间速度剖面的非线性特性越剧烈；两板同相振荡时,若Kn, St 均较小,板间流体受到平板拖动剪切的影响很小,板间速度几乎重叠在一起；在振荡Poiseuille 流动中, St 数增大到一定值时,相位滞后现象减弱；相对于Kn 数, St 数对振荡Couette 和Poiseuille 流中不同位置处速度相位差的产生有较大影响。
High Resolution Simulation of Turbulent Flow in a Channel.
1987-09-25
chosen to maintain the original Poiseuille flow . The introduction of highly unstable disturbances causes transition to turbulence so that the wall...for Turbulent Channel Flow ," Phys. Rev. Lett, Vol. 47, 832-835 (1981). 2. S.A. Orszag and L.C. Kells, "Transition to turbulence in plane Poiseuille and...plane Couette Flow ," J. Fluid Mech., Vol. 96, pp. 159-205. 3. Kreplin, H.-P. and Eckelmann, H., "Behavior of the Three Fluctucting Velocity
ON A PERIMETER-PRESERVING PLANE CURVE FLOW
Institute of Scientific and Technical Information of China (English)
PanShengliang
2001-01-01
The purpose of this paper is to investigate a new type of evolution problem for closedconvex plane curves which will preserves the perimeter of the curve but expands the enclosedarea and the final limiting curve is a circle in the Hausdorff metric in the plane.
Hydrodynamic Interactions between Two Equally Sized Spheres in Viscoelastic Fluids in Shear Flow
Snijkers, F.; Pasquino, R.; Vermant, J.
2013-01-01
The effect of using a viscoelastic suspending medium, on the;in-plane hydrodynamic interaction between two equally sized spheres in shear flow is studied experimentally to understand flow-induced assembly behavior (i.e., string formation). A counterrotating device equipped with a Couette geometry is
A NEW APPROACH TO THE NONLINEAR STABILITY OF PARALLEL SHEAR FLOWS
Institute of Scientific and Technical Information of China (English)
XU Lan-xi; HUANG Yong-nian
2005-01-01
Lyapunov's second method was used to study the nonlinear stability of parallel shear flows for stress-free boundaries. By introducing an energy functional, it was shown that the plane Couette and plane Poiseuille flows are conditionally and asymptotically stable for all Reynolds numbers. In particular, to two-dimensional perturbations, by defining new energy functionals the unconditional stability of the basic flows was proved.
Hodographic study of non-Newtonian MHD aligned steady plane fluid flows
Directory of Open Access Journals (Sweden)
P. V. Nguyen
1990-01-01
Full Text Available A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.
Exact solutions for steady flows of second-grade fluids
Institute of Scientific and Technical Information of China (English)
ZHANG Dao-xiang; FENG Su-xiao; LU Zhi-ming; LIU Yu-lu
2009-01-01
This paper aims to investigate exact solutions for a second-grade fluid flow with the inverse method.By assuming the relation between the vorticity field and the streamfunction,the exact solutions of the motion of plane second-grade fluids are investigated and obtained.The solutions obtained include simple Couette flows,slit jet flows and uniform flows over a series of distributed obstacles.
Flow of Polymer Melts in Plane- and Axi-Symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
1998-01-01
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in all...
Flow of Polymer Melts in Plane- and Axi-symmetric Converging Dies
DEFF Research Database (Denmark)
Lauridsen, Carsten Linding; Kjær, Erik Michael; Haudrum, Jan
1997-01-01
The extensional flow has considerable influence on the pressure loss in converging flows, which are present in both extrusion and injection moulding. Both plane- and axi-symmetric converging flows have been studied with LDPE, HDPE and PS. The transient extensional viscosities are determined in all...
The Compressible Flow Past Various Plane Profiles Near Sonic Velocity
Goethert, B.; Kawalki, K. H.
1949-01-01
In an earlier report UM No.1117 by Gothert,the single-source method was applied to the compressible flow around circles, ellipses, lunes, and around an elongated body of revolution at different Mach numbers and the results compared as far as possible with the calculations by Lamla ad Busemann. Essentially, it was found that with favorable source arrangement the single-source method is in good agreement with the calculations of the same degree of approximation by.Lamla and Busemann. Near sonic velocity the number of steps must be increased considerably in order to sufficiently approximate the adiabatic curve. After exceeding a certain Mach number where local supersonic fields occur already, it was no longer possible, in spite of the substantially increased number of steps, to obtain a systematic solution because the calculation diverged. This result,was interpreted to mean that above this point of divergence the symmetrical type of flow ceases to exist and changes into the unsymmetrical type characterized by compressibility shocks.
Numerical simulations of aerodynamic contribution of flows about a space-plane-type configuration
Matsushima, Kisa; Takanashi, Susume; Fujii, Kozo; Obayashi, Shigeru
1987-01-01
The slightly supersonic viscous flow about the space-plane under development at the National Aerospace Laboratory (NAL) in Japan was simulated numerically using the LU-ADI algorithm. The wind-tunnel testing for the same plane also was conducted with the computations in parallel. The main purpose of the simulation is to capture the phenomena which have a great deal of influence to the aerodynamic force and efficiency but is difficult to capture by experiments. It includes more accurate representation of vortical flows with high angles of attack of an aircraft. The space-plane shape geometry simulated is the simplified model of the real space-plane, which is a combination of a flat and slender body and a double-delta type wing. The comparison between experimental results and numerical ones will be done in the near future. It could be said that numerical results show the qualitatively reliable phenomena.
LIF Measurement of Interacting Gas Jet Flow with Plane Wall
Yanagi, A.; Kurihara, S.; Yamazaki, S.; Ota, M.; Maeno, K.
2011-05-01
Discharging rarefied gas jets in low-pressure conditions are interesting and important phenomena from an engineering point of view. For example they relate to the attitude control of the space satellite, or the semiconductor technology. The jets, however, deform to the complicated shapes by interacting with solid walls. In this paper we have performed the experiments the flow visualization as a first step by applying the LIF (Laser Induced Fluorescence) method on the jet-wall interaction. Jet is spouting out from a φ1.0 mm circular hole into the low pressure air chamber, impinging on a flat plate. The LIF visualization of interacting rarefied gas jet is carried out by using the iodine (I2) tracer and argon ion laser.
SCOUR DEPTH AND FLOW PATTERN OF ERODING PLANE JETS
Institute of Scientific and Technical Information of China (English)
A.KURNIAWAN; M.S.ALTINAKAR; W.H.GRAF
2004-01-01
Local scour may occur when a hydraulic structure is positioned in a channel with an erodible bed.Herewith investigated experimentally are the erosion and flow pattern due to a water jet passing over a channel bed at the asymptotic (final) state. The development of the scour hole, its maximum scour depth and length, are recorded and compared with available scour-depth relations. Two sets of experiments (see Table 1) were carried out. Set 1 (3 runs) was concerned with measuring the vertical instantaneous velocity distribution in the scour hole. The scour hole at the asymptotic (final) state, t ≈100 [h] was investigated. Set 2 (5 runs) was concerned with studying the physics of scouring. The scour hole at about mid-state, t ≈ 0.5 [h], was investigated; subsequently the scour-hole depth was linearly extended on the semi-log scale to 72 [h]; no velocity measurements were performed. The present data are put in context with some (popular) existing relations; recommended is a modification of some of these relations.
Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions
Institute of Scientific and Technical Information of China (English)
ZHENG Yu-Ming; FUCHS Christian; FAESSLER Amand; SHEKHTER Kirril; SRISAWAD Pornrad; KOBDAJ Chinorat; YAN Yu-Peng
2004-01-01
The influence of the chiral mean field on the K+ in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the inmedium kaon dynamics and strongly counterbalances the influence of the vector potential on the K+ in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization,which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the K+ in-plane flow.
A Dual-Plane PIV Study of Turbulent Heat Transfer Flows
Wernet, Mark P.; Wroblewski, Adam C.; Locke, Randy J.
2016-01-01
Thin film cooling is a widely used technique in turbomachinery and rocket propulsion applications, where cool injection air protects a surface from hot combustion gases. The injected air typically has a different velocity and temperature from the free stream combustion flow, yielding a flow field with high turbulence and large temperature differences. These thin film cooling flows provide a good test case for evaluating computational model prediction capabilities. The goal of this work is to provide a database of flow field measurements for validating computational flow prediction models applied to turbulent heat transfer flows. In this work we describe the application of a Dual-Plane Particle Image Velocimetry (PIV) technique in a thin film cooling wind tunnel facility where the injection air stream velocity and temperatures are varied in order to provide benchmark turbulent heat transfer flow field measurements. The Dual-Plane PIV data collected include all three components of velocity and all three components of vorticity, spanning the width of the tunnel at multiple axial measurement planes.
Mamatsashvili, G R; Gogichaishvili, D Z; Chagelishvili, G D; Horton, W
2014-04-01
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity), and threaded by a parallel uniform background magnetic field. This flow is spectrally stable, so the turbulence is subcritical by nature and hence it can be energetically supported just by a transient growth mechanism due to shear flow non-normality. This mechanism appears to be essentially anisotropic in the spectral (wave-number) plane and operates mainly for spatial Fourier harmonics with streamwise wave numbers less than the ratio of flow shear to Alfvén speed, kymagnetohydrodynamic (MHD) turbulence research. We find similarity of the nonlinear dynamics to the related dynamics in hydrodynamic flows: to the bypass concept of subcritical turbulence. The essence of the analyzed nonlinear MHD processes appears to be a transverse redistribution of kinetic and magnetic spectral energies in the wave-number plane [as occurs in the related hydrodynamic flow; see Horton et al., Phys. Rev. E 81, 066304 (2010)] and differs fundamentally from the existing concepts of (anisotropic direct and inverse) cascade processes in MHD shear flows.
Experimental scaling law for the subcritical transition to turbulence in plane Poiseuille flow.
Lemoult, Grégoire; Aider, Jean-Luc; Wesfreid, José Eduardo
2012-02-01
We present an experimental study of the transition to turbulence in a plane Poiseuille flow. Using a well-controlled perturbation, we analyze the flow by using extensive particle image velocimetry and flow visualization (using laser-induced fluorescence) measurements, and use the deformation of the mean velocity profile as a criterion to characterize the state of the flow. From a large parametric study, four different states are defined, depending on the values of the Reynolds number and the amplitude of the perturbation. We discuss the role of coherent structures, such as hairpin vortices, in the transition. We find that the minimal amplitude of the perturbation triggering transition scales asymptotically as Re(-1).
Flow structures in end-view plane of slender delta wing
Directory of Open Access Journals (Sweden)
Sahin Besir
2017-01-01
Full Text Available Present investigation focuses on unsteady flow structures in end-view planes at the trailing edge of delta wing, X/C=1.0, where consequences of vortex bursting and stall phenomena vary according to angles of attack over the range of 25° ≤ α ≤ 35° and yaw angles, β over the range of 0° ≤ β ≤ 20°. Basic features of counter rotating vortices in end-view planes of delta win with 70° sweep angle, Λ are examined both qualitatively and quantitatively using Rhodamine dye and the PIV system. In the light of present experiments it is seen that with increasing yaw angle, β symmetrical flow structure is disrupted continuously. Dispersed wind-ward side leading edge vortices cover a large part of flow domain, on the other hand, lee-ward side leading edge vortices cover only a small portion of flow domain.
TWO-DIMENSIONAL PLANE WATER FLOW AND WATER QUALITY DISTRIBUTION IN BOSTEN LAKE
Institute of Scientific and Technical Information of China (English)
Feng Min-quan; Zhou Xiao-de; Zheng Bang-min; Min Tao; Zhao Ke-yu
2003-01-01
The two-dimensional plane water flow and water quality was developed by using the techniques of coordinate transformation, alternating directions, staggered grid, linear recurrence, and implicit scheme in the study of large water body in lakes. The model was proved to be suitable for treating the irregular boundary and predicting quickly water flow and water quality. The application of the model to the Bosten Lake in Xinjiang Uygur Autonomous Region of China shows that it is reasonable and practicable.
Directory of Open Access Journals (Sweden)
K. Sumathi
2016-07-01
Full Text Available This paper deals with the influence of Hall and ion slip effects on three dimensional unsteady MHD flow of a viscous ncompressible fluid between the vertical flat porous plates separated by a finite distance in a slip flow regime. The moving plate is subjected to a constant injection V0 and the stationary plate to a transverse sinusoidal suction velocity distribution, so that the flow becomes three dimensional. Approximate solutions for cross flow, main flow velocities, skin friction and rate of heat transfer were found using perturbation techniques. The effects of various parameters involved in the problem on flow characteristics were studied numerically.
Institute of Scientific and Technical Information of China (English)
余钊圣; 邵雪明; R.Tanner
2007-01-01
The shear-induced migration of neutrally-buoyant non-colloidal circular particles in a two-dimensional circular Couette flow is investigated numerically with a distributed Lagrange multiplier based fictitious domain method.The effects of inertia and volume fraction on the particle migration are examined.The results indicate that inertia has a negative effect on the particle migration.In consistence with the experimental observations, the rapid migration of particles near the inner cylinder at the early stage is observed in the simulation, which is believed to be related to the chain-like clustering of particles.The migration of circular particles in a plane Poiseuille flow is also examined in order to further confirm the effect of such clustering on the particle migration at early stage.There is tendency for the particles in the vicinity of outer cylinder in the Couette device to pack into concentric rings at late stage in case of high particle concentration.
Analysis of flow structures in supersonic plane mixing layers using the POD method
Institute of Scientific and Technical Information of China (English)
YANG Qin; FU Song
2008-01-01
The proper orthogonal decomposition (POD) method was applied to analyzing the database obtained from the direct numerical simulation (DNS) of supersonic plane mixing layers. The effect of different forms of the inner products in the POD method was investigated. It was observed that the mean flow contributes to a predominant part of the total flow energy, and the energy spectrum of the turbulence fluctuations covers a wide range of POD modes. The patterns of leading (high energy) POD modes reveal that the flow structures exhibit spanwise counter rotating rolls, as well as oblique vortices. These flow patterns are insensitive to the velocity of the observer. As the convective Mach number increases, the energy spectrum be-comes wider, the leading POD modes contain more complicated structures, and the flow becomes more chaotic.
Analysis of flow structures in supersonic plane mixing layers using the POD method
Institute of Scientific and Technical Information of China (English)
2008-01-01
The proper orthogonal decomposition(POD) method was applied to analyzing the database obtained from the direct numerical simulation(DNS) of supersonic plane mixing layers.The effect of different forms of the inner products in the POD method was investigated.It was observed that the mean flow contributes to a predominant part of the total flow energy,and the energy spectrum of the turbulence fluctuations covers a wide range of POD modes.The patterns of leading(high energy) POD modes reveal that the flow structures exhibit spanwise counter rotating rolls,as well as oblique vortices.These flow patterns are insensitive to the velocity of the observer.As the convective Mach number increases,the energy spectrum be-comes wider,the leading POD modes contain more complicated structures,and the flow becomes more chaotic.
Use of a plane jet for flow-induced noise reduction of tandem rods
Zhao, Kun; Yang, Xi-xiang; Okolo, Patrick N.; Zhang, Wei-hua; Bennett, Gareth J.
2016-06-01
Unsteady wake from upstream components of landing gear impinging on downstream components could be a strong noise source. The use of a plane jet is proposed to reduce this flow-induced noise. Tandem rods with different gap widths were utilized as the test body. Both acoustic and aerodynamic tests were conducted in order to validate this technique. Acoustic test results proved that overall noise emission from tandem rods could be lowered and tonal noise could be removed with use of the plane jet. However, when the plane jet was turned on, in some frequency range it could be the subsequent main contributor instead of tandem rods to total noise emission whilst in some frequency range rods could still be the main contributor. Moreover, aerodynamic tests fundamentally studied explanations for the noise reduction. Specifically, not only impinging speed to rods but speed and turbulence level to the top edge of the rear rod could be diminished by the upstream plane jet. Consequently, the vortex shedding induced by the rear rod was reduced, which was confirmed by the speed, Reynolds stress as well as the velocity fluctuation spectral measured in its wake. This study confirmed the potential use of a plane jet towards landing gear noise reduction. Project partially supported by the European Union FP7 CleanSky Joint Technology Initiative “ALLEGRA” (Grant No. 308225).
Pressure, density, temperature and entropy fluctuations in compressible turbulent plane channel flow
Gerolymos, G A
2013-01-01
We investigate the fluctuations of thermodynamic state-variables in compressible aerodynamic wall-turbulence, using results of direct numerical simulation (DNS) of compressible turbulent plane channel flow. The basic transport equations governing the behaviour of thermodynamic variables (density, pressure, temperature and entropy) are reviewed and used to derive the exact transport equations for the variances and fluxes (transport by the fluctuating velocity field) of the thermodynamic fluctuations. The scaling with Reynolds and Mach number of compressible turbulent plane channel flow is discussed. Correlation coefficients and higher-order statistics of the thermodynamic fluctuations are examined. Finally, detailed budgets of the transport equations for the variances and fluxes of the thermodynamic variables from a well-resolved DNS are analysed. Implications of these results both to the understanding of the thermodynamic interactions in compressible wall-turbulence and to possible improvements in statistical...
On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field
Xu, Lanxi; Lan, Wanli
2016-10-01
Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M , where M is the maximum of the absolute value of the velocity field of the laminar flow.
Energy flow analysis of out-of-plane vibration in coplanar coupled finite Mindlin plates
Directory of Open Access Journals (Sweden)
Park Young-Ho
2015-01-01
Full Text Available In this paper, an Energy Flow Analysis (EFA for coplanar coupled Mindlin plates was performed to estimate their dynamic responses at high frequencies. Mindlin plate theory can consider the effects of shear distortion and rotatory inertia, which are very important at high frequencies. For EFA for coplanar coupled Mindlin plates, the wave transmission and reflection relationship for progressing out-of-plane waves (out-of-plane shear wave, bending dominant flexural wave, and shear dominant flexural wave in coplanar coupled Mindlin plates was newly derived. To verify the validity of the EFA results, numerical analyses were performed for various cases where coplanar coupled Mindlin plates are excited by a harmonic point force, and the energy flow solutions for coplanar coupled Mindlin plates were compared with the classical solutions in the various conditions.
Optimal disturbances in shearing and swirling flows
Daly, Conor
2011-11-01
Over the past twenty years transient energy density growth of linearly stable disturbances has shown to be the likely instigator for transition to turbulence in parallel shear flows. In this vein, optimal linear perturbations are calculated for two flows which have a mixture of forces acting on the fluid body. These are; rotating plane Couette flow (RPCF), which combines pressure-driven shear and swirl, and cylindrical Couette-Poiseuille flow (CCPF), which combines pressure-driven and Couette shear. Contours are presented of the maximum achievable linear transient growth, G, over the full range of wavenumbers within the linearly stable parameter regimes. Reference is made to experimental works on each flow and we examine the role that optimal disturbances have in the different transition phenomena that are observed. It is found that the contours of G fall qualitatively alongside the points of transition in the two flows, in support of the notion that large linear transient growth can act a precursor to transition. Despite the combination of effects acting on each fluid, transition in both flows falls in the range 102 flows the same mechanism may be at work. This work is funded by EPSRC.
Institute of Scientific and Technical Information of China (English)
卢志明; 刘宇陆; 蒋剑波
2001-01-01
Turbulent features of streamwise and vertical components of velocity in the negative transport region of asymmetric plane channel flow have been studied experimentally in details. Experiments show that turbulent fluctuations in negative transport region are suppressed, and their probability distributions are far from Gaus sian. Besides, the skewness factors attain their negative maxima at the position of the maximum mean velocity, whereas the flatness factors attain their positive maxima at the same position.
DEFF Research Database (Denmark)
Carretta, Y.; Boman, R.; Bech, Jakob Ilsted
2017-01-01
such as compression sliding tests, strip drawing and cold rolling. It leads to local friction drop and wear reduction. It is therefore critical to achieve a good understanding of this phenomenon. To move towards that goal, a multiscale fluid-structure interaction (FSI) model is developed to model lubricant flows...... at the microscopic scale. These simulations are made possible through the use of the Arbitrary Lagrangian Eulerian (ALE) formalism. In this paper, this methodology is used to study plane strip drawing. The numerical model is able to predict the onset of lubricant escape and the amount of lubricant flowing...
High-order exact solutions for pseudo-plane ideal flows
Sun, Che
2016-08-01
A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.
Numerical Computation of the Chemically Reacting Flow around the National Aero-Space Plane
Tannehill, J. C.
1999-01-01
This final report summarizes the research accomplished. The research performed during the grant period can be divided into the following major areas: (1) Computation of chemically reacting Supersonic combustion ramjet (scramjet) flowfields. (2) Application of a two-equation turbulence model to supersonic combustion flowfields. (3) Computation of the integrated aerodynamic and propulsive flowfields of a generic hypersonic space plane. (4) Computation of hypersonic flows with finite-catalytic walls. (5) Development of an upwind Parabolized Navier-Stokes (PNS) code for thermo-chemical nonequilibrium flows.
Nasibullayev, I S; Krekhov, A P; Kramer, L
2005-01-01
We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane {\\em Couette} or {\\em Poiseuille} flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external {\\em electric} and/or {\\em magnetic} field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semi-analytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analysed.
Directory of Open Access Journals (Sweden)
Taha Sochi
2015-01-01
Full Text Available We use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile, and volumetric flow rate.
Zammert, Stefan
2016-01-01
The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. In contrast to other shear flows, PPF has a number of different coherent states that are relevant for the transition. We here discuss the different states, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux, the ones for constant pressure drop are always higher. The Tollmien-Schlichting waves bifurcate subcritically from the laminar profile at $Re=5772$ and reach down to $Re=2609$ (at a different optimal wave length). Their localized counter part bifurcates at the even lower value $Re=2334$. Three dimensional exact solutions appear at much lower Reynolds numbers. We describe one exact solutions that is spanwise localized and has a critical Reynolds number o...
Directory of Open Access Journals (Sweden)
Salama Faiza A.
2011-01-01
Full Text Available An analysis is carried out to study the effect of heat and mass transfer on a non-Newtonian-fluid between two infinite parallel walls, one of them moving with a uniform velocity under the action of a transverse magnetic field. The moving wall moves with constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at permeable surface. The governing equations for the flow are transformed into a system of nonlinear ordinary differential equations by perturbation technique and are solved numerically by using the shooting technique with fourth order Runge-Kutta integration scheme. The effect of non-Newtonian parameter, magnetic pressure parameter, Schmidt number, Grashof number and modified Grashof number on velocity, temperature, concentration and the induced magnetic field are discussed. Numerical results are given and illustrated graphically for the considered Problem.
Aerodynamic analysis of the aerospaceplane HyPlane in supersonic rarefied flow
Zuppardi, Gennaro; Savino, Raffaele; Russo, Gennaro; Spano'Cuomo, Luca; Petrosino, Eliano
2016-06-01
HyPlane is the Italian aerospaceplane proposal targeting, at the same time, both the space tourism and point-to-point intercontinental hypersonic flights. Unlike other aerospaceplane projects, relying on boosters or mother airplanes that bring the vehicle to high altitude, HyPlane will take off and land horizontally from common runways. According to the current project, HyPlane will fly sub-orbital trajectories under high-supersonic/low-hypersonic continuum flow regimes. It can go beyond the von Karman line at 100 km altitude for a short time, then starting the descending leg of the trajectory. Its aerodynamic behavior up to 70 km have already been studied and the results published in previous works. In the present paper some aspects of the aerodynamic behavior of HyPlane have been analyzed at 80, 90 and 100 km. Computer tests, calculating the aerodynamic parameters, have been carried out by a Direct Simulation Monte Carlo code. The effects of the Knudsen, Mach and Reynolds numbers have been evaluated in clean configuration. The effects of the aerodynamic surfaces on the rolling, pitching and yawing moments, and therefore on the capability to control attitude, have been analyzed at 100 km altitude. The aerodynamic behavior has been compared also with that of another aerospaceplane at 100 km both in clean and flapped configuration.
Linear stability of plane Poiseuille flow over a generalized Stokes layer
Energy Technology Data Exchange (ETDEWEB)
Quadrio, Maurizio [Dip. Ing. Aerospaziale, Politecnico di Milano, Campus Bovisa, I-20156 Milano (Italy); Martinelli, Fulvio; Schmid, Peter J, E-mail: maurizio.quadrio@polimi.it [Laboratoire d' Hydrodynamique (LadHyX), CNRS-Ecole Polytechnique, F-91128 Palaiseau (France)
2011-12-22
Linear stability of plane Poiseuille flow subject to spanwise velocity forcing applied at the wall is studied. The forcing is stationary and sinusoidally distributed along the streamwise direction. The long-term aim of the study is to explore a possible relationship between the modification induced by the wall forcing to the stability characteristic of the unforced Poiseuille flow and the signifcant capabilities demonstrated by the same forcing in reducing turbulent friction drag. We present in this paper the statement of the mathematical problem, which is considerably more complex that the classic Orr-Sommerfeld-Squire approach, owing to the streamwise-varying boundary condition. We also report some preliminary results which, although not yet conclusive, describe the effects of the wall forcing on modal and non-modal characteristics of the flow stability.
Self-similar decay of high Reynolds number Taylor-Couette turbulence
Verschoof, R.A.; Huisman, S.G.; Veen, van der R.C.A.; Sun, C.; Lohse, D.
2016-01-01
We study the decay of high-Reynolds-number Taylor-Couette turbulence, i.e., the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Re i =2×10 6 , the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the syst
Cell disaggregation behavior in shear flow.
Snabre, P; Bitbol, M; Mills, P
1987-05-01
The disaggregation behavior of erythrocytes in dextran saline solution was investigated by a light reflectometry technique in a Couette flow and in a plane Poiseuille flow. Dextran concentration and mass average molecular weight of the polymer fraction strongly influence the shear stress dependence of the erythrocyte suspension reflectivity in shear flow and the critical hydrodynamic conditions (shear rate or shear stress) for near-complete cell dispersion. We investigated the influence of cell volume fraction and membrane deformability (heat treatment of the erythrocytes) on the reflectivity of the flowing suspension. This study indicates that the intercell adhesiveness and the shear stress are the only parameters that influence rouleau break-up in steady uniform shear flow, thus eliminating cell volume fraction and membrane deformability as possible factors. However, the critical cross-sectional average shear stress for near-complete cell dispersion through the flow cross-section is shown to depend on the flow pattern. The rotation of cells in a shear flow or the nonuniform shear field in Poiseuille flow indeed increases the flow resistance of cell aggregates. We give a theoretical description of the shear-induced cell disaggregation process in Couette flow and in plane Poiseuille flow. The quantitation of shear forces for cell dispersion provides a way for estimating the surface adhesive energy of the bridging membranes by fluid mechanical technique.
Institute of Scientific and Technical Information of China (English)
代向艳; 欧阳洁
2011-01-01
通过耦合Brown构形场的有限体积法,对基于FENE(Finite Extension Non-linear Elastic)殊一簧链分子模型的平板Couette流动进行了模拟.不但得到了流动过程中的速度、应力等宏观信息,还得到了分子链的位形、分子链的取向角以及拉伸量等微观信息.另外,还研究了弹簧的最大拉伸长度b和weissenberg数We对聚合物稀溶液流变性质及分子构象的影响.模拟结果表明,随着b和We增大,代表弹性的第一法向应力差增大,分子链的拉伸量增大,取向角减小.但是,6和We对剪切应力的影响相反,即b增大,剪切应力增大;We增大,剪切应力则减小.%Brownian configuration field coupled with finite volume method was used to capture the most important features of dynamics of dilute polymer solution. The efficiency of numerical schemes was evaluated by performing FENE bead-spring chain models in transient planar Couette flow. The velocity and stress also the orientation and stretch of polymer molecule were captured. Additionally, the influences of the dimensionless finite extersibility parameter of spring b and Weissenberg number We on rheological properties and molecular configuration of dilute polymer solution were analyzed. The results of simulation show that the increment of b and We makes the first normal stress difference and the polymer molecular extension increase, but the orientation angle of polymer molecule decrease. However, considering the shear stress, the influence of b and We are opposite. Namely, the shear stress increases with increasing b, while the shear stress decreases with increasing We.
Linear stability of plane Poiseuille flow in an infinite elastic medium and volcanic tremors
Sakuraba, Ataru; Yamauchi, Hatsuki
2014-12-01
The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastic media was investigated with the aim of explaining the excitation of volcanic tremors. Our results show that there are several regimes of instability, and the nature of stability significantly depends on the symmetry of oscillatory fluid and solid motion. It has been shown that long-wave symmetric instability occurs at a very small value of the Reynolds number, but it is unlikely that this is the cause of volcanic tremors. We show that antisymmetric (flexural) instability also occurs, involving two parallel Rayleigh waves traveling against the Poiseuille flow, but the critical flow speed is faster than that of symmetric instability. However, if the basic flow profile is nonparabolic because of a nonuniform driving force or nonuniform viscosity, the critical flow speed of antisymmetric instability can be considerably slower than that of symmetric instability. Based on numerical calculations and analytical consideration, we conclude that this anomalous antisymmetric instability is possibly produced by a basaltic magma flow of a few meters per second through a dike with thickness of 1 m and extending for several kilometers; this origin can explain some of the characteristics of volcanic tremors.
Receptivity of plane Poiseuille flow to local micro-vibration disturbance on wall
Directory of Open Access Journals (Sweden)
Wei-dong CAO
2015-04-01
Full Text Available The receptivity of plane Poiseuille flow to local single-period micro-vibration disturbances with different phases at the top and bottom walls was investigated through direct numerical simulation of three-dimensional incompressible Navier-Stokes equations. Results show that the disturbance presents a symmetrical distribution in the spanwise direction when the micro-vibration on the wall ends, and the initial disturbance velocities and spatial distribution of the disturbance structure are different at the top and bottom walls. The disturbance’s velocity, amplitude, and high- and low-speed streaks increase with time, and the amplitude of streamwise disturbance velocity is larger than those of spanwise and vertical disturbance velocities. However, no significant Tollmien-Schlichting wave was found in the flow field. The number of disturbance vortex cores gradually increases with the disturbance area. High-speed disturbance fluid concentrates near the wall and its normal velocity largely points to the wall, while low-speed disturbance fluid largely deviates from the wall. Furthermore, the streamwise velocity profiles near the top and bottom walls both become plump because of the existence of the disturbances, and the streamwise velocity profiles show a trend of evolving into turbulent velocity profiles. The shear stress near the wall increases significantly. The local micro-vibration disturbance on the wall in plane Poiseuille flow can induce the development of a structure similar to turbulent spots.
Kovalenko, V. M.; Byehkov, N. M.; Kisel, G. A.; Dikovskaia, N. D.
1984-03-01
Measurements have been made of pressure distributions and pulsations in a cross flow past a circular cylinder placed near a plane screen of finite length. The experiments reported here have been carried out under low turbulence conditions over a range of Reynolds numbers that includes the critical values. The boundary layer separation points and the evolution of the front critical point and other characteristic zones with the distance to the screen are determined. The components of the aerodynamic force acting on the cylinder and the Strouhal number are calculated on the basis of the predominant pulsation frequencies on the cylinder.
A Flow-dependent Quadratic Steiner Tree Problem in the Euclidean Plane
Brazil, Marcus; Thomas, Doreen
2011-01-01
We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner points, such that $\\displaystyle\\sum_{e \\in E(T)}f(e)|e|^2$ is a minimum, where $f(e)$ is the flow on edge $e$. The edges are uncapacitated and the flows are determined additively, i.e., the flow on an edge leaving a node $u$ will be the sum of the flows on all edges entering $u$. Our motivation for studying this problem is its utility as a model for relay augmentation of wireless sensor networks. In these scenarios one seeks to optimise power consumption -- which is predominantly due to communication and, in free space, is proportional to the square of transmission distance -- in the network by introducing additional relays. We prove several geometric and combinatorial results on the structure of optimal and locally optimal solution-trees (under various strategies for bound...
Measuring In-Plane Micro-Motion of Micro-Structure Using Optical Flow
Institute of Scientific and Technical Information of China (English)
JIN Cuiyun; JIN Shijiu; LI Dachao; WANG Jianlin
2009-01-01
Optical flow method is one of the most important methods of analyzing motion images.Optical flow field is used to analyze characteristics of motion objects.According to motion features of micro-electronic mechanical system(MEMS)micro-structure,the optical algorithm based on label field and neighborhood optimization is presented to analyze the in-plane micro-motion of micro-structure.Firstly,high speed motion states for each frequency segment of micro-structure in cyclic motion are frozen based on stroboscopic principle.Thus a series of image sequences,and can obtain reliable and precise optical field and reduce computing time.As micro-resonator of urement precision of the presented algorithm is high,and measurement repeatability reaches 40 am under the same experiment condition.
Instability of plane-parallel flow of incompressible liquid over a saturated porous medium
Lyubimova, T. P.; Lyubimov, D. V.; Baydina, D. T.; Kolchanova, E. A.; Tsiberkin, K. B.
2016-07-01
The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
Motion and deformation of immiscible droplet in plane Poiseuille flow at low Reynolds number
Institute of Scientific and Technical Information of China (English)
潘定一; 林雨青; 张凌新; 邵雪明
2016-01-01
Droplet migration in plane Poiseuille flow is numerically investigated with a dissipative particle dynamics method. The single droplet deformation in the channel flow is first studied to verify the current method and the physical model. The effect of the viscosity ratio between the droplet and the solvent and the effect of the confinement are systematically investigated. The droplet is in an off-centerline equilibrium position with a specific selection of the parameters. A large viscosity ratio makes the droplet locate in a near-wall equilibrium position, and a large capillary number makes the droplet migrate to the near-centerline region of the channel. For the droplet migration at the same Capillary number, there is a critical width of the channel, which is less than twice of the droplet diameter, and the droplet will only migrate to the channel centerline if the width is less than this critical value.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
Rawat, Subhendu; Rincon, François
2016-01-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi- streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, upper branch of travelling-wave solutions develop multiple streaks when Lz is increased. Upper branch travelling-wave solutions can be continued into coherent solutions of the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Moyers-Gonzalez, Miguel; Mak, Julian
2010-01-01
We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the microstructure upon a gradual increase of the external forcing is governed by a structural variable (the concentration of solid material elements) which decays smoothly from unity to zero as the stresses are gradually increased beyond the yield point. Stability results are in close conformity with the ones of a pseudo-plastic fluid. Destabilizing effects are related to the presence of an intermediate transition zone where elastic solid elements coexist with fluid elements. This region brings an elastic contribution which does modify the stability of the flow.
CFD simulation of bubbly turbulent Tayor-Couette flow☆
Institute of Scientific and Technical Information of China (English)
Xi Gao; Bo Kong; R. Dennis Vigil
2016-01-01
Bubbly gas–liquid Taylor–Couette vortex flow has been the subject of several recent investigations both because of interest in bubble-induced drag reduction and because such devices have potential applications to a variety of chemical and biochemical processing problems. In order to quantitatively describe the hydrodynamics of highly turbulent two phase Taylor–Couette flow, a rigorous two-fluid computational fluid dynamics (CFD) model was developed and compared with previously published experimental data. This model includes a comprehensive description of the constitutive closure for inter-phase forces and turbulence was simulated using both the k–εand k–ωmodels. In addition, the mechanism by which the dispersed fluid attains a non-uniform radial and axial distribution is analyzed and the relative importance of various interphase forces is discussed. Lastly the model was validated by comparison of simulation predictions with experimental data, and it is shown that the CFD model correctly predicts phase velocity, velocity fluctuation, and gas distribution, and may provide guidance for reactor design and scale-up.
Plane-wave transverse oscillation for high-frame-rate 2-D vector flow imaging.
Lenge, Matteo; Ramalli, Alessandro; Tortoli, Piero; Cachard, Christian; Liebgott, Hervé
2015-12-01
Transverse oscillation (TO) methods introduce oscillations in the pulse-echo field (PEF) along the direction transverse to the ultrasound propagation direction. This may be exploited to extend flow investigations toward multidimensional estimates. In this paper, the TOs are coupled with the transmission of plane waves (PWs) to reconstruct high-framerate RF images with bidirectional oscillations in the pulse-echo field. Such RF images are then processed by a 2-D phase-based displacement estimator to produce 2-D vector flow maps at thousands of frames per second. First, the capability of generating TOs after PW transmissions was thoroughly investigated by varying the lateral wavelength, the burst length, and the transmission frequency. Over the entire region of interest, the generated lateral wavelengths, compared with the designed ones, presented bias and standard deviation of -3.3 ± 5.7% and 10.6 ± 7.4% in simulations and experiments, respectively. The performance of the ultrafast vector flow mapping method was also assessed by evaluating the differences between the estimated velocities and the expected ones. Both simulations and experiments show overall biases lower than 20% when varying the beam-to-flow angle, the peak velocity, and the depth of interest. In vivo applications of the method on the common carotid and the brachial arteries are also presented.
Bounds on the Phase Velocity in the Linear Instability of Viscous Shear Flow Problem in the -Plane
Indian Academy of Sciences (India)
R G Shandil; Jagjit Singh
2003-05-01
Results obtained by Joseph (J. Fluid Mech. 33 (1968) 617) for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived.
Directory of Open Access Journals (Sweden)
Hifdi Ahmed
2012-07-01
Full Text Available The linear stability of plan Poiseuille flow of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field is investigated numerically. The fourth-order Sommerfeld equation governing the stability analysis is solved by spectral method with expansions in lagrange’s polynomials, based on collocation points of Gauss-Lobatto. The critical values of Reynolds number, wave number and wave speed are computed. The results are shown through the neutral curve. The main purpose of this work is to check the combined effect of magnetic field and fluid’s elasticity on the stability of the plane Poiseuille flow. Based on the results obtained in this work, the magnetic field is predicted to have a stabilizing effect on the Poiseuille flow of viscoelastic fluids. Hence, it will be shown that for second-order fluids (K 0 is that the critical Reynolds numbers Rec increase when the Hartman number M increases for certain value of elasticity number K and decrease for others. The latter result is in contrast to previous studies.
Multi-layer film flow down an inclined plane: experimental investigation
Henry, Daniel
2014-11-19
We report the results from an experimental study of the flow of a film down an inclined plane where the film itself is comprised of up to three layers of different liquids. By measuring the total film thickness for a broad range of parameters including flow rates and liquid physical properties, we provide a thorough and systematic test of the single-layer approximation for multi-layer films for Reynolds numbers Re = ρQ/μ≈0.03-60. In addition, we also measure the change in film thickness of individual layers as a function of flow rates for a variety of experimental configurations. With the aid of high-speed particle tracking, we derive the velocity fields and free-surface velocities to compare to the single-layer approximation. Furthermore, we provide experimental evidence of small capillary ridge formations close to the point where two layers merge and compare our experimental parameter range for the occurrence of this phenomenon to those previously reported.
Free convective flow of a stratified fluid through a porous medium bounded by a vertical plane
Directory of Open Access Journals (Sweden)
H. K. Mondal
1994-01-01
Full Text Available Steady two-dimensional free convection flow of a thermally stratified viscous fluid through a highly porous medium bounded by a vertical plane surface of varying temperature, is considered. Analytical expressions for the velocity, temperature and the rate of heat transfer are obtained by perturbation method. Velocity distribution and rate of heat transfer for different values of parameters are shown in graphs. Velocity distribution is also obtained for certain values of the parameters by integrating the coupled differential equations by Runge-Kutta method and compared with the analytical solution. The chief concern of the paper is to study the effect of equilibrium temperature gradient on the velocity and the rate of heat transfer.
UNSTEADY PLANE MHD BOUNDARY LAYER FLOW OF A FLUID OF VARIABLE ELECTRICAL CONDUCTIVITY
Directory of Open Access Journals (Sweden)
Zoran B Boričić
2010-01-01
Full Text Available This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic (MHD boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogenous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multiparametric (generalized similarity method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.
Structure and mechanism of turbulence under dynamical restriction in plane Poiseuille flow
Farrell, Brian F; Jiménez, Javier; Constantinou, Navid C; Lozano-Duran, Adrián; Nikolaidis, Marios-Andreas
2015-01-01
The perspective of statistical state dynamics (SSD) has been applied to the study of mechanisms underlying turbulence in various physical systems. An example application of SSD is that of the second order closure, referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence and the emergence and maintenance of the roll/streak structure. This closure eliminates nonlinear interactions among the perturbations restricting nonlinearity to that of the mean equation and interaction between the mean and perturbations. Simulations at modest $Re$ reveal that the essential features of wall-turbulence dynamics are retained with the dynamics restricted in this manner. Here this restriction of the dynamics is used to obtain a closely related dynamical system, referred to as the restricted non-linear (RNL) system, which is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high $Re$. Remarkably, the RNL system spontane...
Directory of Open Access Journals (Sweden)
Armaghani Taher
2016-01-01
Full Text Available In this article, a numerical study is carried out to analyze the effect of nanoparticle volume fraction over flow and thermal characteristics of laminar 2-D plane jet. Al2O3-water and TiO2-water nanofluids are considered in this investigation with lowest and highest values of particle volume concentration equals to 0 and 0.02 respectively. This paper propose four correlations for describing the relation between the solid volume fraction, δt and δu. The results show that the cross stream thermal diffusion depth and cross stream hydraulic diffusion depth are increased when particles volume concentration is increased and mean temperature and mean velocity decreases when the solid volume fraction is increased. The effects of nanoparticle volume fraction in velocity and temperature time histories are also studied and discussed.
Fast color flow mode imaging using plane wave excitation and temporal encoding
Udesen, Jesper; Gran, Fredrik; Jensen, Jorgen A.
2005-04-01
In conventional ultrasound color flow mode imaging, a large number (~500) of pulses have to be emitted in order to form a complete velocity map. This lowers the frame-rate and temporal resolution. A method for color flow imaging in which a few (~10) pulses have to be emitted to form a complete velocity image is presented. The method is based on using a plane wave excitation with temporal encoding to compensate for the decreased SNR, resulting from the lack of focusing. The temporal encoding is done with a linear frequency modulated signal. To decrease lateral sidelobes, a Tukey window is used as apodization on the transmitting aperture. The data are beamformed along the direction of the flow, and the velocity is found by 1-D cross correlation of these data. First the method is evaluated in simulations using the Field II program. Secondly, the method is evaluated using the experimental scanner RASMUS and a 7 MHz linear array transducer, which scans a circulating flowrig. The velocity of the blood mimicking fluid in the flowrig is constant and parabolic, and the center of the scanned area is situated at a depth of 40 mm. A CFM image of the blood flow in the flowrig is estimated from two pulse emissions. At the axial center line of the CFM image, the velocity is estimated over the vessel with a mean relative standard deviation of 2.64% and a mean relative bias of 6.91%. At an axial line 5 mm to the right of the center of the CFM image, the velocity is estimated over the vessel with a relative standard deviation of 0.84% and a relative bias of 5.74%. Finally the method is tested on the common carotid artery of a healthy 33-year-old male.
Assoudi, Ali; Habli, Sabra; Mahjoub Saïd, Nejla; Bournot, Hervé; Le Palec, Georges
2016-11-01
An experimental and numerical investigation of the flow field of variable density turbulent offset jet is presented. The velocity measurements are performed using a Velocimetry Laser Doppler technique for an offset height h. Three cases of variable-density turbulent plane jets discharging from a rectangular nozzle into a quiescent medium are studied. The variation density jets considered were revealed at different Reynolds numbers. In the second step of this work, a numerical three-dimensional model of the problem is simulated through the resolution of the Navier-Stokes equations by means of the finite volume method and the Reynolds stress model second-order turbulent closure model. A non-uniform mesh system tightened close to the emitting nozzle and both the vertical and horizontal walls is also adopted. A good level of agreement was achieved, between the experiments and the calculations. Once the model validated, our model allowed the evaluation of the influence of the variation density on the characterizing features of the resulting flow filed. It is found that the centerline velocity and concentration of the heavier jet decays much faster than in the two other jets, and a similar behavior for the vertical profiles in the three variable-density jets is well reproduced in the simulation.
Instabilities of a liquid film flowing down an inclined porous plane
Liu, Rong; Liu, Qiusheng
2009-09-01
The problem of a film flowing down an inclined porous layer is considered. The fully developed basic flow is driven by gravitation. A careful linear instability analysis is carried out. We use Darcy’s law to describe the porous layer and solve the coupling equations of the fluid and the porous medium rather than the decoupled equations of the one-sided model used in previous works. The eigenvalue problem is solved by means of a Chebyshev collocation method. We compare the instability of the two-sided model with the results of the one-sided model. The result reveals a porous mode instability which is completely neglected in previous works. For a falling film on an inclined porous plane there are three instability modes, i.e., the surface mode, the shear mode, and the porous mode. We also study the influences of the depth ratio d̂ , the Darcy number δ , and the Beavers-Joseph coefficient αBJ on the instability of the system.
Simple models for shear flow transition
Barkley, Dwight
2011-11-01
I will discuss recent developments in modeling transitional shear flows with simple two-variable models. Both pipe flow and plane Couette flow are considered. The essential insight is that most large-scale features of these shear flows can be traced to a change from excitability to bistability in the local dynamics. Models are presented in two variables, turbulence intensity and mean shear. A PDE model of pipe flow captures the essence of the puff-slug transition as a change from excitability to bistability. Extended models with turbulence as deterministic transient chaos or multiplicative noise reproduce almost all large-scale features of transitional pipe flow. In particular they capture metastable localized puffs, puff splitting, slugs, localized edge states, a continuous transition to sustained turbulence via spatiotemporal intermittency (directed percolation), and a subsequent increase in turbulence fraction towards uniform, featureless turbulence. A model that additionally takes into account the symmetries of plane Couette flow reproduces localized turbulence and periodic turbulent-laminar bands.
Ding, Ting; Hu, Hong; Bai, Chen; Guo, Shifang; Yang, Miao; Wang, Supin; Wan, Mingxi
2016-07-01
Cavitation plays important roles in almost all high-intensity focused ultrasound (HIFU) applications. However, current two-dimensional (2D) cavitation mapping could only provide cavitation activity in one plane. This study proposed a three-dimensional (3D) ultrasound plane-by-plane active cavitation mapping (3D-UPACM) for HIFU in free field and pulsatile flow. The acquisition of channel-domain raw radio-frequency (RF) data in 3D space was performed by sequential plane-by-plane 2D ultrafast active cavitation mapping. Between two adjacent unit locations, there was a waiting time to make cavitation nuclei distribution of the liquid back to the original state. The 3D cavitation map equivalent to the one detected at one time and over the entire volume could be reconstructed by Marching Cube algorithm. Minimum variance (MV) adaptive beamforming was combined with coherence factor (CF) weighting (MVCF) or compressive sensing (CS) method (MVCS) to process the raw RF data for improved beamforming or more rapid data processing. The feasibility of 3D-UPACM was demonstrated in tap-water and a phantom vessel with pulsatile flow. The time interval between temporal evolutions of cavitation bubble cloud could be several microseconds. MVCF beamformer had a signal-to-noise ratio (SNR) at 14.17dB higher, lateral and axial resolution at 2.88times and 1.88times, respectively, which were compared with those of B-mode active cavitation mapping. MVCS beamformer had only 14.94% time penalty of that of MVCF beamformer. This 3D-UPACM technique employs the linear array of a current ultrasound diagnosis system rather than a 2D array transducer to decrease the cost of the instrument. Moreover, although the application is limited by the requirement for a gassy fluid medium or a constant supply of new cavitation nuclei that allows replenishment of nuclei between HIFU exposures, this technique may exhibit a useful tool in 3D cavitation mapping for HIFU with high speed, precision and resolution
LES/FDF simulation of particle dispersion in a gas-particle two phase plane wake flow
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A filtered density function (FDF) transport equation was derived for the fluid velocity seen by the particles in gas-particle two-phase flow. An LES/FDF simulation of a two-phase plane wake flow was carried out. The simulation results were compared with both the experimental photograph and the simulation results without using the FDF model, and proved that the LES/FDF model can clearly improve the spatial dispersion of the particle phase.
Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro
2016-12-01
Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases
A Wall-Function Approach to Incorporating Knudsen-Layer Effects in Gas Micro Flow Simulations
2005-07-13
7) Planar Couette and Poiseuille Flow Simulations To test this proposed wall-function approach, we use a simple centered finite-difference...numerical scheme to solve the Navier-Stokes equations for monatomic gas flow in benchmark one-dimensional planar Couette and Poiseuille systems. Figures 2...and compressible flows . The limited test cases we have investigated (planar Couette flow , planar Poiseuille flow , and low-Reynolds number flow around
Observation of Magnetocoriolis Waves in a Liquid Metal Taylor-Couette Experiment
Energy Technology Data Exchange (ETDEWEB)
Nornberg, M. D.; Ji, H.; Schartman, E.; Roach, A.; Goodman, J.
2009-09-14
The first observation of fast and slow magnetocoriolis (MC) waves in a laboratory experiment is reported. Rotating nonaxisymmetric modes arising from a magnetized turbulent Taylor-Couette flow of liquid metal are identified as the fast and slow MC waves by the dependence of the rotation frequency on the applied field strength. The observed slow MC wave is marginally damped but will become destabilized by the magnetorotational instability with a modest increase in rotation rate.
Drag reduction in numerical two-phase Taylor–Couette turbulence using an Euler–Lagrange approach
Arza, Vamsi Spandan; Ostilla-Monico, Rodolfo; Verzicco, Roberto; Lohse, Detlef
2016-01-01
Two-phase turbulent Taylor–Couette (TC) flow is simulated using an Euler–Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using direct numerical simulations (DNS) in
Taylor-Couette instability in thixotropic yield stress fluids
Jenny, Mathieu; Kiesgen de Richter, Sébastien; Louvet, Nicolas; Skali-Lami, Salahedine; Dossmann, Yvan
2017-02-01
We consider the flow of thixotropic yield stress fluids between two concentric cylinders. To account for the fluid thixotropy, we use Hou\\vska's model [Hou\\vska, Ph.D. thesis, Czech Technical University, Prague, 1981] with a single structural parameter driven by a kinetic equation. Because of the yield stress and the geometric inhomogeneity of the stress, only a part of the material in the gap may flow. Depending on the breakdown rate of the structural parameter, the constitutive relation can lead to a nonmonotonic flow curve. This nonmonotonic behavior is known to induce a discontinuity in the slope of the velocity profile within the flowing material, called shear banding. Thus, for fragile structures, a shear-banded flow characterized by a very sharp transition between the flowing and the static regions may be observed. For stronger structures, the discontinuity disappears and a smooth transition between the flowing and the static regions is observed. The consequences of the thixotropy on the linear stability of the azimuthal flow are studied in a large range of parameters. Although the thixotropy allows shear banding in the base flow, it does not modify fundamentally the linear stability of the Couette flow compared to a simple yield stress fluid. The apparent shear-thinning behavior depends on the thixotropic parameters of the fluid and the results about the onset of the Taylor vortices in shear-thinning fluids are retrieved. Nevertheless, the shear banding modifies the stratification of the viscosity in the flowing zone such that the critical conditions are mainly driven by the width of the flowing region.
Universal decay of high Reynolds number Taylor-Couette turbulence
Verschoof, Ruben A; van der Veen, Roeland C A; Sun, Chao; Lohse, Detlef
2015-01-01
We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder ($Re_i = 2 \\cdot 10^6$, the outer cylinder is at rest) was suddenly stopped. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Next, the radial profile of the azimuthal velocity is found to be self-similar, i.e. when normalizing it with the mean velocity, it is universal. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way ...
Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow
Staben, Michelle E.; Zinchenko, Alexander Z.; Davis, Robert H.
2003-06-01
A new boundary-integral algorithm for the motion of a particle between two parallel plane walls in Poiseuille flow at low Reynolds number was developed to study the translational and rotational velocities for a broad range of particle sizes and depths in the channel. Instead of the free-space Green's function more commonly employed in boundary-integral equations, we used the Green's function for the domain between two infinite plane walls [Liron and Mochon, J. Eng. Math. 10, 287 (1976)]. This formulation allows us to directly incorporate the effects of the wall interactions into the stress tensor, without discretizing the bounding walls, and use well-established iterative methods. Our results are in good agreement with previous computations [Ganatos et al., J. Fluid Mech. 99, 755 (1980)] and limiting cases, over their range of application, with additional results obtained for very small particle-wall separations of less than 1% of the particle radius. In addition to the boundary-integral solution in the mobility formulation, we used the resistance formulation to derive the near-field asymptotic forms for the translational and rotational velocities, extending the results to even smaller particle-wall separations. The decrease in translational velocity from the unperturbed fluid velocity increases with particle size and proximity of the particle to one or both of the walls. The rotational velocity exhibits a maximum magnitude between the centerline and either wall, due to the competing influences of wall retardation and the greater fluid velocity gradient near the walls. The average particle velocity for a uniform distribution of particles was generally found to exceed the average fluid velocity, due in large part to exclusion of the particle centers from the region of slowest fluid near the walls. The maximum average particle velocity is 18% greater than the average fluid velocity and occurs for particle diameters that are 42% of the channel height; particles with
Fu, Thomas C; Judge, Carolyn Q; Dommermuth, Douglas G; Brucker, Kyle A; Wyatt, Donald C
2014-01-01
Over the past few years much progress has been made in Computational Fluid Dynamics (CFD) in its ability to accurately simulate the hydrodynamics associated with a deep-V monohull planing craft. This work has focused on not only predicting the hydrodynamic forces and moments, but also the complex multiphase free-surface flow field generated by a deep-V monohull planing boat at high Froude numbers. One of these state of the art CFD codes is Numerical Flow Analysis (NFA). NFA provides turnkey capabilities to model breaking waves around a ship, including both plunging and spilling breaking waves, the formation of spray, and the entrainment of air. NFA uses a Cartesian-grid formulation with immersed body and volume-of-fluid methods.
Energy Technology Data Exchange (ETDEWEB)
Boualit, A.; Boualit, S. [Unite de recherche appliquee en energies renouvelables, Ghardaia (Algeria); Zeraibi, N. [Universite de Boumerdes, Faculte des hydrocarbures dept. Transport et equipement, Boumerdes (Algeria); Amoura, M. [Universite des Sciences et de la Technologie Houari Boumedienne, Faculte de Physique, Dept. Energetique, Alger (Algeria)
2011-01-15
The thermal development of the hydrodynamically developing laminar flow of a viscoplastic fluid (fluid of Bingham) between two plane plates maintained at a constant temperature has been studied numerically. This analysis has shown the effect caused by inertia and the rheological behaviour of the fluid on the velocity, pressure and temperature fields. The effects of Bingham and Peclet numbers on the Nusselt values with the inclusion of viscous dissipation are also discussed. (authors)
NUMERICAL SIMULATION OF AN OSCILLATING FLOW PAST A CIRCULAR CYLINDER IN THE VICINITY OF A PLANE WALL
Institute of Scientific and Technical Information of China (English)
SHAH Syed Bilai Hussain; LU Xi-yun
2008-01-01
Oscillating flow around a circular cylinder in the vicinity of a plane wall was investigated by solving the two-dimensional incompressible Navier-Stokes equations with a finite element Galarkin residual method. The effect of the gap G/D between the cylinder surface and the wall on the flow behavior was studied. For the case of G/D ≤ 0.25, the periodicity in the flow is attributed to both the outer shear layer instability and the oscillating frequency. As G/D > 0.25, vortex shedding occurs and the periodicity in the flow is mainly due to the competition of the oscillating frequency and the vortex shedding frequency from an isolated stationary cylinder.
Doss, C E; Swisdak, M
2016-01-01
We investigate magnetic reconnection in systems simultaneously containing asymmetric (anti-parallel) magnetic fields, asymmetric plasma densities and temperatures, and arbitrary in-plane bulk flow of plasma in the upstream regions. Such configurations are common in the high-latitudes of Earth's magnetopause and in tokamaks. We investigate the convection speed of the X-line, the scaling of the reconnection rate, and the condition for which the flow suppresses reconnection as a function of upstream flow speeds. We use two-dimensional particle-in-cell simulations to capture the mixing of plasma in the outflow regions better than is possible in fluid modeling. We perform simulations with asymmetric magnetic fields, simulations with asymmetric densities, and simulations with magnetopause-like parameters where both are asymmetric. For flow speeds below the predicted cutoff velocity, we find good scaling agreement with the theory presented in Doss et al., J.~Geophys.~Res., 120, 7748 (2015). Applications to planetary...
Pandey, Gaurav; Linga, Praveen; Sangwai, Jitendra S.
2017-02-01
Conventional rheometers with concentric cylinder geometries do not enhance mixing in situ and thus are not suitable for rheological studies of multiphase systems under high pressure such as gas hydrates. In this study, we demonstrate the use of modified Couette concentric cylinder geometries for high pressure rheological studies during the formation and dissociation of methane hydrate formed from pure water and water-decane systems. Conventional concentric cylinder Couette geometry did not produce any hydrates in situ and thus failed to measure rheological properties during hydrate formation. The modified Couette geometries proposed in this work observed to provide enhanced mixing in situ, thus forming gas hydrate from the gas-water-decane system. This study also nullifies the use of separate external high pressure cell for such measurements. The modified geometry was observed to measure gas hydrate viscosity from an initial condition of 0.001 Pa s to about 25 Pa s. The proposed geometries also possess the capability to measure dynamic viscoelastic properties of hydrate slurries at the end of experiments. The modified geometries could also capture and mimic the viscosity profile during the hydrate dissociation as reported in the literature. The present study acts as a precursor for enhancing our understanding on the rheology of gas hydrate formed from various systems containing promoters and inhibitors in the context of flow assurance.
Chen, Xiaoliang; Zhao, Bin; Ma, Shoujiang; Chen, Cen; Hu, Daoyun; Zhou, Wenshuang; Zhu, Zuqing
2015-03-23
In this paper, we study how to improve the control plane resiliency of software-defined elastic optical networks (SD-EONs) and design a master-slave OpenFlow (OF) controller arrangement. Specifically, we introduce two OF controllers (OF-Cs), i.e., the master and slave OF-Cs, and make them work in a collaborative way to protect the SD-EON against controller failures. We develop a controller communication protocol (CCP) to facilitate the cooperation of the two OF-Cs. With the CCP, the master OF-C (M-OF-C) can synchronize network status to the slave OF-C (S-OF-C) in real time, while S-OF-C can quickly detect the failure of M-OF-C and take over the network control and management (NC&M) tasks timely to avoid service disruption. We implement the proposed framework in an SD-EON control plane testbed built with high-performance servers, and perform NC&M experiments with different network failure scenarios to demonstrate its effectiveness. Experimental results indicate that the proposed system can restore services in both the data and control planes of SD-EON jointly while maintaining relatively good scalability. To the best of our knowledge, this is the first demonstration that realizes control plane resiliency in SD-EONs.
In Vivo High Frame Rate Vector Flow Imaging Using Plane Waves and Directional Beamforming
DEFF Research Database (Denmark)
Jensen, Jonas; Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo
2016-01-01
Directional beamforming (DB) estimates blood flowvelocities accurately when the flow angle is known. However, forautomatically finding the flow angle a computationally expensive approach is used. This work presents a method for estimating the flow angle using a combination of inexpensive transverse...
Fast color flow mode imaging using plane wave excitation and temporal encoding
DEFF Research Database (Denmark)
Udesen, Jesper; Gran, Fredrik; Jensen, Jørgen Arendt
2005-01-01
velocity image is presented. The method is based on using a plane wave excitation with temporal encoding to compensate for the decreased SNR, resulting from the lack of focusing. The temporal encoding is done with a linear frequency modulated signal. To decrease lateral sidelobes, a Tukey window is used...
NARROW-GAP POINT-TO-PLANE CORONA WITH HIGH VELOCITY FLOWS
The article discusses a mathematical model developed to describe a narrow- gap point- to- plane corona system used in the detoxification of chemical agents or their simulants, for which the degree of destruction depends on the strength of the electric field or electron energy. Na...
Energy Technology Data Exchange (ETDEWEB)
Kauder, K.; Sachs, R. [Dortmund Univ. (Germany). FG Fluidenergiemaschinen
1998-12-31
Gas flows in screw-type machines are effecting the energy conversion of the machine by the leakage mass flows and entropy flows inside the machine. The profile meshing clearance and the housing gap have an essential influence. Here the gas flow at the housing gap with non moving gap bounds is investigated. The used and developed measuring and image analysis technique is explained. Qualitative Schlieren pictures of the flow at three different tooth tips, i.e. gap styles are following to enable a comparison of the flow shapes. The application of a plane screw type machine model with moving gap bounds will be meant to be a contribution towards the investigation of the gas flow conditions in the gaps. (orig.) [Deutsch] Gasspaltstroemungen in Schraubenmaschinen wirken als Leckmassen- und Entropiestroeme erheblich auf die Energiewandlungsguete der Maschine. Besonderen Einfluss haben der Profileingriffs- sowie der Gehaeusespalt. In diesem Beitrag wird die Gehaeusespaltstroemung am Nebenrotor mit feststehender Stroemungsberandung untersucht. Nach Erlaeuterungen zur verwendeten und entwickelten Mess- und Bildverarbeitungstechnik folgen qualitative Schlierenbilder der Stroemung an drei unterschiedlichen Zahnkopf- und damit Spaltformen, die einen Vergleich der Stroemungsformen ermoeglichen. Der naechste Schritt zur Klaerung der Stroemungsverhaeltnisse in den Spalten besteht aus der Einfuehrung eines ebenen Schraubenmaschinenmodells mit drehenden Rotorscheiben. (orig.)
Interaction of monopoles, dipoles, and turbulence with a shear flow
Marques Rosas Fernandes, V. H.; Kamp, L. P. J.; van Heijst, G. J. F.; Clercx, H. J. H.
2016-09-01
Direct numerical simulations have been conducted to examine the evolution of eddies in the presence of large-scale shear flows. The numerical experiments consist of initial-value-problems in which monopolar and dipolar vortices as well as driven turbulence are superposed on a plane Couette or Poiseuille flow in a periodic two-dimensional channel. The evolution of the flow has been examined for different shear rates of the background flow and different widths of the channel. Results found for retro-grade and pro-grade monopolar vortices are consistent with those found in the literature. Boundary layer vorticity, however, can significantly modify the straining and erosion of monopolar vortices normally seen for unbounded domains. Dipolar vortices are shown to be much more robust coherent structures in a large-scale shear flow than monopolar eddies. An analytical model for their trajectories, which are determined by self-advection and advection and rotation by the shear flow, is presented. Turbulent kinetic energy is effectively suppressed by the shearing action of the background flow provided that the shear is linear (Couette flow) and of sufficient strength. Nonlinear shear as present in the Poiseuille flow seems to even increase the turbulence strength especially for high shear rates.
Fast Plane Wave 2-D Vector Flow Imaging Using Transverse Oscillation and Directional Beamforming
DEFF Research Database (Denmark)
Jensen, Jonas; Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo
2017-01-01
Several techniques can estimate the 2-D velocity vector in ultrasound. Directional beamforming (DB) estimates blood flow velocities with a higher precision and accuracy than transverse oscillation (TO), but at the cost of a high beamforming load when estimating the flow angle. In this paper......, it is proposed to use TO to estimate an initial flow angle, which is then refined in a DB step. Velocity magnitude is estimated along the flow direction using cross-correlation. It is shown that the suggested TO-DB method can improve the performance of velocity estimates compared to TO, and with a beamforming...... but within 4% for TO-DB. The same trends are observed in measurements although with a slightly larger bias. Simulations of realistic flow in a carotid bifurcation model provide visualization of complex flow, and the spread of velocity magnitude estimates is 7.1 cm/s for TO-DB, while it is 11.8 cm/s using...
Intelligent Tester for Geotextiles Products-Determination of Water Flow Capacity in their Plane
Institute of Scientific and Technical Information of China (English)
FENG Yu-sheng; SONG Bai-ping
2004-01-01
Geotextiles and geotextile-related products Determination of water flowcapacity in their plane has just National standard. But has not a formal instrument at present. There are many kinds of geotextile and also lots of factors influential to the penetration coefficient thereof. The intelligent tester may be involved in testing penetration coefficient under different pressures/gradients resulted in fine repeatability controlled intelligently by microcomputer system.
Directory of Open Access Journals (Sweden)
Ramya M
2016-03-01
Full Text Available The transmission of a traffic flows with a certain bandwidth demand over a single network path is either not possible or not cost-effective. In these cases, it is veritably periodic usable to improve focus the network's bandwidth appliance by breaking the traffic flow upon multiple qualified paths. Using multiple paths for the equivalent traffic flow increases the certainty of the network, it absorbs deluxe forwarding resources from the network nodes and also it overcomes link failure provide security. In this paper, we illustrate several problems related to splitting a traffic flow over multiple paths while minimizing the absorption of forwarding resources mitigates failures and implementing security.
Guilbaud, Maxime
2016-01-01
Most studies of anisotropy flow phenomena have assumed a global flow phase angle (or event plane angle) that is boost invariant in pseudorapidity ($\\eta$). It was realized in recent years that this assumption may not be valid in presence of initial-state fluctuations, especially along the longitudinal direction. The effect of eta-dependent event plane fluctuations would break the factorization relation of Fourier coefficients from two-particle azimuthal correlations into a product of single-particle anisotropy Fourier harmonics as a function of $\\eta$. First study of factorization breakdown effect in $\\eta$ is carried out using the CMS detector, which covers a wide $\\eta$ range of 10 units. A novel method is employed to suppress nonflow correlations at small pseudorapidity gaps of two particles. Significant eta-dependent factorization breakdown is observed in both PbPb and high-multiplicity pPb collisions. The measurements are presented for various orders of flow harmonics as a function of centrality or event...
Subcritical transition to turbulence in planar shear flows
Orszag, S. A.; Patera, A. T.
1981-01-01
The two-dimensional steady and time dependent properties of plane Poiseuille and plane Couette flows are analyzed using iterative techniques and full numerical simulation of the Navier-Stokes equations. It is shown that the finite-amplitude two-dimensional states investigated are strongly unstable to very small three-dimensional perturbations. It is also shown, through full numerical simulation, that this explosive secondary instability can explain the subcritical transitions that occur in real flows. Finally, it is shown that the three-dimensional instability can be analyzed by a linear stability analysis of a two-dimensional flow consisting of the basic parallel flow and a steady (or quasi-steady) finite-amplitude two-dimensional cellular motion.
Influence of magnetic field on the turbulence of plane high temperature gas flow
Energy Technology Data Exchange (ETDEWEB)
Levitan, Yu.S.
1977-01-01
Expressions are obtained within the framework of the Prandtl hypothesis and proposition on local-isotropic turbulence for turbulent friction and thermal flow in a channel flow of an electrical-conducting medium with a current along the channel's axis in the internal magnetic field, and which account for temperature fluctuations of the medium. 6 references.
Applications and limitations of a rheology for granular flows
Cawthorn, Chris; Hinch, John; Huppert, Herbert
2007-11-01
In order to assess the validity of the rheological law for granular flows proposed by Jop, Pouliquen and Forterre [Nature, vol. 441, pp.727-730], we present its application to a number of different problems. Whilst it works well for steady flow on a confined sandpile, or in an inclined channel, we will show that the law fails to qualitatively predict flow some simple geometries, such as annular Couette flow and vertical chute flow. In addition, we consider perturbations to 2D flow on an inclined plane and 3D flow in an inclined channel, where the effect of the confining vertical walls becomes important. Implications for the use of Jop's rheology for more complicated problems, particularly those involving dam-break or column collapse will also be addressed.
Chirality-specific lift forces of helix under shear flows: Helix perpendicular to shear plane.
Zhang, Qi-Yi
2017-02-01
Chiral objects in shear flow experience a chirality-specific lift force. Shear flows past helices in a low Reynolds number regime were studied using slender-body theory. The chirality-specific lift forces in the vorticity direction experienced by helices are dominated by a set of helix geometry parameters: helix radius, pitch length, number of turns, and helix phase angle. Its analytical formula is given. The chirality-specific forces are the physical reasons for the chiral separation of helices in shear flow. Our results are well supported by the latest experimental observations.
Transition to turbulence for flows without linear criticality
Nagata, Masato
2010-12-01
It is well known that plane Couette flow (PCF) and pipe flow (PF) are linearly stable against arbitrary three-dimensional perturbations at any finite Reynolds number, so that transitions from the basic laminar states, if they exist, must be abrupt. Due to this lack of linear criticality, weakly nonlinear analysis does not work in general and numerical approaches must be resorted to. It is only recently that non-trivial nonlinear states for these flows have been discovered numerically at finite Reynolds number as solutions bifurcating from infinity. The onset of turbulence in a subcritical transition is believed to be related to the appearance of steady/travelling wave states caused by disturbances of finite amplitude that take the flows out of the basin of attraction of the laminar state in phase space. In this paper, we introduce other flows that, in a similar way to PCF and PF, exhibit no linear critical point for the laminar states, namely flow in a square duct and sliding Couette flow in an annulus with a certain range of gap ratio. We shall show our recent numerical investigations on these flows where nonlinear travelling wave states are found for the first time by a homotopy approach. We believe that these states constitute the skeleton around which a time-dependent trajectory in the phase space is organized and help in understanding non-equilibrium turbulent processes.
Computation and Modeling of Heat Transfer in Wall-Bounded Turbulent Flows
2010-05-31
Dissimilarity in a Turbulent Channel Flow, Mecánica Computacional , Vol. XXVI, pp. 3644-3663, Ed. by Elaskar, S.A., E.A. Pilotta, and G.A. Torres. (http...Natural Dissimilarity in a Turbulent Plane Couette Flow, In Mecánica Computacional Vol. XXVII, Ed. by A. Cardona, M. Storti, and C. Zuppa, pp.1619-1636...Past a Circular Cylinder , In Mecánica Computacional Vol. XXVII, Ed. by A. Cardona, M. Storti, and C. Zuppa, pp.249-264, 2008. http://venus.ceride.gov.ar/twiki/bin/view/AMCA/ListadoDePublicaciones). xii
Granular flows down inclined and vibrated planes: influence of basal friction
Directory of Open Access Journals (Sweden)
Gaudel Naïma
2017-01-01
Full Text Available We present an experimental study about granular avalanches when external mechanical vibrations are applied. The results of the flow properties highlight the existence of two distinct regimes: (i a gravity-driven regime at large angles where scaling laws are in agreement with those reported in the literature for non-vibrating granular flows and (ii a vibration-driven regime at small angles where no flow occurs without applied vibrations. The flow in this regime is well described by a vibrationinduced activated process. We also propose an empirical law to capture the evolution of the thickness of the deposits as a function of the vibration intensity and the inclination angle.
Plane Poiseuille flow: Near continuum results for a rigid sphere gas
Loyalka, S. K.; Hickey, K. A.
1989-10-01
In Poiseuille flow between two parallel plates, the bulk flow is characterized by the Burnett distribution. We report explicit results for this distribution by solving numerically the relevant integral equations for a rigid sphere gas in the context of the linearized Boltzmann equation. Then, we use this distribution together with the Chapman-Enskog distribution to obtain asymptotic results (near-continuum) for mass and heat fluxes corresponding to planar thermal transpiration and mechanocaloric effects.
Improving double patterning flow by analyzing the diffractive orders in the pupil plane
Zeggaoui, N.; Farys, V.; Besacier, M.; Li, Q.; Yesilada, E.; Trouiller, Y.
2011-04-01
To print sub 22nm node features, current lithography technology faces some tool limitations. One possible solution to overcome these problems is to use the double patterning technique (DPT). The principle of the double patterning technique is pitch splitting where two adjacent features must be assigned opposite masks (colors) corresponding to different exposures if their pitch is less than a predefined minimum coloring pitch. However, certain design orientations for which pattern features separated by more than the minimum coloring pitch cannot be imaged with either of the two exposures. In these directions, the contrast and the process window are degraded because constructive interferences between diffractive orders in the pupil plane are not sufficient. The 22nm and 16nm nodes require the use of very coherent sources that will be generated using SMO (source mask cooptimization). Such pixelized sources while helpful in improving the contrast for selected configurations, can lead to degrade it for configurations which have not been counted for during the SMO process. Therefore, we analyze the diffractive orders interactions in the pupil plane in order to detect these limited orientations in the design and thus propose a new double patterning decomposition algorithm to enlarge the process window and the contrast of each mask.
Wen, Fufang; Wang, Gang
2016-01-01
Recent charge-dependent azimuthal correlation measurements in high-energy heavy-ion collisions have observed charge-separation signals perpendicular to the reaction plane, and the observations have been related to the chiral magnetic effect (CME). However, the correlation signal is contaminated with the background contributions due to the collective motion (flow) of the collision system, and it remains elusive to effectively remove the background from the correlation. We present a method study with Monte Carlo simulations and a multi-phase transport model, and develop a scheme to reveal the true CME signal via the event-shape engineering with the flow vector, $\\overrightarrow{q}$. An alternative approach using the ensemble averages of observables is also discussed.
Fraternale, Federico; Staffilani, Gigliola; Tordella, Daniela
2016-01-01
By deriving conditions for no transient enstrophy growth for two-dimensional small perturbations in the plane Couette and Poiseuille flows, we show that transient kinetic energy growth for small traveling waves is not a sufficient condition for the enstrophy growth. It should be recalled that the vorticity perturbation problem in wall parallel flows was addressed at the beginning of the 20th century by J. L. Synge in an original way and as an alternative and equivalent way of determining flow stability with respect to the classical kinetic energy analysis. However, mathematical difficulties related to the vorticity boundary conditions left the problem open since then. Historically, the discovery of nonmodal perturbation growth and its link to the subcritical transition to turbulence lead to a preferential energy-based analysis. Here, we follow Synge's procedure and extend its work to the nonmodal approach and thus to the initial value problem capable to describe possible transient vorticity growth. Our calcul...
Institute of Scientific and Technical Information of China (English)
Bing Yang; Fuping Gao; DongSheng Jeng; Yingxiang Wu
2009-01-01
In this study, the vortex-induced vibrations of a cylinder near a rigid plane boundary in a steady flow are studied experimentally. The phenomenon of vortex-induced vibrations of the cylinder near the rigid plane boundary is reproduced in the flume. The vortex shedding frequency and mode are also measured by the methods of hot film velocime-ter and hydrogen bubbles. A parametric study is carded out to investigate the influences of reduced velocity, gap-to-diame-ter ratio, stability parameter and mass ratio on the amplitude and frequency responses of the cylinder. Experimental results indicate: (1) the Strouhal number (St) is around 0.2 for the stationary cylinder near a plane boundary in the sub-criti-cal flow regime; (2) with increasing gap-to-diameter ratio (eo/D), the amplitude ratio (A/D) gets larger but frequency ratio (f/fn) has a slight variation for the case of larger val-ues of e0/D(e0/D 0.66 in this study); (3) there is a clear difference of amplitude and frequency responses of the cylin-der between the larger gap-to-diameter ratios (e0/D 0.66) and the smaller ones (e0/D < 0.3); (4) the vibration of the cylinder is easier to occur and the range of vibration in terms of Vr number becomes more extensive with decrease of the stability parameter, but the frequency response is affected slightly by the stability parameter; (5) with decreasing mass ratio,the width of the lock-in ranges in terms of Vr and the frequency ratio(f/fn)become large.
Fast color flow mode imaging using plane wave excitation and temporal encoding
DEFF Research Database (Denmark)
Udesen, Jesper; Gran, Fredrik; Jensen, Jørgen Arendt
2005-01-01
In conventional ultrasound color flow mode imaging, a large number (~500) of pulses have to be emitted in order to form a complete velocity map. This lowers the frame-rate and temporal resolution. A method for color flow imaging in which a few (~10) pulses have to be emitted to form a complete...... deviation of 0.84% and a relative bias of 5.74%. Finally the method is tested on the common carotid artery of a healthy 33-year-old male....
Huang, Hsin-Fu; Zahn, Markus; LEMAIRE, Elisabeth
2010-01-01
International audience; A continuum mechanical model is presented to analyze the negative electrorheological responses of a particle-liquid mixture with the suspended micro-particles undergoing Quincke rotation for both Couette and Poiseuille flow geometries by combining particle electromechanics and continuum antisymmetric/couple stress analyses in the zero spin viscosity limit. We propose a phenomenological polarization relaxation model to incorporate both the micro-particle rotation speed ...
On the origin of streaks in turbulent shear flows
Waleffe, Fabian; Kim, John
1991-01-01
The paper substantiates the notion that selective amplification and direct resonance, based on linear theory, does not provide a selection mechanism for the well-defined streak spacing of about 100 wall units observed in wall-bounded turbulent shear flows. For the direct resonance theory, it is shown that the streaks are created by the nonlinear self-interaction of the vertical velocity rather than that of the directly forced vertical vorticity. It is proposed that the selection mechanism must be inherently nonlinear and correspond to a self-sustaining process. For the case of plane Poiseuille flow the 100-wall-unit criterion corresponds to a critical Reynolds number of 1250, based on the centerline velocity and the channel half-width, which is close to the usually quoted value of about 1000. In plane Couette flow, it corresponds to a critical Reynolds number of 625, based on the half-velocity difference and the half-width.
Turbulent patterns in wall-bounded flows: a Turing instability?
Manneville, Paul
2012-01-01
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the pipe flow transition involving reaction-diffusion concepts, we consider plane Couette flow in the same perspective and transform Waleffe's classical four-variable model of self-sustaining process into a reaction-diffusion model. We show that, upon fulfillment of a condition on the relative diffusivities of its variables, the featureless turbulent regime becomes unstable against patterning as the result of a Turing instability. A reduced two-variable model helps us to delineate the appropriate region of parameter space. An {\\it intrinsic} status is therefore given to the pattern's wavelength for the first time. Virtues and limitations of the model are discussed, calling for a microscopic support of the phenomenological approach.
Unstable manifold computations for the two-dimensional plane Poiseuille flow
Energy Technology Data Exchange (ETDEWEB)
Casas, Pablo S. [Universidad Politecnica de Cataluna, Departamento de Matematica Aplicada I, Barcelona (Spain); Jorba, Angel [Universidad de Barcelona, Departamento de Matematica Aplicada y Analisis, Barcelona (Spain)
2004-11-01
We follow the unstable manifold of periodic and quasi-periodic solutions in time for the Poiseuille problem, using two formulations: holding a constant flux or mean pressure gradient. By means of a numerical integrator of the Navier-Stokes equations, we let the fluid evolve from an initially perturbed unstable solution until the fluid reaches an attracting state. Thus, we detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with two or three basic frequencies, and more complex sets that we have not been able to classify. These connections make possible the location of new families of solutions, usually hard to find by means of numerical continuation of curves, and show the richness of the dynamics of the Poiseuille flow. (orig.)
Developing flow of a power-law liquid film on an inclined plane
Weinstein, Steven J.; Ruschak, Kenneth J.; Ng, Kam C.
2003-10-01
Developing flow of a liquid film along a stationary inclined wall is analyzed for a power-law constitutive equation. For films with appreciable inertia and therefore small interfacial slopes, the boundary-layer approximation may be used. The boundary-layer equations are solved numerically through the von Mises transformation that gives a partial differential equation over a semi-infinite strip and approximately by the method of von Kármán and Polhausen that gives an ordinary differential equation for the film thickness, called a film equation. Film equations derived from self-similar velocity profiles fail when the film thickens and the flow undergoes a supercritical to subcritical transition; a nonremovable singularity arises at the critical point, the location of the flow transition. A film equation is developed that accommodates this transition. Predictions exhibit a standing wave where hydrostatic pressure becomes important and opposes inertia. This thickening effect is accentuated for small angles of inclination at moderate Reynolds numbers. In the limit of small film thickness in which gravitational effects are negligible, the thickness profile is nonlinear in agreement with an independent and new similarity solution. This result contrasts with the established linear thickness profile for a Newtonian liquid. The circumstances in which the film equation gives results close to the full boundary layer equation are identified.
Off-plane motion of a non-spherical capsule in simple shear flow
Omori, Toshihiro; Ishikawa, Takuji; Imai, Yohsuke; Yamaguchi, Takami
2012-11-01
Dynamics of a capsule and a biological cell in fluid flow is now of great interest in chemical engineering and bioengineering. In this study, we numerically investigated the motion of a spheroid capsule in simple shear flow including a red blood cell type biconcave disk. The membrane of a capsule was modeled by a two-dimensional hyperelastic material, and its large deformation was solved by a finite element method. The motion of internal and external liquids was estimated as a Stokes flow and solved by a boundary element method. The results showed that the orientation of a spheroid capsule is variant under time reversal, though that of a rigid spheroid is invariant. The final orientation of a spheroid capsule over a long time duration tends to converge to a certain direction depending on the shear rate despite initial placement with random orientation. These results can be utilized for a particle alignment technique and form a fundamental basis of the suspension mechanics of capsules and biological cells.
El-Mistikawy, Tarek M. A.
2011-12-01
In their article (Fundamental flows with nonlinear slip conditions: exact solutions, R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 (2010) 877-888.), the authors considered three simple cases of the steady flow of a third grade fluid between parallel plates with slip conditions; namely, Couette flow, Poiseuille flow, and generalized Couette flow. They obtained exact solutions, which were utilized in a way that did not lead to useful results. Their conclusion that the Couette flow cannot be obtained from the generalized Couette flow, by dropping the pressure gradient, is incorrect. Meaningful results based on their solution are herein presented.
Simulations of turbulent flow between a rotating and a stationary disk
Energy Technology Data Exchange (ETDEWEB)
Lygren, Magne
2001-07-01
The main focus of this thesis is turbulent flow between a rotating and a stationary disk. The extension of the disks is assumed to be large enough to prevent the outer boundary conditions to influence the flow at the region of interest. This flow is driven by the shear between the disks, but an imbalance between centrifugal and pressure forces in the radial direction induces a radial cross flow. The result is a complex three-dimensional flow where the direction of the mean flow varies with the axial position. Direct numerical simulations (DNS) and large eddy simulations (LES) have been used to investigate the flow. The simulations utilised a special set of quasi-periodic boundary conditions which allowed the use of a computational domain which captured only a section of the flow. Locally, the disk flow is characterised by a rotational Reynolds number and a local gap ratio of 0.02. Turbulence statistics were compared to results from the turbulent plane Couette flow and from an experimental investigation of an enclosed rotor-stator flow. The plane Couette flow is a two-dimensional equivalence to the flow between the disks. Although the turbulence statistics had many similarities in the two cases, there were differences caused by three-dimensionality of the mean-flow in the disk case. In the disk flow the direction of the Reynolds shear stress vector was not aligned with the mean-gradient vector and the ratio of the magnitude of the shear stress vector to the mean turbulent kinetic energy was reduce compared to the Couette flow. The flow between the disks statistically stationary. It is therefore a suitable case for studying effects of mean-flow three-dimentionality on the underlying coherent structures in the boundary layers. Ensemble averages, probability-density functions and a quadrant analysis of conditional averages in the regions near the disks were performed in order to study the coherent quasistreamwise vortices. By comparing with corresponding conditional
Initialization effects via the nuclear radius on transverse in-plane flow and its disappearance
Directory of Open Access Journals (Sweden)
Bansal Rajni
2014-04-01
Full Text Available We study the dependence of collective transverse flow and its disappearance on initialization effects via the nuclear radius within the framework of the Isospin-dependent Quantum Molecular Dynamics (IQMD model. We calculate the balance energy using different parametrizations of the radius available in the literature for the reaction of 12C+12C to explain its measured balance energy. A mass-dependent analysis of the balance energy through out the periodic table is also carried out by changing the default liquid drop IQMD radius.
Flow features that arise due to the interaction of a plane shock wave with concave profiles
CSIR Research Space (South Africa)
MacLucas, David A
2012-10-01
Full Text Available capable of providing both qualitative and quantitative information ? Quantitative information would aid in understanding the variation of shock strength affecting shock focus process Research applications Kulkarny, V.A. (1975) The focusing of weak... stream_source_info MacLucas_2012.pdf.txt stream_content_type text/plain stream_size 5569 Content-Encoding ISO-8859-1 stream_name MacLucas_2012.pdf.txt Content-Type text/plain; charset=ISO-8859-1 Flow features that arise...
Directory of Open Access Journals (Sweden)
Hector Barrios-Piña
2015-01-01
Full Text Available This work focuses on the evolution of a free plane laminar jet in the near-nozzle region. The jet is buoyant because it is driven by a continuous addition of both buoyancy and momentum at the source. Buoyancy is given by a temperature difference between the jet and the environment. To study the jet evolution, numerical simulations were performed for two Richardson numbers: the one corresponding to a temperature difference slightly near the validity of the Boussinesq approximation and the other one corresponding to a higher temperature difference. For this purpose, a time dependent numerical model is used to solve the fully dimensional Navier-Stokes equations. Density variations are given by the ideal gas law and flow properties as dynamic viscosity and thermal conductivity are considered nonconstant. Particular attention was paid to the implementation of the boundary conditions to ensure jet stability and flow rates control. The numerical simulations were also reproduced by using the Boussinesq approximation to find out more about its pertinence for this kind of flows. Finally, a stability diagram is also obtained to identify the onset of the unsteady state in the near-nozzle region by varying control parameters of momentum and buoyancy. It is found that, at the onset of the unsteady state, momentum effects decrease almost linearly when buoyancy effects increase.
Energy Technology Data Exchange (ETDEWEB)
Lok, Yian Yian [Academic Service Center, Kolej Universiti Teknikal Kebangsaan Malaysia, 75450 Ayer Keroh, Melaka (Malaysia); Amin, Norsarahaida [Department of Mathematics, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400, CP 253, Cluj (Romania)
2003-11-01
The growth of the boundary layer flow of a viscous and incompressible micro-polar fluid started impulsively from rest near the rear stagnation point of a two-dimensional plane surface is studied theoretically. The transformed non-similar boundary-layer equations are solved numerically using a very efficient finite-difference method known as Keller-box method. This method may present well-behaved solutions for the transient (small time) solution up to the separation boundary layer flow. Numerical results are given for the reduced velocity and micro-rotation profiles, as well as for the skin friction coefficient when the material parameter K takes the values K=0 (Newtonian fluid), 0.5, 1, 1.1, 1.5, 2, 2.5 and 3 with the boundary condition for micro-rotation n=0 (strong concentration of microelements) and n=1/2 (weak concentration of microelements), respectively. Important features of these flow characteristics are shown on graphs and in tables. (authors)
Simplex finite element analysis of viscous incompressible flow with penalty function formulation
Allaire, P. E.; Rosen, M. C.; Rice, J. G.
1985-01-01
Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constraint and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.
Institute of Scientific and Technical Information of China (English)
严以新; 诸裕良; 薛鸿超
1999-01-01
Based upon the long-term observation of field data, a two-dimensional numerical model is applied to simulating the tidal flow covering from the neap tide to spring tide in the radial sandbank area in the southern Yellow Sea. From the development of tidal current ridges under the hydrodynamic action, multi-purpose analysis and study are carried out, which include the propagation process of tidal wave, the distributions of tidal wave energy rate and tidal range, the tidal ellipses and traces. It is shown that the tidal current is the major dynamic factor for the formation and development of the radial sandbanks, and the differences of tidal wave energy rate and current strength determine the distinct plane shapes of ridges and troughs in this region.
Dallaston, Michael C; McCue, Scott W
2016-01-01
Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.
Gerolymos, G A
2016-01-01
The paper studies the budgets of the dissipation tensor $\\varepsilon_{ij}$ in plane channel flow, obtained from novel DNS computations. Particular emphasis is given on the component-by-component comparison of various mechanisms (production, diffusion, redistribution, destruction) in the $\\varepsilon_{ij}$-transport budgets with the corresponding mechanisms in the transport equations for the Reynolds-stresses $r_{ij}$. The wall-asymptotics of different terms in the transport equations are studied in detail, and examined using the DNS data. The anisotropy of the destruction-of-dissipation tensor $\\varepsilon_{\\varepsilon_{ij}}$ is fundamentally different from that of $r_{ij}$ or $\\varepsilon_{ij}$, never approaching the 2-component (2-C) state at the solid wall.
Energy Technology Data Exchange (ETDEWEB)
Angelique, J.C.; Bizard, G.; Brou, R.; Cussol, D.; Kerambrun, A.; Patry, J.P.; Peter, J.; Regimbart, R.; Steckmeyer, J.C.; Tamain, B.; Vient, E. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire; Popescu, R.; Buta, A. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire]|[Central Inst. of Physics, Bucharest (Romania). Inst. of Physics and Nuclear Engineering; He, Z.Y. [Caen Univ., 14 (France). Lab. de Physique Corpusculaire]|[Lanzhou Univ., GS (China). Dept. of Modern Physics; Auger, G.; Peghaire, A.; Saint-Laurent, F. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France); Cabot, C. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)]|[Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire; Crema, E. [Grand Accelerateur National d`Ions Lourds (GANIL), 14 - Caen (France)]|[Sao Paulo Univ., SP (Brazil). Inst. de Fisica; Hagel, K.; Wada, R. [Texas A and M Univ., College Station, TX (United States). Cyclotron Inst.; Gonin, M. [Texas A and M Univ., College Station, TX (United States). Cyclotron Inst.]|[Brooklyn Coll., NY (United States). Dept. of Chemistry; Eudes, P.; Lebrun, C. [Nantes Univ., 44 (France). Lab. de Physique Nucleaire; El Masri, Y. [Universite Catholique de Louvain (UCL), Louvain-la-Neuve (Belgium); Rosato, E. [Istituto Nazionale di Fisica Nucleare, Naples (Italy)
1994-05-01
The azimuthal distributions of light particles relative to the reaction plane have been measured for several bins of experimentally estimated impact parameter in the reactions of {sup 64}Zn + {sup 58}Ni at energies between 35 and 79 MeV/u. An in-plane enhancement for mid-rapidity Z = 1, 2, 3 particles is observed at low incident energy but gradually evolves to out-of plane enhancement (squeeze-out effect) with increasing energy. This evolution depends on the impact parameter in a way similar to the flow parameter. The energies for this system at which the azimuthal distribution is uniform are lower than the corresponding balance energies. (authors). 22 refs.
Numerical simulation of entry flow over blunt swept-wing planes
Li, C. P.
1992-01-01
Viscous, heat-conducting flow with chemical and vibrational relaxation processes of the constituent gases surrounding winged spacecraft is considered in the continuum regime. The Navier-Stokes equations are appended by additional vibrational energy and species rate equations and supplemented by the equations of state and the phenomenological laws based on mixture rules or collisional cross sections. Numerical convective flux can be obtained from several forms of one-dimensional Riemann solver, with or without entropy correction. High-order accuracy is obtained from two types of reconstructive interpolation. A number of explicit and implicit numerical schemes have been implemented as a means to yield converged solutions. Both shock-fitting, finite-difference and shock-capturing, finite-volume techniques have been tested for configurations such as a sphere, double ellipsoid, blunt-edge delta wing, a European Hermes vehicle, and the U.S. Shuttle Orbiter. The shock-fitting code provides excellent results only for simple configurations, whereas the shock-capturing code leads to overall satisfying solutions for complex geometries.
Experimental investigation of a plane wall jet subjected to an external lateral flow
Kaffel, Ahmed; Moureh, Jean; Harion, Jean-Luc; Russeil, Serge
2015-05-01
The present work aims to experimentally investigate the aerodynamic behavior of a wall jet subjected to external lateral stream by means of time-resolved PIV measurement technique. The experiments are performed on a reduced-scale model representing a generic configuration of a refrigerated display cabinet by focusing on the near-field region ( x/ e < 10) where strong interactions are expected between the jet core, wall boundary and external lateral stream. Comparisons of experimental data obtained with and without external perturbation make it possible to quantify the effect of the perturbation on the time-averaged wall jet characteristics such as airflow patterns, velocity profiles, maximum velocity decay, half-width jet growth, jet entrainment, RMS velocities and coherent structures as well as those related to the development of instabilities. Temporal PIV visualizations have allowed gaining insight on the effect of external lateral perturbation at the outer edge of the jet on the topology of Kelvin-Helmholtz vortices that dominate the early stages of wall jet transition process and play a relevant role on the jet entrainment inwards. Special attention was paid to bring new knowledge of the flow physics related to mutual interactions between outer and inner layer of the wall jet after the break-up of vortex filaments in the braid region due to the external perturbation.
Stability of the flow in a plane microchannel with one or two superhydrophobic walls
Pralits, Jan O.; Alinovi, Edoardo; Bottaro, Alessandro
2017-01-01
The modal and nonmodal linear stability of the flow in a microchannel with either one or both walls coated with a superhydrophobic material is studied. The topography of the bounding wall(s) has the shape of elongated microridges with arbitrary alignment with respect to the direction of the mean pressure gradient. The superhydrophobic walls are modeled using the Navier slip condition through a slip tensor, and the results depend parametrically on the slip length and orientation angle of the ridges. The stability analysis is carried out in the temporal framework; the modal analysis is performed by solving a generalized eigenvalue problem, and the nonmodal, optimal perturbation analysis is done with an adjoint optimization approach. We show theoretically and verify numerically that Squire's theorem does not apply in the present settings, despite the fact that Squire modes are found to be always damped. The most notable result is the appearance of a streamwise wall-vortex mode at very low Reynolds numbers when the ridges are sufficiently inclined with respect to the mean pressure gradient, in the case of a single superhydrophobic wall. When two walls are rendered water repellent, the exponential growth of the instability results from either a two-dimensional or a three-dimensional Orr-Sommerfeld mode, depending on the ridges' orientation and amplitude. Nonmodal results for either one or two superhydrophobic wall(s) display but a mild modification of the no-slip case.
Energy Technology Data Exchange (ETDEWEB)
Meziane, M.; Eichwald, O.; Ducasse, O.; Marchal, F. [Universite de Toulouse, UPS, INPT, LAPLACE (Laboratoire Plasma et Conversion d' Energie), Toulouse Cedex 9 F-31062 (France); Sarrette, J. P.; Yousfi, M. [Universite de Toulouse, UPS, INPT, LAPLACE (Laboratoire Plasma et Conversion d' Energie), Toulouse Cedex 9 F-31062 (France); CNRS, LAPLACE, Toulouse F-31062 (France)
2013-04-21
The present paper is devoted to the 2D simulation of an Atmospheric Corona Discharge Reactor (ACDR) involving 10 pins powered by a DC high voltage and positioned 7 mm above a grounded metallic plane. The corona reactor is periodically crossed by thin mono filamentary streamers with a natural repetition frequency of some tens of kHz. The simulation involves the electro-dynamic, chemical kinetic, and neutral gas hydrodynamic phenomena that influence the kinetics of the chemical species transformation. Each discharge stage (including the primary and the secondary streamers development and the resulting thermal shock) lasts about one hundred nanoseconds while the post-discharge stages occurring between two successive discharge phases last one hundred microseconds. The ACDR is crossed by a lateral air flow including 400 ppm of NO. During the considered time scale of 10 ms, one hundred discharge/post-discharge cycles are simulated. The simulation involves the radical formation and thermal exchange between the discharges and the background gas. The results show how the successive discharges activate the flow gas and how the induced turbulence phenomena affect the redistribution of the thermal energy and the chemical kinetics inside the ACDR.
Meziane, M.; Eichwald, O.; Sarrette, J. P.; Ducasse, O.; Yousfi, M.; Marchal, F.
2013-04-01
The present paper is devoted to the 2D simulation of an Atmospheric Corona Discharge Reactor (ACDR) involving 10 pins powered by a DC high voltage and positioned 7 mm above a grounded metallic plane. The corona reactor is periodically crossed by thin mono filamentary streamers with a natural repetition frequency of some tens of kHz. The simulation involves the electro-dynamic, chemical kinetic, and neutral gas hydrodynamic phenomena that influence the kinetics of the chemical species transformation. Each discharge stage (including the primary and the secondary streamers development and the resulting thermal shock) lasts about one hundred nanoseconds while the post-discharge stages occurring between two successive discharge phases last one hundred microseconds. The ACDR is crossed by a lateral air flow including 400 ppm of NO. During the considered time scale of 10 ms, one hundred discharge/post-discharge cycles are simulated. The simulation involves the radical formation and thermal exchange between the discharges and the background gas. The results show how the successive discharges activate the flow gas and how the induced turbulence phenomena affect the redistribution of the thermal energy and the chemical kinetics inside the ACDR.
Bretheim, Joel U; Gayme, Dennice F
2014-01-01
Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a logarithmic region is observed, its von-K\\'arm\\'an constant is not consistent with the standard logarithmic law. In half-channel flow we show that limiting the streamwise-varying wavenumber support of RNL turbulence to one or few empirically determined modes improves its predictions considerably. In particular, the mean velocity profiles obtained with the band-limited RNL model follow standard logarithmic behavior for the higher Reynolds numbers in this study.
Directory of Open Access Journals (Sweden)
Yariv I
2016-10-01
Full Text Available Inbar Yariv,1 Menashe Haddad,2,3 Hamootal Duadi,1 Menachem Motiei,1 Dror Fixler1 1Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan, Israel; 2Sackler School of Medicine, Tel-Aviv University, Tel-Aviv, Israel; 3Mayanei Hayeshua Medical Center, Benei Brak, Israel Abstract: Physiological substances pose a challenge for researchers since their optical properties change constantly according to their physiological state. Examination of those substances noninvasively can be achieved by different optical methods with high sensitivity. Our research suggests the application of a novel noninvasive nanophotonics technique, ie, iterative multi-plane optical property extraction (IMOPE based on reflectance measurements, for tissue viability examination and gold nanorods (GNRs and blood flow detection. The IMOPE model combines an experimental setup designed for recording light intensity images with the multi-plane iterative Gerchberg-Saxton algorithm for reconstructing the reemitted light phase and calculating its standard deviation (STD. Changes in tissue composition affect its optical properties which results in changes in the light phase that can be measured by its STD. We have demonstrated this new concept of correlating the light phase STD and the optical properties of a substance, using transmission measurements only. This paper presents, for the first time, reflectance based IMOPE tissue viability examination, producing a decrease in the computed STD for older tissues, as well as investigating their organic material absorption capability. Finally, differentiation of the femoral vein from adjacent tissues using GNRs and the detection of their presence within blood circulation and tissues are also presented with high sensitivity (better than computed tomography to low quantities of GNRs (<3 mg. Keywords: Gerchberg-Saxton, optical properties, gold nanorods, blood vessel, tissue viability
Silva, Goncalo; Semiao, Viriato
2017-07-01
The first nonequilibrium effect experienced by gaseous flows in contact with solid surfaces is the slip-flow regime. While the classical hydrodynamic description holds valid in bulk, at boundaries the fluid-wall interactions must consider slip. In comparison to the standard no-slip Dirichlet condition, the case of slip formulates as a Robin-type condition for the fluid tangential velocity. This makes its numerical modeling a challenging task, particularly in complex geometries. In this work, this issue is handled with the lattice Boltzmann method (LBM), motivated by the similarities between the closure relations of the reflection-type boundary schemes equipping the LBM equation and the slip velocity condition established by slip-flow theory. Based on this analogy, we derive, as central result, the structure of the LBM boundary closure relation that is consistent with the second-order slip velocity condition, applicable to planar walls. Subsequently, three tasks are performed. First, we clarify the limitations of existing slip velocity LBM schemes, based on discrete analogs of kinetic theory fluid-wall interaction models. Second, we present improved slip velocity LBM boundary schemes, constructed directly at discrete level, by extending the multireflection framework to the slip-flow regime. Here, two classes of slip velocity LBM boundary schemes are considered: (i) linear slip schemes, which are local but retain some calibration requirements and/or operation limitations, (ii) parabolic slip schemes, which use a two-point implementation but guarantee the consistent prescription of the intended slip velocity condition, at arbitrary plane wall discretizations, further dispensing any numerical calibration procedure. Third and final, we verify the improvements of our proposed slip velocity LBM boundary schemes against existing ones. The numerical tests evaluate the ability of the slip schemes to exactly accommodate the steady Poiseuille channel flow solution, over
Bifurcating fronts for the Taylor-Couette problem in infinite cylinders
Hărăguş-Courcelle, M.; Schneider, G.
We show the existence of bifurcating fronts for the weakly unstable Taylor-Couette problem in an infinite cylinder. These fronts connect a stationary bifurcating pattern, here the Taylor vortices, with the trivial ground state, here the Couette flow. In order to show the existence result we improve a method which was already used in establishing the existence of bifurcating fronts for the Swift-Hohenberg equation by Collet and Eckmann, 1986, and by Eckmann and Wayne, 1991. The existence proof is based on spatial dynamics and center manifold theory. One of the difficulties in applying center manifold theory comes from an infinite number of eigenvalues on the imaginary axis for vanishing bifurcation parameter. But nevertheless, a finite dimensional reduction is possible, since the eigenvalues leave the imaginary axis with different velocities, if the bifurcation parameter is increased. In contrast to previous work we have to use normalform methods and a non-standard cut-off function to obtain a center manifold which is large enough to contain the bifurcating fronts.
Thermal stability for a reactive viscous flow in a slab
Okoya, S S
2002-01-01
The paper deals with the effect of dimensionless non - Newtonian coefficient on the thermal stability of a reactive viscous liquid in steady flow between parallel heated plates. It is assumed that the liquid is symmetrically heated and the flow fully developed. Approximate analytical solution is obtained for the velocity of the flow and the criterion for which this solution is valid is determined. After the velocity distribution is known, the temperature distribution may be calculated. Criticality and disappearance of criticality (transition values) are obtained in the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. We have observed that nonlinear effect from velocity and temperature fields introduced decaying for the transitional values of the dimensionless central temperature. Other effects of this nonlinearity are reported. We also give results for the plane - Couette flow problem. The results help to enhance understanding of the interplay between Newtonian and ...
Meshless lattice Boltzmann method for the simulation of fluid flows.
Musavi, S Hossein; Ashrafizaadeh, Mahmud
2015-02-01
A meshless lattice Boltzmann numerical method is proposed. The collision and streaming operators of the lattice Boltzmann equation are separated, as in the usual lattice Boltzmann models. While the purely local collision equation remains the same, we rewrite the streaming equation as a pure advection equation and discretize the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The meshless feature of the proposed method makes it a more powerful lattice Boltzmann solver, especially for cases in which using meshes introduces significant numerical errors into the solution, or when improving the mesh quality is a complex and time-consuming process. Three well-known benchmark fluid flow problems, namely the plane Couette flow, the circular Couette flow, and the impulsively started cylinder flow, are simulated for the validation of the proposed method. Excellent agreement with analytical solutions or with previous experimental and numerical results in the literature is observed in all the simulations. Although the computational resources required for the meshless method per node are higher compared to that of the standard lattice Boltzmann method, it is shown that for cases in which the total number of nodes is significantly reduced, the present method actually outperforms the standard lattice Boltzmann method.
Understanding the sub-critical transition to turbulence in wall flows
Manneville, Paul
2008-01-01
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that currently are the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A review of the situation is given. An alternative to the temporal theory of the transition to turbulence in terms of chaotic transients in such globally subcritical flows is proposed, which invokes spatio-temporal intermittence and the ...
Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
Seshasayanan, K
2015-01-01
On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for the spatiotemporal dynamics in the plane of the flow. Truncating this set beyond lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at cruder effective wall-normal resolution. Perspectives opened by the approach are discussed.
On Exact Solutions of the Navier-Stokes Equations for Uni-directional Flows
Lam, F
2015-01-01
In the present note, we show that the uni-directional flows in a rectangular channel and in a circular pipe are exact spatio-temporal solutions of the Navier-Stokes equations over a short time interval. We assert that the classical plane Poiseuille-Couette flow and Hagen-Poiseuille flow are time-independent approximations of the exact solutions if an appropriate initial velocity distribution at starting location is specified. Conceptually, there do not exist absolute steady flows starting from unspecified initial data. The classic experimental measurements by Poiseuille can be explained in terms of the evolutional solutions. In particular, the pipe flow does not have a time-independent characteristic velocity. The orthodox notion that the parabolic profile exists for arbitrary Reynolds numbers is unwarranted.
Transition to turbulence in wall-bounded flows: Where do we stand?
Manneville, Paul
2016-01-01
In this essay, we recall the specificities of the transition to turbulence in wall-bounded flows and present recent achievements in the understanding of this problem. The transition is abrupt with laminar-turbulent coexistence over a finite range of Reynolds numbers, the transitional range. The archetypical cases of Poiseuille pipe flow and plane Couette flow are first reviewed at the phenomenological level, together with a few other flow configurations. Theoretical approaches are then examined with particular emphasis on the existence of special nontrivial solutions to the Navier-Stokes equations at finite distance from laminar flow. Dynamical systems theory is most appropriate to analyze their role, in particular with respect to the transient character of turbulence in the lower transitional range. The extensions needed to deal with the prominent spatiotemporal features of the transition are then discussed. Turbulence growth/decay in terms of statistical physics of many-body systems and the relevance of dir...
Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation
Ortiz de Zárate, José M.; Sengers, Jan V.
2013-02-01
We use fluctuating hydrodynamics to evaluate the enhancement of thermally excited fluctuations in laminar fluid flow using plane Couette flow as a representative example. In a previous publication (J. Stat. Phys. 144:774, 2011) we derived the energy amplification arising from thermally excited wall-normal fluctuations by solving a fluctuating Orr-Sommerfeld equation. In the present paper we derive the energy amplification arising from wall-normal vorticity fluctuation by solving a fluctuating Squire equation. The thermally excited wall-normal vorticity fluctuations turn out to yield the dominant contribution to the energy amplification. In addition, we show that thermally excited streaks, even in the absence of any externally imposed perturbations, are present in laminar fluid flow.
Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
Energy Technology Data Exchange (ETDEWEB)
Seshasayanan, K [Laboratoire de Physique Statistique, CNRS UMR 8550, École Normale Supérieure, F-75005 Paris (France); Manneville, P, E-mail: paul.manneville@polytechnique.edu [Laboratoire d’Hydrodynamique, CNRS UMR7646, École Polytechnique, F-91128, Palaiseau (France)
2015-06-15
On its way to turbulence, plane Couette flow–the flow between counter-translating parallel plates–displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier–Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for spatiotemporal dynamics in the plane of the flow. Truncating this set beyond the lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at the cruder effective wall-normal resolution. Perspectives opened by this approach are discussed. (paper)
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Woo [School of Mechanical Engineering, Kumoh National Institute of Technology, 1 Yangho-dong, Gumi, Gyeongbuk 730-701 (Korea, Republic of)], E-mail: swlee@kumoh.ac.kr; Moon, Hyun Suk; Lee, Seong Eun [School of Mechanical Engineering, Kumoh National Institute of Technology, 1 Yangho-dong, Gumi, Gyeongbuk 730-701 (Korea, Republic of)
2009-04-15
The effects of tip gap height-to-chord ratio, h/c, on the flow structure and heat/mass transfer over the plane tip surface of a large-scale high-turning turbine rotor blade have been investigated for h/c = 1.0%, 2.0%, 3.0% and 4.0%. For near-wall tip gap flow visualizations, a high-resolution oil film method is employed, and the naphthalene sublimation technique is used for local heat/mass transfer rate measurements. From the tip surface visualizations, a pair of vortices named 'tip gap vortices' is identified in the leading edge region within the tip gap. The overall tip gap flow is characterized not only by the tip gap vortices but also by the flow separation/re-attachment process along the pressure-side tip edge. Within the separation bubble, there exist complicated near-wall flows moving toward a mid-chord flow converging area. With increasing h/c, the tip gap vortices, the flow separation/re-attachment, and the converging flows within the separation bubble tend to be intensified. In general, higher thermal load is found along the loci of the tip gap vortices and along the re-attachment line, while lower thermal load is observed behind the tip gap vortex system and near the mid-chord flow converging area. Heat/mass transfer characteristics with the variation of h/c are discussed in detail in conjunction with the tip gap flow features. Based on the flow visualizations and heat/mass transfer data, new realistic tip gap flow models have been proposed for h/c = 1.0 and 4.0%.
Spiral and Taylor vortex fronts and pulses in axial through-flow
Pinter, A; Hoffmann, C; Hoffmann, Ch.
2003-01-01
The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through-flow strengths Re and different rates of co- and counterrotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with m=+1 and m=-1. For each of these three different vortex varieties we have investigated (i) axially extended vortex structures, (ii) axially localized vortex pulses, and (iii) vortex fronts. The complex dispersion relations of the linearized NSE for vortex modes with the three different m are evaluated for real axial wave numbers for (i) and over the plane of complex axial wave numbers for (ii,iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictio...
Mcfarland, E. R.
1981-01-01
A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.
A Unified View of Global Instability of Compressible Flow over Open Cavities
2006-03-28
predict instability in Hagen- Poiseuille (pipe) flow , aggravated by the erroneous predictions of BiGlobal theory of stability of pressure-gradient driven... flow in a square duct (Tatsumi and Yoshimura 1990) and wall-bounded Couette flow . It thus becomes of interest, before investing efforts in the... Couette flow at φ = π / 2 which is (erroneously predicted by BiGlobal analysis to be) stable. The introduction of a third velocity component by the lid
Application of the Moment Method in the Slip and Transition Regime for Microfluidic Flows
2011-01-01
the mean free path. For flows in simply geometries, such as Couette and Poiseuille flows , the above linearised moment equations can be decoupled into...Rarefied Channel Flows ,” Phys. Rev. E 78, 046301 (2008). [18] Taheri, P. Torrilhon, M. & Struchtrup, H., “ Couette and Poiseuille Microflows...the velocity in the other directions is zero. All derivatives in the x direction, except pressure gradient in Poiseuille flow , are zero everywhere and
Theory of margination and cell-free layer thickness in blood flow
Graham, Michael
2016-11-01
A mechanistic model is developed to describe segregation in confined multicomponent suspensions such as blood during Couette or plane Poiseuille flow. We focus attention on the case of a binary suspension with a deformable primary component (e.g. red blood cells) that completely dominates the collision dynamics in the system. The model captures the phenomena of depletion layer formation and margination observed in confined multicomponent suspensions of deformable particles. The depletion layer thickness of the primary component is predicted to follow a master curve relating it in a specific way to confinement ratio and volume fraction. Results from experiments and detailed simulations with different parameters (flexibility, viscosity ratio, confinement) collapse onto this curve with only one adjustable parameter. In a binary suspension, several regimes of segregation arise, depending on the value of a "margination parameter" M. Most importantly, in both Couette and Poiseuille flows there is a critical value of M below which a sharp "drainage transition" occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes.
Blokhin, Alexander; Tkachev, Dmitry
2016-10-01
We study the classical problem for a flow of stationary inviscid non-heat-conducting gas in thermodynamical equilibrium moving onto a planar infinite wedge. Under the fulfillment of the Lopatinski condition on the shock (neutral stability) the correctness of the linearized mixed problem (main solution is a weak shock) is proven and the representation of the classical solution is obtained and in that case (unlike the case of a uniform Lopatinski condition i.e. absolutely stable attached shock) there are additionally plane waves in representation. For finite initial data solution goes to prescribed regime given infinite time.
Fedosov, Dmitry A; Karniadakis, George Em; Caswell, Bruce
2010-04-14
Polymer fluids are modeled with dissipative particle dynamics (DPD) as undiluted bead-spring chains and their solutions. The models are assessed by investigating their steady shear-rate properties. Non-Newtonian viscosity and normal stress coefficients, for shear rates from the lower to the upper Newtonian regimes, are calculated from both plane Couette and plane Poiseuille flows. The latter is realized as reverse Poiseuille flow (RPF) generated from two Poiseuille flows driven by uniform body forces in opposite directions along two-halves of a computational domain. Periodic boundary conditions ensure the RPF wall velocity to be zero without density fluctuations. In overlapping shear-rate regimes the RPF properties are confirmed to be in good agreement with those calculated from plane Couette flow with Lees-Edwards periodic boundary conditions (LECs), the standard virtual rheometer for steady shear-rate properties. The concentration and the temperature dependence of the properties of the model fluids are shown to satisfy the principles of concentration and temperature superposition commonly employed in the empirical correlation of real polymer-fluid properties. The thermodynamic validity of the equation of state is found to be a crucial factor for the achievement of time-temperature superposition. With these models, RPF is demonstrated to be an accurate and convenient virtual rheometer for the acquisition of steady shear-rate rheological properties. It complements, confirms, and extends the results obtained with the standard LEC configuration, and it can be used with the output from other particle-based methods, including molecular dynamics, Brownian dynamics, smooth particle hydrodynamics, and the lattice Boltzmann method.
Multicompartment/CFD modelling of transport and reaction processes in Couette-Taylor photobioreactor
Directory of Open Access Journals (Sweden)
Papáček Š.
2007-11-01
Full Text Available A hybrid multicompartment/CFD modelling approach, introduced by Bezzo et al. (2003, describing processes with much faster fluid dynamics time-scale than the reaction rate, is used to characterise microalgal growth in a photobioreactor. Our system of interest, the Couette-Taylor bioreactor (CTBR, is divided into a network of wellmixed compartments. Photosynthetic reactions and other related phenomena are described in each compartment by an ordinary differential equation (ODE. The flow of neutrally-buoyant particles, representing a continuous mass flow of microalgal cells inside CTBR, is simulated by a steady-state computational fluid dynamics (CFD computations. The flow rates between adjacent compartments are derived from several thousand predicted trajectories, post-processed using MATLAB, accordingly to our original method. The resulting governing equations are formed as a system of n_c (total number of compartments ODE’s, which are easier to handle than the large system of equations rising from a reaction phenomena incorporated in CFD models.
Numerical solutions for unsteady rotating high-porosity medium channel Couette hydrodynamics
Zueco, Joaquin; Bég, O. Anwar; Bég, Tasveer A.
2009-09-01
We investigate theoretically and numerically the unsteady, viscous, incompressible, hydrodynamic, Newtonian Couette flow in a Darcy-Forchheimer porous medium parallel-plate channel rotating with uniform angular velocity about an axis normal to the plates. The upper plate is translating at uniform velocity with the lower plate stationary. The two-dimensional reduced Navier-Stokes equations are transformed to a pair of nonlinear dimensionless momentum equations, neglecting convective inertial terms. The network simulation method, based on a thermoelectric analogy, is employed to solve the transformed dimensionless partial differential equations under prescribed boundary conditions. We examine here graphically the effect of Ekman number, Forchheimer number and Darcy number on the shear stresses at the plates over time. Excellent agreement is also obtained for the infinite permeability i.e. purely fluid (vanishing porous medium) case (Da→∞) with the analytical solutions of Guria et al (2006 Int. J. Nonlinear Mechanics 41 838-43). Backflow is observed in certain cases. Increasing Ekman number, Ek (corresponding to decreasing Coriolis force) is found to accentuate the primary shear stress component (τx) considerably but to reduce magnitudes of the secondary shear stress component (τy). The flow is also found to be accelerated generally with increasing Darcy number and decelerated with increasing Forchheimer number. The present model has applications in geophysical flows, chemical engineering systems and also fundamental studies in fluid dynamics.
Turbulent shear flow downstream of a sphere with and without an o-ring located over a plane boundary
Directory of Open Access Journals (Sweden)
Sahin Besir
2012-04-01
Full Text Available Flow-structure interaction of separated shear flow from the sphere and a flat plate was investigated by using dye visualization and the particle image velocimetry technique. Later, a passive control method was applied with 2mm oring located on the sphere surface at 55° from front stagnation point. The experiments were carried out in open water channel for Reynolds number value of Re=5000. Flow characteristics have been examined in terms of the 2-D instantaneous and time-averaged velocity vectors, patterns of vorticity, streamlines, rms of velocity fluctuations and Reynolds stress variations and discussed from the point of flow physics, vortex formation, lengths of large-scale Karman Vortex Streets and Kelvin-Helmholtz vortices depending on the sphere locations over the flat plate. It is demonstrated that the gap flow occurring between the sphere bottom point and the flat plate surface has very high scouring effect until h/d=0.25 and then unsymmetrical flow structure of the wake region keeps up to h/D=1.0 for smooth sphere. For the sphere with o-ring, the wake flow structure becomes symmetrical at smaller gap ratios and reattachment point on the flat plate surface occurs earlier. Moreover, o-ring on the sphere diminishes peak magnitudes of the flow characteristics and thus it is expected that the flow-induced forces will be lessened both on the sphere and flat plate surface. Vortex formation lengths and maximum value occurring points become closer locations to the rear surface of the sphere with o-ring.
Turbulent shear flow downstream of a sphere with and without an o-ring located over a plane boundary
Ozgoren, Muammer; Okbaz, Abdulkerim; Dogan, Sercan; Sahin, Besir; Akilli, Huseyin
2012-04-01
Flow-structure interaction of separated shear flow from the sphere and a flat plate was investigated by using dye visualization and the particle image velocimetry technique. Later, a passive control method was applied with 2mm oring located on the sphere surface at 55° from front stagnation point. The experiments were carried out in open water channel for Reynolds number value of Re=5000. Flow characteristics have been examined in terms of the 2-D instantaneous and time-averaged velocity vectors, patterns of vorticity, streamlines, rms of velocity fluctuations and Reynolds stress variations and discussed from the point of flow physics, vortex formation, lengths of large-scale Karman Vortex Streets and Kelvin-Helmholtz vortices depending on the sphere locations over the flat plate. It is demonstrated that the gap flow occurring between the sphere bottom point and the flat plate surface has very high scouring effect until h/d=0.25 and then unsymmetrical flow structure of the wake region keeps up to h/D=1.0 for smooth sphere. For the sphere with o-ring, the wake flow structure becomes symmetrical at smaller gap ratios and reattachment point on the flat plate surface occurs earlier. Moreover, o-ring on the sphere diminishes peak magnitudes of the flow characteristics and thus it is expected that the flow-induced forces will be lessened both on the sphere and flat plate surface. Vortex formation lengths and maximum value occurring points become closer locations to the rear surface of the sphere with o-ring.
Noble, Pascal
2012-01-01
In this paper we derive consistent shallow water equations for thin films of power law fluids down an incline. These models account for the streamwise diffusion of momentum which is important to describe accurately the full dynamic of the thin film flows when instabilities like roll-waves arise. These models are validated through a comparison with Orr Sommerfeld equations for large scale perturbations. We only consider laminar flow for which the boundary layer issued from the interaction of the flow with the bottom surface has an influence all over the transverse direction to the flow. In this case the concept itself of thin film and its relation with long wave asymptotic leads naturally to flow conditions around a uniform free surface Poiseuille flow. The apparent viscosity diverges at the free surface which, in turn, introduces a singularity in the formulation of the Orr-Sommerfeld equations and in the derivation of shallow water models. We remove this singularity by introducing a weaker formulation of Cauc...
Institute of Scientific and Technical Information of China (English)
Oluwole Daniel Makinde
2009-01-01
This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new com-implemented in MAPLE. This semi-numerical scheme offers some advantages over solu-tions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.
Mamori, Hiroya; Yamaguchi, Kyotaro; Sasamori, Monami; Iwamoto, Kaoru; Murata, Akira
2016-11-01
We perform a dual-plane stereoscopic particle image velocimetry (DPS-PIV) measurement to investigate vortical structure over a sinusoidal riblet surface in the turbulent channel flow. In the sinusoidal riblet surface, its lateral spacing of the adjacent walls varies in the streamwise direction and 12% of the drag reduction rate has been confirmed in the turbulent channel flow. The DPS-PIV measurement system consists of four high-speed CCD cameras and the two laser sheets. In the flat case, the profile of the velocity statistics shows a good agreement with previous data. In the ribet case, the velocity statistics decrease in the region close to the wall as compared with that of the flat case. Since all velocity components are measured on adjacent laser sheets simultaneously, vortical structures can be obtained by a second invariant of the tensor i.e. the Q value. According to an analysis for the Q value, we found that the vortical structure is shifted up and attenuated owing to the riblet. Moreover, the riblet prevents the approaching of the vortical structure: the upward and downward flows in the region near the wall are generated by the riblet; if the vortical structure approaches the wall, it is shifted away from the wall due to the upward flow.
Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence
Zhu, Xiaojue; Lohse, Detlef
2016-01-01
Direct numerical simulations (DNSs) are performed to analyze the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number $Ta=10^{10}$. The dimensionless torque $Nu_\\omega$ shows an effective scaling of $Nu_\\omega \\propto Ta^{0.42\\pm0.01}$, which is steeper than the ultimate regime effective scaling $Nu_\\omega \\propto Ta^{0.38}$ seen for smooth walls. It is found that at the inner wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to $Nu_\\omega$. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. The energy dissipation rate at the wall of inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transpo...
Identifying coherent structures and vortex clusters in Taylor-Couette turbulence
Spandan, Vamsi; Ostilla-Monico, Rodolfo; Lohse, Detlef; Verzicco, Roberto
2016-04-01
The nature of the underlying structures in Taylor-Couette (TC) flow, the flow between two co-axial and independently rotating cylinders is investigated by two methods. First, the quadrant analysis technique for identifying structures with intense radial-azimuthal stresses (also referred to as ‘Q’s) of Lozano-Durán et al., (J. Fluid Mech. 694, 100-130) is used to identify the main structures responsible for the transport of angular velocity. Second, the vortex clusters are identified based on the analysis by del Álamo et al., (J. Fluid. Mech., 561, 329-358). In order to test these criteria, two different radius ratios η = ri/ro are considered, where ri and ro are the radii of inner and outer cylinder, respectively: (i) η = 0.5 and (ii) η = 0.909, which correspond to high and low curvature geometries, respectively and have different underlying structures. The Taylor rolls, i.e. the large-scale coherent structures, are effectively captured as ‘Q’s for the low curvature setup and it is observed that curvature plays a dominant role in influencing the size and volumes of these ‘Q’s. On the other hand, the vortex clusters are smaller in size when compared to the ‘Q’ structures. These vortex clusters are found to be taller in the case of η = 0.909, while the distribution of the lengths of these clusters is almost homogenous for both radius ratios.
Doi, Toshiyuki
2016-09-01
Transient motion of and heat transfer in a rarefied gas between plane parallel walls with different surface properties are studied based on kinetic theory. It is assumed that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary, and the transient behavior of the gas caused by a sudden heating of one of the walls is studied. The linearized Boltzmann equation for a hard-sphere molecular gas is numerically studied using the modified hybrid scheme of the characteristic coordinate and finite difference methods, to correctly describe the discontinuities in the velocity distribution function. The transient motion of the gas from an early time stage to the final time-independent state is studied over a wide range of the mean free path and the accommodation coefficient of the boundary. Between the two transient flows caused by the heating of the respective walls, the values of the heat flow on the heated wall are different, whereas those on the unheated wall coincide identically. This property, which is a consequence of the symmetric relation of the linearized Boltzmann equation, is numerically confirmed over a wide range of the mean free path. The long time behavior of the heat flow on the walls is quite similar to that of the shear stress in the Couette flow problem, whereas a distinct wavy behavior is observed in an early time stage.
Directory of Open Access Journals (Sweden)
Eric Mucunguzi-Rugwebe
2013-09-01
Full Text Available In this study, the results of the effect of water-flow rate and air fraction component on intensity, I, are presented and discussed. The study which was carried out at Bergen University in Norway, presents the impact of monochromatic defects on polarization and measurements of small oil fractions of various crude oils are presented. When there was refraction, it was observed that in static sea-water &mustatic = 0.38 and in running water &muflow = 0.42 When refraction was eliminated by grafting windows in the pipe, &mustatic = 0, &muflow = 0.11 and in both cases &muflow was independent of the flow rate. Air fraction component, &alpha> = 0.12 reduced light intensity. With rate flow Q = 13.6m3/h and Q = 27.2 m3/h critical air fraction was found at &alphac = 0.18 and &alphac = 0.12 respectively. For &alphac = 0.18 up to &alpha 0.87 at Q = 13.6m3/h and &alphac = 0.12 up to &alpha = 0.78 at Q = 27.2 m3/h light intensity was found independent of &alpha. The highest rotation was found in Gullfaks crude oil, followed by Heidrun, the rotation is Statfjord crude oil was less than one in Heidrun and the least rotation was observed in 0A sg 0a rd crude oil. At 40ppm, the rotation was as follows: Gullfaks &empty = 27.0±0.20, Heidrun &empty = 23.9±0.20, Statfjord &empty = 20.0±0.20 and 0Asg 0ard &empty = 10.0±0.10. This method studys very well when small oil fractions from 5.0-70 ppm are in sea-water flow. This technique can be deployed to monitor the environment and to control the re-injected process water.
Iori, F.; Grechy, L.; Corbett, R. W.; Gedroyc, W.; Duncan, N.; Caro, C. G.; Vincent, P. E.
2015-03-01
Arterio-Venous Fistulae (AVF) are the preferred method of vascular access for patients with end stage renal disease who need hemodialysis. In this study, simulations of blood flow and oxygen transport were undertaken in various idealized AVF configurations. The objective of the study was to understand how arterial curvature affects blood flow and oxygen transport patterns within AVF, with a focus on how curvature alters metrics known to correlate with vascular pathology such as Intimal Hyperplasia (IH). If one subscribes to the hypothesis that unsteady flow causes IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto the outer-curvature of a curved artery. However, if one subscribes to the hypothesis that low wall shear stress and/or low lumen-to-wall oxygen flux (leading to wall hypoxia) cause IH within AVF, then the results suggest that in order to avoid IH, AVF should be formed via a vein graft onto a straight artery, or the inner-curvature of a curved artery. We note that the recommendations are incompatible—highlighting the importance of ascertaining the exact mechanisms underlying development of IH in AVF. Nonetheless, the results clearly illustrate the important role played by arterial curvature in determining AVF hemodynamics, which to our knowledge has been overlooked in all previous studies.
Evolution of turbulence and in-plane vortices in the near field flow behind multi-scale planar grids
Gan, L.; Krogstad, P.-Å.
2016-08-01
In this experimental work, we carry out detailed two-dimensional particle image velocimetry investigations for the near field wakes behind a conventional and two multi-scale planar grids, using stitched camera fields of view. Statistical independent measurements are conducted focusing on the first few mesh distances downstream of the grid. It is found that the multiple integral length scales originated from the grids loose their importance on the turbulence development after about three mesh distances downstream, much earlier than the distance where the turbulence becomes homogeneous. The largest eddy size, represented by the integral length scales, does not show clear differences in its growth rate among the three grids after an initial development of three times the largest grid size downstream. Nevertheless, when examining individual vortex behaviours using conditional averaging and filtering processes, clear differences are found. The grids are found to have different decay rates of peak vorticity and projected vortex strengths. Despite these differences, the in-plane vorticity correlation function reveals that the mean vortex shape of all the grids shows a universal near-Gaussian pattern which does not change much as the turbulence decays.
Shear-dependant toroidal vortex flow
Energy Technology Data Exchange (ETDEWEB)
Khorasani, Nariman Ashrafi; Haghighi, Habib Karimi [Payame Noor University, Tehran (Iran, Islamic Republic of)
2013-01-15
Pseudoplastic circular Couette flow in annulus is investigated. The flow viscosity is dependent on the shear rate, which directly affects the conservation equations that are solved in the present study by the spectral method in the present study. The pseudoplastic model adopted here is shown to be a suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of shear rate term in the viscosity expression was considered to ease the numerical manipulations, in the present study takes the term containing the quadratic power into account. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.
Kweon, Jae Ryong
2016-09-01
In this paper, when the initial density has a jump across an interior curve in a bounded domain, we show unique existence, piecewise regularity and jump discontinuity dynamics for the density and the velocity vector governed by the Navier-Stokes equations of compressible viscous barotropic flows. A critical difficulty is in controlling the gradient of the pressure across the jump curve. This is resolved by constructing a vector function associated with the pressure jump value on the convecting curve and extending it to the whole domain.
Energy Technology Data Exchange (ETDEWEB)
Andronic, A. E-mail: A.Andronic@gsi.de; Stoicea, G.; Petrovici, M.; Simion, V.; Crochet, P.; Alard, J.P.; Averbeck, R.; Barret, V.; Basrak, Z.; Bastid, N.; Bendarag, A.; Berek, G.; Caplar, R.; Devismes, A.; Dupieux, P.; Dzelalija, M.; Eskef, M.; Finck, Ch.; Fodor, Z.; Gobbi, A.; Grishkin, Y.; Hartmann, O.N.; Herrmann, N.; Hildenbrand, K.D.; Hong, B.; Kecskemeti, J.; Kim, Y.J.; Kirejczyk, M.; Korolija, M.; Kotte, R.; Kress, T.; Kutsche, R.; Lebedev, A.; Lee, K.S.; Leifels, Y.; Manko, V.; Merlitz, H.; Neubert, W.; Pelte, D.; Plettner, C.; Rami, F.; Reisdorf, W.; De Schauenburg, B.; Schuell, D.; Seres, Z.; Sikora, B.; Sim, K.S.; Siwek-Wilczynska, K.; Smolyankin, V.; Stockmeier, M.R.; Vasiliev, M.; Wagner, P.; Wisniewski, K.; Wohlfarth, D.; Yushmanov, I.; Zhilin, A
2001-01-01
The incident energy at which the azimuthal distributions in semicentral heavy-ion collisions change from in-plane to out-of-plane enhancement -- E{sub tran} is studied as a function of mass of emitted particles, their transverse momentum and centrality for Au+Au collisions. The analysis is performed in a reference frame rotated with the sidewards flow angle ({theta}{sub flow}) relative to the beam axis. A systematic decrease of E{sub tran} as function of mass of the reaction products, their transverse momentum and collision centrality is evidenced. The predictions of a microscopic transport model (IQMD) are compared with the experimental results.
Numerical simulations of two-phase Taylor-Couette turbulence using an Euler-Lagrange approach
Spandan, Vamsi; Verzicco, Roberto; Lohse, Detlef
2015-01-01
Two-phase turbulent Taylor-Couette (TC) flow is simulated using an Euler-Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using Direct Numerical Simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to $\\eta=0.833$, and a maximum inner cylinder Reynolds number of $Re_i=8000$ is reached. We vary the Froude number ($Fr$), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system. In a two-phase TC...
Effects of the computational domain size on DNS of Taylor-Couette turbulence
Mónico, Rodolfo Ostilla; Lohse, Detlef
2014-01-01
In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $\\eta=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is also found to play a significant role, as larger boxes allow for azimuthal wave-like patterns in the Taylor rol...
Nguyen, Anh-Tuan; Yu, Taekyung; Kim, Woo-Sik
2017-07-01
A Couette-Taylor crystallizer is developed to enhance the L-Lysine crystal size distribution and recovery in the case of continuous cooling crystallization. When using the proposed Couette-Taylor (CT) crystallizer, the size distribution and crystal product recovery were much narrower and higher, respectively, than those from a conventional stirred tank (ST) crystallizer. Here, the coefficient of the size distribution for the crystal product from the CT crystallizer was only 0.45, while it was 0.78 in the case of the conventional ST crystallizer at an agitation speed of 700 rpm, mean residence time of 20 min, and feed concentration of 900 (g/L). Furthermore, when using the CT crystallizer, the crystal product recovery was remarkably enhanced up to 100%wt with a mean residence time of only 20 min, while it required a mean residence time of at least 60 min when using the conventional ST crystallizer. This result indicates that the CT crystallizer was much more effective than the conventional ST crystallizer in terms of controlling a narrower size distribution and achieving a 100%wt L-lysine crystal product recovery from continuous cooling crystallization. The advantage of the CT crystallizer over the conventional ST crystallizer was explained based on the higher energy dissipation of the Taylor vortex flow and larger surface area for heat transfer of the CT crystallizer. Here, the energy dissipation of the Taylor vortex flow in the CT crystallizer was 13.6 times higher than that of the random fluid motion in the conventional ST crystallizer, while the surface area per unit volume for heat transfer of the CT crystallizer was 8.0 times higher than that of the conventional ST crystallizer. As a result, the mixing condition and heat transfer of the CT crystallizer were much more effective than those of the conventional ST crystallizer for the cooling crystallization of L-lysine, thereby enhancing the L-lysine crystal size distribution and product recovery.
Institute of Scientific and Technical Information of China (English)
陈元千
2011-01-01
Bear first presented a physical concept and discriminant of the starting pressure gradient in 1972 when he studied the applied lower limit of the Darcy law. And then Professor Ge Jiali introduced the starting pressure gradient to China in 1982. The so-called starting pressure gradient refers to a pressure gradient that makes a fluid in fluid-saturated cores begin to flow. It should be pointed out that the pressure gradient of linear flow is directly proportional to the flow rate, while the starting pressure gradient is a constant. The pressure gradient of plane radial flow is directly proportional to the flow rate but inversely to the radial radius. Moreover, the starting pressure7 gradient at a position of different radial radius is variable. It is controversial for the correctness to have directly applied the Bear's starting pressure gradient and discriminant of linear flow to the plane radial flow equation by some researchers. Theoretically, the paper analyzed both the pressure gradient and starting pressure gradient of linear flow and plane radial flow and proposed the conception of starting flow rate. At the same time, a more applicable method to evaluate the starting drawdown pressure and starting bottomhole flowing pressure of low permeability tight reservoirs was proposed.%启动压力梯度的物理概念及判别式是Bear于1972年在利用岩心测试资料研究达西定律的应用下限时提出来的,葛家理教授首次介绍到我国.所谓启动压力梯度,是指流体在饱和的岩心开始发生流动时的压力梯度.应当指出,线性流的压力梯度与流量成正比,启动压力梯度为常数；平面径向流的压力梯度与流量成正比,与径向半径成反比,而且,不同径向半径位置的启动压力梯度是不同的.有关学者将线性流启动的压力梯度及判别式直接用于平面径向流方程的正确性值得质疑.笔者对线性流和平面径向流的压力梯度和启动压力梯度问题进行了
Energy Technology Data Exchange (ETDEWEB)
Lee, Sang Woo; Kim, Seon Ung [Kumoh National Institute of Technology, School of Mechanical Engineering, Gyeongbuk (Korea, Republic of)
2010-11-15
Tip gap height effects on the flow structure over a cavity squealer tip have been investigated in a linear turbine cascade for power generation, in comparison with the corresponding plane tip results. Oil film flow visualizations are conducted on the tip surface and casing wall for tip gap height-to-chord ratios of h/c=1.0, 2.0, and 3.0%. The squealer tip has a recessed cavity enclosed by a full length squealer with its rim height-to-chord ratio of 5.51%. The results show that most of in-coming fluid entering the tip gap inlet for the cavity squealer tip is entrapped by the suction-side squealer rim, and the cavity fluid is discharged into the blade flow passage over the suction-side squealer rim in the region from the mid-chord to the trailing edge. Regardless of h/c, the cavity squealer tip makes the leakage flow zone narrower than the plane tip, and is superior to the plane tip in reducing the tip leakage mass flow rate. A qualitative flow model describing full flow features over the cavity squealer tip is suggested. In this flow model, the tip gap exit area is classified into four different regions, and the tip gap height effects on the discharge characteristics in each region are discussed in detail. (orig.)
Lee, Sang Woo; Kim, Seon Ung
2010-11-01
Tip gap height effects on the flow structure over a cavity squealer tip have been investigated in a linear turbine cascade for power generation, in comparison with the corresponding plane tip results. Oil film flow visualizations are conducted on the tip surface and casing wall for tip gap height-to-chord ratios of h/c = 1.0, 2.0, and 3.0%. The squealer tip has a recessed cavity enclosed by a full length squealer with its rim height-to-chord ratio of 5.51%. The results show that most of in-coming fluid entering the tip gap inlet for the cavity squealer tip is entrapped by the suction-side squealer rim, and the cavity fluid is discharged into the blade flow passage over the suction-side squealer rim in the region from the mid-chord to the trailing edge. Regardless of h/c, the cavity squealer tip makes the leakage flow zone narrower than the plane tip, and is superior to the plane tip in reducing the tip leakage mass flow rate. A qualitative flow model describing full flow features over the cavity squealer tip is suggested. In this flow model, the tip gap exit area is classified into four different regions, and the tip gap height effects on the discharge characteristics in each region are discussed in detail.
Criterion of Turbulent Transition in Pressure Driven Flows
Dou, Hua-Shu; Khoo, Boo Cheong
2012-11-01
It has been found from numerical simulations and experiments that velocity inflection could result in turbulent transition in viscous parallel flows. However, there are exceptions, for example, in the plane Poiseuille-Couette flow. Thus, whether velocity inflection necessarily leads to turbulent transition is still not clear. To-date, there is still no consensus on the physics of turbulence transition in the scientific community. In this study, the mechanism of turbulent transition is investigated using the energy gradient method. It is found that the transition to turbulence from a laminar flow depends on the magnitudes of the energy gradient function and the energy of the disturbance imposed (including both the amplitude and the frequency). Our study further reveals that the criterion of turbulent transition is different in pressure and shear driven flows. In pressure driven parallel flows, it is found that the necessary and sufficient condition of turbulent transition is the existence of an inflection point on the velocity profile. This criterion is found to be consistent with the available experimental data and numerical simulation results. On contrast, velocity inflection in shear driven flows does not necessarily lead to turbulent transition.
Motion stability of a suspended particle in a MHD flow
Energy Technology Data Exchange (ETDEWEB)
Shvarts, I.A.
1977-07-01
An examination is made of the motion instability of a suspended particle in a plane-parallel laminar flow with a velocity profile U(y,A) where A is certain parameter. An expression was obtained for the critical Reynolds number Re = ..cap alpha../delta/U/delta y/:the coefficient ..cap alpha.. is associated with dimensions and form of the particle. The results of the common theory are used for studying the motion instability of suspended spherical particle in Couette--Hartmann MHD flows. At large Hartmann numbers Re*/Ha was shown to be constant. This agrees well with experimental data on the hydrodynamic stability of the MHD flow itself. A definite correlation also takes place between Re/sub kr/(Ha) of a MHD flow and the Reynolds numbers that determine the stability of suspended particles when the Hartmann numbers are small. Thus, in a number of cases it is possible to examine the hydrodynamic stability of a MHD flow by the motion stability of solid particles introduced into the flow. 8 references, 2 illustrations.
Surface Effects on Nanoscale Gas Flows
Beskok, Ali; Barisik, Murat
2010-11-01
3D MD simulations of linear Couette flow of argon gas confined within nano-scale channels are performed in the slip, transition and free molecular flow regimes. The velocity and density profiles show deviations from the kinetic theory based predictions in the near wall region that typically extends three molecular diameters (s) from each surface. Utilizing the Irwin-Kirkwood theorem, stress tensor components for argon gas confined in nano-channels are investigated. Outside the 3s region, three normal stress components are identical, and equal to pressure predicted using the ideal gas law, while the shear stress is a constant. Within the 3s region, the normal stresses become anisotropic and the shear stress shows deviations from its bulk value due to the surface virial effects. Utilizing the kinetic theory and MD predicted shear stress values, the tangential momentum accommodation coefficient for argon gas interacting with FCC structured walls (100) plane facing the fluid is calculated to be 0.75; this value is independent of the Knudsen number. Results show emergence of the 3s region as an additional characteristic length scale in nano-confined gas flows.
Molecular dynamics simulation of nanochannel flows with effects of wall lattice-fluid interactions.
Soong, C Y; Yen, T H; Tzeng, P Y
2007-09-01
In the present paper, molecular dynamics simulations are performed to explore the effects of wall lattice-fluid interactions on the hydrodynamic characteristics in nanochannels. Couette and Poiseuille flows of liquid argon with channel walls of face-centered cubic (fcc) lattice structure are employed as the model configurations. Truncated and shifted Lennard-Jones (LJ) 12-6 potentials for evaluations of fluid-fluid and wall-fluid interactions, and a nonlinear spring potential for wall-wall interaction, are used as interatomistic or molecular models. The hydrodynamics at various flow orientation angles with respect to channel walls of lattice planes (111), (100), and (110) are explored. The present work discloses that the effects of key parameters, such as wall density, lattice plane, flow orientation, and LJ interaction energy, have a very significant impact on the nanochannel flow characteristics. The related interfacial phenomena and the underlying physical mechanisms are explored and interpreted. These results are significant in the understanding of nanoscale hydrodynamics, as well as in various applications where an accurate nanoscale flow rate control is necessary.
Nonaxisymmetric MHD Instabilities of Chandrasekhar States in Taylor-Couette Geometry
Gellert, M.; Rüdiger, G.; Schultz, M.; Guseva, A.; Hollerbach, R.
2016-06-01
We consider axially periodic Taylor-Couette geometry with insulating boundary conditions. The imposed basic states are so-called Chandrasekhar states, where the azimuthal flow U ϕ and magnetic field B ϕ have the same radial profiles. Mainly three particular profiles are considered: the Rayleigh limit, quasi-Keplerian, and solid-body rotation. In each case we begin by computing linear instability curves and their dependence on the magnetic Prandtl number {{Pm}}. For the azimuthal wavenumber m = 1 modes, the instability curves always scale with the Reynolds number and the Hartmann number. For sufficiently small {{Pm}} these modes therefore only become unstable for magnetic Mach numbers less than unity, and are thus not relevant for most astrophysical applications. However, modes with m\\gt 1 can behave very differently. For sufficiently flat profiles, they scale with the magnetic Reynolds number and the Lundquist number, thereby allowing instability also for the large magnetic Mach numbers of astrophysical objects. We further compute fully nonlinear, three-dimensional equilibration of these instabilities, and investigate how the energy is distributed among the azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper for large m, reflecting the smoothing action of shear. On the other hand kinetic and magnetic energy spectra exhibit similar behavior: if several azimuthal modes are already linearly unstable they are relatively flat, but for the rigidly rotating case where m = 1 is the only unstable mode they are so steep that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The total magnetic energy exceeds the kinetic energy only for large magnetic Reynolds numbers {{Rm}}\\gt 100.
Some analytical solutions for flows of Casson fluid with slip boundary conditions
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K. Ramesh
2015-09-01
Full Text Available In the present paper, we have studied three fundamental flows namely Couette, Poiseuille and generalized Couette flows of an incompressible Casson fluid between parallel plates using slip boundary conditions. The equations governing the flow of Casson fluid are non-linear in nature. Analytical solutions of the non-linear governing equations with non-linear boundary conditions are obtained for each case. The effect of the various parameters on the velocity and volume flow rate for each problem is studied and the results are presented through graphs. It is observed that, the presence of Casson number decreases the velocity and volume flow rate of the fluid. Increasing of slip parameter increases the velocity and volume flow rate in both Poiseuille and generalized Couette flows.