Lagrangian viscoelastic flow computations using the Rivlin-Sawyers constitutive model
Rasmussen, Henrik Koblitz
2000-01-01
A new finifte element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represent a further development of the 3D Lagrangian integral method (3D-LIM) from an upper...... convected Maxwell fluid to a fluid described by an integral constitutive equation of the Rivlin-Sawyers type. This includes the K-BKZ model. The convergence of the method is demonstrated on the axisymmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring....
Rasmussen, Henrik Koblitz
2000-01-01
Lagrangian Integral Method) is a finite element method where Galerkons method is used for solving the governing equation in rectangular coordinates numerically. In the present implementation the velocity and pressure fields are approximated with tri-linear and constant shape functions, respectivly.The 3D LIM......) and polymeric solutions. Secondly, the 3D-LIM has also been applied to calculate the inflation of a thick sheet of a polymeric melt into a elliptic cylinder. These problems all include free surfaces. As the governing equations are solved for the particle positions, the motion of surfaces can be followed easily......A new technique for the numerical 3D simulation of time dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. The fluid is described by the Rivlin Sawyer integral constitutive equation. The method (referred to as the 3D...
Rasmussen, Henrik Koblitz
2000-01-01
The 3D-LIM has as yet been used to simulate the following two three-dimensional problems. First, the method has been used to simulete for viscoelastic end-plate instability that occurs under certain conditions in the transient filament stretching apparatus for pressure sensitive adhesives...... (polymeric melts) and polymeric solutions. Secondly, the 3D-LIM has also been applied to calculate the inflation of a thick sheet of a polymer melt into an elliptic cylinder. These problems all include free surfaces. As the governing equations are solved for the particle positions, the motion of surfaces can...... be followed easily even in 3D viscoelastic flow....
Hamiltonian and Lagrangian theory of viscoelasticity
Hanyga, A.; Seredyńska, M.
2008-03-01
The viscoelastic relaxation modulus is a positive-definite function of time. This property alone allows the definition of a conserved energy which is a positive-definite quadratic functional of the stress and strain fields. Using the conserved energy concept a Hamiltonian and a Lagrangian functional are constructed for dynamic viscoelasticity. The Hamiltonian represents an elastic medium interacting with a continuum of oscillators. By allowing for multiphase displacement and introducing memory effects in the kinetic terms of the equations of motion a Hamiltonian is constructed for the visco-poroelasticity.
Simulation of Transient Viscoelastic Flow
Rasmussen, Henrik Koblitz; Hassager, Ole
1993-01-01
The Lagrangian kinematic description is used to develop a numerical method for simulation of time-dependent flow of viscoelastic fluids described by integral models. The method is shown to converge to first order in the time step and at least second order in the spatial discretization. The method...
Simulation of Transient Viscoelastic Flow
Rasmussen, Henrik Koblitz; Hassager, Ole
1993-01-01
The Lagrangian kinematic description is used to develop a numerical method for simulation of time-dependent flow of viscoelastic fluids described by integral models. The method is shown to converge to first order in the time step and at least second order in the spatial discretization. The method...
Simulation of transient viscoelastic flow with second order time integration
Rasmussen, Henrik Koblitz; Hassager, Ole
1995-01-01
The Lagrangian Integral Method (LIM) for the simulation of time-dependent flow of viscoelastic fluids is extended to second order accuracy in the time integration. The method is tested on the established sphere in a cylinder benchmark problem.......The Lagrangian Integral Method (LIM) for the simulation of time-dependent flow of viscoelastic fluids is extended to second order accuracy in the time integration. The method is tested on the established sphere in a cylinder benchmark problem....
Viscoelastic flow simulations in model porous media
De, S.; Kuipers, J. A. M.; Peters, E. A. J. F.; Padding, J. T.
2017-05-01
We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016), 10.1016/j.jnnfm.2016.04.002]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.
A hybrid Eulerian-Lagrangian flow solver
Palha, Artur; Ferreira, Carlos Simao; van Bussel, Gerard
2015-01-01
Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...
Rasmussen, Henrik Koblitz
1999-01-01
A new technique for the numerical simulation of 3D time dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematic description of the fluid flow and represent a further development of the 2D Lagrangian integral method (LIM). The convergence of the method...... is demonstrated on the problem of a sphere moving in a cylinder filled with an upper convected Maxwell fluid....
Applications the Lagrangian description in aperiodic flows
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
Target Lagrangian kinematic simulation for particle-laden flows
Murray, S.; Lightstone, M. F.; Tullis, S.
2016-09-01
The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.
A perturbative approach to Lagrangian flow networks
Fujiwara, Naoya; Donges, Jonathan F; Donner, Reik V
2016-01-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (a...
Lagrangian Transport Through Surfaces in Volume-Preserving Flows
Karrasch, Daniel
2015-01-01
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The recent development of highly accurate semi-Lagrangian methods for solving scalar conservation laws and of Lagrangian approaches to coherent structures in turbulent (geophysical) fluid flows necessitate a new approach to transport from the (Lagrangian) material perspective. We present a Lagrangian framework for calculating transport of conserved quantities through a given surface in $n$-dimensional, fully aperiodic, volume-preserving flows. Our approach does not involve any dynamical assumptions on the surface or its boundary.
Lagrangian statistics in turbulent channel flow: implications for Lagrangian stochastic models
Stelzenmuller, Nickolas; Polanco, Juan Igancio; Vinkovic, Ivana; Mordant, Nicolas
2016-11-01
Lagrangian acceleration and velocity correlations in statistically one-dimesional turbulence are presented in the context of the development of Lagrangian stochastic models of inhomogeneous turbulent flows. These correlations are measured experimentally by 3D PTV in a high aspect ratio water channel at Reτ = 1450 , and numerically from DNS performed at the same Reynolds number. Lagrangian timescales, key components of Lagrangian stochastic models, are extracted from acceleration and velocity autocorrelations. The evolution of these timescales as a function of distance to the wall is presented, and compared to similar quantities measured in homogeneous isotropic turbulence. A strong dependance of all Lagrangian timescales on wall distance is present across the width of the channel. Significant cross-correlations are observed between the streamwise and wall-normal components of both acceleration and velocity. Lagrangian stochastic models of this flow must therefore retain dependance on the wall-normal coordinate and the components of acceleration and velocity, resulting in significantly more complex models than those used for homogeneous isotropic turbulence. We gratefully acknowledge funding from the Agence Nationale de la Recherche, LabEx Tec 21, and CONICYT Becas Chile.
A Lagrangian-Lagrangian Model for Two-Phase Bubbly Flow around Circular Cylinder
M. Shademan
2014-06-01
Full Text Available A Lagrangian-Lagrangian model is developed using an in-house code to simulate bubble trajectory in two-phase bubbly flow around circular cylinder. Random Vortex Method (RVM which is a Lagrangian approach is used for solving the liquid phase. The significance of RVM relative to other RANS/LES methods is its capability in directly modelling the turbulence. In RVM, turbulence is modeled by solving the vorticity transport equation and there is no need to use turbulence closure models. Another advantage of RVM relative to other CFD approaches is its independence from mesh generation. For the bubbles trajectory, equation of motion of bubbles which takes into account effect of different forces are coupled with the RVM. Comparison of the results obtained from current model with the experimental data confirms the validity of the model. Effect of different parameters including flow Reynolds number, bubble diameter and injection point on the bubbles' trajectory are investigated. Results show that increase in the Reynolds number reduces the rising velocity of the bubbles. Similar behavior is observed for the bubbles when their diameter was decreased. According to the analysis carried out, present Lagrangian-Lagrangian model solves the issues of mesh generation and turbulence modelling which exist in common two phase flow modelling schemes.
Numerical simulations of viscoelastic flows with free surfaces
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2013-01-01
We present a new methodology to simulate viscoelastic flows with free-surfaces. These simulations are motivated by the modelling of polymers manufacturing techniques, such as extrusion and injection moulding. One of the consequences of viscoelasticity is that polymeric materials have a “memory...
Rasmussen, Henrik Koblitz
2000-01-01
A new finite element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represents a further development of the 3D Lagrangian integral method (3D-LIM) from an upper...... convected Maxwell fluid to a fluid described by an integral constitutive equation of the Rivlin-Sawyers type. This includes the K-BKZ model. The convergence of the method is demonstrated on the axisymmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring....
The viscoelastic flow behavior of pitches
Fleurot, Olivier
1998-11-01
For the first time, a commercial impregnating coal-tar pitch was air-blown (or heat-treated) for various periods of time to produce series of treated pitches. Each pitch was chemically and rheologically characterized. During air-blowing, the formation of large, aromatic, cross- linked molecules increased the elasticity of the pitch and prevented mesophase formation. During heat-treatment, large, planar, aromatic molecules formed and aggregated in mesophase spheres. These two-phase materials exhibited yield stress behavior. Also, their elasticity was similar to that of air-blown pitches. The flow/microstructure relationship in mesophase pitches was investigated. It was found that the steady and transient shear behaviors of mesophase pitches were qualitatively similar to that of LCPs. Also, the size of the structure decreased with increasing shear rate. Upon cessation of flow, the structure slowly coarsened. New techniques were proposed to estimate (1) relaxation time for structure recovery, and (2) the average elastic constant of mesophase pitches. Using Marrucci's model (originally designed for LCPs) it was possible for the first time to predict mesophase pitches' structure shrinkage during pure shear. Finally, the flow-induced structural development that occurs during extrusion of mesophase pitch through capillaries was observed and accurately predicted by coupling computational fluid dynamics (CFD) to Marrucci's model. Using a viscoelastic stress tensor to characterize the pitch flow behavior, the model was able to accurately predict the magnitude of the vortex experimentally observed at the spinnerette capillary counterbore as well as the extend of die swell at the exit of the capillary.
Lagrangian structures in time-periodic vortical flows
S. V. Kostrykin
2006-01-01
Full Text Available The Lagrangian trajectories of fluid particles are experimentally studied in an oscillating four-vortex velocity field. The oscillations occur due to a loss of stability of a steady flow and result in a regular reclosure of streamlines between the vortices of the same sign. The Eulerian velocity field is visualized by tracer displacements over a short time period. The obtained data on tracer motions during a number of oscillation periods show that the Lagrangian trajectories form quasi-regular structures. The destruction of these structures is determined by two characteristic time scales: the tracers are redistributed sufficiently fast between the vortices of the same sign and much more slowly transported into the vortices of opposite sign. The observed behavior of the Lagrangian trajectories is quantitatively reproduced in a new numerical experiment with two-dimensional model of the velocity field with a small number of spatial harmonics. A qualitative interpretation of phenomena observed on the basis of the theory of adiabatic chaos in the Hamiltonian systems is given. The Lagrangian trajectories are numerically simulated under varying flow parameters. It is shown that the spatial-temporal characteristics of the Lagrangian structures depend on the properties of temporal change in the streamlines topology and on the adiabatic parameter corresponding to the flow. The condition for the occurrence of traps (the regions where the Lagrangian particles reside for a long time is obtained.
NUMERICAL SIMULATIONS OF VISCOELASTIC FLOWS THROUGH ONE SLOT CHANNEL
YIN Hong-jun; ZHONG Hui-ying; FU Chun-quan; WANG Lei
2007-01-01
In this article, the Modified Upper-Convected Maxwell equation (MUCM) is proposed. The viscoelastic polymer solution flow characteristics are described by the numerical method. The stream function contour, velocity contour and stress modulus contour of fluid in slot channel are drawn. The non-Newtonian power law property and viscoelasticity of MUCM fluid influence on the stream function are analyzed. The velocity contour move towards dead oil area with the viscoelasticity increase, flow area increase and the sweep area enlarges, so the sweep efficiency is enhanced.
Oscillatory and electrohydrodynamic instabilities in flow over a viscoelastic gel
R M Thaokar
2015-05-01
The stability of oscillatory flows over compliant surfaces is studied analytically and numerically. The type of compliant surfaces studied is the incompressible viscoelastic gel model. The stability is determined using the Floquet analysis, where amplitude of perturbations at time intervals separated by one time period is examined to determine whether perturbations grow or decay. Oscillatory flows pas viscoelastic gels exhibit an instability in the limit of zero Reynolds number, and the transition amplitude of the oscillatory velocity increases with the frequency of oscillations. The transition amplitude has a minimum at a finite wavenumber for the viscoelastic gel model. The instability is found to depend strongly on the gel viscosity $\\eta_{g}$, and the effect of oscillations on the continuation of viscous modes at intermediate Reynolds number shows a complicated dependence on the oscillation frequency. Experimental studies are carried out on the stability of an oscillatory flow past a viscoelastic gel at zero Reynolds number, and these confirm the theoretical predictions.
Lid-driven cavity flow of viscoelastic liquids
Sousa, R G; Afonso, A M; Pinho, F T; Oliveira, P J; Morozov, A; Alves, M A
2016-01-01
The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical methods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation formulation, is used in this work to probe the effect of viscoelasticity on the appearance of such instabilities in two-dimensional lid-driven cavities for a wide range of aspect ratios (0.125 < height/length < 4.0), at different Deborah numbers under creeping-flow conditions and to understand the effects of regularization of the lid velocity. The effect of the viscoelasticity on the steady-state results and on the critical conditions for the onset of the elastic instabilities are described and compared to experimental results.
New Lagrangian diagnostics for characterizing fluid flow mixing
Mundel, Ruty; Gildor, Hezi; Rom-Kedar, Vered
2014-01-01
A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two- (and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.
Lagrangian statistics and flow topology in forced 2-D turbulence
Kadoch, B. [Universite d' Aix-Marseille; Del-Castillo-Negrete, Diego B [ORNL; Bos, W.J.T. [CNRS, Ecole Centrale de Lyon, Universite Claude Bernard Lyon; Schneider, Kai [Universite d' Aix-Marseille
2011-01-01
A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order - 2.
HYDROMAGNETIC DIVERGENT CHANNEL FLOW OF A VISCOELASTIC ELECTRICALLY CONDUCTING FLUID
RITA CHOUDHURY
2011-10-01
Full Text Available A theoretical study for the two-dimensional boundary layer flow through a divergent channel of a visco-elastic electrically conducting fluid in presence of transverse magnetic field has been considered. Similarity solutions are obtained by considering a special form of magnetic field. The analytical expressions for velocity and skin friction at the wall have been obtained and numerically worked out for different values of the flow parametersinvolved in the solution. The velocity and the skin friction coefficient have been presented graphically to observe the visco-elastic effects for various values of the flow parameters across the boundary layer.
The Lagrangian Deformation Structure of Three-Dimensional Steady Flow
Lester, Daniel R; Borgne, Tanguy Le; de Barros, Felipe P J
2016-01-01
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures (LCSs). To understand and model these processes it is necessary to quantify Lagrangian deformation in terms of Eulerian flow properties, currently an open problem. To elucidate this link we develop a Protean (streamline) coordinate transform for steady three-dimensional (3D) flows which renders both the velocity gradient and deformation gradient upper triangular. This frame not only simplifies computation of fluid deformation metrics such as fi?nite-time Lyapunov exponents (FTLEs) and elucidates the deformation structure of the flow, but moreover explicitly recovers kinematic and topological constraints upon deformation such as those related to helicity density and the Poincar\\'{e}-Bendixson theorem. We apply this transform to several classes of steady 3D flow, including helical ...
Simulations of flow induced ordering in viscoelastic fluids
Santos de Oliveira, I.S.
2012-01-01
In this thesis we report on simulations of colloidal ordering phenomena in shearthinning viscoelastic fluids under shear flow. Depending on the characteristics of the fluid, the colloids are observed to align in the direction of the flow. These string-like structures remain stable as long as the she
Lagrangian chaos in three- dimensional steady buoyancy-driven flows
Contreras, Sebastian; Speetjens, Michel; Clercx, Herman
2016-11-01
Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. The Lagrangian dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices
Huhn, F.; van Rees, W. M.; Gazzola, M.; Rossinelli, D.; Haller, G.; Koumoutsakos, P.
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
Quantitative flow analysis of swimming dynamics with coherent Lagrangian vortices.
Huhn, F; van Rees, W M; Gazzola, M; Rossinelli, D; Haller, G; Koumoutsakos, P
2015-08-01
Undulatory swimmers flex their bodies to displace water, and in turn, the flow feeds back into the dynamics of the swimmer. At moderate Reynolds number, the resulting flow structures are characterized by unsteady separation and alternating vortices in the wake. We use the flow field from simulations of a two-dimensional, incompressible viscous flow of an undulatory, self-propelled swimmer and detect the coherent Lagrangian vortices in the wake to dissect the driving momentum transfer mechanisms. The detected material vortex boundary encloses a Lagrangian control volume that serves to track back the vortex fluid and record its circulation and momentum history. We consider two swimming modes: the C-start escape and steady anguilliform swimming. The backward advection of the coherent Lagrangian vortices elucidates the geometry of the vorticity field and allows for monitoring the gain and decay of circulation and momentum transfer in the flow field. For steady swimming, momentum oscillations of the fish can largely be attributed to the momentum exchange with the vortex fluid. For the C-start, an additionally defined jet fluid region turns out to balance the high momentum change of the fish during the rapid start.
NUMERICAL ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW
穆君; 冯民富
2004-01-01
We present the numerical analysis of a coupled method for the numerical simulation of transient viscoelastic flow obeying a differential constitutive equation with a Newtonian viscosity. The scheme used is based on Euler implicit method in time and maintains at each time step a couple of the velocity u and the viscoelastic part of the stress σ. Approximation in space is made by finite element method. The approximate stress, velocity and pressure are, respectively, P1-continuous, p2-continuous, and p1continuous. Upwinding needed for convection of σ is made by a "Streamline Upwind Petrov Galerkin" method (SUPG).
Flow of Viscoelastic Polymer Solutions through Filter Screens
Machač, Ivan; Surý, Alexander; Šiška, Bedřich
2011-07-01
In this contribution, the measurements are presented of the pressure drop in the creeping flow of viscoelastic solution of polyacrylamides through metal wire screens, differing in wire diameter, aperture dimension, and type of weaving. In this flow, a strong elastic pressure drop excess manifest itself. Analysing the extensive set of experimental data, it was verified that for engineering estimation of the pressure drop excess, a simple form of the corrective Deborah number function can be used.
Finite Spectral Semi-Lagrangian Method for Incompressible Flows
LI Shao-Wu; WANG Jian-Ping
2012-01-01
A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability. The finite spectrai basis function is C1 continuous at the boundary and is easy to construct. Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady Sows around airfoil with different angles of attack.%A new semi-Lagrangian (SL) scheme is proposed by using finite spectral regional interpolation and adequate numerical dissipation to control the nonlinear instability.The finite spectral basis function is C1 continuous at the boundary and is easy to construct.Comparison between numerical and experimental results indicates that the present method works well in solving incompressible Navier-Stokes equations for unsteady flows around airfoil with different angles of attack.
Advances in the analysis and prediction of turbulent viscoelastic flows
Gatski, T. B.; Thais, L.; Mompean, G.
2014-08-01
It has been well-known for over six decades that the addition of minute amounts of long polymer chains to organic solvents, or water, can lead to significant turbulent drag reduction. This discovery has had many practical applications such as in pipeline fluid transport, oil well operations, vehicle design and submersible vehicle projectiles, and more recently arteriosclerosis treatment. However, it has only been the last twenty-five years that the full utilization of direct numerical simulation of such turbulent viscoelastic flows has been achieved. The unique characteristics of viscoelastic fluid flow are dictated by the nonlinear differential relationship between the flow strain rate field and the extra-stress induced by the additive polymer. A primary motivation for the analysis of these turbulent fluid flows is the understanding of the effect on the dynamic transfer of energy in the turbulent flow due to the presence of the extra-stress field induced by the presence of the viscoelastic polymer chain. Such analyses now utilize direct numerical simulation data of fully developed channel flow for the FENE-P (Finite Extendable Nonlinear Elastic - Peterlin) fluid model. Such multi-scale dynamics suggests an analysis of the transfer of energy between the various component motions that include the turbulent kinetic energy, and the mean polymeric and elastic potential energies. It is shown that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer.
A Galerkin least squares approach to viscoelastic flow.
Rao, Rekha R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schunk, Peter Randall [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-10-01
A Galerkin/least-squares stabilization technique is applied to a discrete Elastic Viscous Stress Splitting formulation of for viscoelastic flow. From this, a possible viscoelastic stabilization method is proposed. This method is tested with the flow of an Oldroyd-B fluid past a rigid cylinder, where it is found to produce inaccurate drag coefficients. Furthermore, it fails for relatively low Weissenberg number indicating it is not suited for use as a general algorithm. In addition, a decoupled approach is used as a way separating the constitutive equation from the rest of the system. A Pressure Poisson equation is used when the velocity and pressure are sought to be decoupled, but this fails to produce a solution when inflow/outflow boundaries are considered. However, a coupled pressure-velocity equation with a decoupled constitutive equation is successful for the flow past a rigid cylinder and seems to be suitable as a general-use algorithm.
Near critical swirling flow of a viscoelastic fluid
Ly, Nguyen; Rusak, Zvi; Tichy, John; Wang, Shixiao
2016-11-01
The interaction between flow inertia and elasticity in high Re, axisymmetric, and near-critical swirling flows of a viscoelastic fluid in a finite-length straight circular pipe is studied. The viscous stresses are described by the Giesekus constitutive model. The application of this model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It explores the complicated interactions between flow inertia, swirl, and fluid viscosity and elasticity. An effective Re that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development and on the critical swirl for the appearance of vortex breakdown are explored. Decreasing the ratio of the viscoelastic characteristic times from one increases the critical swirl for breakdown. Increasing the Weissenberg number from zero or increasing the fluid mobility parameter from zero cause a similar effect. Results may explain changes in the appearance of breakdown zones as a function of swirl level that were observed in Stokes et al. (2001) experiments, where Boger fluids were used.
k Spectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows
Antonsen, Thomas M., Jr.; Fan, Zhencan Frank; Ott, Edward
1995-08-01
An eikonal-type description for the evolution of k spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar k spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law k spectrum and its diffusive cutoff.
Lagrangian transported MDF methods for compressible high speed flows
Gerlinger, Peter
2017-06-01
This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).
Nonexistence of self-similar singularities in ideal viscoelastic flows
Anthony Suen
2012-06-01
Full Text Available We prove the nonexistence of finite time self-similar singularities in an ideal viscoelastic flow in R^3. We exclude the occurrence of Leray-type self-similar singularities under suitable integrability conditions on velocity and deformation tensor. We also prove the nonexistence of asymptotically self-similar singularities in our system. The present work extends the results obtained by Chae in the case of magnetohydrodynamics (MHD.
Floquet stability analysis of viscoelastic flow over a cylinder
Richter, David
2011-06-01
A Floquet linear stability analysis has been performed on a viscoelastic cylinder wake. The FENE-P model is used to represent the non-Newtonian fluid, and the analysis is done using a modified version of an existing nonlinear code to compute the linearized initial value problem governing the growth of small perturbations in the wake. By measuring instability growth rates over a wide range of disturbance spanwise wavenumbers α, the effects of viscoelasticity were identified and compared directly to Newtonian results.At a Reynolds number of 300, two unstable bands exist over the range 0. ≤ α≤ 10 for Newtonian flow. For the low α band, associated with the "mode A" wake instability, a monotonic reduction in growth rates is found for increasing polymer extensibility L. For the high α band, associated with the "mode B" instability, first a rise, then a significant decrease to a stable state is found for the instability growth rates as L is increased from L= 10 to L= 30. The mechanism behind this stabilization of both mode A and mode B instabilities is due to the change of the base flow, rather than a direct effect of viscoelasticity on the perturbation. © 2011 Elsevier B.V.
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.
A perturbation-theoretic approach to Lagrangian flow networks
Fujiwara, Naoya; Kirchen, Kathrin; Donges, Jonathan F.; Donner, Reik V.
2017-03-01
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.
Stochastic Simulation of Lagrangian Particle Transport in Turbulent Flows
Sun, Guangyuan
This dissertation presents the development and validation of the One Dimensional Turbulence (ODT) multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent-particle mixing and transport at low computational cost. The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes. The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle-eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively. The Type-IC model combines the features of the Type-I and -C models. The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet. Particle dispersion, dispersion coefficients, and velocity statistics are predicted and compared with experimental data. The models accurately reproduces the experimental data sets and capture particle inertial effects and trajectory crossing effect. A new adjustable particle parameter is introduced into the ODT model, and sensitivity analysis is performed to facilitate parameter estimation and selection. A novel algorithm of the two-way momentum coupling between the particle and carrier phases is developed in the ODT multiphase model. Momentum exchange between the phases is accounted for through particle source terms in the viscous diffusion. The source term is implemented in eddy events through a new kernel transformation and an iterative procedure is required for eddy selection. This model is applied to a particle-laden turbulent jet flow, and simulation results are compared with experimental measurements. The effect of particle addition on the velocities of the gas phase is investigated. The development of
Particle migration in two-phase, viscoelastic flows
Jaensson, Nick; Hulsen, Martien; Anderson, Patrick
2014-11-01
Particles suspended in creeping, viscoelastic flows can migrate across stream lines due to gradients in normal stresses. This phenomenon has been investigated both numerically and experimentally. However, particle migration in the presence of fluid-fluid interfaces is hardly studied. We present results of simulations in 2D and 3D of rigid spherical particles in two-phase flows, where either one or both of the fluids are viscoelastic. The fluid-fluid interface is assumed to be diffuse and is described using Cahn-Hilliard theory. The particle boundary is assumed to be sharp and is described by a boundary-fitted, moving mesh. The governing equations are solved using the finite element method. We show that differences in normal stresses between the two fluids can induce a migration of the particle towards the interface in a shear flow. Depending on the magnitude of the surface tension and the properties of the fluids, particle migration can be halted due to the induced Laplace pressure, the particle can be adsorbed at the interface, or the particle can cross the interface into the other fluid. Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands.
Grilli, Muzio; Vázquez-Quesada, Adolfo; Ellero, Marco
2013-04-26
Using Lagrangian simulations of a viscoelastic fluid modeled with an Oldroyd-B constitutive equation, we demonstrate that the flow through a closely spaced linear array of cylinders confined in a channel undergoes a transition to a purely elastic turbulent regime above a critical Weissenberg number (We). The high-We regime is characterized by an unsteady motion and a sudden increase in the flow resistance in qualitative agreement with experimental observations. Furthermore, a power-law scaling behavior of the integral quantities as well as enhanced mixing of mass is observed. A stability analysis based on the dynamic mode decomposition method allows us to identify the most energetic modes responsible for the unsteady behavior, which correspond to filamental structures of polymer over- or underextension advected by the main flow preserving their shape. These time-dependent flow features strictly resemble the elastic waves reported in recent numerical simulations.
Equilibrium circulation and stress distribution in viscoelastic creeping flow
Biello, Joseph A
2015-01-01
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both, as an asymptotic parameter and a regularization parameter. The structure of the singular part of polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point; a smoothed $\\delta$-distribution whose width is proportional to the square-root of the diffusion coefficient. The amplitude of the stress island scales with the Wiessenberg number and, although singular in the limit of vanishing diffusion, it is integrable in the cross stream direction due to its vanishing width; this yields a convergent secondary flow. The leading order velocity response to this...
Vibrational shear flow of anisotropic viscoelastic fluid with small amplitudes
韩式方
2008-01-01
Using the constitutive equation of co-rotational derivative type for anisotropic viscoelastic fluid-liquid crystalline(LC),polymer liquids was developed.Two relaxation times are introduced in the equation:λn represents relaxation of the normal-symmetric stress components;λs represents relaxation of the shear-unsymmetric stress components.A vibrational rotating flow in gap between cylinders with small amplitudes is studied for the anisotropic viscoelastic fluid-liquid crystalline polymer.The time-dependent constitutive equation are linearized with respect to parameter of small amplitude.For the normal-symmetric part of stress tensor analytical expression of the shear stress is obtained by the constitutive equation.The complex viscosity,complex shear modulus,dynamic and imaginary viscosities,storage modulus and loss modulus are obtained for the normal-symmetric stress case which are defined by the common shear rate.For the shear-unsymmetric stress part,two shear stresses are obtained thus two complex viscosities and two complex shear modulus(i.e.first and second one) are given by the constitutive equation which are defined by rotating shear rate introduced by author.The dynamic and imaginary viscosities,storage modulus and loss modulus are given for each complex viscosities and complex shear modulus.Using the constituive equation the rotating flow with small amplitudes in gap between two coaxial cylinders is studied.
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.
Fast multipole method applied to Lagrangian simulations of vortical flows
Ricciardi, Túlio R.; Wolf, William R.; Bimbato, Alex M.
2017-10-01
Lagrangian simulations of unsteady vortical flows are accelerated by the multi-level fast multipole method, FMM. The combination of the FMM algorithm with a discrete vortex method, DVM, is discussed for free domain and periodic problems with focus on implementation details to reduce numerical dissipation and avoid spurious solutions in unsteady inviscid flows. An assessment of the FMM-DVM accuracy is presented through a comparison with the direct calculation of the Biot-Savart law for the simulation of the temporal evolution of an aircraft wake in the Trefftz plane. The role of several parameters such as time step restriction, truncation of the FMM series expansion, number of particles in the wake discretization and machine precision is investigated and we show how to avoid spurious instabilities. The FMM-DVM is also applied to compute the evolution of a temporal shear layer with periodic boundary conditions. A novel approach is proposed to achieve accurate solutions in the periodic FMM. This approach avoids a spurious precession of the periodic shear layer and solutions are shown to converge to the direct Biot-Savart calculation using a cotangent function.
A Study on Viscoelastic Fluid Flow in a Square-Section 90-Degrees Bend
Mizue Munekata; Kazuyoshi Matsuzaki; Hideki Ohba
2003-01-01
It is well known that the drag-reducing effect is obtained in a surfactant solution flow in a straight pipe. We investigate about a viscoelastic fluid flow such as a surfactant solution flow in a square-section 90° bend. In the experimental study, drag-reducing effect and velocity field in a surfactant solution flow are investigated by measurements of wall pressure loss and LDV measurements. For the numerical method, LES with FENE-P model is used in the viscoelastic fluid flow in the bend. The flow characteristics of viscoelastic fluid are discussed compared with that of a Newtonian fluid.
Viscoelastic Multicomponent Fluids in confined Flow-Focusing Devices
Gupta, Anupam
2015-01-01
The effects of elasticity on the break-up of liquid threads in microfluidic cross-junctions is investigated using numerical simulations based on the "lattice Boltzmann models" (LBM). Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) and droplet formation downstream of the cross-junction (DC) (Liu & Zhang, ${\\it Phys. Fluids.}$ ${\\bf 23}$, 082101 (2011)). Viscoelasticity is found to influence the break-up point of the threads, which moves closer to the cross-junction and stabilizes. This is attributed to an increase of the polymer feedback stress forming in the corner flows, where the side channels of the device meet the main channel.
Viscoelastic capillary flow: the case of whole blood
David Rabaud
2016-07-01
Full Text Available The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.In this work we consider the Herschel-Bulkley (HB rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids, the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM law for power-law fluids. Although HB model cannot reduce to Casson’s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.
Intermittent Lagrangian velocities and accelerations in three-dimensional porous medium flow.
Holzner, M; Morales, V L; Willmann, M; Dentz, M
2015-07-01
Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.
Bridging from Eulerian to Lagrangian statistics in 3D hydro- and magnetohydrodynamic turbulent flows
Homann, H [CNRS, Universite de Nice-Sophia Antipolis, Observatoire de la Cote d' Azur, Lab. Cassiopee, Bd. de l' Observatoire, 06300 Nice (France); Kamps, O [Center for Nonlinear Science, Universitaet Muenster, 48149 Muenster (Germany); Friedrich, R [Theoretische Physik, Universitaet Muenster, 48149 Muenster (Germany); Grauer, R [Theoretische Physik I, Ruhr-Universitaet, 44780 Bochum (Germany)], E-mail: grauer@tp1.rub.de
2009-07-15
We present measurements of conditional probability density functions (PDFs) that allow one to systematically bridge from Eulerian to Lagrangian statistics in fully developed 3D turbulence. The transition is investigated for hydro- as well as magnetohydrodynamic flows and comparisons are drawn. Significant differences in the transition PDFs are observed for these flows and traced back to the differing coherent structures. In particular, we address the problem of an increasing degree of intermittency going from Eulerian to Lagrangian coordinates by means of the conditional PDFs involved in this transformation. First simple models of these PDFs are investigated in order to distinguish different contributions to the degree of Lagrangian intermittency.
Spherical particle sedimenting in weakly viscoelastic shear flow
Einarsson, J
2016-01-01
We consider the dynamics of a small spherical particle driven through an unbounded viscoelastic shear flow by an external force. We give analytical solutions to both the mobility problem (velocity of forced particle) and the resistance problem (force on fixed particle), valid to second order in the dimensionless Deborah and Weissenberg numbers, which represent the elastic relaxation time of the fluid relative to the rate of translation and the imposed shear rate. We find a shear-induced lift at $O({\\rm Wi})$, a modified drag at $O({\\rm De}^2)$ and $O({\\rm Wi}^2)$, and a second lift that is orthogonal to the first, at $O({\\rm Wi}^2)$. The relative importance of these effects depends strongly on the orientation of the forcing relative to the shear. We discuss how these forces affect the terminal settling velocity in an inclined shear flow. We also describe a new basis set of symmetric Cartesian tensors, and demonstrate how they enable general tensorial perturbation calculations such as the present theory. In pa...
An Eulerian-Lagrangian open source solver for bubbly flow in vertical pipes
Pena-Monferrer, C.; Munoz-Cobo, J. L.; Monros-Andreu, G.; Martinez-Cuenca, R.; Chiva, S.
2014-07-01
Air-water two-phase flow is present in natural and industrial processes of different nature as nuclear reactors. An accurate local prediction of the boiling flow could support safety and operation analyses of nuclear reactors. An Eulerian-Lagrangian approach is investigated in this contribution as it can be used as a virtual facility to investigate the two-phase flow phenomena. A solver based on the PISO algorithm coupled with the Lagrangian equation of motion have been implemented for computing incompressible bubbly flows. (Author)
Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid
Sufian Munawar
2014-01-01
Full Text Available This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0≤τ<∞. Flow properties of the viscoelastic fluid are discussed through graphs.
A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows
Felici, Helene Marie
1992-06-01
A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.
Lagrangian filtered density function for LES-based stochastic modelling of turbulent dispersed flows
Innocenti, A; Chibbaro, S
2016-01-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study turbulent dispersed flows when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGS) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves for a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided b...
A non-conventional discontinuous Lagrangian for viscous flow
Scholle, M.; Marner, F.
2017-02-01
Drawing an analogy with quantum mechanics, a new Lagrangian is proposed for a variational formulation of the Navier-Stokes equations which to-date has remained elusive. A key feature is that the resulting Lagrangian is discontinuous in nature, posing additional challenges apropos the mathematical treatment of the related variational problem, all of which are resolvable. In addition to extending Lagrange's formalism to problems involving discontinuous behaviour, it is demonstrated that the associated equations of motion can self-consistently be interpreted within the framework of thermodynamics beyond local equilibrium, with the limiting case recovering the classical Navier-Stokes equations. Perspectives for applying the new formalism to discontinuous physical phenomena such as phase and grain boundaries, shock waves and flame fronts are provided.
Stochastic Lagrangian dynamics for charged flows in the E-F regions of ionosphere
Tang, Wenbo; Mahalov, Alex
2013-03-01
We develop a three-dimensional numerical model for the E-F region ionosphere and study the Lagrangian dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic Lagrangian motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using Lagrangian coherent structures (LCS). LCS objectively depict the flow topology—the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using Lagrangian measures such as the finite-time Lyapunov exponents, we locate the Lagrangian skeletons for mixing in plasma, hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic Lagrangian motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.
Machicoane, Nathanaël
2015-01-01
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization using two-time models (for instance Saw-ford's). As particles are tracked over long times in the quasi totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly usef...
Pratt, J; Mueller, W -C; Chapman, S C; Watkins, N W
2014-01-01
Local regions of anomalous particle dispersion, and intermittent events that occur in turbulent flows can greatly influence the global statistical description of the flow. These local behaviors can be identified and analyzed by comparing the growth of neighboring convex hulls of Lagrangian tracer particles. Although in our simulations of homogeneous turbulence the convex hulls generally grow in size, after the Lagrangian particles that define the convex hulls begin to disperse, our analysis reveals short periods when the convex hulls of the Lagrangian particles shrink, evidence that particles are not dispersing simply. Shrinkage can be associated with anisotropic flows, since it occurs most frequently in the presence of a mean magnetic field or thermal convection. We compare dispersion between a wide range of statistically homogeneous and stationary turbulent flows ranging from homogeneous isotropic Navier-Stokes turbulence over different configurations of magnetohydrodynamic turbulence and Boussinesq convect...
Stability of a Two-Dimensional Poiseuille-Type Flow for a Viscoelastic Fluid
Endo, Masakazu; Giga, Yoshikazu; Götz, Dario; Liu, Chun
2017-03-01
A viscoelastic flow in a two-dimensional layer domain is considered. An L 2-stability of the Poiseuille-type flow is established provided that both Poiseuille flow and perturbation is sufficiently small. Our analysis is based on a stream function formulation introduced by Lin et al. (Commun Pure Appl Math 58(11):1437-1471, 2005).
Exact Solution of Unsteady Flow of Viscoelastic Fluid in a Pipe with Fractional Maxwell Model
无
2007-01-01
The unsteady flow of viscoelastic fluid in a cylindrical pipe was investigated using the fractional Maxwell model. Two special cases of unsteady pipe flow were expressed. The first is start-up flow, and the second is oscillating flow. The exact solution of start-up flow under a constant pressure gradient was obtained by using the theories of Laplace transform and Fourier-Bessel series for fractional derivatives. The exact solution of oscillating flow was obtained by utilizing the separation of variables.
Implementation of the Log-Conformation Formulation for Two-Dimensional Viscoelastic Flow
Jensen, K E; Okkels, F
2015-01-01
We have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a cross-slot geometry for a FENE-CR fluid, and we describe the changes required for performing simulations with the Phan-Thien-Tanner (PTT), Giesekus and FENE-P models. Finally, we calculate the flow of a FENE-CR fluid in a geometry with three in- and outlets. The implementation is included in the supplementary material, and we hope that it can inspire new as well as experienced researchers in the field of differential constitutive equations for viscoelastic flow.
Oscillatory squeeze flow for the study of linear viscoelastic behavior
Wingstrand, Sara Lindeblad; Alvarez, Nicolas J.; Hassager, Ole
2016-01-01
The squeezing of a sample between parallel plates has been used for many years to characterize the rheological behavior of soft, purely viscous materials, and in recent times, small-amplitude oscillatory squeezing has been proposed as a means to determine the linear viscoelastic properties of mol...
Consistent treatment of viscoelastic effects at junctions in one-dimensional blood flow models
Müller, Lucas O.; Leugering, Günter; Blanco, Pablo J.
2016-06-01
While the numerical discretization of one-dimensional blood flow models for vessels with viscoelastic wall properties is widely established, there is still no clear approach on how to couple one-dimensional segments that compose a network of viscoelastic vessels. In particular for Voigt-type viscoelastic models, assumptions with regard to boundary conditions have to be made, which normally result in neglecting the viscoelastic effect at the edge of vessels. Here we propose a coupling strategy that takes advantage of a hyperbolic reformulation of the original model and the inherent information of the resulting system. We show that applying proper coupling conditions is fundamental for preserving the physical coherence and numerical accuracy of the solution in both academic and physiologically relevant cases.
Nonlinear dynamics aspects of subcritical transitions and singular flows in viscoelastic fluids
Becherer, Paul
2008-01-01
Recently, there has been a renewed interest in theoretical aspects of flows of viscoelastic fluids (such as dilute polymer solutions). This thesis addresses two distinct issues related to such flows. Motivated by the possible occurrence of subcritical (finite-amplitude) instabilities in parallel flo
Haitao Qi; Hui Jin
2006-01-01
The fractional calculus is used in the constitutive relationship model of viscoelastic fluid.A generalized Maxwell model with fractional calculus is considered.Based on the flow conditions described,two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.
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
k Spectrum of Finite Lifetime Passive Scalars in Lagrangian Chaotic Fluid Flows
Nam, Keeyeol; Antonsen, Thomas M., Jr.; Guzdar, Parvez N.; Ott, Edward
1999-10-01
The power law exponent for the wave number power spectrum of a passive scalar field in Lagrangian chaotic flows is found to differ from the classical value of -1 (Batchelor's law) when the passive particles have a finite lifetime for exponential decay. A theory based on the chaotic dynamics of the passive scalar is developed and compared to numerical simulation results.
Besse, Nicolas; Frisch, Uriel
2017-04-01
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.
Besse, Nicolas; Frisch, Uriel
2017-01-01
The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.
Lagrangian flows within reflecting internal waves at a horizontal free-slip surface
Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA (United Kingdom); Diamessis, Peter J. [School of Civil and Environmental Engineering, Cornell University, Ithaca, New York 14853 (United States)
2015-12-15
In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider Lagrangian flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking Lagrangian fluid particles in direct numerical simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian mean flow due to wave-wave interaction and wave-induced Stokes drift cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero Lagrangian mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean Lagrangian flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean Lagrangian drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.
The flow of a viscoelastic fluid in a spherical pendulum
Nikolakis, D.
Stationary drift in a spherical cavity filled with viscoelastic fluid and in constant pendular motion suspended from a hinged rod is investigated analytically. The derivation of the governing equations is outlined, and numerical results from parametric studies are presented in graphs and streamline diagrams. It is shown that a reversal can occur in the stationary drift near the meridian plane due to the 'competition' between normal stress and inertia.
Heat Transfer to MHD Oscillatory Viscoelastic Flow in a Channel Filled with Porous Medium
Rita Choudhury
2012-01-01
Full Text Available The combined effect of a transverse magnetic field and radiative heat transfer on unsteady flow of a conducting optically thin viscoelastic fluid through a channel filled with saturated porous medium and nonuniform walls temperature has been discussed. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. Closed-form analytical solutions are constructed for the problem. The effects of the radiation and the magnetic field parameters on velocity profile and shear stress for different values of the viscoelastic parameter with the combination of the other flow parameters are illustrated graphically, and physical aspects of the problem are discussed.
FINITE VOLUME METHOD FOR SIMULATION OF VISCOELASTIC FLOW THROUGH A EXPANSION CHANNEL
FU Chun-quan; JIANG Hai-mei; YIN Hong-jun; SU Yu-chi; ZENG Ye-ming
2009-01-01
A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number (We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.
On the Study of Viscoelastic Walters' B Fluid in Boundary Layer Flows
Seyed Ali Madani Tonekaboni
2012-01-01
Full Text Available Viscoelastic Walters' B fluid flows for three problems, stagnation-point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth-order predictor-corrector finite-difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter's B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second-order approximation of viscoelastic fluids in each case of study.
A mixed finite element scheme for viscoelastic flows with XPP model
Xianhong Han; Xikui Li
2008-01-01
A mixed finite element formulation for viscoe-lastic flows is derived in this paper, in which the FIC (finite incremental calculus) pressure stabilization process and the DEVSS (discrete elastic viscous stress splitting) method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractio-nal step algorithm. The SU (streamline-upwind) method is particularly chosen to tackle the convective terms in constitu-tive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpola-tion approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP (extended Pom-Pom) consti-tutive model for describing viscoelastic behaviors is particu-larly integrated into the proposed scheme. The numerical results for the 4:1 sudden contraction flow problem demons-trate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of the Weissenberg number, particularly the capability in reproducing the results, which can be used to explain the "die swell" phenomenon observed in the polymer injection molding process.
Modeling and simulation challenges in Eulerian-Lagrangian computations of multiphase flows
Diggs, Angela; Balachandar, S.
2017-01-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Grid-Based (GB) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Particle-Based (PB) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of PB methods. By evaluating the total error and its components we compare the performance of GB and PB methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities.
Viscoelastic fluid-structure interaction between a non-Newtonian fluid flow and flexible cylinder
Dey, Anita; Modarres-Sadeghi, Yahya; Rothstein, Jonathan
2016-11-01
It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to a purely elastic flow instability. In this talk, we will present a series of experiments investigating the response of a flexible cylinder placed in the cross flow of a viscoelastic fluid. The elastic flow instabilities occurring at high Weissenberg numbers can exert fluctuating forces on the flexible cylinder thus leading to nonlinear periodic oscillations of the flexible structure. These oscillations are found to be coupled to the time-dependent state of viscoelastic stresses in the wake of the flexible cylinder. The static and dynamic responses of the flexible cylinder will be presented over a range of flow velocities, along with measurements of velocity profiles and flow-induced birefringence, in order to quantify the time variation of the flow field and the state of stress in the fluid.
Santos de Oliveira, I.S.; Otter, den W.K.; Briels, W.J.
2013-01-01
Computer simulations are presented of colloids, bidisperse in size, suspended in a shear-thinning viscoelastic fluid with the flow characteristics of a surfactant solution. The worm-like micelles are modeled in Responsive Particle Dynamics (RaPiD) as single soft particles obeying a generalized Brown
Nguyen, T.; Berg, van den A.; Eijkel, J.C.T.
2015-01-01
We present an in-depth analysis and analytical solution for AC hydrodynamic flow (driven by a timedependent pressure gradient and/or electric fields) of viscoelastic fluid through cylindrical micro-, nanochannels. Particularly, for this purpose we solve the linearized Poisson-Boltzmann equation tog
Lagrangian analysis of fluid transport in empirical vortex ring flows
Shadden, Shawn C.; Dabiri, John O.; Marsden, Jerrold E.
2006-01-01
In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynami...
Innocenti, Alessio; Marchioli, Cristian; Chibbaro, Sergio
2016-11-01
The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is provided by LES and then used to advance the SDEs in time. The model consistency is assessed in the limit of particles with zero inertia, when "duplicate fields" are available from both the Eulerian LES and the Lagrangian tracking. Tests with inertial particles were performed to examine the capability of the model to capture the particle preferential concentration and near-wall segregation. Upon comparison with DNS-based statistics, our results show improved accuracy and considerably reduced errors with respect to the case in which no SGS model is used in the equations of particle motion.
AN UNSTEADY SEEPAGE FLOW MODEL OF VISCO-ELASTIC POLYMER SOLUTION
YIN Hong-jun; FU Chun-quan; LV Yan-ping
2004-01-01
With the consideration of the visco-elasticity,the adsorption effect and the variation of rheological parameters, a seepage flow model of visco-elastic polymer solutions was established. The model was numerically treated with the finite difference method. Then curves of Bottom Hole Pressure (BHP) and formation pressure were drawn. The influences of the relaxation time, the injection rate, the permeability reduction co efficient, the consistency coefficient and the power-law exponent of the injected fluid on pressure performance were analyzed. This study shows that it is necessary to consider the visco-elasticity of non-Newtonian fluid in analyzing of pressure performance in the polymer flooding.
Role of viscoelasticity in instability in plane shear flow over a deformable solid
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.
A new Lagrangian method for three-dimensional steady supersonic flows
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
In this report, the new Lagrangian method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) scheme is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.
Pressure-field extraction from Lagrangian flow measurements: first experiences with 4D-PTV data
Neeteson, N. J.; Bhattacharya, S.; Rival, D. E.; Michaelis, D.; Schanz, D.; Schröder, A.
2016-06-01
As a follow-up to a previous proof-of-principle study, a novel Lagrangian pressure-extraction technique is analytically evaluated, and experimentally validated using dense 4D-PTV data. The technique is analytically evaluated using the semi-three-dimensional Taylor-Green vortex, and it is found that the Lagrangian technique out-performs the standard Eulerian technique when Dirichlet boundary conditions are enforced. However, the Lagrangian technique produces worse estimates of the pressure field when Neumann boundary conditions are enforced on boundaries with strong pressure gradients. The technique is experimentally validated using flow data obtained for the case of a free-falling, index-matched sphere at Re=2100. The experimental data were collected using a four-camera particle tracking velocimetry measurement system, and processed using 4D-PTV. The pressure field is then extracted using both the Eulerian and Lagrangian techniques, and the resulting pressure fields are compared. Qualitatively, the pressure fields agree; however, quantitative differences are found with respect to the magnitude of the pressure minima on the side of the sphere. Finally, the pressure-drag coefficient is estimated using each technique, and the two techniques are found to be in very close agreement. A comparison to a reference value from literature confirms that the drag coefficient estimates are reasonable, demonstrating the validity of the technique.
Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary
Stankiewicz, W.; Roszak, R.; Morzyński, M.
2013-06-01
Flow-induced deflections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like flutter or buffeting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the flow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-fidelity computations. The motion of the boundary and mesh is defined in Arbitrary Lagrangian-Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a flow around an oscillating wing.
A semi-Lagrangian gas-kinetic scheme for smooth flows
Wang, Peng
2014-01-01
In this paper, a semi-Lagrangian gas-kinetic scheme is developed for smooth flows based on the Bhatnagar-Gross-Krook (BGK) equation. As a finite-volume scheme, the evolution of the average flow variables in a control volume is under the Eulerian framework, whereas the construction of the numerical flux across the cell interface comes from the Lagrangian perspective. The adoption of the Lagrangian aspect makes the collision and the transport mechanisms intrinsically coupled together in the flux evaluation. As a result, the time step is independent of the particle collision time and solely determined by the Courant-Friedrichs-Lewy (CFL) conditions. A set of simulations are carried out to validate the performance of the new scheme. The results show that with second-order spatial accuracy, the scheme exhibits low numerical dissipation, and can accurately capture the Navier-Stokers solutions for the smooth flows with viscous heat dissipation from the low-speed incompressible to hypersonic compressible regimes.
Hiong Yap Gan
2012-12-01
Full Text Available Viscoelastically induced flow instabilities, via a simple planar microchannel, were previously used to produce rapid mixing of two dissimilar polymeric liquids (i.e. at least a hundredfold different in shear viscosity even at a small Reynolds number. The unique advantage of this mixing technology is that viscoelastic liquids are readily found in chemical and biological samples like organic and polymeric liquids, blood and crowded proteins samples; their viscoelastic properties could be exploited. As such, an understanding of the underlying interactions will be important especially in rapid microfluidic mixing involving multiple-stream flow of complex (viscoelastic fluids in biological assays. Here, we use the same planar device to experimentally show that the elasticity ratio (i.e. the ratio of stored elastic energy to be relaxed between two liquids indeed plays a crucial role in the entire flow kinematics and the enhanced mixing. We demonstrate here that the polymer stretching dynamics generated in the upstream converging flow and the polymer relaxation events occurring in the downstream channel are not exclusively responsible for the transverse flow mixing, but the elasticity ratio is also equally important. The role of elasticity ratio for transverse flow instability and the associated enhanced mixing were illustrated based on experimental observations. A new parameter Deratio = Deside / Demain (i.e. the ratio of the Deborah number (De of the sidestream to the mainstream liquids is introduced to correlate the magnitude of energy discontinuity between the two liquids. A new Deratio-Demain operating space diagram was constructed to present the observation of the effects of both elasticity and energy discontinuity in a compact manner, and for a general classification of the states of flow development.
Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel
Lim, C. P.; Lam, Y. C., E-mail: myclam@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798 (Singapore); BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602 (Singapore); Han, J. [BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602 (Singapore); Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2015-07-15
Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO) and another immiscible fluid (silicone oil). A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxation times. The flows were shown to be chaotic through the computation of their correlation dimension (D{sub 2}) and the largest Lyapunov exponent (λ{sub 1}), with D{sub 2} being fractional and λ{sub 1} being positive. Contour maps of D{sub 2} and λ{sub 1} of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D{sub 2} and λ{sub 1} maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.
Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel
C. P. Lim
2015-07-01
Full Text Available Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO and another immiscible fluid (silicone oil. A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxation times. The flows were shown to be chaotic through the computation of their correlation dimension (D2 and the largest Lyapunov exponent (λ1, with D2 being fractional and λ1 being positive. Contour maps of D2 and λ1 of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D2 and λ1 maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.
RICHTER, DAVID
2010-03-29
The results from a numerical investigation of inertial viscoelastic flow past a circular cylinder are presented which illustrate the significant effect that dilute concentrations of polymer additives have on complex flows. In particular, effects of polymer extensibility are studied as well as the role of viscoelasticity during three-dimensional cylinder wake transition. Simulations at two distinct Reynolds numbers (Re = 100 and Re = 300) revealed dramatic differences based on the choice of the polymer extensibility (L2 in the FENE-P model), as well as a stabilizing tendency of viscoelasticity. For the Re = 100 case, attention was focused on the effects of increasing polymer extensibility, which included a lengthening of the recirculation region immediately behind the cylinder and a sharp increase in average drag when compared to both the low extensibility and Newtonian cases. For Re = 300, a suppression of the three-dimensional Newtonian mode B instability was observed. This effect is more pronounced for higher polymer extensibilities where all three-dimensional structure is eliminated, and mechanisms for this stabilization are described in the context of roll-up instability inhibition in a viscoelastic shear layer. © 2010 Cambridge University Press.
Lagrangian viscoelastic flow computations using a generalized molecular stress function model
Rasmussen, Henrik K.
2002-01-01
–Sawyers fluid to a fluid described by a generalized molecular stress function (MSF) model allowing the use of dissipative convective constraint release in the constitutive equation. The convergence of the method is demonstrated on the axis-symmetric problem of the inflation of a polymeric membrane only...
Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids.
Ferrás, L L; Afonso, A M; Alves, M A; Nóbrega, J M; Pinho, F T
2014-04-15
In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.
The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves
Takahashi, M.; Uryu, M.
1981-01-01
The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane. It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant. Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height. In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height. In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations.
The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows
Lufkin, Eric A.; Hawley, John F.
1993-01-01
We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.
Elasto-inertial particle focusing under the viscoelastic flow of DNA solution in a square channel.
Kim, Bookun; Kim, Ju Min
2016-03-01
Particle focusing is an essential step in a wide range of applications such as cell counting and sorting. Recently, viscoelastic particle focusing, which exploits the spatially non-uniform viscoelastic properties of a polymer solution under Poiseuille flow, has attracted much attention because the particles are focused along the channel centerline without any external force. Lateral particle migration in polymer solutions in square channels has been studied due to its practical importance in lab-on-a-chip applications. However, there are still many questions about how the rheological properties of the medium alter the equilibrium particle positions and about the flow rate ranges for particle focusing. In this study, we investigated lateral particle migration in a viscoelastic flow of DNA solution in a square microchannel. The elastic property is relevant due to the long relaxation time of a DNA molecule, even when the DNA concentration is extremely low. Further, the shear viscosity of the solution is essentially constant irrespective of shear rate. Our current results demonstrate that the particles migrate toward the channel centerline and the four corners of a square channel in the dilute DNA solution when the inertia is negligible (elasticity-dominant flow). As the flow rate increases, the multiple equilibrium particle positions are reduced to a single file along the channel centerline, due to the elasto-inertial particle focusing mechanism. The current results support that elasto-inertial particle focusing mechanism is a universal phenomenon in a viscoelastic fluid with constant shear viscosity (Boger fluid). Also, the effective flow rate ranges for three-dimensional particle focusing in the DNA solution were significantly higher and wider than those for the previous synthetic polymer solution case, which facilitates high throughput analysis of particulate systems. In addition, we demonstrated that the DNA solution can be applied to focus a wide range of
Yatou, Hiroki
2010-09-01
We numerically find three types of steady solutions of viscoelastic flows and flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Weissenberg (Wi) and Reynolds (Re) numbers using a spectral element method. The solutions are called "convective," "transition," and "elastic" in ascending order of Wi. In the convective region in the Wi-Re parameter space, convective effect and pressure gradient balance on average. As Wi increases, elastic effect becomes comparable, and the first transition sets in. Through the transition, a separation vortex disappears, and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; the viscous drag significantly drops, and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic effect becomes greater than the convective effect, the second transition occurs but it is relatively moderate. The second transition seems to be governed by the so-called Weissenberg effect. These transitions are not sensitive to driving forces. By a scaling analysis, it is shown that the stress component is proportional to the Reynolds number on the boundary of the first transition in the Wi-Re space. This scaling coincides well with the numerical result.
C. Mendoza
2012-08-01
Full Text Available This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the climate impact of ocean transport processes, we illustrate a 2-D application on altimeter data sets over the area of the Kuroshio Current, although the proposed techniques are general and applicable to arbitrary time dependent aperiodic flows. The first challenge for describing transport in aperiodical time dependent flows is obtaining a representation of the phase portrait where the most relevant dynamical features may be identified. areas that are related to confinement regions. This representation is accomplished by using global Lagrangian descriptors that when applied for instance to the altimeter data sets retrieve over the ocean surface a phase portrait where the geometry of interconnected dynamical systems is visible. The phase portrait picture is essential because it evinces which transport routes are acting on the whole flow. Once these routes are roughly recognised, it is possible to complete a detailed description by the direct computation of the finite time stable and unstable manifolds of special hyperbolic trajectories that act as organising centres of the flow.
Viscoelastic flow modeling in the extrusion of a dough-like fluid.
Dhanasekharan, M; Kokini, J L
2000-08-01
This work attempts to investigate the effect of viscoelasticity and three-dimensional geometry in screw channels. The Phan-Thien Tanner (PTT) constitutive equation with simplified model parameters was solved in conjunction with the flow equations. Polyflow, a commercially available finite element code was used to solve the resulting nonlinear partial differential equations. The PTT model predicted one log scale lower pressure buildup compared to the equivalent Newtonian results. However, the velocity profile did not show significant changes for the chosen PTT model parameters. Past Researchers neglected viscoelastic effects and also the three dimensional nature of the flow in extruder channels. The results of this paper provide a starting point for further simulations using more realistic model parameters, which may enable the food engineer to more accurately scale-up and design extrusion processes.
A stable and convergent scheme for viscoelastic flow in contraction channels
Trebotich, David; Colella, Phillip; Miller, Gregory
2004-02-15
We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel's formula and discretize the resulting PDEs using a semi-implicit finite difference method based on a Lax-Wendroff method for hyperbolic terms. In particular, we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well-posed. A projection method is used to impose the incompressibility constraint. We are able to compute the full range of elastic flows in an abrupt contraction channel--from the viscous limit to the elastic limit--in a stable and convergent manner for elastic Mach numbers less than one. We demonstrate the method for unsteady Oldroyd-B and Maxwell fluids in planar contraction channels.
A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow
Jiang, T.; Ren, J. L.; Lu, W. G.; Xu, B.
2017-02-01
In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.
Viscoelastic flow modeling in the extrusion of a dough-like fluid
Dhanasekharan, M.; Kokini, J. L.; Janes, H. W. (Principal Investigator)
2000-01-01
This work attempts to investigate the effect of viscoelasticity and three-dimensional geometry in screw channels. The Phan-Thien Tanner (PTT) constitutive equation with simplified model parameters was solved in conjunction with the flow equations. Polyflow, a commercially available finite element code was used to solve the resulting nonlinear partial differential equations. The PTT model predicted one log scale lower pressure buildup compared to the equivalent Newtonian results. However, the velocity profile did not show significant changes for the chosen PTT model parameters. Past Researchers neglected viscoelastic effects and also the three dimensional nature of the flow in extruder channels. The results of this paper provide a starting point for further simulations using more realistic model parameters, which may enable the food engineer to more accurately scale-up and design extrusion processes.
Lagrangian mass-flow investigations of inorganic contaminants in wastewater-impacted streams
Barber, L.B.; Antweiler, R.C.; Flynn, J.L.; Keefe, S.H.; Kolpin, D.W.; Roth, D.A.; Schnoebelen, D.J.; Taylor, H.E.; Verplanck, P.L.
2011-01-01
Understanding the potential effects of increased reliance on wastewater treatment plant (WWTP) effluents to meet municipal, agricultural, and environmental flow requires an understanding of the complex chemical loading characteristics of the WWTPs and the assimilative capacity of receiving waters. Stream ecosystem effects are linked to proportions of WWTP effluent under low-flow conditions as well as the nature of the effluent chemical mixtures. This study quantifies the loading of 58 inorganic constituents (nutrients to rare earth elements) from WWTP discharges relative to upstream landscape-based sources. Stream assimilation capacity was evaluated by Lagrangian sampling, using flow velocities determined from tracer experiments to track the same parcel of water as it moved downstream. Boulder Creek, Colorado and Fourmile Creek, Iowa, representing two different geologic and hydrologic landscapes, were sampled under low-flow conditions in the summer and spring. One-half of the constituents had greater loads from the WWTP effluents than the upstream drainages, and once introduced into the streams, dilution was the predominant assimilation mechanism. Only ammonium and bismuth had significant decreases in mass load downstream from the WWTPs during all samplings. The link between hydrology and water chemistry inherent in Lagrangian sampling allows quantitative assessment of chemical fate across different landscapes. ?? 2011 American Chemical Society.
Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow
Frisch, Uriel
2014-01-01
Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to G\\"ottingen University, contain major discoveries on vorticity dynamics whose impact is now quickly increasing. Cauchy found a Lagrangian formulation of 3D ideal incompressible flow in terms of three invariants that generalize to three dimensions the now well-known law of conservation of vorticity along fluid particle trajectories for two-dimensional flow. This has very recently been used to prove analyticity in time of fluid particle trajectories for 3D incompressible Euler flow and can be extended to compressible flow, in particular to cosmological dark matter. Hankel showed that Cauchy's formulation gives a very simple Lagrangian derivation of the Helmholtz vorticity-flux invariants and, in the middle of the proof, derived an intermediate result which is the conservation of the circulation of the velocity around a closed contour moving with the fluid. This circulation the...
Tran, Steven; Sahni, Onkar; RPI Team
2015-11-01
Large eddy simulations (LES) provide high fidelity in which the large-scale turbulent structures are resolved while their interactions with the subgrid scales are modeled. In a Smagorinsky-based LES approach, the unresolved stresses are modeled using an eddy viscosity which in-turn involves a model parameter that is unknown a priori and varies in space and time for complex problems. Therefore, dynamic procedures are employed to determine this parameter where averaging is applied to make the procedure robust. When applicable, spatial averaging is applied across homogeneous directions. However, for complex flows the Lagrangian subgrid-scale model employing averaging over pathlines becomes attractive. In contrast to the dynamic Smagorinsky model, variational multiscale (VMS) models have also been developed for LES. In this study, we investigate dynamic mixed models for LES based on the combinations of the Lagrangian subgrid-scale model and the residual-based VMS (RBVMS) approach to study complex, inhomogeneous turbulent flows on unstructured meshes. Applications range from flow through a channel to flow over an airfoil at a moderate angle of attack. Experimental and DNS data are used to make comparisons.
Eulerian-Lagrangian Simulations of Bubbly Flows in A Vertical Square Duct
Liu, Rui; Vanka, Surya P.; Thomas, Brian G.
2013-11-01
We report results of Eulerian-Lagrangian simulations of developing upward and downward bubbly flows in a vertical square duct with a bulk Reynolds number of 5000. The continuous fluid is simulated with DNS, solving the Navier-Stokes equations by a second-order accurate finite volume fractional step method. Bubbles of sizes comparable to the Kolmogorov scale are injected at the duct entrance with a mean bulk volume fraction below 10-2. A two-way coupling approach is adopted for the interaction between the continuous fluid phase and dispersed bubble phase. The bubbles are tracked by a Lagrangian method including drag and lift forces due to buoyancy and Saffman lift. A in-house code, CU-FLOW, implemented on Graphic Processing Unit (GPU) is used for simulations in this work. The preferential distributions of bubbles and their impact on local turbulence structures and their effects on turbulent kinetic energy budgets are studied. Results between an upward flow and a downward flow with the bubbles are compared. Work Supported by Continuous Casting Consortium at UIUC.
Simulation of Time-Dependent Viscoelastic Fluid Flows by Spectral Elements
Jafari, Azadeh
2011-01-01
The research work reported in this dissertation is aimed to develop efficient and stable numerical schemes in order to obtain accurate numerical solution for viscoelastic fluid flows within the spectral element context. The present research consists in the transformation of a large class of differential constitutive models into an equation where the main variable is the logarithm of the conformation tensor or a quantity related to it in a simple way. ...
Computing 3-D steady supersonic flow via a new Lagrangian approach
Loh, C. Y.; Liou, M.-S.
1993-01-01
The new Lagrangian method introduced by Loh and Hui (1990) is extended for 3-D steady supersonic flow computation. Details of the conservation form, the implementation of the local Riemann solver, and the Godunov and the high resolution TVD schemes are presented. The new approach is robust yet accurate, capable of handling complicated geometry and reactions between discontinuous waves. It keeps all the advantages claimed in the 2-D method of Loh and Hui, e.g., crisp resolution for a slip surface (contact discontinuity) and automatic grid generation along the stream.
A Lagrangian finite element method for the simulation of flow of non-newtonian liquids
Hassager, Ole; Bisgaard, C
1983-01-01
A Lagrangian method for the simulation of flow of non-Newtonian liquids is implemented. The fluid mechanical equations are formulated in the form of a variational principle, and a discretization is performed by finite elements. The method is applied to the slow of a contravariant convected Maxwell...... liquid around a sphere moving axially in a cylinder. The simulations show that the friction factor for a sphere in a narrow cylinder is a rapidly decreasing function of the Deborah number, while the friction factor for a sphere in a very wide cylinder is not significantly affected by fluid elasticity...
Yatou, Hiroki
2010-01-01
We find three types of steady solutions and remarkable flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical simulations with spectral element method. The solutions are called "convective", "transition", and "elastic" in ascending order of Wi. In the convective region in the Re-Wi parameter space, the convective effect and the pressure gradient balance on average. As Wi increases, the elastic effect becomes suddenly comparable and the first transition sets in. Through the transition, a separation vortex disappears and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; The viscous drag significantly drops and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic eff...
程怀玉; 龙新平; 季斌; 祝叶; 周加建
2016-01-01
Unsteady cavitating turbulent flow around twisted hydrofoil is simulated with Zwart cavitation model combined with the filter-based density correction model (FBDCM). Numerical results simulated the entire process of the 3-D cavitation shedding including the re-entrant jet and side-entrant jet dynamics and were compared with the available experimental data. The distribution of finite-time Lyapunov exponent (FTLE) was used to analyze the 3-D behavior of the re-entrant jet from the Lagrangian viewpoint, which shows that it can significantly influence the particle trackers in the attached cavity. Further analysis indicates that the different flow behavior on the suction side with different attack angle can be identified with Lagrangian coherent structures (LCS). For the area with a large attack angle, the primary shedding modifies the flow pattern on the suction side. With the decrease in attack angle, the attached cavity tends to be steady, and LCS A is close to the upper wall. A further decrease in attack angle eliminates LCS A in the boundary layer. The FTLE distribution also indicates that the decreasing attack angle induces a thinner boundary layer along the foil surface on the suction side.
Energy amplification in channel flows of viscoelastic fluids
Hoda, Nazish; Jovanovi?, Mihailo R.; Kumar, Satish
Energy amplification in channel flows of Oldroyd-B fluids is studied from an input-output point of view by analysing the ensemble-average energy density associated with the velocity field of the linearized governing equations. The inputs consist of spatially distributed and temporally varying body forces that are harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyse Newtonian fluid flows. It is found that the energy density increases with a decrease in viscosity ratio (ratio of solvent viscosity to total viscosity) and an increase in Reynolds number and elasticity number. In most of the cases, streamwise-constant perturbations are most amplified and the location of maximum energy density shifts to higher spanwise wavenumbers with an increase in Reynolds number and elasticity number and a decrease in viscosity ratio. For similar parameter values, the maximum in the energy density occurs at a higher spanwise wavenumber for Poiseuille flow, whereas the maximum energy density achieves larger maxima for Couette flow. At low Reynolds numbers, the energy density decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.
Viscoelastic flow simulations through an array of cylinders
Gillissen, J.J.J.
2013-01-01
Polymer solution flow is studied numerically in a periodic, hexagonal array of cylinders as a model for a porous medium. We use a lattice Boltzmann method supplemented by a polymer stress, where the polymers are modeled as finitely extensible, nonlinear, elastic dumbbells. The simulated, nonmonotoni
Shaw, Emily C.; Phinn, Stuart R.; Tilbrook, Bronte; Steven, Andy
2014-01-01
Coral reef calcification is predicted to decline as a result of ocean acidification and other anthropogenic stressors. The majority of studies predicting declines based on in situ relationships between environmental parameters and net community calcification rate have been location-specific, preventing accurate predictions for coral reefs globally. In this study, net community calcification and production were measured on a coral reef flat at One Tree Island, Great Barrier Reef, using Lagrangian flow respirometry and slack water methods. Net community calcification, daytime net photosynthesis and nighttime respiration were higher under the flow respirometry method, likely due to increased water flow relative to the slack water method. The two methods also varied in the degrees to which they were influenced by potential measurement uncertainties. The difference in the results from these two commonly used methods implies that some of the location-specific differences in coral reef community metabolism may be due to differences in measurement methods. PMID:25426626
Investigation of vortical flows over oscillating body using fast Lagrangian vortex method
Baoshan ZHU
2009-01-01
A computational method facilitating long-time and high-resolution unsteady vortical flows is developed with the advantages of the discrete vortex methods. Both the velocity and pressure distribution of the flow field are calculated by integral formulations in combination with a fast summation algorithm. The vorticity field is described by Lagrangian representation, which is well suited to the moving boundary. Viscosity diffusion of the vorticity is considered with the core spreading model corrected by an adaptive splitting and merging algorithm. The effective-ness of the present method is examined by comparing the numerical results of unsteady separated flows which pass a cylinder and a thin cambered blade undergoing rotational oscillations with available experimental results. Interesting results about vortex shedding patterns and lock-in characteristics are provided for the thin cambered blade.
Emily C Shaw
Full Text Available Coral reef calcification is predicted to decline as a result of ocean acidification and other anthropogenic stressors. The majority of studies predicting declines based on in situ relationships between environmental parameters and net community calcification rate have been location-specific, preventing accurate predictions for coral reefs globally. In this study, net community calcification and production were measured on a coral reef flat at One Tree Island, Great Barrier Reef, using Lagrangian flow respirometry and slack water methods. Net community calcification, daytime net photosynthesis and nighttime respiration were higher under the flow respirometry method, likely due to increased water flow relative to the slack water method. The two methods also varied in the degrees to which they were influenced by potential measurement uncertainties. The difference in the results from these two commonly used methods implies that some of the location-specific differences in coral reef community metabolism may be due to differences in measurement methods.
Model for natural convective flow of visco-elastic nanofluid past an isothermal vertical plate
Mustafa, M.; Mushtaq, Ammar
2015-09-01
The present article addresses the classical problem of the natural convection flow past a vertical plate by considering visco-elastic nanofluid. The mathematical model is constructed by following the constitutive equations of the upper-convected Maxwell (UCM) fluid. The novel aspects of Brownian motion and thermophoresis are taken into account. The recently proposed condition of passively controlled wall nanoparticle volume fraction is used. The shooting approach combined with the fourth-fifth-order Runge-Kutta integration procedure is utilized for computing the numerical solutions. The results are in agreement with the available studies in limiting sense. Our results indicate that the velocity profile is parabolic and it decreases with an increment in the visco-elastic parameter.
Prediction of Viscoelastic Behavior of Blood Flow in Plaque Deposited Capillaries
Muhammad Anwar Solangi
2012-10-01
Full Text Available The paper investigates the viscoelastic behaviour of blood over low value of elasticity, to analyse the influence of inertia in the presence of elasticity. For viscoelastic fluids shear-thinning and strainsoftening PTT (Phan-Thien/Tanner constitutive model is employed to identify the influence of elasticity. The computational method adopted is based on a finite element semi-implicit time stepping Taylor- Galerkin/pressure-correction scheme. Simulations are conducted via atherosclerotic vessels along with various percentages of deposition at distinct values of Reynolds numbers. The numerical simulations are performed for recirculation flow structure and development of recirculation length to investigate the impact of atherosclerosis on partially blocked plaque deposited vessels.
Viscoelastic flow simulations through an array of cylinders.
Gillissen, J J J
2013-02-01
Polymer solution flow is studied numerically in a periodic, hexagonal array of cylinders as a model for a porous medium. We use a lattice Boltzmann method supplemented by a polymer stress, where the polymers are modeled as finitely extensible, nonlinear, elastic dumbbells. The simulated, nonmonotonic behavior of the effective viscosity μ(eff) as a function of the Weissenberg number We is in qualitative agreement with experiments in the literature. An analytical model, which replaces the flexible polymers by rods and that replaces the flow field in the porous medium by a superposition of shear and elongation, correctly reproduces the simulated μ(eff) as a function of the polymer extensibility parameter b in the limit of large We.
Relating surface pressure to Lagrangian wake topology around a circular cylinder in cross flow
Rockwood, Matthew; Green, Melissa
2016-11-01
The tracks of Lagrangian saddles, identified as non-parallel intersections of positive and negative-time finite-time Lyapunov exponent (FTLE) ridges, have been shown to indicate the timing of von Karman vortex shedding in the wake of bluff bodies. The saddles are difficult to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the topological changes without direct access to the FTLE, the saddle dynamics are correlated to measurable surface quantities on a circular cylinder in cross flow. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex has been shown to accelerate away from the cylinder surface as the vortex sheds. In previous numerical results at Re = 150 , this acceleration coincides with the peak in lift force over the cylinder, and also with a minimum in the static pressure at a location slightly upstream of the mean separation location. In the current work, this result is compared with experimental data at Re = O (10 , 000) . Successful validation would provide a strategy for locating sensitive regions on the cylinder surface where vortex shedding could be detected using simple pressure transducers. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.
Rotor wake and flow analysis using a coupled Eulerian–Lagrangian method
Yongjie Shi
2016-01-01
Full Text Available A coupled Eulerian–Lagrangian methodology was developed in this paper in order to provide an efficient and accurate tool for rotor wake and flow prediction. A Eulerian-based Reynolds-averaged Navier–Stokes (RANS solver was employed to simulate the grid-covered near-body zone, and a grid-free Lagrangian-based viscous wake method (VWM was implemented to model the complicated rotor-wake dynamics in the off-body wake zone. A carefully designed coupling strategy was developed to pass the flow variables between two solvers. A sample case of a forward flying rotor was performed first in order to show the capabilities of the VWM for wake simulations. Next, the coupled method was applied to rotors in several representative flight conditions. Excellent agreement regarding wake geometry, chordwise pressure distribution and sectional normal force with available experimental data demonstrated the validity of the method. In addition, a comparison with the full computational fluid dynamics (CFD method is presented to illustrate the efficiency and accuracy of the proposed coupled method.
Flow Kinematics and Lagrangian Mixing Dynamics in a Darcy Scale Heterogeneous Porous Medium
Dentz, M.; de Barros, F.; Le Borgne, T.
2013-12-01
We study the mixing behavior of a solute blob that is transported through a two-dimensional Darcy scale heterogeneous porous medium. Flow heterogeneity is induced by spatial variability in hydraulic conductivity. The fundamental mechanism governing the evolution of the solute blob are the competition of the stretching and compression action within a fluid element, and diffusion. We formulate the transport problem in a Lagrangian framework and consider the motion of solute particles that form the blob, in the coordinate system attached to the fluid element on which it originates. The blob evolution is fully characterized by the time series of stretching and shear rates of the material segment in its own coordinate system. Associated stirring protocols, or spreading protocols may be different from the ones encountered in chaotic and turbulent flow and can be related to the evolution of center of mass velocities of an ensemble of solute blobs. The permeability variability is modeled using a stochastic approach, which renders the stretching and shear rate time series as stochastic processes. Theses stochastic series are investigated numerically using random walk particle tracking simulations, and quantified analytically in terms of multiplicative and additive stochastic processes for the strip elongation and shear deformation. In this stochastic framework, we study the ensemble concentration PDF, concentration entropy and scalar dissipation rate. We relate the mixing properties to the appearance of coherent structures as quantified by the Okubo-Weiss measure and its Lagrangian counterpart.
Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil
Wu, Qin; Huang, Biao; Wang, Guoyu
2016-02-01
The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier-Stokes flow computations. In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equation γ {-Re}_θ transition model, is used for the turbulence closure. Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0° to 15° then back to 0° at a moderate Reynolds number Re=7.5× 105. The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case, it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observed and the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times, which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows, and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.
A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our...... calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume...
A new numerical framework to simulate viscoelastic free-surface flows with the finite-volume method
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2015-01-01
A new method for the simulation of 2D viscoelastic flow is presented. Numerical stability is obtained by the logarithmic-conformation change of variable, and a fully-implicit pure-streamfunction flow formulation, without use of any artificial diffusion. As opposed to other simulation results, our...... calculations predict a hydrodynamic instability in the 4:1 contraction geometry at a Weissenberg number of order 4. This new result is in qualitative agreement with the prediction of a non-linear subcritical elastic instability in Poiseuille flow. Our viscoelastic flow solver is coupled with a volume...
Meneveau, Charles; Johnson, Perry; Hamilton, Stephen; Burns, Randal
2016-11-01
An intrinsic property of turbulent flows is the exponential deformation of fluid elements along Lagrangian paths. The production of enstrophy by vorticity stretching follows from a similar mechanism in the Lagrangian view, though the alignment statistics differ and viscosity prevents unbounded growth. In this paper, the stretching properties of fluid elements and vorticity along Lagrangian paths are studied in a channel flow at Reτ = 1000 and compared with prior, known results from isotropic turbulence. To track Lagrangian paths in a public database containing Direct Numerical Simulation (DNS) results, the task-parallel approach previously employed in the isotropic database is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis. Normalized by dissipation rate, the stretching in the buffer layer and below is less efficient due to less favorable alignment statistics. The Cramér function characterizing cumulative Lagrangian stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence. Supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1232825, and by National Science Foundation Grants CBET-1507469, ACI-1261715, OCI-1244820 and by JHU IDIES.
Lagrangian study of temporal changes of a surface flow through the Kamchatka Strait
Prants, S V; Uleysky, M Yu; Budyansky, M V
2014-01-01
Using Lagrangian methods we analyze a 20-year-long estimate of water flux through the Kamchatka Strait in the northern North Pacific based on AVISO velocity field. It sheds new light on the flux pattern and its variability on annual and monthly time scales. Strong seasonality in surface outflow through the strait could be explained by temporal changes in the wind stress over the northern and western Bering Sea slopes. Interannual changes in a surface outflow through the Kamchatka Strait correlate significantly with the Near Strait inflow and Bering Strait outflow. Enhanced westward surface flow of the Alaskan Stream across the $174^\\circ$ E section in the northern North Pacific is accompanied by an increased inflow into the Bering Sea through the Near Strait. In summer, the surface flow pattern in the Kamchatka Strait is determined by passage of anticyclonic and cyclonic mesoscale eddies. The wind stress over the Bering basin in winter - spring is responsible for eddy generation in the region.
Flow-Driven Cloud Formation and Fragmentation: Results From Eulerian and Lagrangian Simulations
Heitsch, Fabian; Walch, Stefanie
2011-01-01
The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian Smoothed Particle Hydrodynamics (SPH) code VINE and the Eulerian grid code Proteus. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydro-dynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300K. For clumps more massive than 1 Msun/pc, the clump mass function has an average slope of -0.8. The internal velocity dispersion of the clumps is nearly an order of ma...
Lagrangian simulation of deposition of CO2 gas-solid sudden expansion flow
2008-01-01
Freezing and blockage resulting from the deposition of solid CO2 formed because of sudden expansion of the downstream pipe during the release of CO2 through safety valves,will endanger the protected equipment.To overcome this problem,the characteristics of the CO2 gas-solid sudden expansion flow are studied by using the disperse Lagrangian model.A comparison of the calculated deposition of the solid CO2 with the experimental results shows that they are in reasonable agreement.The simulation results show that the size of the solid CO2 formed should not be in the range of 0.04-0.07 mm (St number 3.2-9.8).This can be achieved by using an appropriate flow cross section of the safety valve.
Qi, M.; Wegner, J.; Ganzer, L. [Technische Univ. Clausthal, Clausthal-Zellerfeld (Germany). ITE
2013-08-01
Polymer flooding, as an EOR method, has become one of the most important driving forces after water flooding. The conventional believe is that polymer flooding can only improve sweep efficiency, but it has no contribution to residual oil saturation reduction. However, experimental studies indicated that polymer solution can also improve displacement efficiency and decrease residual oil saturation. To get a better understanding of the mechanism to increase the microscopic sweep efficiency and the displacement efficiency, theoretical studies are required. In this paper, we studied the viscoelasticity effect of polymer by using a numerical simulator, which is based on Finite Element Analysis. Since it is showed experimentally that the first normal stress difference of viscoelastic polymer solution is higher than the second stress difference, the Oldroyd-B model was selected as the constitutive equation in the simulation. Numerical modelling of Oldroyd-B viscoelastic fluids is notoriously difficult. Standard Galerkin finite element methods are prone to numerical oscillations, and there is no convergence as the elasticity of fluid increases. Therefore, we use a stabilised finite element model. In order to verify our model, we first built up a model with the same geometry and fluid properties as presented in literature and compared the results. Then, with the tested model we simulated the effect of viscoelastic polymer fluid on dead pores in three simplified pore structures, which are contraction structure, expansion structure and expansion-contraction structure. Correspondingly, the streamlines and velocity contours of polymer solution, with different Reynolds numbers (Re) and Weissenberg numbers (We), flowing in these three structures are showed. The simulation results indicate that the viscoelasticity of polymer solution is the main contribution to increase the micro-scale sweep efficiency. With higher elasticity, the velocity of polymer solution is getting bigger at
The Cauchy-Lagrangian method for numerical analysis of Euler flow
Podvigina, O; Frisch, U
2015-01-01
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by simple recurrence relations that follow from the Cauchy invariants formulation of the Euler equations (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more --- and occasionally much more --- efficient and less prone to instability than Eulerian Runge-Kutta methods and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algor...
Flow Modeling in Pelton Turbines by an Accurate Eulerian and a Fast Lagrangian Evaluation Method
A. Panagiotopoulos
2015-01-01
Full Text Available The recent development of CFD has allowed the flow modeling in impulse hydro turbines that includes complex phenomena like free surface flow, multifluid interaction, and unsteady, time dependent flow. Some commercial and open-source CFD codes, which implement Eulerian methods, have been validated against experimental results showing satisfactory accuracy. Nevertheless, further improvement of accuracy is still a challenge, while the computational cost is very high and unaffordable for multiparametric design optimization of the turbine’s runner. In the present work a CFD Eulerian approach is applied at first, in order to simulate the flow in the runner of a Pelton turbine model installed at the laboratory. Then, a particulate method, the Fast Lagrangian Simulation (FLS, is used for the same case, which is much faster and hence potentially suitable for numerical design optimization, providing that it can achieve adequate accuracy. The results of both methods for various turbine operation conditions, as also for modified runner and bucket designs, are presented and discussed in the paper. In all examined cases the FLS method shows very good accuracy in predicting the hydraulic efficiency of the runner, although the computed flow evolution and the torque curve exhibit some systematic differences from the Eulerian results.
Nguyen, Trieu; van der Meer, Devaraj; van den Berg, Albert
2017-01-01
-Boltzmann equation, together with the incompressible Cauchy momentum equation under no-slip boundary conditions for viscoelastic fluid in the case of a combination of time periodic pressure-driven and electro-osmotic flow. The resulting solutions allow us to predict the electrical current and solution flow rate....... As expected from the assumption of linear viscoelasticity, the results satisfy the Onsager reciprocal relation, which is important since it enables an analogy between fluidic networks in this flow configuration and electric circuits. The results especially are of interest for micro-and nanofluidic energy...
On the unsteady flow of two visco-elastic fluids between two inclined porous plates
P. R. Sengupta
1992-01-01
Full Text Available This study is concerned with both hydrodynamic and hydromagnetic unsteady slow flows of two immiscible visco-elastic fluids of Rivlin-Ericksen type between two porous parallel nonconducting plates inclined at a certain angle to the horizontal. The exact solutions for the velocity fields, skin frictions, and the interface velocity distributions are found for both fluid models. Numerical results are presented in graphs. A comparison is made between the hydrodynamic and hydromagnetic velocity profiles. It is shown that the velocity is diminished due to the presence of a transverse magnetic field.
Spatial-temporal dynamics of Newtonian and viscoelastic turbulence in channel flow
Wang, Sung-Ning; Shekar, Ashwin; Graham, Michael
2016-11-01
Introducing a trace amount of polymer into liquid turbulent flows can result in substantial reduction of friction drag. This phenomenon has been widely used in fluid transport; however, the mechanism is not well understood. Past studies have found that in minimal domain turbulent simulations, there areoccasional time periods when flow exhibits features such as weaker vortices, lower friction drag and larger log-law slope; these have been denoted as "hibernatingturbulence". Here we address the question of whether similar behavior arises spatio-temporally in extended domains, focusing on turbulence at friction Reynolds numbers near transition and Weissenberg numbers resulting in low-medium drag reduction. By using image analysis and conditional sampling tools, we identify the hibernating states in extended domains and show that they display striking similarity as those in minimal domains. The hibernating states among different Weissenberg numbers exhibit similar flow statistics, suggesting they are unaltered by low to medium viscoelasticity. In addition, the polymer is much less stretched during hibernation. Finally, these hibernating states vanish as Reynolds number increases. However, they reoccur and gradually become dominant with increasing viscoelasticity.
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.
Viscoelastic polymer flows and elastic turbulence in three-dimensional porous structures.
Mitchell, Jonathan; Lyons, Kyle; Howe, Andrew M; Clarke, Andrew
2016-01-14
Viscoelastic polymer solutions flowing through reservoir rocks have been found to improve oil displacement efficiency when the aqueous-phase shear-rate exceeds a critical value. A possible mechanism for this enhanced recovery is elastic turbulence that causes breakup and mobilization of trapped oil ganglia. Here, we apply nuclear magnetic resonance (NMR) pulsed field gradient (PFG) diffusion measurements in a novel way to detect increased motion of disconnected oil ganglia. The data are acquired directly from a three-dimensional (3D) opaque porous structure (sandstone) when viscoelastic fluctuations are expected to be present in the continuous phase. The measured increase in motion of trapped ganglia provides unequivocal evidence of fluctuations in the flowing phase in a fully complex 3D system. This work provides direct evidence of elastic turbulence in a realistic reservoir rock - a measurement that cannot be readily achieved by conventional laboratory methods. We support the NMR data with optical microscopy studies of fluctuating ganglia in simple two-dimensional (2D) microfluidic networks, with consistent apparent rheological behaviour of the aqueous phase, to provide conclusive evidence of elastic turbulence in the 3D structure and hence validate the proposed flow-fluctuation mechanism for enhanced oil recovery.
Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
Cameron, Alexandre; Dormy, Emmanuel
2016-01-01
Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \\& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.
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...
HEAT AND MASS TRANSFER FOR VISCO-ELASTIC MHD BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE
Rita Choudhury
2012-07-01
Full Text Available The two-dimensional free convection flow of visco-elastic and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equation by introducing appropriate co-ordinate transformation. The analytical expressions for the velocity, temperature and species concentration fields have been obtained. The corresponding expressions for the non-dimensional rates of heat transfer and mass transfer have beenobtained. The velocity profile and the shearing stress have been illustrated graphically, for various values of flow parameters involved in the solution to observe the effect of visco-elastic parameter.
Shen, Bingyu; Zheng, Liancun, E-mail: liancunzheng@ustb.edu.cn; Chen, Shengting [School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083 (China)
2015-10-15
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
Bingyu Shen
2015-10-01
Full Text Available This paper presents an investigation for magnetohydrodynamic (MHD viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
A FAST LAGRANGIAN SIMULATION METHOD FOR FLOW ANALYSIS AND RUNNER DESIGN IN PELTON TURBINES
ANAGNOSTOPOULOS John S.; PAPANTONIS Dimitris E.
2012-01-01
In the present work,an alternative numerical methodology is developed for a fast and effective simulation and analysis of the complex flow and energy conversion in Pelton impulse hydro turbines.The algorithm is based on the Lagrangian approach and the unsteady free-surface flow during the jet-bucket interaction is simulated by tracking the trajectories of representative fluid particles at very low computer cost.Modern regression tools are implemented in a new parameterization technique of the inner bucket surface.Key-feature of the model is the introduction of additional terms into the particle motion equations to account for various hydraulic losses and the flow spreading,which are regulated and evaluated with the aid of experimental data in a Laboratory Pelton turbine.The model is applied to study the jet-runner interaction in various operation conditions and then to perform numerical design optimization of the bucket shape,using a stochastic optimizer based on evolutionary algorithms.The obtained optimum runner attains remarkably higher hydraulic efficiency in the entire load range.Finally,a new small Pelton turbine (150 kW) is designed,manufactured and tested in the Laboratory,and its performance and efficiency verify the model predictions.
Sedaghatizadeh, N.; Atefi, G.; Fardad, A. A.
2011-01-01
In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite differenc...
Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.
Wang, Xiaofei; Fullana, Jose-Maria; Lagrée, Pierre-Yves
2015-01-01
A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2015-01-01
A new streamfunction/log-conformation formulation of incompressible viscoelastic flows is presented. The log-conformation representation guaranties the positive-definiteness of the conformation tensor and obviates the high Weissenberg number problem. The streamfunction is defined as a vector...... potential of the velocity field, and provides a pressureless formulation of the conservation laws, which automatically enforces the incompressibility. The resulting numerical method is free from velocity-pressure decoupling errors, and can achieve stable calculations for large Courant numbers, which improve...... the robustness and the efficiency of the solver. The two-dimensional flow of an Oldroyd-B fluid inside the lid-driven cavity is simulated for a large range of Weissenberg numbers. The numerical results demonstrate the second-order accuracy of our scheme, and our solutions are in good agreement with the available...
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed
2017-01-01
Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters. PMID:28046011
Vincent, Stéphane; Sarthou, Arthur; Caltagirone, Jean-Paul; Sonilhac, Fabien; Février, Pierre; Mignot, Christian; Pianet, Grégoire
2011-02-01
The numerical simulation of the interaction between a free surface flow and a moving obstacle is considered for the analysis of hydroplaning flows. A new augmented Lagrangian method, coupled to fictitious domains and penalty methods, is proposed for the simulation of multi-phase flows. The augmented Lagrangian parameter is estimated by an automatic analysis of the discretization matrix resulting from the approximation of the momentum equations. The algebraic automatic augmented Lagrangian 3AL approach is validated on the natural convection in a differentially heated cavity, a two-dimensional collapse of a water column, the three-dimensional settling of a particle in a tank and the falling of a dense cylinder in air. Finally, the 3AL method is utilized to simulate the hydroplaning of a tire under various pattern shape conditions.
Kundalkar, Deepak; Singh, Rajkumar; Tewari, Asim
2017-07-01
Friction plays an important role in high-temperature deformation process. Friction affects local displacement field in the tool-workpiece interface region, thus affecting the overall material flow. Under high-temperature compression, macro-indicators like bulge radius and load displacement curves are not sensitive enough to distinguish subtle differences between various friction models. Hence, a new approach to match the experimental Lagrangian flow field with flow field obtained from FE simulation is proposed. For this uniaxial barreling, compression tests at constant temperature were conducted on Gleeble thermo-mechanical simulator. The compression tests were conducted at different strain, strain rate and friction conditions. Finite element simulations employing various friction models and parameters were performed for matching the experimental conditions. Experimental Lagrangian flow fields were obtained from the grain flow lines observed on high-resolution larger area micrographs of the specimen. It was observed that all the investigated friction models provided equally good fit with the macro-experimental indicators (bulge radius and load displacement curves). However, Coulomb friction model was the only friction model that provided the closest fit with the experimentally obtained Lagrangian flow fields. Coulomb friction model provided the best agreement between experimental and numerical simulation for both lubricated and non-lubricated conditions using friction coefficients μ = 0.2993 and μ = 0.3895, respectively.
Theoretical Investigation of Creeping Viscoelastic Flow Transition Around a Rotating Curved Pipe
Hamza, S E E
2015-01-01
The study of creeping motion of viscoelastic fluid around a rotating rigid torus is investigated. The analysis of the problem is performed using a second-order viscoelastic model. The study is carried out in terms of the bipolar toroidal system of coordinates where the toroid is rotating about its axis of symmetry (z-axis). The problem is solved within the frame of slow flow approximation. Therefore, all variables in the governing equations are expanded in a power series of angular velocity. A set of successive partial differential equations is obtained. The equations of motion governing the first and second-order are formulated and solved for the first-order only in this paper. However, the solution of the second-order equations will be the subject of a part two of this series of papers. Analytically, Laplace's equation is solved via the usual method of separation of variables. This method shows that, the solution is given in a form of infinite sums over Legendre functions of the first and second kinds. From...
Karen May-Newman
2016-11-01
Full Text Available A thrombus is a blood clot that forms on a surface, and can grow and detach, presenting a high risk for stroke and pulmonary embolism. This risk increases with blood-contacting medical devices, due to the immunological response to foreign surfaces and altered flow patterns that activate the blood and promote thromboembolism (TE. Abnormal blood transport, including vortex behavior and regional stasis, can be assessed from Lagrangian Coherent Structures (LCS. LCS are flow structures that bound transport within a flow field and divide the flow into regions with maximally attracting/repelling surfaces that maximize local shear. LCS can be identified from finite time Lyapunov exponent (FTLE fields, which are computed from velocity field data. In this study, the goal was to use FTLE analysis to evaluate LCS in the left ventricle (LV using velocity data obtained from flow visualization of a mock circulatory loop. A model of dilated cardiomyopathy (DCM was used to investigate the effect of left ventricular assist device (LVAD support on diastolic filling and transport in the LV. A small thrombus in the left ventricular outflow tract was also considered using data from a corresponding LV model. The DCM LV exhibited a direct flow of 0.8 L/cardiac cycle, which was tripled during LVAD support Delayed ejection flow was doubled, further illustrating the impact of LVAD support on blood transport. An examination of the attracting LCS ridges during diastolic filling showed that the increase is due primarily to augmentation of A wave inflow, which is associated with increased vortex circulation, kinetic energy and Forward FTLE. The introduction of a small thrombus in the left ventricular outflow tract (LVOT of the LV had a minimal effect on diastolic inflow, but obstructed systolic outflow leading to decreased transport compared with the unobstructed LVOT geometry. Localized FTLE in the LVOT increased dramatically with the small thrombus model, which reflects
El-dabe, N. T. M.; Moatimid, G. M.; Hassan, M. A.; Mostapha, D. R.
2016-01-01
The effect of a vertical alternating current, electric field, and heat transfer on a peristaltic flow of a dielectric viscoelastic Oldroyd fluid is studied. This analysis involves uniform and nonuniform annuli having a mild stenosis. The analytical solutions of equations of motion are based on the perturbation technique. This technique depends on two parameters: amplitude ratio and small wave number. Numerical calculations are performed to obtain the effects of several parameters, such as the electrical Rayleigh number, temperature gradient, Reynolds number, wave number, maximum height of stenosis, and Weissenberg numbers, on the distributions of velocity, temperature, electric potential, and wall shear stress. It is found that the above-mentioned distributions in the case of a convergent tapered tube are larger than those in the case of a non-tapered one as well as a diverging tapered tube.
Influence of aligned MHD on convective boundary layer flow of viscoelastic fluid
Aziz, Laila Amera; Kasim, Abdul Rahman Mohd; Al-Sharifi, H. A. M.; Salleh, Mohd Zuki; Mohammad, Nurul Farahain; Shafie, Sharidan; Ali, Anati
2017-05-01
Effects of aligned Magnetohydrodynamics (MHD) on the mixed convection boundary layer flow of viscoelastic fluid past a circular cylinder with Newtonian heating is investigated. Appropriate transformation is applied to the governing partial differential equations to transform them into dimensionless forms which are then solved using finite difference method known as Keller box. For verification purpose, the preliminary numerical solutions of the model are compared with previous study with a particular condition that the magnetic and viscosity effect are both absent. With strong agreement between the previous and current results, the authors believe that the extended outcome produced from the present model is accurate. Findings from the study will be presented in tabular and graphical form.
Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model
Wang, Xiaofei; Lagrée, Pierre-Yves
2013-01-01
In this paper, we present four numerical schemes for a 1D viscoelastic blood flow model. In the case with a small nonlinearity (small amplitude of wave), asymptotic analysis predicts several behaviours of the wave: propagation in a uniform tube, attenuation of the amplitude due to the skin friction, diffusion due to the viscosity of the wall, and reflection and transmission at a branching point. These predictions are compared very favorably with all of the numerical solutions. The schemes are also tested in case with a larger nonlinearity. Finally, we apply all of the schemes on a relatively realistic arterial system with 55 arteries. The schemes are compared in four aspects: the spatial and temporal convergence speed, the ability to capture shock phenomena, the computation speed and the complexity of the implementation. The suitable conditions for the application of the various schemes are discussed.
Three dimensional boundary layer flow of a viscoelastic nanofluid with Soret and Dufour effects
M. Ramzan
2016-03-01
Full Text Available The present research focuses on the three-dimensional flow of viscoelastic fluid in the presence of Soret and Dufour effects. Effects of thermophoresis and Brownian motion are taken into account. Appropriate similarity transformations lead to nonlinear ordinary differential equations. Solution expressions of velocity, temperature and nanoparticle concentration are computed via homotopy analysis method (HAM. Convergence of obtained solutions is analyzed graphically and numerically. Results are plotted and analyzed for the dimensionless velocities, temperature and nanoparticle concentration. Values of local Nusselt and Sherwood numbers are examined through tabular form. It is observed that Temperature field is enhanced for the larger Brownian motion parameter and an increase in Dufour number gives rise to the temperature and thermal boundary layer thickness.
Chemically reacting dusty viscoelastic fluid flow in an irregular channel with convective boundary
R. Sivaraj
2013-03-01
Full Text Available In this paper, we have studied the combined effects of free convective heat and mass transfer on an unsteady MHD dusty viscoelastic (Walters liquid model-B fluid flow between a vertical long wavy wall and a parallel flat wall saturated with porous medium subject to the convective boundary condition. The coupled partial differential equations are solved analytically using perturbation technique. The velocity, temperature and concentration fields have been studied for various combinations of physical parameters such as magnetic field, heat absorption, thermal radiation, radiation absorption, Biot number and chemical reaction parameters. The skin friction, Nusselt number and Sherwood number are also presented and displayed graphically. Further, it is observed that the velocity profiles of dusty fluid are higher than the dust particles.
Zhi-Ying Zheng
2013-01-01
Full Text Available Through embedding an in-house subroutine into FLUENT code by utilizing the functionalization of user-defined function provided by the software, a new numerical simulation methodology on viscoelastic fluid flows has been established. In order to benchmark this methodology, numerical simulations under different viscoelastic fluid solution concentrations (with solvent viscosity ratio varied from 0.2 to 0.9, extensibility parameters (100≤L2≤500, Reynolds numbers (0.1 ≤ Re ≤ 100, and Weissenberg numbers (0 ≤ Wi ≤ 20 are conducted on unsteady laminar flows through a symmetric planar sudden expansion with expansion ratio of 1: 3 for viscoelastic fluid flows. The constitutive model used to describe the viscoelastic effect of viscoelastic fluid flow is FENE-P (finitely extensive nonlinear elastic-Peterlin model. The numerical simulation results show that the influences of elasticity, inertia, and concentration on the flow bifurcation characteristics are more significant than those of extensibility. The present simulation results including the critical Reynolds number for which the flow becomes asymmetric, vortex size, bifurcation diagram, velocity distribution, streamline, and pressure loss show good agreements with some published results. That means the newly established method based on FLUENT software platform for simulating peculiar flow behaviors of viscoelastic fluid is credible and suitable for the study of viscoelastic fluid flows.
Finite-Time Lyapunov Exponents and Lagrangian Coherent Structures in Uncertain Unsteady Flows.
Guo, Hanqi; He, Wenbin; Peterka, Tom; Shen, Han-Wei; Collis, Scott; Helmus, Jonathan
2016-02-29
The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain LCS (U-LCS). The D-FTLE is the probability density function of FTLE values for every spatiotemporal location, which can be visualized with different statistical measurements. The FTLE-D extends the deterministic FTLE by measuring the divergence of particle distributions. It gives a statistical overview of how transport behaviors vary in neighborhood locations. The U-LCS, the probabilities of finding LCSs over the domain, can be extracted with stochastic ridge finding and density estimation algorithms. We show that our approach produces better results than existing variance-based methods do. Our experiments also show that the combination of D-FTLE, FTLE-D, and U-LCS can help users understand transport behaviors and find separatrices in ensemble simulations of atmospheric processes.
Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia); Muhammad, Taseer, E-mail: taseer_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, A.; Alhuthali, M.S. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589 (Saudi Arabia)
2015-07-01
Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect. - Highlights: • Three-dimensional boundary layer flow of viscoelastic nanofluid is examined. • Nonlinear thermal radiation is analyzed. • Brownian motion and thermophoresis effects are present. • Recently developed condition requiring zero nanoparticle mass flux is implemented. • Construction of convergent solutions of nonlinear flow is possible.
TONG Dengke; WANG Ruihe
2004-01-01
In this paper, fractional order derivative, fractal dimension and spectral dimension are introduced into the seepage flow mechanics to establish the relaxation models of non-Newtonian viscoelastic fluids with the fractional derivative in fractal reservoirs. A new type integral transform is introduced, and the flow characteristics of non-Newtonian viscoelastic fluids with the fractional order derivative through a fractal reservoir are studied by using the integral transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions are obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation are also obtained. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite fractal reservoir is studied by using the Stehfest's inversion method of the numerical Laplace transform. It is shown that the clearer the viscoelastic characteristics of the fluid, the more the fluid is sensitive to the order of the fractional derivative. The new type integral transform provides a new analytical tool for studying the seepage mechanics of fluid in fractal porous media.
P H Veena
2017-04-01
Full Text Available In this paper two dimensional flow of a viscoelastic fluid due to stretching surface is considered. Flow analysis is carried out by using closed form solution of fourth order differential equation of motion of viscoelastic fluid. Further (Walters’ liquid B’ model heat transfer analysis is carried out using convective surface condition. The governing equations of flow and heat transfer are non-linear partial differential equations which are unable to solve analytically hence are solved using Runge-Kutta Numerical Method with efficient shooting technique. The flow and heat transfer characteristics are studied through plots drawn. Numerical values of Wall temperature are calculated and presented in the table and compared with earlier published results which are in good agreement
Lagrangian Flow networks: a new way to characterize transport and connectivity in geophysical flows
Ser-Giacomi, Enrico; Hernandez-Garcia, Emilio; Lopez, Cristobal; Rossi, Vincent; Vasile, Ruggero
2015-04-01
Water and air transport are among the basic processes shaping the climate of our planet. Heat and salinity fluxes change sea water density, and thus drive the global thermohaline circulation. Atmospheric winds force the ocean motion, and also transport moisture, heat or chemicals, impacting the regional climate. We describe transport among different regions of the ocean or the atmosphere by flow networks, giving a discrete and robust representation of the fluid advection dynamics. We use network-theory tools to gain insights into transport problem. Local and global features of the networks are extracted from many numerical experiments to give a time averaged description of the system. Classical concepts like dispersion, mixing and connectivity are finally related to a set of network-like objects contributing to build a "dictionary" between network measures and physical quantities in geophysical flows.
Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H
2015-10-01
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.
Atkinson, C.; Hackl, J.; Stegeman, P.; Borrell, G.; Soria, J.
2014-04-01
The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.
Baskan, O.; Clercx, H. J. H [Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Speetjens, M. F. M. [Energy Technology Laboratory, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Metcalfe, G. [Commonwealth Scientific and Industrial Research Organisation, Melbourne, Victoria 3190 (Australia); Swinburne University of Technology, Department of Mechanical Engineering, Hawthorn VIC 3122 (Australia)
2015-10-15
Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
HE Feng-yun; YANG Shu-ren
2008-01-01
The equation governing the unsteady flow of viscoelastic fluids in an eccentric annulus was derived by using the common conversion Maxwell fluid constitutive equation and then discretized by the control volume method. The velocity distribution of flow field was computed by using the ADI method. The influences of the pressure gradient, eccentricity, stroke length, and stroke frequency on the velocity and flow capacity in the flow field was analyzed. The foundation for further research of the eccentric wear problem of the pumping rod in polymer-flood well was laid.
Koppol, Anantha Padmanabha Rao
Flows of viscoelastic polymeric fluids are of great fundamental and practical interest as polymeric materials for commodity and value-added products are processed typically in a fluid state. The nonlinear coupling between fluid motion and microstructure, which results in highly non-Newtonian theology, memory/relaxation and normal stress development or tension along streamlines, greatly complicates the analysis, design and control of such flows. This has posed tremendous challenges to researchers engaged in developing first principles models and simulations that can accurately and robustly predict the dynamical behavior of polymeric flows. Despite this, the past two decades have witnessed several significant advances towards accomplishing this goal. Yet a problem of fundamental and great pragmatic interest has defied solution to years of ardent research by several groups, namely the relationship between friction drag and flow rate in inertialess flows of highly elastic polymer solutions in complex kinematics flows. First principles-based solution of this long-standing problem in non-Newtonian fluid mechanics is the goal of this research. To achieve our objective, it is essential to develop the capability to perform large-scale multiscale simulations, which integrate continuum-level finite element solvers for the conservation of mass and momentum with fast integrators of stochastic differential equations that describe the evolution of polymer configuration. Hence, in this research we have focused our attention on development of a parallel, multiscale simulation algorithm that is capable of robustly and efficiently simulating complex kinematics flows of dilute polymeric solutions using the first principles based bead-spring chain description of the polymer molecules. The fidelity and computational efficiency of the algorithm has been demonstrated via three benchmark flow problems, namely, the plane Couette flow, the Poiseuille flow and the 4:1:4 axisymmetric
Hydrodynamic interactions between two equally sized spheres in viscoelastic fluids in shear flow.
Snijkers, Frank; Pasquino, Rossana; Vermant, Jan
2013-05-14
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 used together with quantitative videomicroscopy. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected that highlight specific constitutive features. These include a reference Newtonian fluid (N), a constant-viscosity, high-elasticity Boger fluid (BF), a wormlike micellar surfactant solution with a single dominant relaxation time (WMS), and a broad spectrum shear-thinning elastic polymer solution (ST). As expected, the trajectories are symmetric in the Newtonian fluid. In the BF, the midpoints of the spheres are observed to remain in the same plane before and after the interaction, as in the Newtonian fluid, although the path lines are in this case no longer symmetric. Interactions in the ST and WMS are highly asymmetric. Two fundamentally different kinds of path lines are observed in the WMS and ST: reversing and open trajectories. The type of trajectory depends on the initial configuration of the spheres with respect to each other and on the shear rate. On the basis of the obtained results, shear-thinning of the viscosity seems to be the key rheological parameter that determines the overall nature of the interactions, rather than the relative magnitude of the normal stress differences.
Augenbaum, J. M.
1985-01-01
A Lagrangian scheme using the Voronoi mesh is applied to study shallow water flow on a sphere. Discrete approximations to the shallow water equations are obtained for the surfaces of a nonrotating and a rotating sphere, and discrete differential operators are defined for the gradient and the divergence on the sphere. Dissipation is put into the model, when needed, by merging fluid points when they get too close to each other. The full numerical scheme is described and results of numerical computations on various test cases are given, including zonal flow and the Riemann problem.
Mielke, Alexander
1991-01-01
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists,...
Mancho, Ana M.; Mendoza, Carolina
2009-11-01
In recent years there has been a lot of progress in the application of dynamical systems concepts to the description of transport in oceanic flows. In these flows the classical dynamical system theory does not apply since they are aperiodic and finite-time defined. Recently, for describing these flows a new definition of distinguished trajectory has been proposed (Madrid & Mancho, Chaos, 2009). Distinguished trajectories act as organizing centres of the geometrical template of aperiodic time-dependent flows, like fixed points and periodic orbits do in time independent or periodic flows. The computation of distinguished trajectories makes use of a function M of which we show contains a lot of Lagrangian information. In this presentation I will discuss how the visualization of this function M, allows identifying relevant Lagrangian features at a glance. In particular we report an application to real altimetry data taken from satellite in the area of the Kuroshio current. The function M also determines the stable and unstable subspaces of the distinguished hyperbolic trajectories which are tangent to the invariant manifolds. From the computation of stable and unstable manifolds we report an accurate description of transport routes in this region.
Hashemabadi, S.H. [Iran Univ. of Science and Technology, Dept. of Chemical Engineering, Tehran (Iran); Etemad, S.Gh. [Isfahan Univ. of Technology, Dept. of Chemical Engineering, Isfahan (Israel); Thibault, J. [Ottawa Univ., Dept. of Chemical Engineering, Ottawa, ON (Canada)
2004-08-01
Heat transfer to viscoelastic fluids is frequently encountered in various industrial processing. In this investigation an analytical solution was obtained to predict the fully developed, steady and laminar heat transfer of viscoelastic fluids between parallel plates. One of the plates was stationary and was subjected to a constant heat flux. The other plate moved with constant velocity and was insulated. The simplified Phan-Thien-Tanner (SPTT) model, believed to be a more realistic model for viscoelastic fluids, was used to represent the rheological behavior of the fluid. The energy equation was solved for a wide range of Brinkman number, dimensionless viscoelastic group, and dimensionless pressure drop. Results highlight the strong effects of these parameters on the heat transfer rate. (Author)
Lie group analysis of viscoelastic MHD aligned flow and heat transfer
Asif Ali; Ahmer Mehmood; Muhammad R. Mohyuddin; Keren Wang; Yunming Chen
2005-01-01
Exact solutions for an incompressible, viscoelastic, electrically conducting MHD aligned fluid are obtained for velocity components and temperature profiles. Lie Group method is applied to obtain the solution and the symmetries used are of translational type.
Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan
2016-12-01
Lagrangian tracking model combined with Eulerian multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The Eulerian approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the Lagrangian way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/h is larger than 0.4.
J. Duan
1997-01-01
Full Text Available In this paper we study Lagrangian transport in the near wake of the flow around an obstacle, which we take to be a cylinder. In this case, for the range of Reynolds numbers investigated, the flow is two-dimensional and time periodic. We use ideas and methods from transport theory in dynamical systems to describe and quantify transport in the near wake. We numerically solve the Navier-Stokes equations for the velocity field and apply these methods to the resulting numerical representation of the velocity field. We show that the method of lobe dynamics can be used in conjunction with computational fluid dynamics methods to give very detailed and quantitative information about Lagrangian transport. In particular, we show how the stable and unstable manifolds of certain saddle-type stagnation points on the cylinder, and one in the wake, can be used to divide the flow into three distinct regions, an upper wake, a lower wake, and a wake cavity. The significance of the division using stable and unstable manifolds lies in the fact that these invariant manifolds form a template on which the transport occurs. Using this, we compute fluxes from the upper and lower wakes into the wake cavity using the associated turnstile lobes. We also compute escape time distributions as well as compare transport properties for two different Reynolds numbers.
Johnson, Perry L.; Hamilton, Stephen S.; Burns, Randal; Meneveau, Charles
2017-01-01
An intrinsic property of turbulent flows is the exponential deformation of fluid elements along Lagrangian paths. The production of enstrophy by vorticity stretching follows from a similar mechanism in the Lagrangian view, though the alignment statistics differ and viscosity prevents unbounded growth. In this paper, the stretching properties of fluid elements and vorticity along Lagrangian paths are studied in a channel flow at Reτ=1000 and compared with prior known results from isotropic turbulence. To track Lagrangian paths in a public database containing direct numerical simulation results, the task-parallel algorithm previously employed in the isotropic database is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis. In the viscous sublayer, these stretching statistics approach values more consistent with an unsteady two-dimensional shear flow, in which exponential stretching no longer occurs. Normalized by dissipation rate, the stretching in the buffer layer and below is less efficient due to less favorable alignment statistics. The Cramér function characterizing cumulative Lagrangian stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence.
Khan, Sami Ullah; Ali, Nasir; Abbas, Zaheer
2015-01-01
An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.
Khan, Sami Ullah; Ali, Nasir; Abbas, Zaheer
2015-01-01
An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD) second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number. PMID:26657931
Kim, Ju Min [Ajou University, Suwon (Korea, Republic of)
2015-12-15
A cross-slot microchannel has been harnessed for a wide range of applications, such as label-free measurements of cell deformability and rheological characterization of complex fluids. This work investigates flow kinematics in a cross-slot microchannel used for the measurements of cell deformability utilizing finite element method (FEM)- based numerical simulation. In a cross-slot microchannel, the cell is stretched near the stagnation of the cross-slot channel, and cell deformation is significantly affected by its trajectory. Two passive methods, inertia- and viscoelasticitybased, which do not rely on any external force such as an electric field, have been applied to focus particles along the channel centerline so that the cell trajectories are unified. However, it is not well understood how the flow kinematics inside the cross-slot channel is altered by the inertial or viscoelastic effect when these two methods are employed. This work demonstrates that the flow kinematics such as the distributions of flow type and strain rate is notably changed with an increase in the Reynolds number when an inertia-based method is employed. On the other hand, flow kinematics does not significantly deviate from that of an inertia-less Newtonian fluid irrespective of the Weissenberg numbers when a viscoelasticity-based method is used. The current work will be helpful for the design and operation of a cross-slot microdevice for measuring cell deformability.
Sami Ullah Khan
Full Text Available An analysis is carried out to study the heat transfer in unsteady two-dimensional boundary layer flow of a magnetohydrodynamics (MHD second grade fluid over a porous oscillating stretching surface embedded in porous medium. The flow is induced due to infinite elastic sheet which is stretched periodically. With the help of dimensionless variables, the governing flow equations are reduced to a system of non-linear partial differential equations. This system has been solved numerically using the finite difference scheme, in which a coordinate transformation is used to transform the semi-infinite physical space to a bounded computational domain. The influence of the involved parameters on the flow, the temperature distribution, the skin-friction coefficient and the local Nusselt number is shown and discussed in detail. The study reveals that an oscillatory sheet embedded in a fluid-saturated porous medium generates oscillatory motion in the fluid. The amplitude and phase of oscillations depends on the rheology of the fluid as well as on the other parameters coming through imposed boundary conditions, inclusion of body force term and permeability of the porous medium. It is found that amplitude of flow velocity increases with increasing viscoelastic and mass suction/injection parameters. However, it decreases with increasing the strength of the applied magnetic field. Moreover, the temperature of fluid is a decreasing function of viscoelastic parameter, mass suction/injection parameter and Prandtl number.
Misra, J C; Rath, H J
2010-01-01
Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter's liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agrement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.
Cimorelli, L.; Cozzolino, L.; D'Aniello, A.; Morlando, F.; Pianese, D.; Singh, V. P.
2016-07-01
In this paper, a new numerical model for the simulation of constituent transport in both steady and unsteady flow conditions is presented. The transport model is a routing procedure in which the advection process is solved by means of the Lagrangian coordinate transformation, while the dispersion process is approximated within each time step by means of the convolution principle, exploiting a multilinear procedure. In order to facilitate the application of the Lagrangian coordinate transformation during unsteady flow conditions, the unsteady velocity field corresponding to the linearized parabolic approximation of the Saint Venant Equations is provided, taking into account appropriate boundary conditions. Finally, classic BOD-DO relationships are embedded into the routing procedure in order to perform water quality applications with reactive constituents. The model is first demonstrated with respect to a numerical water quality model in both steady and unsteady hydraulic conditions, and is then applied to two real-world cases. Because of its characteristics, the proposed model seems suitable for real time forecast of pollutant concentrations when an emergency event occurs, or for water quality management in real rivers.
B. Rostami
2014-01-01
Full Text Available An analytical strong method, the homotopy analysis method (HAM, is employed to study the mixed convective heat transfer in an incompressible steady two-dimensional viscoelastic fluid flow over a wedge in the presence of buoyancy effects. The two-dimensional boundary-layer governing partial differential equations (PDEs are derived by the consideration of Boussinesq approximation. By the use of similarity transformation, we have obtained the ordinary differential nonlinear (ODE forms of momentum and energy equations. The highly nonlinear forms of momentum and energy equations are solved analytically. The effects of different involved parameters such as viscoelastic parameter, Prandtl number, buoyancy parameter, and the wedge angle parameter, which is related to the exponent m of the external velocity, on velocity and temperature distributions are plotted and discussed. An excellent agreement can be seen between the results and the previously published papers for f′′(0 and θ′(0 in some of the tables and figures of the paper for velocity and temperature profiles for various values of viscoelastic parameter and Prandtl number. The effects of buoyancy parameter on the velocity and temperature distributions are completely illustrated in detail.
An explicit Lagrangian finite element method for free-surface weakly compressible flows
Cremonesi, Massimiliano; Meduri, Simone; Perego, Umberto; Frangi, Attilio
2017-07-01
In the present work, an explicit finite element approach to the solution of the Lagrangian formulation of the Navier-Stokes equations for weakly compressible fluids or fluid-like materials is investigated. The introduction of a small amount of compressibility is shown to allow for the formulation of a fast and robust explicit solver based on a particle finite element method. Newtonian and Non-Newtonian Bingham laws are considered. A barotropic equation of state completes the model relating pressure and density fields. The approach has been validated through comparison with experimental tests and numerical simulations of free surface fluid problems involving water and water-soil mixtures.
Semi-Lagrangian off-lattice Boltzmann method for weakly compressible flows.
Krämer, Andreas; Küllmer, Knut; Reith, Dirk; Joppich, Wolfgang; Foysi, Holger
2017-02-01
The lattice Boltzmann method is a simulation technique in computational fluid dynamics. In its standard formulation, it is restricted to regular computation grids, second-order spatial accuracy, and a unity Courant-Friedrichs-Lewy (CFL) number. This paper advances the standard lattice Boltzmann method by introducing a semi-Lagrangian streaming step. The proposed method allows significantly larger time steps, unstructured grids, and higher-order accurate representations of the solution to be used. The appealing properties of the approach are demonstrated in simulations of a two-dimensional Taylor-Green vortex, doubly periodic shear layers, and a three-dimensional Taylor-Green vortex.
Huhn, F.; Schanz, D.; Gesemann, S.; Schröder, A.
2016-09-01
Pressure gradient fields in unsteady flows can be estimated through flow measurements of the material acceleration in the fluid and the assumption of the governing momentum equation. In order to derive pressure from its gradient, almost exclusively two numerical methods have been used to spatially integrate the pressure gradient until now: first, direct path integration in the spatial domain, and second, the solution of the Poisson equation for pressure. Instead, we propose an alternative third method that integrates the pressure gradient field in Fourier space. Using a FFT function, the method is fast and easy to implement in programming languages for scientific computing. We demonstrate the accuracy of the integration scheme on a synthetic pressure field and apply it to an experimental example based on time-resolved material acceleration data from high-resolution Lagrangian particle tracking with the Shake-The-Box method.
Li, D. [Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2 (Canada); Labropulu, F. [Luther College e Mathematics, University of Regina, Regina, SK S4S 0A2 (Canada); Pop, I. [Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253 (Romania)
2011-09-15
An analysis of the steady mixed convection flow of a viscoelastic fluid stagnating orthogonally on a heated or cooled vertical flat plate has been studied. Using similarity variables, the governing equations are transformed into a system of two coupled non-linear ordinary differential equations. The resulting equations are then solved numerically using the spectral method. It is observed that the skin friction coefficient and the local heat transfer are decreasing when the Weissenberg number We is increasing in both assisting and opposing flow cases. On the other hand, the skin friction is decreasing and the local heat transfer is increasing when the Prandtl number Pr is increasing in the case of assisting flow. In the case of opposing flow, the skin friction and the local heat transfer are increasing as Pr is increasing. (authors)
Detecting and tracking eddies in oceanic flows: A vorticity based Euler-Lagrangian method
Vortmeyer-Kley, Rahel; Gräwe, Ulf; Feudel, Ulrike
2016-04-01
Algae blooms as recurrent events in the Baltic Sea are an increasing natural hazard. Sandulescu et al. show in numerical simulation in [1] that eddies can play the role of an incubator for an algae bloom. Inside the eddy nutrients and plankton are trapped and can then be transported across rather long distances. To gain insight in mechanisms of algae bloom evolution detection and tracking of eddies is of interest. Based on the idea to interpret an eddy as a region that is bounded by manifolds and has an elliptic fixed point inside them, we develop an Euler-Lagrangian eddytracking tool using the idea of Lagrangian descriptors [2] and the vorticity. To test how well the tool detects eddy tracks and shapes, and estimates eddy lifetimes, the method is applied to a synthetic van Karman-Vortex Street. The results are compared to an eddytracking tool by Nencioli et al. [3]. Even velocity fields incorporated with different types of noise are taken into account to test the robustness of the tool. Finally, both methods are applied to velocity fields of the Baltic Sea. [1] M. Sandulescu, C. Lopez, E. Hernandez-Garcia and U. Feudel, Nonlinear Proc. Geophys., 14, 443-454, (2007). [2] J. Jimenez-Madrid and A. Mancho, Chaos, 19, 013111-1-18, (2009). [3] F. Nencioli, C. Dong, T. Dickey, L. Washburn, and J.C. McWilliams, J. Atmos. Ocean Tech., 27, 564-579, (2010).
Güçlü, Yaman
2013-01-01
The term `Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of final cells. As such the CS is a `forward-trajectory' semi-Lagrangian scheme. For multi-dimensional simulations of neutral gas flows, the cell-centered version of this semi-Lagrangian (CCSL) scheme has advantages over other options due to its implementation simplicity, low memory requirements, and easier treatment of boundary conditions. The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2$^{\\text{nd}}$ order remapping that takes place at the end of each time step. By means of a Modified Equation Analysis, it is shown that a high order estimate of the remapping error can be obtained a priori, and a small correction to the final position of the cells can be applied upon remapping, in order to achieve full compensatio...
Bach, P; Hassager, Ole
1985-01-01
An algorithm is constructed for the use of the Lagrangian kinematc specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with t......-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value......., with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel...
Doisneau, François; Arienti, Marco; Oefelein, Joseph C.
2017-01-01
For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.
Doisneau, François, E-mail: fdoisne@sandia.gov; Arienti, Marco, E-mail: marient@sandia.gov; Oefelein, Joseph C., E-mail: oefelei@sandia.gov
2017-01-15
For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.
Adesemowo, Morakinyo; Shelton, John
2016-11-01
Previous experimental and numerical investigations involving lid-driven cavity flows with particle suspensions have primarily focused on particle tracking and the visualization of complex three-dimensional structures that compose the flow field. However, these particle suspensions and their resulting particle-particle interactions could also be viewed as a system of time-dependent perturbation equations to the steady-state Navier-Stokes equations and could affect both the stability and steady-state characteristics of the two-dimensional lid-driven cavity system. In this investigation, an Eulerian-Lagrangian approach to modeling particle suspensions in the lid-driven cavity is utilized in FV-CFD simulations to investigate the effect particle density, area fraction, and Reynolds number have on the two-dimensional flow characteristics of a laminar fluid. Observations have indicated that the development of the primary vortex in the lid-driven cavity varies according to the area fraction of particle suspensions in the system; transitioning from development via an adverse pressure gradient at the top-right corner of the cavity towards particle-laden behavior where particle-particle interactions dominate the development of the primary vortex. Dynamic responses were also observed for particle systems of less dense particles. Finally, a comparison between flows perturbed using disturbance velocities and from particle interactions was performed.
Töger, Johannes; Kanski, Mikael; Carlsson, Marcus; Kovács, Sándor J; Söderlind, Gustaf; Arheden, Håkan; Heiberg, Einar
2012-12-01
Recent studies suggest that vortex ring formation during left ventricular (LV) rapid filling is an optimized mechanism for blood transport, and that the volume of the vortex ring is an important measure. However, due to lack of quantitative methods, the volume of the vortex ring has not previously been studied. Lagrangian Coherent Structures (LCS) is a new flow analysis method, which enables in vivo quantification of vortex ring volume. Therefore, we aimed to investigate if vortex ring volume in the human LV can be reliably quantified using LCS and magnetic resonance velocity mapping (4D PC-MR). Flow velocities were measured using 4D PC-MR in 9 healthy volunteers and 4 patients with dilated ischemic cardiomyopathy. LV LCS were computed from flow velocities and manually delineated in all subjects. Vortex volume in the healthy volunteers was 51 ± 6% of the LV volume, and 21 ± 5% in the patients. Interobserver variability was -1 ± 13% and interstudy variability was -2 ± 12%. Compared to idealized flow experiments, the vortex rings showed additional complexity and asymmetry, related to endocardial trabeculation and papillary muscles. In conclusion, LCS and 4D PC-MR enables measurement of vortex ring volume during rapid filling of the LV.
Huang, C Y; Mow, V C; Ateshian, G A
2001-10-01
articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension-compression nonlinearity.
Sedaghatizadeh, N; Atefi, G; Fardad, A A; Barari, A; Soleimani, Soheil; Khani, S
2011-10-01
In this investigation, semiempirical and numerical studies of blood flow in a viscoelastic artery were performed using the Cosserat continuum model. The large-amplitude oscillatory shear deformation model was used to quantify the nonlinear viscoelastic response of blood flow. The finite difference method was used to solve the governing equations, and the particle swarm optimization algorithm was utilized to identify the non-Newtonian coefficients (k(υ) and γ(υ)). The numerical results agreed well with previous experimental results. Copyright © 2011 Elsevier Ltd. All rights reserved.
M. Ramzan
2015-05-01
Full Text Available This paper deals with steady three dimensional boundary layer flow of an incompressible viscoelastic nanofluid flow in the presence of Newtonian heating. An appropriate transformation is employed to convert the highly non linear partial differential equations into ordinary differential equations. Homotopy Analysis method (HAM is used to find series solution of the obtained coupled highly non linear differential equations. The convergence of HAM solutions is discussed via h-curves. Graphical illustrations displaying the influence of emerging parameters on velocity, temperature and concentration profiles are given. It is observed that γ the conjugate parameter for Newtonian heating show increasing behavior on both temperature and concentration profiles. However, the temperature and concentration profiles are increasing and decreasing functions of Brownian motion parameter Nb respectively.
Shun Zou
2015-02-01
Full Text Available An efficient IBLF-dts scheme is proposed to integrate the bounce-back LBM and FVM scheme to solve the Navier-Stokes equations and the constitutive equation, respectively, for the simulation of viscoelastic fluid flows. In order to improve the efficiency, the bounce-back boundary treatment for LBM is introduced in to improve the grid mapping of LBM and FVM, and the two processes are also decoupled in different time scales according to the relaxation time of polymer and the time scale of solvent Newtonian effect. Critical numerical simulations have been carried out to validate the integrated scheme in various benchmark flows at vanishingly low Reynolds number with open source CFD toolkits. The results show that the numerical solution with IBLF-dts scheme agrees well with the exact solution and the numerical solution with FVM PISO scheme and the efficiency and scalability could be remarkably improved under equivalent configurations.
Yamamoto, T.; Nakamura, K. [Osaka University, Tokyo (Japan). Faculty of Engineering
1998-10-25
Start-up flows of viscoelastic fluids in a two-dimensional 4 to 1 abrupt contraction channel is numerically studied and the transient behavior of viscoelastic fluids is discussed. The multi mode Leonov model is applied to describe the rheological properties of the viscoelastic fluid. The numerical simulation has been carried out for two Weissenberg numbers. The following results are obtained from the present analysis: The corner vortices develop with time and restrict the velocity gradient to relax the growth of the stress field. The circular secondary flow works as a stress relief mechanism. The overshoot of the stress growth is observed at the high Weissenberg number and is not done at the low Weissenberg number. This phenomenon is caused by the unsteady elongational property of the fluid. 15 refs., 9 figs.
Comminal, Raphael Benjamin
This thesis presents a new numerical algorithm for the simulation of two‐dimensional multiphase viscoelastic flows. The simulation of viscoelastic flows has both a scientific importance and practical implications in polymer processing. This work has put the emphasis on the extrusion of polymeric...... materials, where viscoelastic effects cause dynamical instabilities, despite the very simple geometry. This thesis reviews the popular differential constitutive models derived from molecular theories of dilute polymer solutions, polymer networks, and entangled polymer melts, as well as the inelastic...... with data in the literature. Finally, preliminary simulations of extrudate swelling show that the fracture melt extrusion defect could be caused by instabilities in the stress layer at the surface of the die, triggered at moderate Weissenberg numbers....
Nucci, M. C.; Leach, P. G. L.
2007-01-01
Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic ...
Lagrangian vector field and Lagrangian formulation of partial differential equations
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
Su, Xiaohui; Cao, Yuanwei; Zhao, Yong
2016-06-01
In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.
A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow
Xie, Jin-Han
2014-01-01
Wind forcing of the ocean generates a spectrum of inertia-gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the nondissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the glm variant of Soward & Roberts (2010)), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon's (2013) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul's (1997) equation for NIWs with a modified quasi-geostrophic equation. In th...
Yatou, Hiroki
2010-01-01
We find three types of steady solutions and remarkable flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Reynolds (Re) and Weissenberg (Wi) numbers using direct numerical simulations with spectral element method. The solutions are called "convective", "transition", and "elastic" in ascending order of Wi. In the convective region in the Re-Wi parameter space, the convective effect and the pressure gradient balance on average. As Wi increases, th...
Bhukta, D; Dash, G C; Mishra, S R
2014-01-01
An attempt has been made to study the heat and mass transfer effect in a boundary layer flow through porous medium of an electrically conducting viscoelastic fluid over a shrinking sheet subject to transverse magnetic field in the presence of heat source. Effects of radiation, viscous dissipation, and uniform heat sink on the heat transfer have been considered. The method of solution involves similarity transformation. The coupled nonlinear partial differential equations representing momentum, concentration, and nonhomogenous heat equation are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved by applying Kummer's function. The exact solution of temperature field is obtained for power-law surface temperature (PST) as well as power-law heat flux (PHF) boundary condition. The interaction of magnetic field is proved to be counterproductive in enhancing velocity and concentration distribution, whereas presence of porous matrix reduces the temperature field at all points.
Řehoř, Martin; Pr&oring; ša, Vít; T&oring; ma, Karel
2016-10-01
Rigorous analysis of the response of nonlinear materials to step inputs requires one to simultaneously handle the discontinuity, differentiation, and nonlinearity. This task is however beyond the reach of the standard theories such as the classical theory of distributions and presents a considerable mathematical difficulty. New advanced mathematical tools are necessary to handle the challenge. An elegant and relatively easy-to-use framework capable of accomplishing the task is provided by the Colombeau algebra, which is a generalisation of the classical theory of distributions to the nonlinear setting. We use the Colombeau algebra formalism and derive explicit formulae describing the response of incompressible Maxwell viscoelastic fluid subject to step load/deformation in the lubricated squeeze flow setting.
Moreno, P. A.; Bombardelli, F. A.
2012-12-01
Particles laying motionless at the bed of rivers, lakes and estuaries can be put into motion when the shear stress exerted by the flow on the particles exceeds the critical shear stress. When these particles start their motion they can either remain suspended by long periods of time (suspended load) or move close to the bed (bed load). Particles are transported as bed load in three different modes: Sliding, rolling and saltation. Saltation is usually described as the bouncing motion of sediment particles in a layer a few particle diameters thick. The amount of particles and the bed-load mode in which they move depend on the particle size and density, and the flow intensity, usually quantified by the shear velocity. The bottom shear stress in natural streams will most likely be large enough to set saltation as the most important bed-load transport mechanism among all three modes. Thus, studying the saltation process is crucial for the overall understanding of bed-load transport. Particularly, numerical simulations of this process have been providing important insight regarding the relative importance of the physical mechanisms involved in it. Several processes occur when particles are saltating near the bed: i) Particles collide with the bed, ii) they "fly" between collisions with the bed, as a result of their interaction with the fluid flow, iii) and they collide among themselves. These processes can be simulated using a three-dimensional Eulerian-Lagrangian model. In order to mimic these processes we have experimented with an averaged turbulent flow field represented by the logarithmic law of the wall, and with a more involved approach in which a computed turbulent velocity field for a flat plate was used as a surrogate of the three-dimensional turbulent conditions present close to stream beds. Since flat-plate and open-channel boundary layers are essentially different, a dynamic similarity analysis was performed showing that the highly-resolved three
Nucci, M. C.; Leach, P. G. L.
2007-12-01
Searching for a Lagrangian may seem either a trivial endeavor or an impossible task. In this paper, we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H. Goldstein, Classical Mechanics, 2nd edition (Addison-Wesley, Reading, MA, 1980)], and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.
Razmkhah, Somayeh; Razavi, Seyed Mohammad Ali; Mohammadifar, Mohammad Amin
2017-01-01
In this study, rheological properties of cress seed gum (CSG) and its fractions (F1, F2, F3; fractionated using stepwise extraction with water) were investigated. Cress seed gum and its fractions revealed random coil conformation in dilute regimes; chain flexibility and intrinsic viscosity...... increased from F1 to F2 to F3. The mechanical spectra derived from strain sweep and frequency sweep measurements indicated that the gum dispersions had viscoelastic behavior; all of them were classified as weak gels and the gel network got stronger along the series of F1, F2 and F3. Arrhenius-type model...... was used to describe the effect of temperature; F2 and F1 showed the highest and the lowest activation energy, respectively. All gum dispersions displayed thixotropic behavior; hysteresis loop area and structural recovery increased significantly along the series of F1, F2 and F3. In general, the results...
Vié, Aymeric; Pouransari, Hadi; Zamansky, Rémi; Mani, Ali
2015-01-01
International audience; The goal of the present work is to assess the ability of Eulerian moment methods to reproduce the physics of two-way coupled particle-laden turbulent flow systems. Previous investigations have been focused on effects such as preferential concentration, and turbulence modulation, but in regimes in which turbulence is sustained by an imposed external forcing. We show that in such regimes, Eulerian methods need resolutions finer than nominal Kolmogorov scale in order to c...
Lagrangian flow measurements and observations of the 2015 Chilean tsunami in Ventura, CA
Kalligeris, Nikos; Skanavis, Vassilios; Tavakkol, Sasan; Ayca, Aykut; Safty, Hoda El; Lynett, Patrick; Synolakis, Costas
2016-05-01
Tsunami-induced coastal currents are spectacular examples of nonlinear and chaotic phenomena. Due to their long periods, tsunamis transport substantial energy into coastal waters, and as this energy interacts with the ubiquitous irregularity of bathymetry, shear and turbulent features appear. The oscillatory character of a tsunami wave train leads to flow reversals, which in principle can spawn persistent turbulent coherent structures (e.g., large vortices or "whirlpools") that can dominate damage and transport potential. However, no quantitative measurements exist to provide physical insight into this kind of turbulent variability, and no motion recordings are available to help elucidate how these vortical structures evolve and terminate. We report our measurements of currents in Ventura Harbor, California, generated by the 2015 Chilean M8.3 earthquake. We measured surface velocities using GPS drifters and image sequences of surface tracers deployed at a channel bifurcation, as the event unfolded. From the maps of the flow field, we find that a tsunami with a near-shore amplitude of 30 cm at 6 m depth produced unexpectedly large currents up to 1.5 m/s, which is a fourfold increase over what simple linear scaling would suggest. Coherent turbulent structures appear throughout the event, across a wide range of scales, often generating the greatest local currents.
Zehe, Erwin; Jackisch, Conrad; Rodriguez, Nicolas; Klaus, Julian
2017-04-01
Only a minute amount of global fresh water is stored in the unsaturated zone. Yet this tiny compartment controls soil microbial activity and associated trace gas emissions, transport and transformations of contaminants, plant productivity, runoff generation and groundwater recharge. To date, the processes controlling renewal and age of different fractions of the soil water stock are far from being understood. Current theories and process concepts were largely inferred either from over-simplified laboratory experiments, or non-exhaustive point observations and tracer data in the field. Tracer data provide key but yet integrated information about the distribution of travel times of the tracer molecules to a certain depth or on their travel depth distribution within a given time. We hence are able to observe the "effect" of soil structure i.e. partitioning of infiltrating water between fast preferential and slow flow paths and imperfect subsequent mixing between these flow paths in the subsurface and the related plant water uptake. However, we are not able to study the "cause" - because technologies for in-situ observations of flow, flow path topology and exchange processes at relevant interfaces have up to now not been at hand. In the present study we will make use of a Lagrangian model for subsurface water dynamics to explore how subsurface heterogeneity and mixing among different storage fractions affects residence time distribution in the unsaturated zone in a forward approach. Soil water is represented by particles of constant mass, which travel according to the Itô form of the Fokker Planck equation. The model concept builds on established soil physics by estimating the drift velocity and the diffusion term based on the soil water characteristics. The model has been shown to simulate capillary driven soil moisture dynamics in good accordance with a) the Richards equation and b) observed soil moisture data in different soil. The particle model may furthermore
Goyal, M.; Bhargava, R.
2014-05-01
This paper deals with the double-diffusive boundary layer flow of non-Newtonian nanofluid over a stretching sheet. In this model, where binary nanofluid is used, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of the convection features of the nanofluid. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The variational finite element method (FEM) is used to solve these ordinary differential equations. We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, modified Dufour number, viscoelastic parameter, Prandtl number, regular Lewis number, Dufour Lewis number, and nanofluid Lewis number on the flow field and heat transfer characteristics. Graphical display of the numerical examine are performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, reduced Nusselt, reduced Sherwood and reduced nanofluid Sherwood number distributions. The present study has many applications in coating and suspensions, movement of biological fluids, cooling of metallic plate, melt-spinning, heat exchangers technology, and oceanography.
Puragliesi, R., E-mail: riccardo.puragliesi@psi.ch [Nuclear Energy and Safety Research Department, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Laboratoire d' Ingenierie Numerique, Ecole Polytechnique Federale de Lausanne, Station 9, CH-1015 Lausanne (Switzerland); Dehbi, A., E-mail: abdel.dehbi@psi.ch [Nuclear Energy and Safety Research Department, Paul Scherrer Institut, CH-5232 Villigen PSI (Switzerland); Leriche, E., E-mail: emmanuel.leriche@univ-st-etienne.fr [Universite de Lyon, F-42023 Saint-Etienne, LMFA-UJM St-Etienne, CNRS UMR 5509 Universite de St-Etienne, 23 rue Docteur Paul Michelon, F-42023 Saint-Etienne (France); Soldati, A., E-mail: soldati@uniud.it [Dipartimento di Energetica e Macchine, Universita di Udine, Via delle Scienze 208, IT-33100 Udine (Italy); Deville, M.O., E-mail: michel.deville@epfl.ch [Laboratoire d' Ingenierie Numerique, Ecole Polytechnique Federale de Lausanne, Station 9, CH-1015 Lausanne (Switzerland)
2011-10-15
Highlights: > 2D study of micro-size particle depletion driven by chaotic natural convective flows in square domains. > Description of velocity and temperature first and second moments with changing in the Rayleigh number. > Strong decoupling between the turbulent kinetic energy and the dissipation rate. > Particle recirculation sustained by the vertical hot boundary layer. > Deposition mostly induced by gravity, thermophoretic and lift forces are negligible. - Abstract: In this work we investigate numerically particle deposition in the buoyancy driven flow of the differentially heated cavity (DHC). We consider two values of the Rayleigh number (Ra = 10{sup 9}, 10{sup 10}) and three values of the particle diameter (d{sub p} = 15, 25, 35 [{mu}m]). We consider the cavity filled with air and particles with the same density of water {rho}{sub w} = 1000 [kg/m{sup 3}] (aerosol). We use direct numerical simulations (DNS) for the continuous phase, and we solve transient Navier-Stokes and energy transport equations written in an Eulerian framework, under the Boussinesq approximation, for the viscous incompressible Newtonian fluid with constant Prandtl number (Pr = 0.71). First- and second-order statistics are presented for the continuous phase as well as important quantities like turbulent kinetic energy (TKE) and temperature variance with the associated production and dissipation fields. The TKE production shows different behaviour at the two Rayleigh numbers. The Lagrangian approach has been chosen for the dispersed phase description. The forces taken into account are drag, gravity, buoyancy, lift and thermophoresis. A first incursion in the sedimentation mechanisms is presented. Current results indicate that the largest contribution to particle deposition is caused by gravitational settling, but a strong recirculating zone, which liftoffs and segregates particles, contributes to decrease settling. Deposition takes place mostly at the bottom wall. The influence of lift
Goyal, Mania; Bhargava, Rama
2014-08-01
The aim of the paper is to analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The obtained ordinary differential equations are solved by variational finite element method (FEM). The effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, viscoelastic parameter, Prandtl number, Lewis number and the slip parameter on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The present study is of great interest in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal-oil slurries, heat exchangers' technology, and materials' processing and exploiting.
AL-SAIF A.S.J.; ZHU Zheng-you
2005-01-01
The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered.A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zeroth-order and first-order approximate governing equations were obtained by means of the perturbation method.To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain.The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM).The matching conditions at the interface between the inner and outer domains were presented.An iterative method for solving these discretized equations was given in this paper.The numerical results obtained agree with existing results.
Takeshi Kitano; S A R Hashmi; Navin Chand
2004-10-01
An experimental study was conducted to observe the effects of parallel-superposed flow condition on viscoelastic properties of LLDPE, Kevlar fibre reinforced LLDPE and hybrid of short glass fibre and Kevlar fibre reinforced LLDPE. Parallel-plate rheometer was employed for these tests. Rheological parameters such as loss modulus (″) and dynamic viscosity (′) do not vary significantly on superposing steady state shear with oscillatory shear in the studied range of experiment at 185°C in un-reinforced LLDPE. Kevlar fibre reinforced LLDPE and Kevlar/glass fibre reinforced LLDPE showed significant changes in the flow behaviour under various sets of superposed conditions. Storage modulus (′), and ″ become highly sensitive to low oscillatory angular frequencies () under superposed conditions. These curves show two different regions with increased value. At low values, parameters ′ and ″ change sharply reaching a certain value, thereafter, changes are moderate with increased . In case of ′ a maxima is observed, position of which, depends upon the value of steady shear rate. Maxima shifts towards higher frequencies with the increased steady shear rate.
Gutierrez-Lemini, Danton
2014-01-01
Engineering Viscoelasticity covers all aspects of the thermo- mechanical response of viscoelastic substances that a practitioner in the field of viscoelasticity would need to design experiments, interpret test data, develop stress-strain models, perform stress analyses, design structural components, and carry out research work. The material in each chapter is developed from the elementary to the advanced, providing the background in mathematics and mechanics that are central to understanding the subject matter being presented. The book examines how viscoelastic materials respond to the application of loads, and provides practical guidelines to use them in the design of commercial, military and industrial applications. This book also: · Facilitates conceptual understanding by progressing in each chapter from elementary to challenging material · Examines in detail both differential and integral constitutive equations, devoting full chapters to each type and using both forms in ...
Muñoz-Cobo, José; Chiva, Sergio; El Aziz Essa, Mohamed; Mendes, Santos
2012-08-01
Two phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the
Stagnation point flow of an non-Newtonian visco-elastic fluid
Teipel, I. [Univ. of Hannover, Inst. of Mechanics, Hannover (Germany)
1985-07-01
In this paper the flow near a two-dimensional stagnation point for a particular non-Newtonian fluid has been studied. Non-Newtonian fluids form a wide class of different materials, which will be used very often in chemical industries. From a practical point of view it is of great importance to obtain some results for example concerning the flow rate and the losses in a tube, the drag and the separation point of a boundary layer flow etc. for such fluids. Therefore it is necessary to assume a particular constitutive equation to calculate various aspects. (author)
Finite element calculations of viscoelastic fluid flow in a spinning and nutating cylinder
Rosenblat, S.; Gooding, A.; Engleman, M. S.
1986-12-01
An investigation has been performed of the flow of a non-Newtonian liquid in a spinning and nutating cylinder. An approximate analysis has been effected on the assumption that the ratio of coning rate to spin rate is small and applied to the case of a cylinder of infinite length. A numerical calculation has been performed for the actual flow of two specified non-Newtonian liquids, using the finite element code FIDAP. Results are presented in both graphical and tabular form showing flow fields and calculated values of the despin moment for ranges of parameters. The question of appropriate representation of the liquid's non-Newtonian behavior is discussed.
Lagrangian Modeling of the Atmosphere
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
Oliveira, J.L.G.; Geld, van der C.W.M.; Kuerten, J.G.M.
2013-01-01
Three-dimensional particle tracking velocimetry (3D-PTV) measurements have provided accurate Eulerian and Lagrangian high-order statistics of velocity and acceleration fluctuations and correlations at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. Spatial resolution requir
An experimental study of heat and momentum transfer in pipe flow of viscoelastic fluids
Ng, K. S.
Heat transfer and pressure drop results are presented for pipe flow of aqueous solutions of polyacrylamide and polyethylene oxide in weight concentration of a few thousand parts per million. Experiments were conducted in two experimental set-ups. The first set-up consisted of two different diameter tubes. The turbulent flow hydrodynamic entry length was found to be 110 pipe diameters. Laminar friction factor data were in good agreement with correlations for purely viscous non-Newtonian fluids. The second set-up consisted of three different diameter tubes with heat transfer length-to-diameter ratio of 282, 489, and 648. The turbulent flow thermal entry length was found to be about 400 pipe diameters. The asymptotic dimensionless heat transfer coefficients were observed to be independent of pipe diameter, polymer molecular weight, and polymer concentration, suggesting the existence of a maximum heat transfer reduction asymptote.
Minier, Jean-Pierre, E-mail: Jean-Pierre.Minier@edf.fr [EDF R and D, Mécanique des Fluides, Energie et Environnement, 6 quai Watier, 78400 Chatou (France); Chibbaro, Sergio [Sorbonne Universités, Institut Jean Le Rond d’Alembert, UPMC Univ Paris 06, CNRS, UMR7190, F-75005 Paris (France); Pope, Stephen B. [Sibley School of Mechanical and Aerospace Engineering, Cornell University, 254 Upson Hall, Ithaca, New York 14853 (United States)
2014-11-15
In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced. This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations. A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future
M. M. Rashidi
2012-01-01
Full Text Available In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid. It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a prescribed surface temperature (PST and (b prescribed heat flux (PHF. The effect of involved parameters on velocity and temperature is investigated.
Verification of mesoscopic models of viscoelastic fluids with a non-monotonic flow curve
Kuznetsova, Julia L.; Skul'skiy, Oleg I.
2016-02-01
The non-monotonic flow curve of a 1 wt.% polyacrylonitrile solution in dimethyl sulfoxide is described by two mesoscopic models: the modified Vinogradov-Pokrovsky model and the model proposed by Remmelgas, Harrison and Leal. To obtain an adequate description of the experimental curve, we have selected suitable internal parameters for these models. Analytical solutions for the Couette-Poiseuille flow problems are determined in parametric form, which allows us to plot the distribution of stress components and anisotropy tensor as well as the velocity profiles containing closed loops and weak tangential discontinuities. It is shown that both models predict a similar qualitative picture of structure evolution, but exhibit a significant discrepancy in the quantitative description of the magnitude of molecular chain stretching.
Lakshminarayanan, Vasudevan; Thyagarajan, K
2002-01-01
Ingeometrical optics, light propagation is analyzed in terms of light rays which define the path of propagation of light energy in the limitofthe optical wavelength tending to zero. Many features oflight propagation can be analyzed in terms ofrays,ofcourse, subtle effects near foci, caustics or turning points would need an analysis based on the wave natureoflight. Allofgeometric optics can be derived from Fermat's principle which is an extremum principle. The counterpart in classical mechanics is of course Hamilton's principle. There is a very close analogy between mechanics ofparticles and optics oflight rays. Much insight (and useful results) can be obtained by analyzing these analogies. Asnoted by H. Goldstein in his book Classical Mechanics (Addison Wesley, Cambridge, MA, 1956), classical mechanics is only a geometrical optics approximation to a wave theory! In this book we begin with Fermat's principle and obtain the Lagrangian and Hamiltonian pictures of ray propagation through various media. Given the ...
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.
Snijkers, F.
2016-03-31
We report upon the characterization of the steady-state shear stresses and first normal stress differences as a function of shear rate using mechanical rheometry (both with a standard cone and plate and with a cone partitioned plate) and optical rheometry (with a flow-birefringence setup) of an entangled solution of asymmetric exact combs. The combs are polybutadienes (1,4-addition) consisting of an H-skeleton with an additional off-center branch on the backbone. We chose to investigate a solution in order to obtain reliable nonlinear shear data in overlapping dynamic regions with the two different techniques. The transient measurements obtained by cone partitioned plate indicated the appearance of overshoots in both the shear stress and the first normal stress difference during start-up shear flow. Interestingly, the overshoots in the start-up normal stress difference started to occur only at rates above the inverse stretch time of the backbone, when the stretch time of the backbone was estimated in analogy with linear chains including the effects of dynamic dilution of the branches but neglecting the effects of branch point friction, in excellent agreement with the situation for linear polymers. Flow-birefringence measurements were performed in a Couette geometry, and the extracted steady-state shear and first normal stress differences were found to agree well with the mechanical data, but were limited to relatively low rates below the inverse stretch time of the backbone. Finally, the steady-state properties were found to be in good agreement with model predictions based on a nonlinear multimode tube model developed for linear polymers when the branches are treated as solvent.
Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model
Muhammad Jamil; Constantin Fetecau; Corina Fetecau
2012-01-01
The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms.The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid.The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions.They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids.Finally,the influence of pertinent parameters on the fluid motion,as well as a comparison between models,is highlighted by graphical illustrations.
Non-modal energy amplification in channel flows of viscoelastic fluids
Jovanovic, Mihailo; Hoda, Nazish; Kumar, Satish
2008-11-01
Energy amplification in channel flows of Oldroyd-B fluids is studied from an input-output point of view by analyzing the responses of the velocity components to spatio-temporal body forces. These inputs into the governing linearized equations are assumed to be harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyze Newtonian fluid flows. It is found that the energy amplification increases with a decrease in viscosity ratio and increase in Reynolds number and elasticity number. In most of the cases, streamwise constant perturbations are most amplified and the location of maximum energy amplification shifts to higher spanwise wavenumbers with an increase in Reynolds number and elasticity number and decrease in viscosity ratio. For streamwise constant perturbations, an explicit Reynolds number scaling of energy amplification from different forcing to different velocity components is developed, showing the same Re-dependence as in Newtonian fluids. At low Reynolds numbers, the energy amplification decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak.
Khayat, Roger E.; Genouvrier, Delphine
2001-05-01
An adaptive (Lagrangian) boundary element approach is proposed for the general three-dimensional simulation of confined free-surface Stokes flow. The method is stable as it includes remeshing capabilities of the deforming free surface and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free-surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several flow problems are presented to illustrate the utility of the approach, particularly as encountered in polymer processing and rheology. These problems illustrate the transient nature of the flow during the processes of extrusion and thermoforming, the elongation of a fluid sample in an extensional rheometer, and the coating of a sphere. Surface tension effects are also explored. Copyright
Lagrangian Quantum Homology for Lagrangian cobordism
Singer, Berit
2015-01-01
We extend the definition of Lagrangian quantum homology to monotone Lagrangian cobordism and establish its general algebraic properties. In particular we develop a relative version of Lagrangian quantum homology associated to a cobordism relative to a part of its boundary and study relations of this invariant to the ambient quantum homology.
Om Prakash; Devendra Kumar; Y K Dwivedi
2012-12-01
The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle . A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.
Federico VÃƒÂ¡zquez
2008-12-01
Full Text Available The heat transfer problem of a zero-mean oscillatory flow of a Maxwell fluid between infinite parallel plates with boundary conditions of the third kind is considered. With these conditions, the amount of heat entering or leaving the system depends on the external temperature as well as on the convective heat transfer coefficient. The local and global time-averaged entropy production are computed, and the consequences of convective cooling of the plates are also assessed. It is found that the global entropy production is a minimum for certain suitable combination of the physical parameters. For a discrete set of values of the oscillatory Reynolds number, the extracted heat from one of the plates shows maxima.
Role of viscoelasticity in mantle convection models
Patocka, Vojtech; Cadek, Ondrej; Tackley, Paul
2015-04-01
A present limitation of global thermo-chemical convection models is that they assume a purely viscous or visco-plastic flow law for solid rock, i.e. elasticity is ignored. This may not be a good assumption in the cold, outer boundary layer known as the lithosphere, where elastic deformation may be important. Elasticity in the lithosphere plays at least two roles: It changes surface topography, which changes the relationship between topography and gravity, and it alters the stress distribution in the lithosphere, which may affect dynamical behaviour such as the formation of plate boundaries and other tectonics features. A method for adding elasticity to a viscous flow solver to make a visco-elastic flow solver, which involves adding advected elastic stress to the momentum equation and introducing an "effective" viscosity has been proposed (e.g. Moresi, 2002). The proposed method is designed primarily for a regional-scale numerical model which employs tracers for advection and co-rotation of the stress field. In this study we test a grid-based version of the method in context of thermal convection in the Boussinesq approximation. A simple finite difference/volume model with staggered grid is used, with the aim to later use the same method to implement viscoelasticity into StagYY (Tackley, 2008). The main obstacle is that Maxwell viscoelastic rheology produces instantaneous deformation if instantaneous change of the driving forces occurs. It is not possible to model such deformation in a velocity formulated convection model, as velocity undergoes a singularity for an instantaneous deformation. For a given Rayleigh number there exists a certain critical value of the Deborah number above which it is necessary to use a thermal time step different from the one used in viscoelastic constitutive equation to avoid this numerical instability from happening. Critical Deborah numbers for various Rayleigh numbers are computed. We then propose a method to decouple the thermal and
S. Abdul Gaffar
2015-01-01
Full Text Available Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (ε, local non-Newtonian parameter based on length scale (δ, Prandtl number (Pr, Biot number (γ, pressure gradient parameter (m, magnetic parameter (M, mixed convection parameter (λ, and dimensionless tangential coordinate (ξ, on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated.
Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow
T.Chinyoka; O.D.Makinde
2013-01-01
This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.
Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids
Román Marín, José Manuel; Rasmussen, Henrik K.
2009-01-01
is assumed to be a thermorheological simple material using the extended Morland and Lee hypothesis by Crochet and Naghdi [M.J. Crochet, P.M. Naghdi, A class of non-isothermal viscoelastic fluids, International Journal of Engineering Science 10 (1972) 755–800], where the real time in the K-BKZ constitutive...... utilizing an implicit variable step backwards differencing (BDF2) scheme, obtaining second order convergence of the temperature in time. A quadratic interpolation in time is applied to approximate the time integral in the K-BKZ equation. This type of scheme ensures third order accuracy with respect...
José L. Muñoz-Cobo
2012-09-01
Full Text Available A set of air-water experiments has been performed under isothermal upward concurrent flow conditions, in a vertical column. The interfacial velocity, the bubble interfacial area and the void fraction distributions have been measured. Numerical simulation of these experiments were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. In the Eulerian solver the velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS. The turbulent kinetic energy k, and the dissipation rate transport equations were simultaneously solved by using the k, epsilon model in a (r,z grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions. The Eulerian Code was upgraded from an axisymmetric 2D code to a 3D code in order to improve the turbulence solution. The results of the 3D CFD code have been tested and show a good agreement with the experimental results. In this paper special attention is given to the coupling between the different models.
Maqbool, Khadija; Anwar Bég, O.; Sohail, Ayesha; Idreesa, Shafaq
2016-05-01
The theoretical analysis of magnetohydrodynamic (MHD) incompressible flows of a Burgers fluid through a porous medium in a rotating frame of reference is presented. The constitutive model of a Burgers fluid is used based on a fractional calculus formulation. Hydrodynamic slip at the wall (plate) is incorporated and the fractional generalized Darcy model deployed to simulate porous medium drag force effects. Three different cases are considered: namely, the flow induced by a general periodic oscillation at a rigid plate, the periodic flow in a parallel plate channel and, finally, the Poiseuille flow. In all cases the plate(s) boundary(ies) are electrically non-conducting and a small magnetic Reynolds number is assumed, negating magnetic induction effects. The well-posed boundary value problems associated with each case are solved via Fourier transforms. Comparisons are made between the results derived with and without slip conditions. Four special cases are retrieved from the general fractional Burgers model, viz. Newtonian fluid, general Maxwell viscoelastic fluid, generalized Oldroyd-B fluid and the conventional Burgers viscoelastic model. Extensive interpretation of graphical plots is included. We study explicitly the influence of the wall slip on primary and secondary velocity evolution. The model is relevant to MHD rotating energy generators employing rheological working fluids.
WANG Yan; CUI Hai-qing; YANG Yuan-jian; GUO Jun-hui; LI Nan
2006-01-01
In this article, the governing equations for the unsteady flow of viscoelastic fluid in the eccentric annulus with the inner cylinder reciprocating axially and the expression of the pressure distribution on the wall of the inner cylinder of the annulus are established and derived, respectively, under the bipolar coordinate system.The equations and the expression are solved and calculated numerically using the finite difference method, respectively.The curves of the pressure distribution on the wall of the inner cylinder of the aqueous solution of Hydrolyzed Polyacrylamide (HPAM) are plotted and the influences of annular eccentricity, stroke, and stroke frequency on the pressure distribution are analyzed.
Jha A.K.
2014-02-01
Full Text Available The present paper deals with the unsteady motion of an MHD free convection flow of an incompressible non- Newtonian viscoelastic fluid past an infinite vertical plate in the presence of a heat source and Soret effect. A parametric study illustrating the influence of various parameters on the temperature, velocity as well as on the skin-friction and rate of heat transfer is conducted. The results of the effect of the magnetic field, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are examined and shown graphically
RAKESH KUMAR,
2011-04-01
Full Text Available The purpose of this paper is to present a theoretical analysis of an unsteady hydromagnetic free convection flow of viscoelastic fluid (Walter’s B’ past an infinite vertical porous flat plate through porous medium. The temperature is assumed to be oscillating with time and the effect of the Hall current is taken into account. Assuming constant suction at the plate, closed form solutions have been obtained for velocity and temperature profiles. The effect of the various parameters, entering into the problem, on the primary, secondary velocity profiles, the axial and transverse components of skin-friction are shown graphically followed by quantitative discussion.
STUDY ON VISCOELASTIC BEHAVIOR OF PAPER COATING
Heng Zhang; Kefu Chen; Rendang Yang
2004-01-01
The flow behavior of paper coating is critical to the coating operation. In this work, the influence of the added agents on the flow behavior and the viscoelastic behavior is investigated using rheometer in steady and dynamic oscillatory modes.
Munoz-Cobo, J.L. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Chiva, S. [Univ. Jaume I, Dept. of Mechnical Engineering and Construction, Castellon (Spain); Abd El Aziz Essa, M. [Univ. Politecnica de Valencia, Inst. de Ingenieria Energetica, Valencia (Spain); Mendes, S. [Univ. Autonoma de Nuevo Leon, Facultad de Ingenieria Mecanica y Electrica (Mexico)
2011-07-01
A set of air-water experiments have been performed under isothermal upward concurrent flow in a vertical column. The interfacial velocity, interfacial area of the bubbles and the void fraction distributions was obtained. Numerical validation of these results for bubbly flow conditions were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. Both Lagrangian and Eulerian calculations were performed in parallel and iterative self-consistent method was developed. The bubbles-induced turbulence is an important issue considered, to obtain good predictions of experimental results. (author)
粘弹性流体模拟的DCQ-QUICK格式∗%Simulating Viscoelastic Flow Field Based on DCQ-QUICK Scheme
周文; 解岩; 欧阳洁; 李强
2015-01-01
流场中对流项的离散是其数值求解的一大难点。本文基于非结构同位网格格心有限体积法，针对流场守恒方程与Oldroyd-B本构方程的对流项，提出了一种耦合高阶Q-QUICK格式的延迟修正格式。通过平面Poiseuille流在不同W e数下数值解与解析解的比较，验证了该方法具有较高的精度和较好的数值稳定性。通过4：1粘弹性收缩流的数值模拟，揭示了不同Re、W e数下流场中压力、应力变化及角涡生长情况，同时也表明了该方法可有效扩大We数的计算范围。%The discrete for the convection term is one of the main diﬃculties for the num-erical solution of viscoelastic fluid flow. In this paper, for the conservation equations and the Oldroyd-B constitutive equation, a deferred correction method coupled with high order Q-QUICK scheme for the computation of the convection flux is proposed. This method is designed based on the finite volume method on unstructured collocated grids. The planar poiseuille viscoelastic flow is simulated numerically to verify the high precision and stability of the proposed method. In the simulation of 4:1 contraction viscoelastic flow, the changes of the stream lines and stresses as well as growing of the salient corner vortex versus the Weissenberg numbers are revealed. The numerical results show that the numerical method is capable of expanding the range of the Weissenberg numbers for nonlinear viscoelastic fluid.
Bilal Ashraf, M.; Alsaedi, A.; Hayat, T.; Shehzad, S. A.
2017-06-01
Heat and mass transfer effects in the three-dimensional mixed convection flow of a viscoelastic fluid with internal heat source/sink and chemical reaction have been investigated in the present work. The flow generation is because of an exponentially stretching surface. Magnetic field normal to the direction of flow is considered. Convective conditions at the surface are also encountered. Appropriate similarity transformations are utilized to reduce the boundary layer partial differential equations into the ordinary differential equations. The homotopy analysis method is used to develop the solution expressions. Impacts of different controlling parameters such as ratio parameter, Hartman number, internal heat source/sink, chemical reaction, mixed convection, concentration buoyancy parameter and Biot numbers on the velocity, temperature and concentration profiles are analyzed. The local Nusselt and Sherwood numbers are sketched and examined.
Zeeshan Khan; Muhammad Altaf Khan; Saeed Islam; Bilal Jan; Fawad Hussain; Haroon Ur Rasheed; Waris Khan
2017-01-01
Wire coating process is a continuous extrusion process for primary insulation of conducting wires with molten polymers for mechanical strength and protection in aggressive environments. Nylon, polysulfide, low/high density polyethylene (LDPE/HDPE) and plastic polyvinyl chloride (PVC) are the common and important plastic resin used for wire coating. In the current study, wire coating is performed using viscoelastic third grade fluid in the presence of applied magnetic field and porous medium. ...
Zeeshan Khan
2017-05-01
Full Text Available Wire coating process is a continuous extrusion process for primary insulation of conducting wires with molten polymers for mechanical strength and protection in aggressive environments. Nylon, polysulfide, low/high density polyethylene (LDPE/HDPE and plastic polyvinyl chloride (PVC are the common and important plastic resin used for wire coating. In the current study, wire coating is performed using viscoelastic third grade fluid in the presence of applied magnetic field and porous medium. The governing equations are first modeled and then solved analytically by utilizing the homotopy analysis method (HAM. The convergence of the series solution is established. A numerical technique called ND-solve method is used for comparison and found good agreement. The effect of pertinent parameters on the velocity field and temperature profile is shown with the help of graphs. It is observed that the velocity profiles increase as the value of viscoelastic third grade parameter β increase and decrease as the magnetic parameter M and permeability parameter K increase. It is also observed that the temperature profiles increases as the Brinkman number B r , permeability parameter K , magnetic parameter M and viscoelastic third grade parameter (non-Newtonian parameter β increase.
On viscoelastic instability in polymeric filaments
Rasmussen, Henrik Koblitz; Hassager, Ole
1999-01-01
The 3D Lagrangian Integral Method is used to simulate the effects of surface tension on the viscoelastic end-plate instability, occuring in the rapid extension of some polymeric filaments between parallel plates. It is shovn that the surface tension delays the onset of the instability. Furthermore...... it is demonstrated that surface tension plays a key role in the selection of the most unstable mode...
Two-phase viscoelastic jetting
Yu, J-D; Sakai, S.; Sethian, J.A.
2008-12-10
A coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations. The ink is modeled by the Oldroyd-B viscoelastic fluid model. The coupled algorithm seamlessly incorporates several things: (1) a coupled level set-projection method for incompressible immiscible two-phase fluid flows; (2) a higher-order Godunov type algorithm for the convection terms in the momentum and level set equations; (3) a simple first-order upwind algorithm for the convection term in the viscoelastic stress equations; (4) central difference approximations for viscosity, surface tension, and upper-convected derivative terms; and (5) an equivalent circuit model to calculate the inflow pressure (or flow rate) from dynamic voltage.
Ito, M. [Nagoya Institute of Technology, Nagoya (Japan). Faculty of Engineering; Moroi, T. [Toyoda Automatic Loom Works, Ltd., Aichi (Japan); Toda, H. [Toray Industries, Inc., Tokyo (Japan)
1998-05-25
Numerical simulations by a finite-difference method have been made for a viscoelastic flow due to a rotating disc enclosed in a cylindrical casing with large axial clearance. The Giesekus model with a single relaxation time was applied as a constitutive equation. We could simulate some typical secondary flow patterns for viscoelastic fluids which were different from Newtonian fluids; e.g., a secondary flow of which circulation direction at very low Reynolds number is reversed compared with that for a Newtonian fluid and a double-cell flow structure which Escudier et. all observed at relatively high Reynolds number. We show that the double-cell flow structure relates to nonlinear terms of the constitutive equation. The secondary flow patterns are characterized by the elasticity number (=Weissenberg number/Reynolds number) from low to high Reynolds numbers. 16 refs., 14 figs., 1 tab.
B.I. Olajuwon
2014-12-01
Full Text Available Heat and mass transfer effects on unsteady flow of a viscoelastic micropolar fluid over an infinite moving permeable plate in a saturated porous medium in the presence of a transverse magnetic field with Hall effect and thermal radiation are studied. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique to obtain the expressions for velocity, microrotation, temperature and concentration. With the help of graphs, the effects of magnetic field parameter M, thermal radiation parameter Nr, Hall current parameter m, K, viscoelastic parameter a, and slip parameter h on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. The result showed that increase in Nr and m increases translational velocity across the boundary layer while (a decreases translational velocity in the vicinity of the plate but the reverse happens when away from the plate. As h increases the translational velocity across the boundary layer increases. The higher the values of Nr, the higher the micro-rotational velocity effect while m lowers it. Also the effects n, a, m, Nr, Pr and Sc on the skin friction coefficient, Nusselt number and Sherwood numbers are presented numerically in tabular form. The result also revealed that increase in n reduces the skin friction coefficient. Pr enhances the rate of heat transfer while Sc enhances the rate of mass transfer.
Hussain Ahmad
2016-01-01
Full Text Available In the present article, radiation effect on mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder with constant heat flux has been numerically analyzed. The governing boundary layer equations are transformed to dimensionless nonlinear partial differential equations. The equations are solved numerically by using Keller-box method. The computed results are in excellent agreement with the previous studies. Skin friction coefficient and Nusselt number are emphasized specifically. These quantities are displayed against the curvature parameter. The effects of pertinent parameters involved in the problem namely effective Prandtl number and mixed convection parameter on skin friction coefficient and Nusselt number are shown through graphs and table. Boundary layer separation points are also calculated with and without radiation and a comparison is shown. The presence of radiation helps to decrease or increase the skin friction coefficient for the negative or positive values of the mixed convection parameter accordingly. The decrease in value of effective Prandtl number helps to increase the value of skin friction coefficient and Nusselt number for viscoelastic fluids.
Pasquino, Rossana; Panariello, Daniele; Grizzuti, Nino
2013-03-15
Flow-Induced Self-Assembly (FISA) is the flow-driven formation of ordered structures in complex fluids. In this paper the effect of shear flow on the microstructure formation of dilute sphere suspensions in a viscoelastic fluid has been studied experimentally by optical microscopy techniques. The system is formed by Polymethylmethacrylate beads suspended in 20 wt.% aqueous solutions of Hydroxypropylcellulose at volume fractions ranging between 0.1% and 1.0%. Experiments show that, under the action of flow, beads migrate from the bulk to the shear walls, there forming strings aligned along the flow direction. Strings grow with time eventually reaching a steady-state final length. The alignment kinetics have been quantified by means of an alignment factor, which is a measure of the average length of the strings. The experimental results indicate that both shear rate and particle concentration are relevant factors in determining the alignment factor kinetics. In particular, it is shown that, upon increasing shear rate, strings grow both faster and longer. As a consequence, the characteristic time of the overall alignment process remains roughly constant. It is also shown that an increase in particle volume fraction determines effects similar to an increase of shear rate.
Ma, Ye; Ng, Chiu-On
2009-05-01
The oscillatory and time-mean motions induced by a propagating wave of small amplitude through a viscous incompressible fluid contained in a prestressed and viscoelastic (modeled as a Voigt material) tube are studied by a perturbation analysis based on equations of motion in the Lagrangian system. The classical problem of oscillatory viscous flow in a flexible tube is re-examined in the contexts of blood flow in arteries or pulmonary gas flow in airways. The wave kinematics and dynamics, including wavenumber, wave attenuation, velocity, and stress fields, are found as analytical functions of the wall and fluid properties, prestress, and the Womersley number for the cases of a free or tethered tube. On extending the analysis to the second order in terms of the small wave steepness, it is shown that the time-mean motion of the viscoelastic tube with sufficient strength is short lived and dies out quickly as a limit of finite deformation is approached. Once the tube has attained its steady deformation, the steady streaming in the fluid can be solved analytically. Results are generated to illustrate the combined effects on the first-order oscillatory flow and the second-order steady streaming due to elasticity, viscosity, and initial stresses of the wall. The present model as applied to blood flow in arteries and gas flow in pulmonary airways during high-frequency ventilation is examined in detail through comparison with models in the literature.
Arbogast, Todd
2012-01-01
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.
Cake Filtration in Viscoelastic Polymer Solutions
Surý, Alexander; Machač, Ivan
2009-07-01
In this contribution, the filtration equations for a cake filtration in viscoelastic fluids are presented. They are based on a capillary hybrid model for the flow of a power law fluid. In order to express the elastic pressure drop excess in the flow of viscoelastic filtrate through the filter cake and filter screen, modified Deborah number correction functions are included into these equations. Their validity was examined experimentally. Filtration experiments with suspensions of hardened polystyrene particles (Krasten) in viscoelastic aqueous solutions of polyacryl amides (0.4% and 0.6%wt. Kerafloc) were carried out at a constant pressure on a cylindrical filtration unit using filter screens of different resistance.
Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md
2013-01-01
In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.
Lubrication of soft viscoelastic solids
Pandey, Anupam; Venner, Kees; Snoeijer, Jacco
2015-01-01
Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin-Voigt-, Standard Linear-, and Power Law-rheology. It is shown how the solid viscoelasticity affects the lubrication process when the timescale of loading becomes comparable to the rheological timescale. We derive asymptotic relations between lift force and sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.
Nakamura, K.; Mori, N.; Matsumura, K. [Osaka University, Osaka (Japan). Faculty of Engineering
1997-04-25
Numerical simulations of viscoelastic flows through an eccentric four-to-one abrupt contraction are carried out using the Giesekus model. The SMAC (Simplified-Marker-and-Cell) method is used to analyze the three-dimensional flows. The velocity profiles along the path line passing through the center of the exit exhibit an overshoot near the entry section, and at high Weissenberg numbers an undershoot follows the overshoot. The magnitude of the stress along the same path line has a peak near the entry, section, and its slow relaxation process indicates that a large downstream length is necessary for fully developed stress conditions to exist. The peak is lower than that for the flow through the concentric four-to-one abrupt contraction ; the decrease in the peak amplitude is understood to be due to the distortion of the path line in the eccentric geometry. A corner vortex, the height of which is a maximum at the widest corner, grows as the Weissenberg number increases. Furthermore, the tangential flow toward the widest section inside the vortex is determined. 19 refs., 10 figs.
Moroi, T. [Toyoda Automatic Loom Works, Ltd., Aichi (Japan); Ito, M.; Fujita, K. [Nagoya Institue of Technology, Nagoya (Japan)
1999-11-25
Numerical simulations by a finite-difference method have been made for a viscoelastic flow due to a rotating disc enclosed in a cylindrical casing with relatively large axial clearance. The Giesekus model, modified Giesekus modal and Phan Thien-Tanner model were applied as the constitutive equations. Using particle tracking velocimetry (PTV), the effects of rheological properties on the distribution of the velocity component V{sub {theta}} and the secondary flow were clarified. By comparing the experimental results with the numerical simulations the validity of the respective viscoelastic fluid models were examined. The secondary flow patters observed by flow visualizations were characterized by the elasticity number (= Weissenberg number/Reynolds number). It was confirmed experimentally that near the rotating axis there was a place where the tangential velocity component was negative for the cases of 0.3 wt% and 1 wt% polyacrylamide aqueous solutions. (author)
Cohen Stuart, D.C.; Kleijn, C.R.; Kenjeres, S.
2010-01-01
In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the Magnetic Drug Targeting (MDT) technique, on which th
Violato, D.; Moore, P.; Scarano, F.
2010-01-01
This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Karman wake of a cylindrical rod. The
Khan, Sujit Kumar; Abel, M. Subhas [Department of Mathematics, Gulbarga University, Gulbarga - 585 106, Karnataka (India); Sonth, Ravi M. [Department of Mathematics, K.C.T. Engineering College, Gulbarga - 585 104, Karnataka (India)
2003-12-01
The present paper deals with the study of momentum, heat and mass transfer characteristics in a viso-elastic fluid flow over a porous sheet, where the flow is generated due to linear stretching of the sheet and influenced by a uniform magnetic field applied vertically and a continuous injection of the fluid through porous boundary. In the flow region, heat balance is maintained with a temperature dependent heat source/sink, viscous dissipation, dissipation due to elastic deformation and stress work produced as the result of magnetic field on the non-Newtonian fluid. In mass transfer analysis we have taken into account the loss of mass of the chemically reactive diffusive species by means of first order chemical conversion rate. Using suitable similarity transformations on the highly non-linear partial differential equations we derive several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles in the form of confluent hyper geometric (Kummer's) functions and some other elementary functions as its special form, for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature (PST) and prescribed second order power law concentration (ii) wall with prescribed second order power law heat flux (PHF) and prescribed second order power law mass flux. The effect of the non-dimensional magnetic parameter on momentum, heat and mass transfer characteristics for non-isothermal boundary condition and different physical situations of the fluid, having various degrees of visco-elasticity, Prandtl number, heat source/sink strength and Schmidt number, are discussed in detail. Some of the several important findings reported in this paper are: (i) The combined effect of magnetic field, visco-elasticity and impermeability of the wall is to increase skin-friction largely at the wall; (ii) maximum enhancement of wall-temperature profile due to the application of
Optimization of Bistable Viscoelastic Systems
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2014-01-01
We consider the flow of a viscoelastic fluid in a symmetric cross geometry. For small driving pressures the flow is symmetric, but beyond a certain critical pressure the symmetric flow becomes unstable; two stable asymmetric solutions appear, and forcing of the unstable symmetric flow beyond...... find a design that significantly reduces the driving pressure required for bistability, and furthermore is in agreement with the approach followed by experimental researchers. Furthermore, by comparing the two asymmetric solutions, we succesfully apply the same approach to a problem with two fluids...
Moyers-Gonzalez, M.; Frigaard, I. A.; Nouar, Cherif
2010-01-01
Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-l
Moyers-Gonzalez, M.; Frigaard, I. A.; Nouar, Cherif
2010-01-01
Multi-fluid flows are frequently thought of as being less stable than single phase flows. Consideration of different non-Newtonian models can give rise to different types of hydrodynamic instability. Here we show that with careful choice of fluid rheologies and flow paradigm, one can achieve multi-l
Rheology of human blood plasma: Viscoelastic versus Newtonian behavior
Brust, M; Pan, L; Garcia, M; Arratia, P E; Wagner, C; 10.1103/PhysRevLett.110.078305
2013-01-01
We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary break-up rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurements indicate that the viscoelasticity of the plasma might even lead to viscoelastic instabilities under certain conditions. Our findings show that the viscoelastic properties of plasma should not be ignored in future studies on blood flow.
Lagrangian 3D particle tracking in high-speed flows: Shake-The-Box for multi-pulse systems
Novara, Matteo; Schanz, Daniel; Reuther, Nico; Kähler, Christian J.; Schröder, Andreas
2016-08-01
The Shake-The-Box (STB) particle tracking technique, recently introduced for time-resolved 3D particle image velocimetry (PIV) images, is applied here to data from a multi-pulse investigation of a turbulent boundary layer flow with adverse pressure gradient in air at 36 m/s ( Re τ = 10,650). The multi-pulse acquisition strategy allows for the recording of four-pulse long time-resolved sequences with a time separation of a few microseconds. The experimental setup consists of a dual-imaging system and a dual-double-cavity laser emitting orthogonal polarization directions to separate the four pulses. The STB particle triangulation and tracking strategy is adapted here to cope with the limited amount of realizations available along the time sequence and to take advantage of the ghost track reduction offered by the use of two independent imaging systems. Furthermore, a correction scheme to compensate for camera vibrations is discussed, together with a method to accurately identify the position of the wall within the measurement domain. Results show that approximately 80,000 tracks can be instantaneously reconstructed within the measurement volume, enabling the evaluation of both dense velocity fields, suitable for spatial gradients evaluation, and highly spatially resolved boundary layer profiles. Turbulent boundary layer profiles obtained from ensemble averaging of the STB tracks are compared to results from 2D-PIV and long-range micro particle tracking velocimetry; the comparison shows the capability of the STB approach in delivering accurate results across a wide range of scales.
Zhao, Tong; Yao, Jiafeng; Liu, Kai; Takei, Masahiro
2016-03-01
The inertial migration of neutrally buoyant spherical particles in high particle concentration (αpi > 3%) suspension flow in a square microchannel was investigated by means of the multi-electrodes sensing method which broke through the limitation of conventional optical measurement techniques in the high particle concentration suspensions due to interference from the large particle numbers. Based on the measured particle concentrations near the wall and at the corner of the square microchannel, particle cross-sectional migration ratios are calculated to quantitatively estimate the migration degree. As a result, particle migration to four stable equilibrium positions near the centre of each face of the square microchannel is found only in the cases of low initial particle concentration up to 5.0 v/v%, while the migration phenomenon becomes partial as the initial particle concentration achieves 10.0 v/v% and disappears in the cases of the initial particle concentration αpi ≥ 15%. In order to clarify the influential mechanism of particle-particle interaction on particle migration, an Eulerian-Lagrangian numerical model was proposed by employing the Lennard-Jones potential as the inter-particle potential, while the inertial lift coefficient is calculated by a pre-processed semi-analytical simulation. Moreover, based on the experimental and simulation results, a dimensionless number named migration index was proposed to evaluate the influence of the initial particle concentration on the particle migration phenomenon. The migration index less than 0.1 is found to denote obvious particle inertial migration, while a larger migration index denotes the absence of it. This index is helpful for estimation of the maximum initial particle concentration for the design of inertial microfluidic devices.
NUMERICAL SIMULATION OF THE VISCOELASTIC FLOWS FOR PTT MODEL BY THE SPH METHOD%PTT黏弹性流体的光滑粒子动力学方法模拟
杨波; 欧阳洁; 蒋涛; 许晓阳
2011-01-01
运用光滑粒子流体动力学（smoothed particle hydrodynamics，SPH）方法对基于PHan—Thien—Tanner（PTT）模型的黏弹性流动进行了数值模拟．首先，利用SPH方法模拟了基于PTT模型的平板Poiseuille流，通过与文献结果的比较，验证了SPH方法模拟黏弹性流动的准确性和有效性；随后，基于PTT模型对黏弹性自由表面流一液滴碰撞问题进行了SPH模拟，研究了PTT模型中拉伸参数对碰撞过程的影响．为了解决张力不稳定问题，采用简化的人工应力公式．数值结果表明，SPH方法可%The smoothed particle hydrodynamics （SPH） method is applied to simulate the viscoelastic flows governed by the PHan-Thien-Tanner （PTT） constitutive equation. First of all, the validity of the SPH method for viscoelastic flows is verified by comparing the numerical solution of a PTT fluid in the planar Poiseuille flow with those in literatures. And then, a viscoelastic free surface flow is simulated to consider about a drop of a PTT fluid impacting a rigid plate. Furthermore, the effect of the elongational parameter is investigated. The results show the flexibility of the SPH method for viscoelastic free surface problems. In particular, a simplified artificial stress is adopted to resolve the problem of the tensile instability. Numerical results obtained are in good agreement with those simulated by other mesh-based methods.
模拟微可压粘弹性流体的WCCBS_SU方法%A WCCBS_SU method for solving weakly compressible visco-elastic flow problems
栗雪娟; 欧阳洁; 蒋涛; 张小华
2011-01-01
A WCCBS_SU method based on Oldroyd-B constitutive model is developed for solving the weakly compressible visco-elastic flow problems.The planar Poiseuille visco-elastic flow and the 4：1 contraction visco-elastic flow are simulated by WCCBS_SU method under weakly compressible condition.Comparisons between the numerical and analytic solutions for the Poiseuille flow show high accuracy and better stability of the method.In the simulation of the 4：1 contraction visco-elastic flow,the changes of the stream lines and stresses and growing of the lip vortex and salient corner vortex versus the Weissenberg numbers are discussed.All the numerical results show that WCCBS_SU method developed in this paper is valid for the weakly compressible visco-elastic flow problems.%针对微可压缩粘弹性流动问题,发展了微可压缩流的WCCBS方法,详细推导了基于Oldroyd-B本构模型的WCCBS_SU方法的求解过程。在流场微可压的条件下,分别对平面Poiseuille流和4：1粘弹性收缩流进行了数值模拟。Poiseuille流在不同We数下数值结果与解析解的比较,验证了本文方法具有较高的精度和较好的稳定性。在4：1粘弹性收缩流的数值模拟中,讨论了不同We数下流场中流线、应力的变化情况,以及唇涡和凸角涡的生长情况。所有数值结果表明,对于微可压缩粘弹性流的数值模拟,WCCBS_SU方法是
Sousa, Renato G.; Nogueira, S.; Pinto, A. M. F. R.; Riethmuller, M. L.; Campos, J. B. L. M.
2004-07-01
A simultaneous technique employing particle image velocimetry (PIV) and shadowgraphy was used to study vertical slug flow in non-Newtonian fluids. Two aqueous solutions of 0.8 and 1.0 wt% carboxymethylcellulose (CMC) were studied and the flow field around individual Taylor bubbles fully characterized. The rheological fluid properties and pipe dimension yielded Reynolds numbers of 8 and 4 and Deborah numbers of 0.2 and 0.4. A negative wake was found downstream of the Taylor bubbles in both fluids. Below the bubble trailing edge, along the axis region, the fluid flows in the opposite direction to the bubble (negative wake), originating rotational liquid movements in adjacent regions. Even far downward from the bubble, rotational liquid movements are clearly seen and measured. In the 1.0 wt% CMC solution, the bubble trailing edge has the shape of a two-dimensional cusp. This two-dimensional cusp, of small dimensions, is seen in different orientations during the bubble rise-indicating a fast rotational movement. The asymmetrical shape of the trailing edge is responsible for small asymmetries in the flow in the wake region (three-dimensional flow). The asymmetrical shape associated with the rotational movement is responsible for an unsteady flow of small amplitude. In the 0.8 wt% CMC solution, the shape of the trailing edge changes during the bubble rise. An axisymmetric axial oscillation a continuous expansion and contraction of the trailing edge, is the origin of this behaviour. This oscillatory movement is responsible for an unsteady flow of small amplitude in the wake region.
Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.
Holm, Darryl D.
2002-06-01
We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.
Alireza AZIMI
2014-07-01
Full Text Available In this paper the velocity fields associated with the two-dimensional unsteady magnetohydrodynamic (MHD flow of a viscous fluid between moving parallel plates have been investigated. The governing Navier-Stokes equations for the flow are reduced to a fourth order nonlinear ordinary differential equation. The Homotopy Perturbation Method (HPM and Reconstruction of Variational Iteration Method (RVIM have been used to achieve analytical solutions. The obtained approximate results have been compared with numerical ones and results from pervious works in some cases. It has been shown that the current study is accurate and validated and can be used for other nonlinear cases.doi:10.14456/WJST.2014.70
Continuous Time Random Walks for the Evolution of Lagrangian Velocities
Dentz, Marco; Comolli, Alessandro; Borgne, Tanguy Le; Lester, Daniel R
2016-01-01
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have non-stationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and non-stationary conditions. We provide explicit expressions for the Lagrangian velocity statistics, and determine the behaviors of...
Effects of viscoelasticity in the high Reynolds number cylinder wake
Richter, David
2012-01-16
At Re = 3900, Newtonian flow past a circular cylinder exhibits a wake and detached shear layers which have transitioned to turbulence. It is the goal of the present study to investigate the effects which viscoelasticity has on this state and to identify the mechanisms responsible for wake stabilization. It is found through numerical simulations (employing the FENE-P rheological model) that viscoelasticity greatly reduces the amount of turbulence in the wake, reverting it back to a state which qualitatively appears similar to the Newtonian mode B instability which occurs at lower Re. By focusing on the separated shear layers, it is found that viscoelasticity suppresses the formation of the Kelvin-Helmholtz instability which dominates for Newtonian flows, consistent with previous studies of viscoelastic free shear layers. Through this shear layer stabilization, the viscoelastic far wake is then subject to the same instability mechanisms which dominate for Newtonian flows, but at far lower Reynolds numbers. © Copyright Cambridge University Press 2012.
Munoz-Cobo, Jose L., E-mail: jlcobos@iqn.upv.es [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Chiva, Sergio [Department of Mechanical Engineering and Construction, Universitat Jaume I, Castellon (Spain); Essa, Mohamed Ali Abd El Aziz [Instituto de Ingenieria Energetica, Universidad Politecnica de Valencia, Valencia (Spain); Mendes, Santos [Facultad de Ingenieria Mecanica y Electrica, Universidad Autonoma de Nuevo Leon (Mexico)
2012-01-15
Highlights: Black-Right-Pointing-Pointer We have simulated bubbly flow in vertical pipes by coupling a Lagrangian model to an Eulerian one, and to a 3D random walk model. Black-Right-Pointing-Pointer A set of experiments in a vertical column with isothermal co-current two phase flow have been performed and used to validate the previous model. Black-Right-Pointing-Pointer We have investigated the influence of the turbulence induced by the bubbles on the results. Black-Right-Pointing-Pointer Comparison of experimental and computed results has been performed for different boundary conditions. - Abstract: A set of two phase flow experiments for different conditions ranging from bubbly flow to cap/slug flow have been performed under isothermal concurrent upward air-water flow conditions in a vertical column of 3 m height. Special attention in these experiments was devoted to the transition from bubbly to cap/slug flow. The interfacial velocity of the bubbles and the void fraction distribution was obtained using 2 and 4 sensors conductivity probes. Numerical simulations of these experiments for bubbly flow conditions were performed by coupling a Lagrangian code with an Eulerian one. The first one tracks the 3D motion of the individual bubbles in cylindrical coordinates (r, {phi}, z) inside the fluid field under the action of the following forces: buoyancy, drag, lift, wall lubrication. Also we have incorporated a 3D stochastic differential equation model to account for the random motion of the individual bubbles in the turbulent velocity field of the carrier liquid. Also we have considered the deformations undergone by the bubbles when they touch the walls of the pipe and are compressed until they rebound. The velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate {epsilon} transport equations
Fasano, Andrea; Rasmussen, Henrik K.; Marín, J. M. R.
2015-01-01
The process of drawing an optical fiber from a polymer preform is still not completely understood,although it represents one of the most critical steps in the process chain for the fabrication of microstructuredpolymer optical fibers (mPOFs). Here we present a new approach for the numerical...... the numerical modelling of mPOF drawing has mainly beenbased on principles, such as generalized Newtonian fluid dynamics, which are not able to cope with the elasticcomponent in polymer flow. In the present work, we employ the K-BKZ constitutive equation, a non-linearsingle-integral model that combines both...
Lagrangian tetragons and instabilities in Hamiltonian dynamics
Entov, Michael; Polterovich, Leonid
2017-01-01
We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.
Experimental design for drifting buoy Lagrangian test
Saunders, P. M.
1975-01-01
A test of instrumentation fabricated to measure the performance of a free drifting buoy as a (Lagrangian) current meter is described. Specifically it is proposed to distinguish between the trajectory of a drogued buoy and the trajectory of the water at the level of the drogue by measuring the flow relative to the drogue.
Sahin, Mehmet
2010-01-01
A new geometrically conservative arbitrary Lagrangian-Eulerian (ALE) formulation is presented for the moving boundary problems in the swirl-free cylindrical coordinates. The governing equations are multiplied with the radial distance and integrated over arbitrary moving Lagrangian-Eulerian quadrilateral elements. Therefore, the continuity and the geometric conservation equations take very simple form similar to those of the Cartesian coordinates. The continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law (GCL) at the discrete level. The equation of motion of a deforming body is solved in addition to the Navier-Stokes equations in a fully-coupled form. The mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness. The resulting algebraic linear systems are solved using an ILU(k) preconditioned GMRES method provided by the PETSc librar...
Euler-Lagrangian computation for estuarine hydrodynamics
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and Lagrangian computational techniques.
The Mather problem for lower semicontinuous Lagrangians
Gomes, Diogo A.
2013-08-01
In this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
André R. Muniz
2005-03-01
Full Text Available É proposta neste trabalho uma nova metodologia para resolução das equações governantes de fluidos viscoelásticos, baseada no método dos volumes finitos, usando o arranjo co-localizado para as variáveis e malhas estruturadas. São utilizadas aproximações de alta ordem para os fluxos lineares e não-lineares médios nas interfaces dos volumes, e para os termos não-lineares que surgem da discretização das equações constitutivas. Nesta metodologia, os valores médios das variáveis nos volumes são usados durante todo o procedimento de resolução, e os valores pontuais são obtidos ao final, através da deconvolução dos valores médios. O sistema de equações discretizadas é resolvido de forma simultânea, pelo método de Newton. A metodologia é exemplificada para um problema clássico em mecânica de fluidos computacional, o escoamento stick-slip, usando como equação constitutiva o modelo de Oldroyd-B. As soluções obtidas apresentaram boa precisão, sendo livres de oscilações mesmo em regiões de grandes gradientes das variáveis.In this work, a new methodology to solve the governing equations of viscoelastic fluid flows is proposed. This methodology is based on the finite-volume method with co-located arrangement of the variables, using high-order approximations for the linear and nonlinear average fluxes in the interfaces and for the nonlinear terms resulting from the discretization of the constitutive equations. In this methodology, the average values of the variable in the volumes are used during the resolution, and the point values are recovered in the post-processing step by deconvolution of the average values. The nonlinear equations, resulting from the discretization technique, are solved simultaneously, using the Newton's method. The solutions obtained are oscillation-free and accurate, as can be seen in the solution of the stick-slip flow, used as an illustrative example.
Lagrangian Methods Of Cosmic Web Classification
Fisher, J D; Johnson, M S T
2015-01-01
The cosmic web defines the large scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. (2012) is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or halos) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straight forward inclusion of the Hubble flow negating the necessity of a visually defined thresh...
Clarisse, J.M
2007-07-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
方波; 曹丹红; 江体乾
2008-01-01
The viscoelastic micelle systems formed by novel anionic-nonionic dimeric surfactant and conventional cationic surfactant cetyltrimethylammonium(1631) were studied.The viscoelasticity,thixotropy,flow curves and constitutive equation for the novel viscoelastic micelle systems were investigated.The results show that the micelle systems possess viscoelasticity,thixotropy,and shear thinning property.Some micelle systems possess hysteresis loops showing both viscoelasticity and thixotropy.It is proved that the flow curves are characterized by the co-rotational Jeffreys constitutive equation correctly.
Sepe, D.
2013-01-01
The obstruction to construct a Lagrangian bundle over a fixed integral affine manifold was constructed by Dazord and Delzant (J Differ Geom 26:223–251, 1987) and shown to be given by ‘twisted’ cup products in Sepe (Differ GeomAppl 29(6): 787–800, 2011). This paper uses the topology of universal Lagr
Nonlinear Gravitational Lagrangians revisited
Magnano, Guido
2016-01-01
The Legendre transformation method, applied in 1987 to deal with purely metric gravitational Lagrangians with nonlinear dependence on the Ricci tensor, is extended to metric-affine models and is shown to provide a concise and insightful comparison of the dynamical content of the two variational frameworks.
Symmetries in Lagrangian Field Theory
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
Om Prakash
2011-06-01
Full Text Available The present paper is concerned with the study of MHD free convective flow of a visco-elastic (Kuvshinski type dusty gas through a porous medium induced by the motion of a semi-infinite flat plate under the influence of radiative heat transfer moving with velocity decreasing exponentially with time. The expressions for velocity distribution of a dusty gas and dust particles, concentration profile and temperature field are obtained. The effect of Schmidt number (Sc, Magnetic field parameter (M and Radiation parameter (N on velocity distribution of dusty gas and dust particles, concentration and temperature distribution are discussed graphically.
Aspiration of biological viscoelastic drops
Guevorkian, Karine; Durth, Mélanie; Dufour, Sylvie; Brochard-Wyart, Françoise
2010-01-01
Spherical cellular aggregates are in vitro systems to study the physical and biophysical properties of tissues. We present a novel approach to characterize the mechanical properties of cellular aggregates using micropipette aspiration technique. We observe an aspiration in two distinct regimes, a fast elastic deformation followed by a viscous flow. We develop a model based on this viscoelastic behavior to deduce the surface tension, viscosity, and elastic modulus. A major result is the increase of the surface tension with the applied force, interpreted as an effect of cellular mechanosensing.
Undulatory swimming in viscoelastic fluids
Shen, Xiaoning
2011-01-01
The effects of fluid elasticity on the swimming behavior of the nematode \\emph{Caenorhabditis elegans} are experimentally investigated by tracking the nematode's motion and measuring the corresponding velocity fields. We find that fluid elasticity hinders self-propulsion. Compared to Newtonian solutions, fluid elasticity leads to 35% slower propulsion speed. Furthermore, self-propulsion decreases as elastic stresses grow in magnitude in the fluid. This decrease in self-propulsion in viscoelastic fluids is related to the stretching of flexible molecules near hyperbolic points in the flow.
Undulatory swimming in viscoelastic fluids.
Shen, X N; Arratia, P E
2011-05-20
The effects of fluid elasticity on the swimming behavior of the nematode Caenorhabditis elegans are experimentally investigated by tracking the nematode's motion and measuring the corresponding velocity fields. We find that fluid elasticity hinders self-propulsion. Compared to Newtonian solutions, fluid elasticity leads to up to 35% slower propulsion. Furthermore, self-propulsion decreases as elastic stresses grow in magnitude in the fluid. This decrease in self-propulsion in viscoelastic fluids is related to the stretching of flexible molecules near hyperbolic points in the flow.
Symplectic Applicability of Lagrangian Surfaces
Lorenzo Nicolodi
2009-06-01
Full Text Available We develop an approach to affine symplectic invariant geometry of Lagrangian surfaces by the method of moving frames. The fundamental invariants of elliptic Lagrangian immersions in affine symplectic four-space are derived together with their integrability equations. The invariant setup is applied to discuss the question of symplectic applicability for elliptic Lagrangian immersions. Explicit examples are considered.
Viscoelastic properties of cellular polypropylene ferroelectrets
Gaal, Mate; Bovtun, Viktor; Stark, Wolfgang; Erhard, Anton; Yakymenko, Yuriy; Kreutzbruck, Marc
2016-03-01
Viscoelastic properties of cellular polypropylene ferroelectrets (PP FEs) were studied at low frequencies (0.3-33 Hz) by dynamic mechanical analysis and at high frequencies (250 kHz) by laser Doppler vibrometry. Relaxation behavior of the in-plane Young's modulus ( Y11 ' ˜ 1500 MPa at room temperature) was observed and attributed to the viscoelastic response of polypropylene matrix. The out-of-plane Young's modulus is very small ( Y33 ' ≈ 0.1 MPa) at low frequencies, frequency- and stress-dependent, evidencing nonlinear viscoelastic response of PP FEs. The high-frequency mechanical response of PP FEs is shown to be linear viscoelastic with Y33 ' ≈ 0.8 MPa. It is described by thickness vibration mode and modeled as a damped harmonic oscillator with one degree of freedom. Frequency dependence of Y33 * in the large dynamic strain regime is described by the broad Cole-Cole relaxation with a mean frequency in kHz range attributed to the dynamics of the air flow between partially closed air-filled voids in PP FEs. Switching-off the relaxation contribution causes dynamic crossover from the nonlinear viscoelastic regime at low frequencies to the linear viscoelastic regime at high frequencies. In the small strain regime, contribution of the air flow seems to be insignificant and the power-law response, attributed to the mechanics of polypropylene cell walls and closed air voids, dominates in a broad frequency range. Mechanical relaxation caused by the air flow mechanism takes place in the sound and ultrasound frequency range (10 Hz-1 MHz) and, therefore, should be taken into account in ultrasonic applications of the PP FEs deal with strong exciting or receiving signals.
Linear Viscoelasticity, Reptation, Chain Stretching and Constraint Release
Neergaard, Jesper; Schieber, Jay D.; Venerus, David C.
2000-01-01
A recently proposed self-consistent reptation model - alreadysuccessful at describing highly nonlinear shearing flows of manytypes using no adjustable parameters - is used here to interpretthe linear viscoelasticity of the same entangled polystyrenesolution. Using standard techniques, a relaxatio...
Experimental characterisation of a novel viscoelastic rectifier design
Jensen, Kristian Ejlebjærg; Okkels, Fridolin; Szabo, Peter
2012-01-01
A planar microfluidic system with contractions and obstacles is characterized in terms of anisotropic flow resistance due to viscoelastic effects. The working mechanism is illustrated using streak photography, while the diodicity performance is quantified by pressure drop measurements. The point...
Multi-Scale Analysis of Lagrangian Properties of Turbulence
Wilczek, Michael; Lalescu, Cristian
2016-11-01
Turbulence is a multi-scale problem in space and time with a broad range of strongly interacting degrees of freedom. Lagrangian tracer particles advected with the flow sample this spatio-temporal complexity. This naturally leads to the question of how Lagrangian properties are affected by the scales of turbulence. We attempt to answer this question numerically and theoretically adopting a coarse-graining approach. In an extensive DNS (direct numerical simulation) study, we track tracer particles advected by spatially coarse-grained velocity fields. This allows to distinguish the impact of large-scale sweeping effects and small-scale intermittency on Lagrangian aspects of turbulence. In this presentation we will present results on Lagrangian particle dispersion and velocity fluctuations for various coarse-graining scales. The results will furthermore be discussed in the context of Eulerian-Lagrangian bridging relations.
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
Gravity, Time, and Lagrangians
Huggins, Elisha
2010-01-01
Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…
2010-09-30
the vertical interpolation adjustment given by Equation 8 (SL OMT ), NOGAPS SL/SI with non-interpolation in the vertical (SL NIV), and the non semi...interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV) and the non semi-Lagrangian NOGAPS (EULER). Figures 4 and...2009 comparing the control NOGAPS SL/SI with the adjusted vertical interpolation scheme (SL OMT ), the non-interpolating scheme in the vertical (SL NIV
On Attracting Lagrangian Coherent Structures
Karrasch, Daniel
2013-01-01
In this note, we show that in the autonomous, two-dimensional incompressible saddle flow, contrary to common intuition, also attracting Lagrangian Coherent Structures (LCSs) can show up as ridges of the forward finite-time Lyapunov exponent (FTLE) field. This raises the issue of characterization of attracting LCSs from forward time FTLE analysis. First, we extend recent results of Haller & Sapsis (2011) [11] on the relation between forward and backward maximal and minimal stretching rates to the whole finite-time Lyapunov spectrum and to stretching directions by considering the singular value decomposition (SVD) of the deformation gradient. We show two significant advantages of the SVD compared to the usual eigendecomposition of the Cauchy-Green strain tensor: (1) one gains theoretical insight into local deformation under a finite-time dynamical system, and (2) one obtains both complete forward and backward strain information from a single grid advection. Furthermore, we give a short and direct proof of t...
Azua, B.M.; DeMets, C.; Masterlark, Timothy
2002-01-01
Continuous GPS measurements from Colima, Mexico during 4/93-6/01, bracketing the Oct. 9, 1995 M = 8.0 Colima-Jalisco earthquake, provide new constraints on Rivera plate subduction mechanics. Modeling of margin-normal strain accumulation before the earthquake suggests the Rivera-North America subduction interface was fully locked. Transient postseismic motion from 10/ 95-6/97 is well fit by a model that includes logarithmically-decaying fault afterslip, elastic strain from shallow fault relocking, and possibly a minor viscoelastic response, but is fit poorly by models that assume a dominant Maxwell viscoelastic response of the lower crust and upper mantle, independent of the assumed viscosities. Landward, margin-normal motion since mid-1997 is parallel to but ??? 75% slower than the pre-seismic velocity. Afterslip alone fails to account for this slowdown. The viscoelastic response predicted by a FEM correctly resolves the remaining velocity difference within the uncertainties. Both processes thus offset elastic strain accumulating from the relocked subduction interface.
Topology optimization of viscoelastic rectifiers
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2012-01-01
An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...
MECHANISM FOR VISCOELASTIC POLYMER SOLUTION PERCOLATING THROUGH POROUS MEDIA
ZHANG Li-juan; YUE Xiang-an
2007-01-01
The pore throat of porous media is modeled as a constricted channel or expanded channel. The flow of viscoelastic polymer solution in pore throat model is studied by numerical method. Relationship between pressure drop and flow rate is developed, viscoelasticity and throat size are found to be two main factors in high flow resistance. According to pore throat model, 2-D stochastic channel bundle is put forward to model porous media, which is composed of pore throat models in series - parallel connection with size and length accord to Haring - Greenkorn stochastic distribution. Percolation model of viscoelastic fluid is developed on the basis of Darcy equation and pressure drop vs. flow rate relation in 2-D stochastic channel bundle. Results indicate that the seepage ability of viscoelastic polymer solution decreases with the increase of viscoelasticity, injection rate, and heterogeneity as well as the decrease of mean pore size of porous media. The high pressure drop of viscoelastic fluid at the connection of pore to throat plays a great role in its anomalous high flow resistance through porous media.
Viscoelasticity of mixed polyacrylamide solution
徐丽娜
2008-01-01
The viscoelastic behavior of polyacrylamide solution is crucial for its application in various industries.The mixed polyacrylamide solution was prepared by mixing polyacrylamide with different relative molecular masses according to the defined mass fraction.The viscosity and elasticity of mixed polyacrylamide solution were separately tested with RS150 rheometer and capillary breakup extensional rheometer and compared with those of the single polyacrylamide solution which is directly provided by manufacturer without any mixing.The results indicate that the mixed and single polyacrylamide solutions have the same shear viscosity and intrinsic viscosity.However,some mixed polyacrylamide solutions have higher elasticity than single polyacrylamide solution.The flow resistance of mixed polyacrylamide with higher elasticity is also greater than that of single polyacrylamide solution in porous medium.This paper presents an effective method of mixing polyacrylamides with different relative molecular masses,which can enhance the elasticity of polyacrylamide solution and flowing resistance through porous medium.
Introduction to Focus Issue: Lagrangian Coherent Structures.
Peacock, Thomas; Dabiri, John
2010-03-01
The topic of Lagrangian coherent structures (LCS) has been a rapidly growing area of research in nonlinear dynamics for almost a decade. It provides a means to rigorously define and detect transport barriers in dynamical systems with arbitrary time dependence and has a wealth of applications, particularly to fluid flow problems. Here, we give a short introduction to the topic of LCS and review the new work presented in this Focus Issue.
Malkus, David S.
1989-01-01
This project concerned the development of a new fast finite element algorithm to solve flow problems of non-Newtonian fluids such as solutions or melts of polymers. Many constitutive theories for such materials involve single integrals over the deformation history of the particle at the stress evaluation point; examples are the Doi-Edwards and Curtiss-Bird molecular theories and the BKZ family derived from continuum arguments. These theories are believed to be among the most accurate in describing non-Newtonian effects important to polymer process design, effects such as stress relaxation, shear thinning, and normal stress effects. This research developed an optimized version of the algorithm which would run a factor of two faster than the pilot algorithm on scalar machines and would be able to take full advantage of vectorization on machines. Significant progress was made in code vectorization; code enhancement and streamlining; adaptive memory quadrature; model problems for the High Weissenberg Number Problem; exactly incompressible projection; development of multimesh extrapolation procedures; and solution of problems of physical interest. A portable version of the code is in the final stages of benchmarking and testing. It interfaces with the widely used FIDAP fluid dynamics package.
Generalized Superfield Lagrangian Quantization
Lavrov, P M; Moshin, P Y
2002-01-01
We consider an extension of the gauge-fixing procedure in the framework of the Lagrangian superfield BRST and BRST-antiBRST quantization schemes for arbitrary gauge theories, taking into account the possible ambiguity in the choice of the superfield antibracket. We show that this ambiguity is fixed by the algebraic properties of the antibracket and the form of the BRST and antiBRST transformations, realized in terms of superspace translations. The Ward identities related to the generalized gauge-fixing procedure are obtained.
The 3D Lagrangian Integral Method. Henrik Koblitz Rasmussen
Rasmussen, Henrik Koblitz
2003-01-01
with a second order Runge-Kutta integration method. In any development of a numerical method for viscoelastic flow it is important to focus on the constitutive equation associated to the method. For instance the K-BKZ model is not adequate to describe both shear and extensional flow using the same constitutive...
Thermal convection of viscoelastic shear-thinning fluids
Albaalbaki, Bashar; Khayat, Roger E.; Ahmed, Zahir U.
2016-12-01
The Rayleigh-Bénard convection for non-Newtonian fluids possessing both viscoelastic and shear-thinning behaviours is examined. The Phan-Thien-Tanner (PTT) constitutive equation is implemented to model the non-Newtonian character of the fluid. It is found that while the shear-thinning and viscoelastic effects could annihilate one another for the steady roll flow, presence of both behaviours restricts the roll stability limit significantly compared to the cases when the fluid is either inelastic shear-thinning or purely viscoelastic with constant viscosity.
Topological Classification of Lagrangian Fibrations
Sepe, D
2009-01-01
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of Lagrangian fibrations with base $\\rpr$ and fixed monodromy representation, generalising a construction due to Bates.
Viscoelastic properties of the false vocal fold
Chan, Roger W.
2004-05-01
The biomechanical properties of vocal fold tissues have been the focus of many previous studies, as vocal fold viscoelasticity critically dictates the acoustics and biomechanics of phonation. However, not much is known about the viscoelastic response of the ventricular fold or false vocal fold. It has been shown both clinically and in computer simulations that the false vocal fold may contribute significantly to the aerodynamics and sound generation processes of human voice production, with or without flow-induced oscillation of the false fold. To better understand the potential role of the false fold in phonation, this paper reports some preliminary measurements on the linear and nonlinear viscoelastic behavior of false vocal fold tissues. Linear viscoelastic shear properties of human false fold tissue samples were measured by a high-frequency controlled-strain rheometer as a function of frequency, and passive uniaxial tensile stress-strain response of the tissue samples was measured by a muscle lever system as a function of strain and loading rate. Elastic moduli (Young's modulus and shear modulus) of the false fold tissues were calculated from the measured data. [Work supported by NIH.
PLANE SURFACE SUDDENLY SET IN MOTION IN A VISCOELASTIC FLUID WITH FRACTIONAL MAXWELL MODEL
谭文长; 徐明瑜
2002-01-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model
Wenchang, Tan; Mingyu, Xu
2002-08-01
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak.
Micro-mechanisms of residual oil mobilization by viscoelastic fluids
Zhang Lijuan; Yue Xiang'an; Guo Fenqiao
2008-01-01
Four typical types of residual oil, residual oil trapped in dead ends, oil ganglia in pore throats,oil at pore comers and oil film adhered to pore walls, were studied. According to main pore structure characteristics and the fundamental morphological features of residual oil, four displacement models for residual oil were proposed, in which pore-scale flow behavior of viscoelastic fluid was analyzed by a numerical method and micro-mechanisms for mobilization of residual oil were discussed. Calculated results indicate that the viscoelastic effect enhances micro displacement efficiency and increases swept volume. For residual oil trapped in dead ends, the flow field of viscoelastic fluid is developed in dead ends more deeply, resulting in more contact with oil by the displacing fluid, and consequently increasing swept volume. In addition, intense viscoelastic vortex has great stress, under which residual oil becomes small oil ganglia, and finally be carried into main channels. For residual oil at pore throats, its displacement mechanisms are similar to the oil trapped in dead ends. Vortices are developed in the depths of the throats and oil ganglia become smaller. Besides, viscoelastic fluid causes higher pressure drop on oil ganglia, as a driving force, which can overcome capillary force, consequently, flow direction can be changed and the displacing fluid enter smaller throats. For oil at pore comers, viscoelastic fluid can enhance displacement efficiency as a result of greater velocity and stress near the comers. For residual oil adhered to pore wall,viscoelastic fluid can provide a greater displacing force on the interface between viscoelastic fluid and oil,thus, making it easier to exceed the minimum interfacial tension for mobilizing the oil film.
D' Ambros, Alder C.; Vitorassi, Pedro H.; Franco, Admilson T.; Morales, Rigoberto E.M. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Matins, Andre Leibsohn [PETROBRAS S.A., Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES). Tecnologia de Engenharia de Perfuracao
2008-07-01
The success of oil well drilling process depends on the correct prediction of the velocities and stresses fields inside the gap between the drill string and the rock formation. Using CFD is possible to predict the behavior of the drilling fluid flow along the annular space, from the bottom to the top of the well. Commonly the drilling fluid is modeled as a Herschel-Bulkley fluid. An alternative is to employ a non-linear viscoelastic model, like the one developed by Phan-Thien-Tanner (PTT). In the present work the PTT constitutive equation is used to model the drilling fluid flow along the annular space. Thus, this work investigates the influence of the Deborah number on the laminar flow pattern through the numerical solution of the equations formed by the coupled velocity-pressure-stress fields. The results are analyzed and validated against the analytical solution for the fully developed annular pipe flow. The relation between the Deborah number (De) and the entry length is investigated, along with the influence of high values of Deborah number on the friction factor, stress and velocity fields. (author)
STABILITY ANALYSIS OF VISCOELASTIC CURVED PIPES CONVEYING FLUID
WANG Zhong-min; ZHANG Zhan-wu; ZHAO Feng-qun
2005-01-01
Based on the Hamilton's principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.
Lagrangian methods of cosmic web classification
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.
Lagrangian-Only Quantum Theory
Wharton, K B
2013-01-01
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path integral or quantum field theory, a promising alternative is to only consider field histories for which the Lagrangian density is always zero. With this change, it appears possible to replace amplitudes with equally-weighted probabilities. This paper demonstrates a proof-of-principle for this approach, using a toy Lagrangian that corresponds to an arbitrary spin state. In this restricted framework one can derive both the Born rule and its limits of applicability. The fact that the Lagrangian obeys future boundary constraints also results in the first continuous, spacetime-based, hidden-variable description of a Bell-inequality-violating system.
The Lagrangian in Quantum Mechanics
Dirac, P. A. M.
Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics. Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is the more fundamental. In the first place the Lagrangian method allows one to collect together all the equations of motion and express them as the stationary property of a certain action function. (This action function is just the time-integral of the Lagrangian.) There is no corresponding action principle in terms of the coordinates and momenta of the Hamiltonian theory. Secondly the Lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; while the Hamiltonian method is essentially non-relativistic in form, since it marks out a particular time variable as the canonical conjugate of the Hamiltonian function. For these reasons it would seem desirable to take up the question of what corresponds in the quantum theory to the Lagrangian method of the classical theory. A little consideration shows, however, that one cannot expect to be able to take over the classical Lagrangian equations in any very direct way. These equations involve partial derivatives of the Lagrangian with respect to the coordinates and velocities and no meaning can be given to such derivatives in quantum mechanics. The only differentiation process that can be carried out with respect to the dynamical variables of
Lagrangian description of nonlinear chromatography
LIANG Heng; LIU Xiaolong
2004-01-01
Under the framework of non-equilibrium thermodynamic separation theory (NTST), Local Lagrangian approach (LLA) was proposed to deal with the essential issues of the convection and diffusion (shock waves) phenomena in nonlinear chromatography with recursion equations based on the three basic theorems, Lagrangian description, continuity axiom and local equilibrium assumption (LEA). This approach remarkably distinguished from the system of contemporary chromatographic theories (Eulerian description-partial differential equations), and can felicitously match modern cybernetics.
Presymplectic structures and intrinsic Lagrangians
Grigoriev, Maxim
2016-01-01
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the...
A Lagrangian fluctuation-dissipation relation for scalar turbulence
Drivas, Theodore D
2016-01-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation ...
Yue Yang
2016-01-01
The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in vis-cous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian struc-tures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.
Lagrangian Coherent Structures: Introduction and Applications
Haller, George
2008-11-01
Lagrangian Coherent Structures (LCS) are distinguished material surfaces that organize the global mixing and transport of fluid particles. While these surfaces define a skeleton that governs all mixing events even in turbulent flows, LCS remain hidden to traditional coherent structure detecting methods based on vorticity, pressure, streamlines, or other frame-dependent quantities. Here we review the mathematical foundations of LCS and discuss how they can be located in an objective (frame-independent) way in complex flows. We also highlight applications to experimental and numerical flow data analysis. Examples include two-dimensional rotating turbulence, hairpin vortices in three-dimensional numerical simulations, passive ocean pollution control and atmospheric clear-air turbulence detection. Some of these examples will be discussed in more detail in later talks within this minisymposium.
Lagrangian Coherent Structures in the Trieste Gulf
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Self-propulsion in viscoelastic fluids: pushers vs. pullers
Zhu, Lailai; Brandt, Luca
2012-01-01
We use numerical simulations to address locomotion at zero Reynolds number in viscoelastic (Giesekus) fluids. The swimmers are assumed to be spherical, to self-propel using tangential surface deformation, and the computations are implemented using a finite element method. The emphasis of the study is on the change of the swimming kinematics, energetics, and flow disturbance from Newtonian to viscoelastic, and on the distinction between pusher and puller swimmers. In all cases, the viscoelastic swimming speed is below the Newtonian one, with a minimum obtained for intermediate values of the Weissenberg number, $We$. An analysis of the flow field places the origin of this swimming degradation in non-Newtonian elongational stresses. The power required for swimming is also systematically below the Newtonian power, and always a decreasing function of $We$. A detail energetic balance of the swimming problem points at the polymeric part of the stress as the primary $We$-decreasing energetic contribution, while the c...
A remapped particle-mesh semi-Lagrangian advection scheme
Cotter, C.J.; Frank, J.E.; Reich, S.
2007-01-01
We describe the remapped particle-mesh advection method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the conservation property, the remapped pa
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan [Department of Physics, Faculty of Science and Mathematics, University of Nis, Visegradska 33, P.O. Box 224, 18000 Nis (Serbia)
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
Experimental investigation of Lagrangian structure functions in turbulence
Berg, Jacob; Ott, Søren; Mann, Jakob
2009-01-01
Lagrangian properties obtained from a particle tracking velocimetry experiment in a turbulent flow at intermediate Reynolds number are presented. Accurate sampling of particle trajectories is essential in order to obtain the Lagrangian structure functions and to measure intermittency at small...... temporal scales. The finiteness of the measurement volume can bias the results significantly. We present a robust way to overcome this obstacle. Despite no fully developed inertial range, we observe strong intermittency at the scale of dissipation. The multifractal model is only partially able to reproduce...
Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean
2016-07-01
In this paper we study 3D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body (GMB/GZB) including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter full waveform inversion for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parameterization can be related to the counterparts using P- and S- velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high performance computing resources and the field data are available.
Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean
2016-10-01
In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.
Particle Paths of Lagrangian Velocity Distribution Simulating the Spiral Arms of Galaxy M51
Tzu-Fang Chen; Georgios H. Vatistas; Sui Lin
2008-01-01
Galaxies are huge families of stars held together by their own gravities. The system M51 is a spiral galaxy. It possesses billions of stars. The range of the spiral arms extends hundred thousand light years. The present study is in an attempt in using the particle paths of the Lagrangian flow field to simulate the spiral arms of Galaxy M51.The Lagrangian flow field is introduced. The initial locations of fluid particles in the space between two concentric cylinders are first specified. Then a linear velocity distribution of the fluid particles is used with different angle rotations of the particles to obtain the particle paths in the Lagrangian diagram. For simulating the spiral arms of Galaxy M51, the Lagrangian M51 diagram is developed. The particle paths of the Lagrangian M51 diagram agree quite well with the spiral arms of Galaxy M51.
Lebon, Luc; Limat, Laurent; Gaillard, Antoine; Beaumont, Julien; Lhuissier, Henri; Laboratoire MSC Team
2015-11-01
We have investigated experimentally the properties and stability of viscoelastic curtains, falling from a long thin slot and maintained laterally by two highly wetting wires. We have observed several original facts, compared to the seminal work of Brown and Taylor on Newtonian curtains: (1) The stability with respect to breaking is considerably enhanced by the use of appropriate polymers. Even strange tree-like falling filament structures can be also stabilised, though less interesting for applications. (2) Specific instabilities can be observed, when the amount of polymers is excessive, with spatial and temporal modulations of the coating thickness. (3) Even the base state is modified, and does NOT reduce at large scale to a free fall, even slightly displaced vertically from the expected profile. We present this experimental exploration and also some attempts of analytical modeling based on Rheological theories of complex fluids.
Watanabe, H.; Hasegawa, T.; Narumi, T. [Niigata University, Niigata (Japan). Faculty of Engineering; Tamano, K. [Mitsubishi Electric Corp., Tokyo (Japan)
1995-02-25
In detergent engineering and polymer processing, it is important to study the force exerted on an obstacle placed near a wall. In the present study, we numerically analyze the flow of viscoelastic fluids past a minute cylinder which is set at or near an inside wall of a two-dimensional channel. The upper convected Maxwell model and the finite-element method are used as the constitutive equation and the numerical method, respectively. Drag and lift of the cylinder are calculated for low Reynolds numbers (Re) and various Weissenberg numbers (Wi) of positive and negative values. Drag coefficient (C{sub D}) slightly changes with Wi. Lift coefficient (C{sub L}) monotonously decreases with increasing Wi irrespective of the sign of Wi. C{sub L} is greatly changed with Wi and is more sensitive to the elasticity of the fluid than C{sub D}. C{sub D} and C{sub L} decrease as the cylinder is separated from the wall. 11 refs., 12 figs.
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
A hybrid Eulerian Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
E. Kaas
2013-07-01
Full Text Available A new hybrid Eulerian Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place, i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
A Student's Guide to Lagrangians and Hamiltonians
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
Lagrangian multi-particle statistics
Lüthi, Beat; Berg, Jacob; Ott, Søren
2007-01-01
Combined measurements of the Lagrangian evolution of particle constellations and the coarse-grained velocity derivative tensor. partial derivative(u) over tilde (i) /partial derivative x(j) are presented. The data are obtained from three-dimensional particle tracking measurements in a quasi isotr...
Galilean invariance in Lagrangian mechanics
Mohallem, J. R.
2015-10-01
The troublesome topic of Galilean invariance in Lagrangian mechanics is discussed in two situations: (i) A particular case involving a rheonomic constraint in uniform motion and (ii) the general translation of an entire system and the constants of motion involved. A widespread impropriety in most textbooks is corrected, concerning a condition for the equality h = E to hold.
Stationary solutions of equations of incompressible viscoelastic polymer liquid
Bambaeva, N. V.; Blokhin, A. M.
2014-05-01
The equations describing flows of an incompressible viscoelastic polymer liquid are studied. Stationary solutions similar to the Poiseuille and Couette solutions for the system of the Navier-Stokes equations are constructed. Stationary discontinuous solutions of the polymer liquid equation are also considered.
Theoretical and Experimental Studies of the Mechanics of Viscoelastic Liquids.
1985-02-15
Ref. 6 D. D. Joseph, M. Renardy, and J-C. Saut , "Hyper- bolicity and change of type in the flow of viscoelastic fluids," Archive for Rational Mechanics...J. C. Saut and D. D. Joseph, "Fading Memory," Archive for Rational Mechanics and Analysis, Vol. 81(1), pp. 53-95, 1983. Fading memory expresses the
Theory of viscoelasticity an introduction
Christensen, R
1982-01-01
Theory of Viscoelasticity: An Introduction, Second Edition discusses the integral form of stress strain constitutive relations. The book presents the formulation of the boundary value problem and demonstrates the separation of variables condition.The text describes the mathematical framework to predict material behavior. It discusses the problems to which integral transform methods do not apply. Another topic of interest is the thermoviscoelastic stress analysis. The section that follows describes the heat conduction, glass transition criterion, viscoelastic Rayleigh waves, optimal str
Viscoelastic behavior of concrete pile
丁科; 唐小弟
2008-01-01
Based on constitutive theory of viscoelasticity,the viscoelastic behaviour of concrete pile was investigated.The influence of viscosity coefficient on the stress,displacement and velocity response was discussed.With the increase of viscosity coefficient,the amplitude of stress wave decreases,and the maximum value of the stress wave shifts to deeper position of the pile.In other words,the viscosity coefficient behaves as lag effect to stress wave.
无
2000-01-01
New form of the constitutive equations for the Oldroyd-B model, which have physical meaning, is developed to facilitate theoretical analysis. The new equations are used to simulate planar 4∶1 contraction flow of a Maxwell fluid using a third-order upwind finite volume method. The numerical results compare well with the theoretical solutions and the results of other references to show the effectiveness of the numerical method. Numerical experiments suggest that the present method not only converges fairly rapidly, but can also generate a highly resolved approximation to an Oldroyd-B fluid flow at a high Weissenberg number.
Data Assimilation With Regional Lagrangian Models
1999-09-30
Journal of Marine Systems . RESULTS We are able to fit the inviscid Lagrangian model with synthetic Lagrangian data for short periods of time (1-2 days...Mead and A.F. Bennett, 1999. Towards regional assimilation of data: The Lagrangian form of the reduced gravity model and its inverse, (submitted), Journal of Marine Systems .
Momeni, M.; Jamshidi, N.; Barari, Amin
2011-01-01
Purpose - In this paper a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet channel is presented and the Homotopy Analysis Method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential...... equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the Homotopy Analysis Method in comparison with the numerical method in solving this problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear...... conclusion can be drawn from the numerical method results that the HAM provides highly accurate solutions for nonlinear differential equations. Design/methodology/approach - In this paper a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet channel...
Lagrangian based methods for coherent structure detection
Allshouse, Michael R., E-mail: mallshouse@chaos.utexas.edu [Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Peacock, Thomas, E-mail: tomp@mit.edu [Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Three dimensional Lagrangian structures in the Antarctic Polar Vortex.
Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen
2017-04-01
Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as Lagrangian Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use Lagrangian Descriptors [1,2,3,4] (function M) for visualizing 3D Lagrangian structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. Lagrangian descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A
Anchored Lagrangian submanifolds and their Floer theory
Fukaya, Kenji; Ohta, Hiroshi; Ono, Kaoru
2009-01-01
We introduce the notion of (graded) anchored Lagrangian submanifolds and use it to study the filtration of Floer' s chain complex. We then obtain an anchored version of Lagrangian Floer homology and its (higher) product structures. They are somewhat different from the more standard non-anchored version. The anchored version discussed in this paper is more naturally related to the variational picture of Lagrangian Floer theory and so to the likes of spectral invariants. We also discuss rationality of Lagrangian submanifold and reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.
Droplet breakup dynamics of weakly viscoelastic fluids
Marshall, Kristin; Walker, Travis
2016-11-01
The addition of macromolecules to solvent, even in dilute quantities, can alter a fluid's response in an extensional flow. For low-viscosity fluids, the presence of elasticity may not be apparent when measured using a standard rotational rheometer, yet it may still alter the response of a fluid when undergoing an extensional deformation, especially at small length scales where elastic effects are enhanced. Applications such as microfluidics necessitate investigating the dynamics of fluids with elastic properties that are not pronounced at large length scales. In the present work, a microfluidic cross-slot configuration is used to study the effects of elasticity on droplet breakup. Droplet breakup and the subsequent iterated-stretching - where beads form along a filament connecting two primary droplets - were observed for a variety of material and flow conditions. We present a relationship on the modes of bead formation and how and when these modes will form based on key parameters such as the properties of the outer continuous-phase fluid. The results are vital not only for simulating the droplet breakup of weakly viscoelastic fluids but also for understanding how the droplet breakup event can be used for characterizing the extensional properties of weakly-viscoelastic fluids.
Effective Lagrangian for Nonrelativistic Systems
Haruki Watanabe
2014-09-01
Full Text Available The effective Lagrangian for Nambu-Goldstone bosons (NGBs in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
Complex Lagrangians and phantom cosmology
Andrianov, A A; Kamenshchik, A Yu
2006-01-01
Motivated by the generalization of quantum theory for the case of non-Hermitian Hamiltonians with PT symmetry, we show how a classical cosmological model describes a smooth transition from ordinary dark energy to the phantom one. The model is based on a classical complex Lagrangian of a scalar field. Specific symmetry properties analogous to PT in non-Hermitian quantum mechanics lead to purely real equation of motion.
Fujieda, T.; Tanahashi, T.; Okada, A. [Keio University, Tokyo (Japan). Faculty of Science and Technology; Kato, Y. [Asahi Glass Co. Ltd., Tokyo (Japan)
1997-06-25
In this paper, we propose a new GSMAC-FEM (generalized simplified marker and cell-finite element method) which is suited to the numerical analysis of visco-elastic fluids. The equation of continuity and the equation of momentum are solved by the GSMAC-FEM algorithm and the constitutive equation is solved by the finite volume method. This scheme employs the third order MUSCL (Monotone Upstream-centered Schemes for Conservation Law) in order to guarantee the absence of spurious oscillation near the steep gradients of the variable. This method uses a minmod limiter in order to satisfy the TVD (Total Variation Diminishing) condition. The present method employs the simultaneous relaxation of velocity and pressure for the incompressible condition. The flows of Maxwell fluid through two-dimensional planer abrupt contraction are calculated by the present method and the effects the Weissenberg number and the Reynolds number are discussed. 13 refs., 12 figs.
Viscoelastic tides: models for use in Celestial Mechanics
Ragazzo, C.; Ruiz, L. S.
2016-11-01
This paper contains equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body. The goal is to present good models for the tidal forces that take into account the possibly different rheology of each body. The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main contribution is a procedure to associate to each spring-dashpot model, which defines the rheology of a body, a potential and a dissipation function for the body deformation variables. The theory is applied to the Earth (solid part plus oceans) and a comparison between model and observation of the following quantities is made: norm of the Love numbers, rate of tidal energy dissipation, Chandler period, and Earth-Moon distance increase.
Absolute instability in viscoelastic mixing layers
Ray, Prasun K.; Zaki, Tamer A.
2014-01-01
The spatiotemporal linear stability of viscoelastic planar mixing layers is investigated. A one-parameter family of velocity profiles is used as the base state with the parameter, S, controlling the amount of shear and backflow. The influence of viscoelasticity in dilute polymer solutions is modeled with the Oldroyd-B and FENE-P constitutive equations. Both models require the specification of the ratio of the polymer-relaxation and convective time scales (the Weissenberg number, We) and the ratio of solvent and solution viscosities (β). The maximum polymer extensibility, L, must also be specified for the FENE-P model. We examine how the variation of these parameters along with the Reynolds number, Re, affects the minimum value of S at which the flow becomes locally absolutely unstable. With the Oldroyd-B model, the influence of viscoelasticity is shown to be almost fully captured by the elasticity, E^* equiv (1-β ) We/Re, and Scrit decreases as elasticity is increased, i.e., elasticity is destabilizing. A simple approximate dispersion relation obtained via long-wave asymptotic analysis is shown to accurately capture this destabilizing influence. Results obtained with the FENE-P model exhibit a rich variety of behavior. At large values of the extensibility, L, results are similar to those for the Oldroyd-B fluid as expected. However, when the extensibility is reduced to more realistic values (L ≈ 100), one must consider the scaled shear rate, η _c equiv We S/2L, in addition to the elasticity. When ηc is large, the base-state polymer stress obtained by the FENE-P model is reduced, and there is a corresponding reduction in the overall influence of viscoelasticity on stability. Additionally, elasticity exhibits a stabilizing effect which is driven by the streamwise-normal perturbation polymer stress. As ηc is reduced, the base-state and perturbation normal polymer stresses predicted by the FENE-P model move towards the Oldroyd-B values, and the destabilizing
Acoustic Streaming: An Arbitrary Lagrangian-Eulerian Perspective
Nama, Nitesh; Costanzo, Francesco
2016-01-01
We analyze acoustic streaming flows using an ALE perspective. The formulation stems from an explicit separation of time-scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacosutofluidic devices. After the formulation's exposition, we present numerical re...
Using Lagrangian Coherent Structures to understand coastal water quality
Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.
2012-09-01
The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a Lagrangian circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.
Focusing and alignment of erythrocytes in a viscoelastic medium
Go, Taesik; Byeon, Hyeokjun; Lee, Sang Joon
2017-01-01
Viscoelastic fluid flow-induced cross-streamline migration has recently received considerable attention because this process provides simple focusing and alignment over a wide range of flow rates. The lateral migration of particles depends on the channel geometry and physicochemical properties of particles. In this study, digital in-line holographic microscopy (DIHM) is employed to investigate the lateral migration of human erythrocytes induced by viscoelastic fluid flow in a rectangular microchannel. DIHM provides 3D spatial distributions of particles and information on particle orientation in the microchannel. The elastic forces generated in the pressure-driven flows of a viscoelastic fluid push suspended particles away from the walls and enforce erythrocytes to have a fixed orientation. Blood cell deformability influences the lateral focusing and fixed orientation in the microchannel. Different from rigid spheres and hardened erythrocytes, deformable normal erythrocytes disperse from the channel center plane, as the flow rate increases. Furthermore, normal erythrocytes have a higher angle of inclination than hardened erythrocytes in the region near the side-walls of the channel. These results may guide the label-free diagnosis of hematological diseases caused by abnormal erythrocyte deformability.
Focusing and alignment of erythrocytes in a viscoelastic medium
Go, Taesik; Byeon, Hyeokjun; Lee, Sang Joon
2017-01-01
Viscoelastic fluid flow-induced cross-streamline migration has recently received considerable attention because this process provides simple focusing and alignment over a wide range of flow rates. The lateral migration of particles depends on the channel geometry and physicochemical properties of particles. In this study, digital in-line holographic microscopy (DIHM) is employed to investigate the lateral migration of human erythrocytes induced by viscoelastic fluid flow in a rectangular microchannel. DIHM provides 3D spatial distributions of particles and information on particle orientation in the microchannel. The elastic forces generated in the pressure-driven flows of a viscoelastic fluid push suspended particles away from the walls and enforce erythrocytes to have a fixed orientation. Blood cell deformability influences the lateral focusing and fixed orientation in the microchannel. Different from rigid spheres and hardened erythrocytes, deformable normal erythrocytes disperse from the channel center plane, as the flow rate increases. Furthermore, normal erythrocytes have a higher angle of inclination than hardened erythrocytes in the region near the side-walls of the channel. These results may guide the label-free diagnosis of hematological diseases caused by abnormal erythrocyte deformability. PMID:28117428
Viscoelasticity and shear thinning of nanoconfined water
Kapoor, Karan; Amandeep, Patil, Shivprasad
2014-01-01
Understanding flow properties and phase behavior of water confined to nanometer-sized pores and slits is central to a wide range of problems in science, such as percolation in geology, lubrication of future nano-machines, self-assembly and interactions of biomolecules, and transport through porous media in filtration processes. Experiments with different techniques in the past have reported that viscosity of nanoconfined water increases, decreases, or remains close to bulk water. Here we show that water confined to less than 20-nm-thick films exhibits both viscoelasticity and shear thinning. Typically viscoelasticity and shear thinning appear due to shearing of complex non-Newtonian mixtures possessing a slowly relaxing microstructure. The shear response of nanoconfined water in a range of shear frequencies (5 to 25 KHz) reveals that relaxation time diverges with reducing film thickness. It suggests that slow relaxation under confinement possibly arises due to existence of a critical point with respect to slit width. This criticality is similar to the capillary condensation in porous media.
Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri
2016-05-01
This paper is the second part of a series of two. It follows [44], in which the positivity-preservation property of methods solving one-dimensional Lagrangian gas dynamics equations, from first-order to high-orders of accuracy, was addressed. This article aims at extending this analysis to the two-dimensional case. This study is performed on a general first-order cell-centered finite volume formulation based on polygonal meshes defined either by straight line edges, conical edges, or any high-order curvilinear edges. Such formulation covers the numerical methods introduced in [6,32,5,41,43]. This positivity study is then extended to high-orders of accuracy. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. It is important to point out that even if this paper is concerned with purely Lagrangian schemes, the theory developed is of fundamental importance for any methods relying on a purely Lagrangian step, as ALE methods or non-direct Euler schemes.
Effect of Fluid Viscoelasticity on Turbulence and Large-Scale Vortices behind Wall-Mounted Plates
Takahiro Tsukahara
2014-03-01
Full Text Available Direct numerical simulations of turbulent viscoelastic fluid flows in a channel with wall-mounted plates were performed to investigate the influence of viscoelasticity on turbulent structures and the mean flow around the plate. The constitutive equation follows the Giesekus model, valid for polymer or surfactant solutions, which are generally capable of reducing the turbulent frictional drag in a smooth channel. We found that turbulent eddies just behind the plates in viscoelastic fluid decreased in number and in magnitude, but their size increased. Three pairs of organized longitudinal vortices were observed downstream of the plates in both Newtonian and viscoelastic fluids: two vortex pairs were behind the plates and the other one with the longest length was in a plate-free area. In the viscoelastic fluid, the latter vortex pair in the plate-free area was maintained and reached the downstream rib, but its swirling strength was weakened and the local skin-friction drag near the vortex was much weaker than those in the Newtonian flow. The mean flow and small spanwise eddies were influenced by the additional fluid force due to the viscoelasticity and, moreover, the spanwise component of the fluid elastic force may also play a role in the suppression of fluid vortical motions behind the plates.
Chagras, V.
2004-03-15
The aim of this work is to contribute to the numerical modeling of turbulent gas-solid flows in vertical or horizontal non isothermal pipes, which can be found in many industrial processes (pneumatic transport, drying, etc). The model is based on an Eulerian-Lagrangian approach allowing a fine description of the interactions between the two phases (action of the fluid upon the particles (dispersion), action of the particles upon the fluid (two way coupling) and between particles (collisions)), more or less influential according to the characteristics of the flow. The influence of the gas phase turbulence on the particle motion is taken into account using a non-isotropic dispersion model, which allows the generation of velocity and temperature fluctuations of the fluid seen by the particles. The numerical developments brought to the model for vertical and horizontal pipe flow have been validated by comparison with available experimental results from the literature. The sensitivity tests highlight the influence of the dispersion model, collisions and turbulence modulation (direct and non direct modifications ) on the dynamic and thermal behavior of the suspension. The model is able to predict the heat exchanges in the presence of particles for a wide range of flows in vertical and horizontal pipes. However numerical problems still exist in two-way coupling for very small particles and loading ratios above one. This is related to the problems encountered when modeling the coupling terms between the two phases (parameters C{sub {epsilon}}{sub 2} and C{sub {epsilon}}{sub 3} ) involved in the turbulence dissipation balance. (author)
Alternative expression for the electromagnetic Lagrangian
Saldanha, Pablo L
2015-01-01
We propose an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields. The proposed Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. The total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. The proposed Lagrangian is equivalent to the traditional one in their domain of validity and provides an interesting description of the Aharonov-Bohm effect.
B. Rutherford
2012-12-01
Full Text Available The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation.
Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance.
The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.
Viscoelastic behavior of rubbery materials
Roland, C M
2011-01-01
The gigantic size of polymer molecules makes them viscoelastic - their behavior changes depending on how fast and for how long the material is used. This book looks at the latest discoveries in the field from a fundamental molecular perspective, in order to guide the development of better and new applications for soft materials.
Viscoelastic behaviour of pumpkin balloons
Gerngross, T.; Xu, Y.; Pellegrino, S.
2008-11-01
The lobes of the NASA ULDB pumpkin-shaped super-pressure balloons are made of a thin polymeric film that shows considerable time-dependent behaviour. A nonlinear viscoelastic model based on experimental measurements has been recently established for this film. This paper presents a simulation of the viscoelastic behaviour of ULDB balloons with the finite element software ABAQUS. First, the standard viscoelastic modelling capabilities available in ABAQUS are examined, but are found of limited accuracy even for the case of simple uniaxial creep tests on ULDB films. Then, a nonlinear viscoelastic constitutive model is implemented by means of a user-defined subroutine. This approach is verified by means of biaxial creep experiments on pressurized cylinders and is found to be accurate provided that the film anisotropy is also included in the model. A preliminary set of predictions for a single lobe of a ULDB is presented at the end of the paper. It indicates that time-dependent effects in a balloon structure can lead to significant stress redistribution and large increases in the transverse strains in the lobes.
Gupta, Anupam
2015-01-01
Based on mesoscale lattice Boltzmann (LB) numerical simulations, we investigate the effects of viscoelasticity on the break-up of liquid threads in microfluidic cross-junctions, where droplets are formed by focusing a liquid thread of a dispersed (d) phase into another co-flowing continuous (c) immiscible phase. Working at small Capillary numbers, we investigate the effects of non-Newtonian phases in the transition from droplet formation at the cross-junction (DCJ) to droplet formation downstream of the cross-junction (DC) (Liu $\\&$ Zhang, ${\\it Phys. ~Fluids.}$ ${\\bf 23}$, 082101 (2011)). We will analyze cases with ${\\it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed phase, as well as cases with ${\\it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous phase. Moderate flow-rate ratios $Q \\approx {\\cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in ...
Comparing High-latitude Ionospheric and Thermospheric Lagrangian Coherent Structures
Wang, N.; Ramirez, U.; Flores, F.; Okic, D.; Datta-Barua, S.
2015-12-01
Lagrangian Coherent Structures (LCSs) are invisible boundaries in time varying flow fields that may be subject to mixing and turbulence. The LCS is defined by the local maxima of the finite time Lyapunov exponent (FTLE), a scalar field quantifying the degree of stretching of fluid elements over the flow domain. Although the thermosphere is dominated by neutral wind processes and the ionosphere is governed by plasma electrodynamics, we can compare the LCS in the two modeled flow fields to yield insight into transport and interaction processes in the high-latitude IT system. For obtaining thermospheric LCS, we use the Horizontal Wind Model 2014 (HWM14) [1] at a single altitude to generate the two-dimensional velocity field. The FTLE computation is applied to study the flow field of the neutral wind, and to visualize the forward-time Lagrangian Coherent Structures in the flow domain. The time-varying structures indicate a possible thermospheric LCS ridge in the auroral oval area. The results of a two-day run during a geomagnetically quiet period show that the structures are diurnally quasi-periodic, thus that solar radiation influences the neutral wind flow field. To find the LCS in the high-latitude ionospheric drifts, the Weimer 2001 [2] polar electric potential model and the International Geomagnetic Reference Field 11 [3] are used to compute the ExB drift flow field in ionosphere. As with the neutral winds, the Lagrangian Coherent Structures are obtained by applying the FTLE computation. The relationship between the thermospheric and ionospheric LCS is analyzed by comparing overlapping FTLE maps. Both a publicly available FTLE solver [4] and a custom-built FTLE computation are used and compared for validation [5]. Comparing the modeled IT LCSs on a quiet day with the modeled IT LCSs on a storm day indicates important factors on the structure and time evolution of the LCS.
Stress memory effect in viscoelastic stagnant lid convection
Patočka, V.; Čadek, O.; Tackley, P. J.; Čížková, H.
2017-06-01
Present thermochemical convection models of planetary evolution often assume a purely viscous or viscoplastic rheology. Ignoring elasticity in the cold, outer boundary layer is, however, questionable since elastic effects may play an important role there and affect surface topography as well as the stress distribution within the stiff cold lithosphere. Here we present a modelling study focused on the combined effects of Maxwell viscoelastic rheology and a free surface in the stagnant lid planetary convection. We implemented viscoelastic rheology in the StagYY code using a tracer-based stress advection scheme that suppresses subgrid oscillations. We apply this code to perform thermal convection models of the cooling planetary mantles and we demonstrate that while the global characteristics of the mantle flow do not change significantly when including viscoelasticity, the stress state of the cold lithosphere may be substantially different. Transient cooling of an initially thin upper thermal boundary layer results in a complex layered stress structure due to the memory effects of viscoelastic rheology. The stress state of the lid may thus contain a record of the planetary thermal evolution.
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
An example of special Lagrangian fibration
FU Jixiang
2005-01-01
On the total space of the line bundle π: π*1T*P1(◎)π2*T*P1 → P1× P1, acomplete Ricci-flat Kaehler metric and a smooth special Lagrangian fibration are given.This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4directions.
Electroweak Chiral Lagrangian for Neutral Higgs Boson
WANG Shun-Zhi; WANG Qing
2008-01-01
A neutral Higgs boson is added into the traditional electroweak chiral Lagrangian by writing down all possible high dimension operators. The matter part of the Lagrangian is investigated in detail. We find that if Higgs field dependence of Yukawa couplings can be factorized out, there will be no flavour changing neutral couplings; neutral Higgs can induce coupling between light and heavy neutrinos.
A functional LMO invariant for Lagrangian cobordisms
Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël
2008-01-01
Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le–Murakami–Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category...
Anomalous effective lagrangians and vector resonance models
Pallante, E.; Petronzio, R.
1993-01-01
Chiral lagrangians including vector resonances have been shown to saturate the finite part of some of the counterterms needed to regularize ordinary one-loop effective lagrangians of pseudoscalar interactions with external currents. The equivalence between different models has been discussed in the
The hybrid Eulerian Lagrangian numerical scheme tested with Chemistry
A. B. Hansen
2012-11-01
Full Text Available A newly developed advection scheme, the Hybrid Eulerian Lagrangian (HEL scheme, has been tested, including a module for atmospheric chemistry, including 58 chemical species, and compared to two other traditional advection schemes; a classical pseudospectral Eulerian method the Accurate Space Derivative (ASD scheme and the bi-cubic semi-Lagrangian (SL scheme using classical rotation tests. The rotation tests have been designed to test and compare the advection schemes for different spatial and temporal resolutions in different chemical conditions (rural and urban and for different shapes (cone and slotted cylinder giving the advection schemes different challenges with respect to relatively slow or fast chemistry and smooth or sharp gradients, respectively. In every test, error measures have been calculated and used for ranking of the advection schemes with respect to performance, i.e. lowest overall errors for all chemical species. Furthermore, the HEL and SL schemes have been compared in a shallow water model, demonstrating the performance in a more realistic non-linear deformation flow.
The results in this paper show that the new advection scheme, HEL, by far outperforms both the Eulerian and semi-Lagrangian schemes with very low error estimates compared to the two other schemes. Although no analytic solution can be obtained for the performance in the non-linear shallow water model flow, the tracer distribution appears realistic as compared to LMCSL when a mixing between local parcel concentrations is introduced in HEL.
A Lagrangian approach to classical thermodynamics
Stokes, A.
2017-02-01
The specification of microstates of interacting dynamical systems is different in Lagrangian and Hamiltonian approaches whenever the interaction Lagrangian depends on generalised velocities. In almost all cases of physical interest however, velocity-dependent interaction Lagrangians do not couple velocities belonging to different subsystems. For these cases we define reduced system and bath Lagrangian macrostates, which like the underlying microstates differ from their Hamiltonian counterparts. We then derive exact first and second laws of thermodynamics without any modification of the original system and bath quantities. This approach yields manifestly gauge-invariant definitions of work and free energy, and a gauge-invariant Jarzynski equality is derived. The formalism is applied in deriving the thermodynamic laws for a material system within the radiation reservoir. The Lagrangian partition of the total energy is manifestly gauge-invariant and is in accordance with Poynting's theorem.
Time-Dependent Lagrangian Biomechanics
Ivancevic, Tijana T
2009-01-01
In this paper we present the time-dependent generalization of an 'ordinary' autonomous human musculo-skeletal biomechanics. We start with the configuration manifold of human body, given as a set of its all active degrees of freedom (DOF). This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. On this extended configuration space we develop time-dependent biomechanical Lagrangian dynamics, using derived jet spaces of velocities and accelerations, as well as the underlying geometric evolution of the mass-inertia matrix. Keywords: Human time-dependent biomechanics, configuration manifold, jet spaces, geometric evolution
Yasutake, Nobutoshi; Fujisawa, Kotaro; Yamada, Shoichi
2016-12-01
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle with a triangulated mesh. It treats not only barotropic but also baroclinic equations of state. We compare the various stellar equilibria obtained by our new scheme with those by Hachisu's self-consistent field scheme for the barotropic case, and those by Fujisawa's self-consistent field scheme for the baroclinic case. Included in these rotational configurations are those with shellular-type rotations, which are commonly assumed in the evolution calculation of rotating stars. Although radiation processes, convections and meridional flows have not been taken into account in this study, we have in mind the application of this method to the two-dimensional evolution calculations of rotating stars, for which the Lagrangian formulation is best suited.
Viscoelastic properties of heavy oils
Rojas Luces, Maria Alejandra
Rheological low frequency measurements were carried out to analyze the viscoelastic properties of four heavy oil samples. At room conditions, the heavy oil samples exhibit non-Newtonian or viscoelastic behavior since they have a viscous component and an elastic component. The latter becomes very important for temperatures below 30°C, and for seismic to ultrasonic frequencies. Above this temperature, the viscous component increases significantly in comparison to the elastic component, and for seismic frequencies heavy oils can be considered as Newtonian fluids. A new viscosity model based on the concept of activation energy was derived to predict viscosity in terms of frequency and temperature for temperatures below 60°C. A new frequency-temperature dispersion model was derived to address the variation of the complex shear modulus (G*) with frequency and temperature for the heavy oil samples. This model fits the data well for seismic and sonic frequencies but it overpredicts G* at ultrasonic frequencies.
Viscoelastic behavior of dense microemulsions
Cametti, C.; Codastefano, P.; D'arrigo, G.; Tartaglia, P.; Rouch, J.; Chen, S. H.
1990-09-01
We have performed extensive measurements of shear viscosity, ultrasonic absorption, and sound velocity in a ternary system consisting of water-decane-sodium di(2-ethylhexyl)sulfo- succinate(AOT), in the one-phase region where it forms a water-in-oil microemulsion. We observe a rapid increase of the static shear viscosity in the dense microemulsion region. Correspondingly the sound absorption shows unambiguous evidence of a viscoelastic behavior. The absorption data for various volume fractions and temperatures can be reduced to a universal curve by scaling both the absorption and the frequency by the measured static shear viscosity. The sound absorption can be interpreted as coming from the high-frequency tail of the viscoelastic relaxation, describable by a Cole-Cole relaxation formula with unusually small elastic moduli.
Dynamical problem of micropolar viscoelasticity
Rajneesh Kumar; Suman Choudhary
2001-09-01
The dynamic problem in micropolar viscoelastic medium has been investigated by employing eigen value approach after applying Laplace and Fourier transformations. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inverted by using a numerical technique to obtain the displacement components, force stresses, couple stress and microrotation in the physical domain. The results for these quantities are given and illustrated graphically.
Davoodi, M.; Norouzi, M.
2016-10-01
In the present study, an investigation of the motion and shape deformation of drops is carried out in creeping flow to highlight the effect of viscoelastic properties on the problem. A perturbation method is employed to derive an analytical solution for the general case that both interior and exterior fluids are viscoelastic, both fluids obeying the Giesekus model. An experiment is also performed for the limiting case of an immiscible drop of a 0.03% (w/w) polyacrylamide in an 80:20 glycerol/water solution falling through a viscous Newtonian silicon oil (410 cP polydimethylsiloxane oil) in order to check the accuracy of the analytical solution. It is shown that the addition of elastic properties to the interior fluid may cause a decrease in the terminal velocity of the droplet while an increase in the elastic properties of the exterior fluid results in the opposite behavior and increases the terminal velocity. The well-known spherical shape of creeping drops for Newtonian fluids is modified by elasticity into either prolate or oblate shapes. Using the analytical solution, it is shown that normal stresses play a key role on the final steady-state shape of the drops. To keep the drops spherical in viscoelastic phases, it is shown that the effect of normal stresses on the interior and exterior media can cancel out under certain conditions. The results presented here may be of interest to industries dealing with petroleum and medicine processing, paint and power-plant related fields where knowledge of the shape and terminal velocity of descending droplets is of great importance.
Stress-energy-momentum tensors in Lagrangian field theory; 2, gravitational superpotential
Giachetta, G
1995-01-01
Our investigation of differential conservation laws in Lagrangian field theory is based on the first variational formula which provides the canonical decomposition of the Lie derivative of a Lagrangian density by a projectable vector field on a bundle (Part 1: gr-qc/9510061). If a Lagrangian density is invariant under a certain class of bundle isomorphisms, its Lie derivative by the associated vector fields vanishes and the corresponding differential conservation laws take place. If these vector fields depend on derivatives of parameters of bundle transformations, the conserved current reduces to a superpotential. This Part of the work is devoted to gravitational superpotentials. The invariance of a gravitational Lagrangian density under general covariant transformations leads to the stress-energy-momentum conservation law where the energy-momentum flow of gravity reduces to the corresponding generalized Komar superpotential. The associated energy-momentum (pseudo) tensor can be defined and calculated on solu...
Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
Beron-Vera, F J; Haller, G; Farazmand, M; Trinanes, J; Wang, Y
2014-01-01
Recent developments in dynamical systems theory have revealed long-lived and coherent Lagrangian (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent Lagrangian eddies. Here we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent Lagrangian eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent Lagrangian eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satell...
Gupta, Renu; Bansal, Ajay
2013-08-01
Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of BoL number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The BoL numbers were observed to increase with increase in liquid flow rate and consistency index 'K' for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Critical Point Theory for Lagrangian Systems
Mazzucchelli, Marco
2012-01-01
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange's reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more spec
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
An Augmented Lagrangian Approach for Scheduling Problems
Nishi, Tatsushi; Konishi, Masami
The paper describes an augmented Lagrangian decomposition and coordination approach for solving single machine scheduling problems to minimize the total weighted tardiness. The problem belongs to the class of NP-hard combinatorial optimization problem. We propose an augmented Lagrangian decomposition and coordination approach, which is commonly used for continuous optimization problems, for solving scheduling problems despite the fact that the problem is nonconvex and non-differentiable. The proposed method shows a good convergence to a feasible solution without heuristically constructing a feasible solution. The performance of the proposed method is compared with that of an ordinary Lagrangian relaxation.
An unconditionally stable fully conservative semi-Lagrangian method
Lentine, Michael
2011-04-01
Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had. © 2011 Elsevier Inc.
Micro-Macro Simulation of Viscoelastic Fluids in Three Dimensions
Rüttgers, Alexander; Griebel, Michael
2012-11-01
The development of the chemical industry resulted in various complex fluids that cannot be correctly described by classical fluid mechanics. For instance, this includes paint, engine oils with polymeric additives and toothpaste. We currently perform multiscale viscoelastic flow simulations for which we have coupled our three-dimensional Navier-Stokes solver NaSt3dGPF with the stochastic Brownian configuration field method on the micro-scale. In this method, we represent a viscoelastic fluid as a dumbbell system immersed in a three-dimensional Newtonian liquid which leads to a six-dimensional problem in space. The approach requires large computational resources and therefore depends on an efficient parallelisation strategy. Our flow solver is parallelised with a domain decomposition approach using MPI. It shows excellent scale-up results for up to 128 processors. In this talk, we present simulation results for viscoelastic fluids in square-square contractions due to their relevance for many engineering applications such as extrusion. Another aspect of the talk is the parallel implementation in NaSt3dGPF and the parallel scale-up and speed-up behaviour.
Wave propagation and energy dissipation in viscoelastic granular media
无
2001-01-01
In terms of viscoelasticity, the relevant theory of wave in granular media is analyzed in this paper.Under the conditions of slight deformation of granules, wave equation, complex number expressions of propagation vector and attenuation vector, attenuation coefficient expressions of longitudinal wave and transverse wave,etc, are analyzed and deduced. The expressions of attenuation coefficients of viscoelastic longitudinal wave and transverse wave show that the attenuation of wave is related to frequency. The higher the frequency is, the more the attenuation is, which is tested by the laboratory experiment. In addition, the energy dissipation is related to the higher frequency wave that is absorbed by granular media. The friction amongst granular media also increase the energy dissipation. During the flowing situation the expression of transmission factor of energy shows that the granular density difference is the key factor which leads to the attenuation of vibrating energy.This has been proved by the experiment results.
Chemical control of the viscoelastic properties of vinylogous urethane vitrimers
Denissen, Wim; Droesbeke, Martijn; Nicolaÿ, Renaud; Leibler, Ludwik; Winne, Johan M.; Du Prez, Filip E.
2017-03-01
Vinylogous urethane based vitrimers are polymer networks that have the intrinsic property to undergo network rearrangements, stress relaxation and viscoelastic flow, mediated by rapid addition/elimination reactions of free chain end amines. Here we show that the covalent exchange kinetics significantly can be influenced by combination with various simple additives. As anticipated, the exchange reactions on network level can be further accelerated using either Brønsted or Lewis acid additives. Remarkably, however, a strong inhibitory effect is observed when a base is added to the polymer matrix. These effects have been mechanistically rationalized, guided by low-molecular weight kinetic model experiments. Thus, vitrimer elastomer materials can be rationally designed to display a wide range of viscoelastic properties.
Geometric Time and Causal Time in Relativistic Lagrangian Mechanics
Brunet, Olivier
2016-01-01
In this article, we argue that two distinct types of time should be taken into account in relativistic physics: a geometric time, which emanates from the structure of spacetime and its metrics, and a causal time, indicating the flow from the past to the future. A particularity of causal times is that its values have no intrinsic meaning, as their evolution alone is meaningful. In the context of relativistic Lagrangian mechanics, causal times corresponds to admissible parameterizations of paths, and we show that in order for a langragian to not depend on any particular causal time (as its values have no intrinsic meaning), it has to be homogeneous in its velocity argument. We illustrate this property with the example of a free particle in a potential. Then, using a geometric Lagrangian (i.e. a parameterization independent Lagrangian which is also manifestly covariant), we introduce the notion of ageodesicity of a path which measures to what extent a path is far from being a geodesic, and show how the notion ca...
Direct Numerical Simulation of Particle Migration in a Simple Shear Flow
LV Hong; TANG Sheng-Li; ZHOU Wen-Ping
2011-01-01
@@ Motion of a rectangular particle in a two-dimensional vertical shear flow of Newtonian fluid and viscoelastic fluid with different parameters is studied using the finite element arbitrary Lagrangian-Eulerian domain method.The results show that the centerline of the channel is a stable equilibrium position for the neutrally buoyant rectangular particle in a vertical shear flow.Inertia causes the particle to migrate towards the centerline of the channel.In addition, a critical elasticity number exists.When the elasticity number is below the critical value,the rectangular particle migrates to the centerline; otherwise the centerline of the channel is apparently no longer a global attractor of trajectories of the particle.
Tsunami intrusion in wide meandering channels: a Lagrangian numerical experiment
Couston, L. A.; Alam, M. R.
2015-12-01
Among the many difficulties of tsunami forecast, wave runup on sloped beaches remains a major obstacle in numerical simulations. Traditional Eulerian models must adjust the fluid flow domain continuously due to the moving shorelines, which can significantly affect the computational cost and results accuracy. An efficient though uncommon alternative for accurate runup predictions still exists, consisting in using a Lagrangian model as recently shown by e.g. Couston et al. (2015) who studied the runup of landslide tsunamis in lakes with a non-dispersive Lagrangian model. Here we introduce a fully-nonlinear Boussinesq-type model derived in the Lagrangian framework to investigate various cases of long-wave runup on curved beaches and meandering channels. The governing equations are expressed in terms of curvilinear Lagrangian coordinates, making the model suitable for accurate runup computations at shorelines of arbitrary geometry while retaining the inherent simplicity of a physical model discretized on a fixed and structured grid. We implement an elliptic grid generation algorithm to map the physical space to the computational space, and a high-order finite-difference scheme for time integration. The numerical model has a linear complexity in the number of unknowns when neglecting dispersive effects. We show that the formation of edge waves due to the sloped banks of a wide channel has a significant influence on the capability of a meander or constriction in reflecting the intruding tsunami, and we investigate the effect of dispersion. Reference: Couston, L.-A., Mei, C. C., & Alam, M.-R. (2015). Landslide tsunamis in lakes. Journal of Fluid Mechanics, 772, 784-804.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Multi-Lagrangians for Integrable Systems
Nutku, Y
2001-01-01
We propose a general scheme to construct multiple Lagrangians for completely integrable non-linear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new Lagrangian and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit $N$-fold first order local Hamiltonian structure can be cast into variational form with $2N-1$ Lagrangians which will be local functionals of Clebsch potentials. Furthermore we construct a new Lagrangian for polytropic gas dynamics in 1+1 dimensions which is a {\\it local} functional of the physical field variables, namely density and velocity.
Effective Lagrangians and Light Gravitino Phenomenology
Luty, M A; Luty, Markus A.; Ponton, Eduardo
1998-01-01
We construct the low-energy effective lagrangian for supersymmetry breaking models with a light gravitino. Our effective lagrangian is written in terms of the spin-1/2 Goldstino (the longitudinal component of the gravitino) transforming under a non-linear realization of supersymmetry. The Goldstino is derivatively coupled. We use this lagrangian to place bounds on the supersymmetry breaking scale \\sqrt{F} from Goldstino phenomenology. The most stringent bounds come from the coupling of a single photon to Goldstino pairs. For gauge-mediated models, this coupling arises at one loop in the effective lagrangian, and supernova cooling allows \\sqrt{F} > 610 GeV or \\sqrt{F} 140 GeV for tan\\beta = 2.
Detecting Lagrangian fronts with favourable fishery conditions
Prants, S V; Uleysky, M Yu
2012-01-01
Lagrangian fronts in the ocean delineate boundaries between surface waters with different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps of the drift of synthetic tracers, their Lyapunov exponents, and other Lagrangian indicators. Using Russian ship's catch and location data for a number of commercial fishing seasons in the region of the northwest Pacific with one of the richest fishery in the world, it is shown that the saury fishing grounds with maximal catches are located mainly along those Lagrangian fronts where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts with the altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions in both the cases the front locations may serve good indicators of potential fishing grou...
A Lagrangian particle/panel method for the barotropic vorticity equations on a rotating sphere
Bosler, Peter; Krasny, Robert [Department of Mathematics, University of Michigan, Ann Arbor, MI 48109 (United States); Wang, Lei [Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201 (United States); Christiane Jablonowski, E-mail: krasny@umich.edu [Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109 (United States)
2014-06-01
We present a Lagrangian particle/panel method for geophysical fluid flow described by the barotropic vorticity equations on a rotating sphere. The particles carry vorticity and the panels are used in discretizing the Biot–Savart integral for the velocity. Adaptive panel refinement and a new Lagrangian remeshing scheme are applied to reduce the computational cost and maintain accuracy as the flow evolves. Computed examples include a Rossby–Haurwitz wave, a Gaussian vortex, and a perturbed zonal jet. To validate the method, a comparison is made with results obtained using the Lin–Rood finite–volume scheme. (papers)
On invariant sets in Lagrangian graphs
无
2010-01-01
In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.
Lagrangian Formulation of Todorov-Komar Model
Gomis, J.; Kamimura, K.; Pons, J. M.
1984-05-01
The multi-temporal Hamiltonian model of relativistic particle interaction (Todorov-Komar model) is studied from the viewpoint of the Lagrangian formalism. The action is constructed and the gauge structure is clarified.The mathematical coordinates used to describe the Lagrangian are not gauge invariant and are disqualified as the physical coordinates of the interacting particles. The position of the particles is defined as the function of the canonical variables so that the world lines are invariant under the gauge transformations.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu [Karlsruhe Institute of Technology (KIT), Institute of Physical Chemistry, Theoretical Chemistry Group, KIT Campus South, P.O. Box 6980, 76049 Karlsruhe (Germany)
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
The visco-elastic multilayer program VEROAD
Hopman, P.C.
1996-01-01
The mathematical principles and derivation of a linear visco-elastic multilayer computer program are described. The mathematical derivation is based on Fourier Transformation. The program is called VEROAD, which is an acronym for Visco-Elastic ROad Analysis Delft. The program allows calculation of p
Shape recovery of viscoelastic beams after stowage
Kwok, Kawai
2015-01-01
The deployment of viscoelastic structures that have been held stowed for a given time duration can be formulated as a viscoelastic boundary value problem in which the prescribed condition switches from constant displacement to constant traction. This paper presents closed-form expressions...
Linear viscoelastic characterization from filament stretching rheometry
Wingstrand, Sara Lindeblad; Alvarez, Nicolas J.; Hassager, Ole
viscoelasticity well into the nonlinear regime. Therefore at present, complete rheological characterization of a material requires two apparatuses: a shear and an extensional rheometer. This work is focused on developing a linear viscoelastic protocol for the filament stretching rheometer (FSR) in order...
Nonlinear Viscoelastic Characterization of Structural Adhesives.
1983-06-01
neat resin properties 20. ABSTRACT (Cainlnuo OR revaWco aide II necessay amd identify br blck number) Measurements of the nonlinear viscoelastic...which is utilized. 17. Key Words and Document Analysis. l7a. Descriptors Adhesives, nonlinear viscoelasticity, FM-73 and FM-300 neat resin properties 17b
Matsuura, Yusuke; Hirano, Taichi; Sakai, Keiji
2017-07-01
In this study, we developed a novel type of rheological measurement system. Here, a spherical probe is driven to rotate periodically by applying torques using quadruple electromagnets in a noncontact manner. Moreover, this system is an enhancement of our electromagnetically spinning (EMS) viscometer, which is widely used for measuring rheological flow curves in various industrial fields. The quadruple EMS method provides the frequency spectrum of viscoelasticity, in addition to shear viscosity, in a steady flow by switching the operation modes of the driving torque. We show the results obtained for Newtonian fluids and viscoelastic materials and demonstrate the validity of the system.
Convective heat transfer for viscoelastic fluid in a curved pipe
Norouzi, M.; Kayhani, M.H. [Shahrood University of Technology, Mechanical Engineering Department, Shahrood (Iran); Nobari, M.R.H. [Amirkabir University of Technology, Mechanical Engineering Department, Tehran (Iran); Joneidi, A.A. [Eindhoven University of Technology, Mechanical-Polymer Technology Group, Eindhoven (Netherlands)
2010-10-15
In this paper, fully developed convective heat transfer of viscoelastic flow in a curved pipe under the constant heat flux at the wall is investigated analytically using a perturbation method. Here, the curvature ratio is used as the perturbation parameter and the Oldroyd-B model is applied as the constitutive equation. In the previous studies, the Dirichlet boundary condition for the temperature at the wall has been used to simplify the solution, but here exactly the non-homogenous Neumann boundary condition is considered to solve the problem. Based on this solution, the non-axisymmetric temperature distribution of Dean flow is obtained analytically and the effect of flow parameters on the flow field is investigated in detail. The current analytical results indicate that increasing the Weissenberg number, viscosity ratio, curvature ratio, and Prandtl number lead to the increase of the heat transfer in the Oldroyd-B fluid flow. (orig.)
Lagrangian hydrocode simulations of the 1958 Lituya Bay tsunamigenic rockslide
Schwaiger, H. F.; Higman, B.
2007-07-01
The interaction of debris flows, whether subaqueous or subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, corresponding to a large effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. We use this model to simulate the 1958 Lituya Bay rockslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and numerical studies.
Lagrangian Velocity Correlations and Absolute Dispersion in the Midlatitude Troposphere
Sukhatme, J
2004-01-01
Employing daily wind data from the ECMWF, we perform passive particle advection to estimate the Lagrangian velocity correlation functions (LVCF) associated with the midlatitude tropospheric flow. In particular we decompose the velocity field into time mean and transient (or eddy) components to better understand the nature of the LVCF's.A closely related quantity, the absolute dispersion (AD) is also examined. Given the anisotropy of the flow, meridional and zonal characteristics are considered separately. The zonal LVCF is seen to be non-exponential. In fact, for a broad set of intermediate timescales it is better described as a power law of the form $\\tau^{-\\alpha}$ with $ 0<\\alpha<1$. Indeed, the implied long time correlation in the zonal flow results in a superdiffusive zonal AD regime. On the other hand, the meridional LVCF decays rapidly to zero. Interestingly, before approaching to zero it shows a region of negative correlation. A physical argument based on the rotational inhibition of latitudinal...
THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL
Wang Zhongmin; Zhao Fengqun; Feng Zhenyu; Liu Hongzhao
2000-01-01
Based on the differential constitutive relationship of linear viscoelastic material, a solid-liquid coupling vibration equation for viscoelastic pipe conveying fluid is derived by the D'Alembert's principle. The critical flow velocities and natural frequencies of the cantilever pipe conveying fluid with the Kelvin model ( flutter instability) are calculated with the modified finite difference method in the form of the recurrence for mula. The curves between the complex frequencies of the first, second and third mode and flow velocity of the pipe are plotted. On the basis of the numerical calculation results, the dynamic behaviors and stability of the pipe are discussed. It should be pointed out that the delay time of viscoelastic material with the Kelvin model has a remarkable effect on the dynamic characteristics and stability behaviors of the cantilevered pipe conveying fluid, which is a gyroscopic non-conservative system.
A Comparison of Viscoelastic Properties of Three Root Canal Sealers
Malihe Pishvaei
2013-01-01
Full Text Available Objective: Handling of endodontic sealers is greatly dependent on their elasticity and flow ability. We compared the viscoelastic properties of three root canal sealers.Materials and Methods: AH Plus (Dentsply, De Trey, Konstanz, Germany, Endofill (Dentsply Hero, Petrópolis, Rio de Janeiro, Brazil and AH26 (Dentsply, De Trey, Konstanz, Germany were mixed according to the manufacturers' instructions. The resulted pastes were placed on the plate of a rheometer (MCR 300, Anton-Paar, Graz, Austria. The experiments were performed at 25˚C and 37˚C. Viscoelastic properties of the sealers including loss modulus (G", storage modulus (G´ and complex viscosity (η* were studied using dynamic oscillatory shear tests. The shear module versus frequency (from 0.01 to 100 S-1 curves were gained using frequency deformation sweep test. Three samples of each material were examined at each temperature. The mean of these three measurements were recorded.Results: The storage modulus of AH plus was higher than its loss modulus at two temperatures. Endofill exhibited a crossover region in which the storage modulus crosses the loss modulus in both temperatures. At 25ºC the loss modulus of AH26 was higher than the storage modulus (G">G¢. In contrast, at 37ºC G¢was greater than G² (G¢>G². Both shear modules of AH Plus and Endofill decreased as the temperature raised from 25ºC to 37ºC. On the contrary, the loss modulus and storage modulus of AH26 increased at 37ºC.Conclusion: In both test temperatures, AH Plus behaved like viscoelastic solids and Endofill exhibited a gel-like viscoelastic behavior. AH26 at 25ºC behaved like liquids, while at 37ºC it was an elastic solid-like material
An experimental study of turbulent mixing of viscoelastic fluids
Bartels, Paul Vincent
1988-07-01
The viscoelastic behavior of fluids was related to the hydrodynamics, energy dissipation, and homogenization for turbulent pipeline flow and stirred tank reactors. For both mixing systems a significant influence of viscoelasticity on the hydrodynamics is found in locations with a high shear rate, such as occur in the boundary layer of pipeline flow and in the trailing vortices of the blade of a Rushton turbine. This results in a dramatic drop of the overall energy dissipation for very low values of elasticity number. In tube flow there is a threshold for the drag reduction phenomenon. The friction factor appears to be also a function of the elasticity number. The homogenization process of polymer solutions is also slower due to the lower energy dissipation, causing less dispersion. The energy dissipation and homogenization can be related to a characteristic fluid time and the elasticity number. The effect of inserted mixing elements on turbulent pipe flow was studied. The pressure drop of the mixers is almost independent of the concentration of polyacrylamide, but mixing will be less when the characteristic time of the solutions increases.
The viscoelastic effects on thermal convection of an Oldroyd-B fluid in open-top porous media
NIU Jun; SHI Zai-hong; TAN Wen-chang
2013-01-01
The effects of two viscoelastic parameters on the thermal convection of a viscoelastic Oldroyd-B fluid in an open-top porous square box with constant heat flux are investigated.The results show that the increase of relaxation time is able to destabilize the fluid flow leading to a higher heat transfer rate,while the increase of retardation time tends to stabilize the flow and suppress the heat transfer.The flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time,resulting in more complicated flow patterns in the porous medium.
Directed self-assembly of spheres into a two-dimensional colloidal crystal by viscoelastic stresses.
Pasquino, Rossana; Snijkers, Frank; Grizzuti, Nino; Vermant, Jan
2010-03-02
Ordering induced by shear flow can be used to direct the assembly of particles in suspensions. Flow-induced ordering is determined by the balance between a range of forces, such as direct interparticle, Brownian, and hydrodynamic forces. The latter are modified when dealing with viscoelastic rather than Newtonian matrices. In particular, 1D stringlike structures of spherical particles have been observed to form along the flow direction in shear thinning viscoelastic fluids, a phenomenon not observed in Newtonian fluids at similar particle volume fractions. Here we report on the formation of freestanding crystalline patches in planes parallel to the shearing surfaces. The novel microstructure is formed when particles are suspended in viscoelastic, wormlike micellar solutions and only when the applied shear rate exceeds a critical value. In spite of the very low volume fraction (less than 0.01), particles arrange themselves in 2D crystalline patches along the flow direction. This is a bulk phenomenon because 2D crystals form throughout the whole gap between plates, with the gap thickness being much larger than the particle size. Shear flow may hence be an easy method to drive particles into crystalline order in suspensions with viscoelastic properties. The crystalline structure reported here could be used to design new materials with special mechanical, optical, thermal, or electric properties.
Zhang, Da Peng; Lei, Yong Jun; Shen, Zhi Bin [College of Aerospace Science and Engineering, National University of Defense Technology, Changsha (China); Wang, Cheng Yuan [Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea Wales (United Kingdom)
2017-01-15
Vibration responses were investigated for a viscoelastic Single-walled carbon nanotube (visco-SWCNT) resting on a viscoelastic foundation. Based on the nonlocal Euler-Bernoulli beam model, velocity-dependent external damping and Kelvin viscoelastic foundation model, the governing equations were derived. The Transfer function method (TFM) was then used to compute the natural frequencies for general boundary conditions and foundations. In particular, the exact analytical expressions of both complex natural frequencies and critical viscoelastic parameters were obtained for the Kelvin-Voigt visco-SWCNTs with full foundations and certain boundary conditions, and several physically intuitive special cases were discussed. Substantial nonlocal effects, the influence of geometric and physical parameters of the SWCNT and the viscoelastic foundation were observed for the natural frequencies of the supported SWCNTs. The study demonstrates the efficiency and robustness of the developed model for the vibration of the visco-SWCNT-viscoelastic foundation coupling system.
Rotating convection in a viscoelastic magnetic fluid
Pérez, L.M. [Departamento de Fíisica y Matemática Aplicada, Universidad de Navarra, 31080 Pamplona (Spain); Laroze, D., E-mail: dlarozen@uta.cl [Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica (Chile); Díaz, P. [Departamento de Ciencias Físicas, Universidad de La Frontera, Casilla 54 D, Temuco (Chile); Martinez-Mardones, J. [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Mancini, H.L. [Departamento de Fíisica y Matemática Aplicada, Universidad de Navarra, 31080 Pamplona (Spain)
2014-09-01
We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid under rotation. The viscoelastic properties are given by the Oldroyd model. We obtain explicit expressions for the convective thresholds in terms of the parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic boundary conditions. The effects of the rheology and of the rotation rate on the instability thresholds for a diluted magnetic suspension are emphasized. - Highlights: • Ferrofluids. • Thermal convection. • Viscoelastic model. • Realistic boundary conditions.
Transient vibration of thin viscoelastic orthotropic plates
J. Soukup; F. Vale(s); J. Volek; J. Sko(c)ilas
2011-01-01
This article deals with solutions of transient vibration of a rectangular viscoelastic orthotropic thin 2D plate for particular deformation models according to Flügge and Timoshenko-Mindlin. The linear model, a general standard viscoelastic body, of the rheologic properties of a viscoelastic material was applied. The time and coordinate curves of the basic quantities displacement, rotation, velocity, stress and deformation are compared. The results obtained by an approximate analytic method are compared with numerical results for 3D plate generated by FEM application and with experimental investigation.
Transient waves in visco-elastic media
Ricker, Norman
1977-01-01
Developments in Solid Earth Geophysics 10: Transient Waves in Visco-Elastic Media deals with the propagation of transient elastic disturbances in visco-elastic media. More specifically, it explores the visco-elastic behavior of a medium, whether gaseous, liquid, or solid, for very-small-amplitude disturbances. This volume provides a historical overview of the theory of the propagation of elastic waves in solid bodies, along with seismic prospecting and the nature of seismograms. It also discusses the seismic experiments, the behavior of waves propagated in accordance with the Stokes wave
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Viscoelastic coupling of nanoelectromechanical resonators.
Simonson, Robert Joseph; Staton, Alan W.
2009-09-01
This report summarizes work to date on a new collaboration between Sandia National Laboratories and the California Institute of Technology (Caltech) to utilize nanoelectromechanical resonators designed at Caltech as platforms to measure the mechanical properties of polymeric materials at length scales on the order of 10-50 nm. Caltech has succeeded in reproducibly building cantilever resonators having major dimensions on the order of 2-5 microns. These devices are fabricated in pairs, with free ends separated by reproducible gaps having dimensions on the order of 10-50 nm. By controlled placement of materials that bridge the very small gap between resonators, the mechanical devices become coupled through the test material, and the transmission of energy between the devices can be monitored. This should allow for measurements of viscoelastic properties of polymeric materials at high frequency over short distances. Our work to date has been directed toward establishing this measurement capability at Sandia.
Viscoelastic behavior of stock indices
Gündüz, Güngör; Gündüz, Yalin
2010-12-01
The scattering diagram of a stock index results in a complex network structure, which can be used to analyze the viscoelastic properties of the index. The change along x- or y-direction of the diagram corresponds to purely elastic (or spring like) movement whereas the diagonal change at an angle of 45° corresponds to purely viscous (or dashpot like) movement. The viscous component pushes the price from its current value to any other value, while the elastic component acts like a restoring force. Four indices, namely, DJI, S&P-500, NASDAQ-100, and NASDAQ-composite were studied for the period of 2001-2009. NASDAQ-composite displayed very high elasticity while NASDAQ-100 displayed the highest fluidity in the time period considered. The fluidity of DJI and S&P-500 came out to be close to each other, and they are almost the same in the second half of the period.
When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...
Modeling electrically active viscoelastic membranes.
Sitikantha Roy
Full Text Available The membrane protein prestin is native to the cochlear outer hair cell that is crucial to the ear's amplification and frequency selectivity throughout the whole acoustic frequency range. The outer hair cell exhibits interrelated dimensional changes, force generation, and electric charge transfer. Cells transfected with prestin acquire unique active properties similar to those in the native cell that have also been useful in understanding the process. Here we propose a model describing the major electromechanical features of such active membranes. The model derived from thermodynamic principles is in the form of integral relationships between the history of voltage and membrane resultants as independent variables and the charge density and strains as dependent variables. The proposed model is applied to the analysis of an active force produced by the outer hair cell in response to a harmonic electric field. Our analysis reveals the mechanism of the outer hair cell active (isometric force having an almost constant amplitude and phase up to 80 kHz. We found that the frequency-invariance of the force is a result of interplay between the electrical filtering associated with prestin and power law viscoelasticity of the surrounding membrane. Paradoxically, the membrane viscoelasticity boosts the force balancing the electrical filtering effect. We also consider various modes of electromechanical coupling in membrane with prestin associated with mechanical perturbations in the cell. We consider pressure or strains applied step-wise or at a constant rate and compute the time course of the resulting electric charge. The results obtained here are important for the analysis of electromechanical properties of membranes, cells, and biological materials as well as for a better understanding of the mechanism of hearing and the role of the protein prestin in this mechanism.
The physics of aerobreakup. III. Viscoelastic liquids
Theofanous, T. G.; Mitkin, V. V.; Ng, C. L.
2013-03-01
We extend the work of Theofanous and Li [Phys. Fluids 20, 052103 (2008), 10.1063/1.2907989] on aerobreakup physics of water-like, low viscosity liquid drops, and of Theofanous et al. [Phys. Fluids 24, 022104 (2012), 10.1063/1.3680867] for Newtonian liquids of any viscosity, to polymer-thickened liquids over wide ranges of viscoelasticity. The scope includes the full range of aerodynamics from near incompressible to supersonic flows and visualizations are recorded with μs/μm resolutions. The key physics of Rayleigh-Taylor piercing (RTP, first criticality) and of Shear-Induced Entrainment (SIE, second criticality) are verified and quantified on the same scaling approach as in our previous work, but with modifications due to the shear-thinning and elastic nature of these liquids. The same holds for the onset of surface waves by Kelvin-Helmholtz instability, which is a key attribute of the second criticality. However, in the present case, even at conditions well-past the first criticality, there is no breakup (particulation) to be found; instead the apparently unstable (extensively stretched into sheets) drops rebound elastically to reconstitute an integral mass. Such a resistance to breakup is found also past the second criticality, now with extensive filament formation that maintain a significant degree of cohesiveness, until the gas-dynamic pressure is high enough to cause filament ruptures. Thereby we define the onset of a third criticality peculiar to viscoelastic liquids—SIER, for SIE with ruptures. Past this criticality the extent of particulation increases and the characteristic dimension of fragments generated decreases in a more or less continuous fashion with increasing dynamic pressure. We outline a rheology-based scaling approach for these elasticity-modulated phenomena and suggest a path to similitude (with polymer and solvent variations) in terms of a critical rupture stress that can be measured independently. The advanced stages of breakup and
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-01-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O3 decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Forecasting for a Lagrangian aircraft campaign
A. Stohl
2004-05-01
Full Text Available A forecast system has been developed in preparation for an upcoming aircraft measurement campaign, where the same air parcels polluted by emissions over North America shall be sampled repeatedly as they leave the continent, during transport over the Atlantic, and upon their arrival over Europe. This paper describes the model system in advance of the campaign, in order to make the flight planners familiar with the novel model output. The aim of a Lagrangian strategy is to infer changes in the chemical composition and aerosol distribution occurring en route by measured upwind/downwind differences. However, guiding aircraft repeatedly into the same polluted air parcels requires careful forecasting, for which no suitable model system exists to date. This paper describes a procedure using both Eulerian-type (i.e. concentration fields and Lagrangian-type (i.e. trajectories model output from the Lagrangian particle dispersion model FLEXPART to predict the best opportunities for a Lagrangian experiment. The best opportunities are defined as being highly polluted air parcels which receive little or no emission input after the first measurement, which experience relatively little mixing, and which are reachable by as many aircraft as possible. For validation the system was applied to the period of the NARE 97 campaign where approximately the same air masses were sampled on different flights. Measured upwind/downwind differences in carbon monoxide (CO and ozone (O_{3} decreased significantly as the threshold values used for accepting cases as Lagrangian were tightened. This proves that the model system can successfully identify Lagrangian opportunities.
Lagrangians for the W-Algebra Models
Gaite, J C
1994-01-01
The field algebra of the minimal models of W-algebras is amenable to a very simple description as a polynomial algebra generated by few elementary fields, corresponding to order parameters. Using this description, the complete Landau-Ginzburg lagrangians for these models are obtained. Perturbing these lagrangians we can explore their phase diagrams, which correspond to multicritical points with $D_n$ symmetry. In particular, it is shown that there is a perturbation for which the phase structure coincides with that of the IRF models of Jimbo et al.
Effective Lagrangian in de Sitter Spacetime
Kitamoto, Hiroyuki
2016-01-01
Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.
Maxwell-like Lagrangians for higher spins
Campoleoni, Andrea
2012-01-01
We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.
Learn the Lagrangian: A Vector-Valued RKHS Approach to Identifying Lagrangian Systems.
Cheng, Ching-An; Huang, Han-Pang
2016-12-01
We study the modeling of Lagrangian systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of Lagrangian systems and vector-valued reproducing kernel Hilbert space. We reformulate Lagrangian systems with kernels that embed the governing Euler-Lagrange equation-the Lagrangian kernels-and show that these kernels span a subspace capturing the Lagrangian's projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's Lagrangian, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying Lagrangian systems, despite using only inputs and outputs.
Reaction enhancement of initially distant scalars by Lagrangian coherent structures
Pratt, Kenneth R., E-mail: kenneth.pratt@colorado.edu; Crimaldi, John P., E-mail: john.crimaldi@colorado.edu [Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colorado 80309-0428 (United States); Meiss, James D., E-mail: james.meiss@colorado.edu [Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526 (United States)
2015-03-15
Turbulent fluid flows have long been recognized as a superior means of diluting initial concentrations of scalars due to rapid stirring. Conversely, experiments have shown that the structures responsible for this rapid dilution can also aggregate initially distant reactive scalars and thereby greatly enhance reaction rates. Indeed, chaotic flows not only enhance dilution by shearing and stretching but also organize initially distant scalars along transiently attracting regions in the flow. To show the robustness of this phenomenon, a hierarchical set of three numerical flows is used: the periodic wake downstream of a stationary cylinder, a chaotic double gyre flow, and a chaotic, aperiodic flow consisting of interacting Taylor vortices. We demonstrate that Lagrangian coherent structures (LCS), as identified by ridges in finite time Lyapunov exponents, are directly responsible for this coalescence of reactive scalar filaments. When highly concentrated filaments coalesce, reaction rates can be orders of magnitude greater than would be predicted in a well-mixed system. This is further supported by an idealized, analytical model that was developed to quantify the competing effects of scalar dilution and coalescence. Chaotic flows, known for their ability to efficiently dilute scalars, therefore have the competing effect of organizing initially distant scalars along the LCS at timescales shorter than that required for dilution, resulting in reaction enhancement.
Theory of reciprocating contact for viscoelastic solids
Putignano, Carmine; Carbone, Giuseppe; Dini, Daniele
2016-04-01
A theory of reciprocating contacts for linear viscoelastic materials is presented. Results are discussed for the case of a rigid sphere sinusoidally driven in sliding contact with a viscoelastic half-space. Depending on the size of the contact, the frequency and amplitude of the reciprocating motion, and on the relaxation time of the viscoelastic body, we establish that the contact behavior may range from the steady-state viscoelastic solution, in which traction forces always oppose the direction of the sliding rigid punch, to a more elaborate trend, which is due to the strong interaction between different regions of the path covered during the reciprocating motion. Practical implications span a number of applications, ranging from seismic engineering to biotechnology.
Dynamics and Stability of Rolling Viscoelastic Tires
Potter, Trevor [Univ. of California, Berkeley, CA (United States)
2013-04-30
Current steady state rolling tire calculations often do not include treads because treads destroy the rotational symmetry of the tire. We describe two methodologies to compute time periodic solutions of a two-dimensional viscoelastic tire with treads: solving a minimization problem and solving a system of equations. We also expand on work by Oden and Lin on free spinning rolling elastic tires in which they disovered a hierachy of N-peak steady state standing wave solutions. In addition to discovering a two-dimensional hierarchy of standing wave solutions that includes their N-peak hiearchy, we consider the eects of viscoelasticity on the standing wave solutions. Finally, a commonplace model of viscoelasticity used in our numerical experiments led to non-physical elastic energy growth for large tire speeds. We show that a viscoelastic model of Govindjee and Reese remedies the problem.
Changes in protein solubility, fermentative capacity, viscoelasticity ...
SAM
2014-05-14
May 14, 2014 ... solubility, fermentative capacity and viscoelasticity of frozen dough. In addition to examining ... A dynamic ... ten protein fractions of higher molecular weight and are .... An SE-HPLC system (Varian ProStar equipment, Model.
Understanding Viscoelasticity An Introduction to Rheology
Phan-Thien, Nhan
2013-01-01
This book presents an introduction to viscoelasticity; in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity at a first year graduate level. The main aim is to provide a still compact book, sufficient at the level of first year graduate course for those who wish to understand viscoelasticity and to embark in modeling of viscoelastic multiphase fluids. To this end, a new chapter on Dissipative Particle Dynamics (DPD) was introduced which is relevant to model complex-structured fluids. All the basic ideas in DPD are reviewed,...
Understanding viscoelasticity an introduction to rheology
Phan-Thien, Nhan
2017-01-01
This book presents an introduction to viscoelasticity, in particular, to the theories of dilute polymer solutions and dilute suspensions of rigid particles in viscous and incompressible fluids. These theories are important, not just because they apply to practical problems of industrial interest, but because they form a solid theoretical base upon which mathematical techniques can be built, from which more complex theories can be constructed, to better mimic material behaviour. The emphasis of this book is not on the voluminous current topical research, but on the necessary tools to understand viscoelasticity. This is a compact book for a first year graduate course in viscoelasticity and modelling of viscoelastic multiphase fluids. The Dissipative Particle Dynamics (DPD) is introduced as a particle-based method, relevant in modelling of complex-structured fluids. All the basic ideas in DPD are reviewed. The third edition has been updated and expanded with new results in the meso-scale modelling, links between...
Dynamic response of visco-elastic plates
Kadıoǧlu, Fethi; Tekin, Gülçin
2016-12-01
In this study, a comprehensive analysis about the dynamic response characteristics of visco-elastic plates is given. To construct the functional in the Laplace-Carson domain for the analysis of visco-elastic plates based on the Kirchhoff hypothesis, functional analysis method is employed. By using this new energy functional in the Laplace-Carson domain, moment values that are important for engineers can be obtained directly with excellent accuracy and element equations can be written explicitly. Three-element model is considered for modelling the visco-elastic material behavior. The solutions obtained in the Laplace-Carson domain by utilizing mixed finite element formulation are transformed to the time domain using the Durbin's inverse Laplace transform technique. The proposed mixed finite element formulation is shown to be simple to implement and gives satisfactory results for dynamic response of visco-elastic plates.
Enhanced active swimming in viscoelastic fluids
Riley, Emily E
2014-01-01
Swimming microorganisms often self propel in fluids with complex rheology. While past theoretical work indicates that fluid viscoelasticity should hinder their locomotion, recent experiments on waving swimmers suggest a possible non-Newtonian enhancement of locomotion. We suggest a physical mechanism, based on fluid-structure interaction, leading to swimming in a viscoelastic fluid at a higher speed than in a Newtonian one. Using Taylor's two-dimensional swimming sheet model, we solve for the shape of an active swimmer as a balance between the external fluid stresses, the internal driving moments, and the passive elastic resistance. We show that this dynamic balance leads to a generic transition from hindered rigid swimming to enhanced flexible locomotion. The results are physically interpreted as due to a viscoelastic suction increasing the swimming amplitude in a non-Newtonian fluid and overcoming viscoelastic damping.
Probing Viscoelasticity of Cholesteric Liquid Crystals in a Twisting Cell
Angelo, Joseph; Moheghi, Alireza; Diorio, Nick; Jakli, Antal
2013-03-01
Viscoelastic properties of liquid crystals are typically studied either using Poiseuille flow, which can be produced by a pressure gradient in a capillary tube,[2] or Couette flow, which can be generated by a shear between concentric cylinders.[3] We use a different method in which we twist the liquid crystal sandwiched between two cylindrical glass plates, one of which can rotate about its center, the other of which is fixed. When the cell is twisted, there is a force proportional to the twist angle and the twist elastic constant, and inversely proportional to the pitch and sample thickness, normal to the substrates due to the change in pitch in the cholesteric liquid crystal (CLC). Measuring this force on various CLCs with known pitch we could obtain the twist elastic constants. In addition to the equilibrium force, we observed a transient force during the rotation, which is related to the flow of the material, thus allowing us to determine the Leslie viscosity component α1, which typically cannot be assessed by other methods. We expect this apparatus to be a useful tool to study the visco-elastic properties of liquid crystals. The authors acknowledge support from NSF grant DMR-0907055.
The blistering of a viscoelastic filament of a droplet of saliva
Wagner, Christian; Eggers, Jens
2009-01-01
A fluid dynamics video of the break up of a droplet of saliva is shown. First a viscoelastic filament is formed and than the blistering of this filament is shown. Finally, a flow induced phase separation takes place nanometer sized solid fiber remains that consist out of the biopolymers.
Recent advances in elasticity, viscoelasticity and inelasticity
Rajagopal, KR
1995-01-01
This is a collection of papers dedicated to Prof T C Woo to mark his 70th birthday. The papers focus on recent advances in elasticity, viscoelasticity and inelasticity, which are related to Prof Woo's work. Prof Woo's recent work concentrates on the viscoelastic and viscoplastic response of metals and plastics when thermal effects are significant, and the papers here address open questions in these and related areas.
Visco-elastic response of thermoplastics
Kristensen, Vegard Berge
2013-01-01
In this study a recently developed visco-elastic visco-plastic material model has been evaluated with the intention of improving the simulated behaviour of polymers. In order for polymers to become a more reliable construction material the behaviour has to be rendered realistically in simulations. A set of eleven experimental tests have been conducted to establish a database for further simulations. By use of some of these experimental tests the visco-elastic visco-plastic material model has ...
VISCOELASTIC STRUCTURAL MODEL OF ASPHALT CONCRETE
V. Bogomolov
2016-06-01
Full Text Available The viscoelastic rheological model of asphalt concrete based on the generalized Kelvin model is offered. The mathematical model of asphalt concrete viscoelastic behavior that can be used for calculation of asphalt concrete upper layers of non-rigid pavements for strength and rutting has been developed. It has been proved that the structural model of Burgers does not fully meet all the requirements of the asphalt-concrete.
Dynamic response of a viscoelastic Timoshenko beam
Kalyanasundaram, S.; Allen, D. H.; Schapery, R. A.
1987-01-01
The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.
Computing Lagrangian coherent structures from their variational theory.
Farazmand, Mohammad; Haller, George
2012-03-01
Using the recently developed variational theory of hyperbolic Lagrangian coherent structures (LCSs), we introduce a computational approach that renders attracting and repelling LCSs as smooth, parametrized curves in two-dimensional flows. The curves are obtained as trajectories of an autonomous ordinary differential equation for the tensor lines of the Cauchy-Green strain tensor. This approach eliminates false positives and negatives in LCS detection by separating true exponential stretching from shear in a frame-independent fashion. Having an explicitly parametrized form for hyperbolic LCSs also allows for their further in-depth analysis and accurate advection as material lines. We illustrate these results on a kinematic model flow and on a direct numerical simulation of two-dimensional turbulence.
Droplet impact on soft viscoelastic surfaces
Chen, Longquan; Bonaccurso, Elmar; Deng, Peigang; Zhang, Haibo
2016-12-01
In this work, we experimentally investigate the impact of water droplets onto soft viscoelastic surfaces with a wide range of impact velocities. Several impact phenomena, which depend on the dynamic interaction between the droplets and viscoelastic surfaces, have been identified and analyzed. At low We , complete rebound is observed when the impact velocity is between a lower and an upper threshold, beyond which droplets are deposited on the surface after impact. At intermediate We , entrapment of an air bubble inside the impinging droplets is found on soft surfaces, while a bubble entrapment on the surface is observed on rigid surfaces. At high We , partial rebound is only identified on the most rigid surface at We ≳92 . Rebounding droplets behave similarly to elastic drops rebounding on superhydrophobic surfaces and the impact process is independent of surface viscoelasticity. Further, surface viscoelasticity does not influence drop spreading after impact—as the surfaces behave like rigid surfaces—but it does affect drop recoiling. Also, the postimpact drop oscillation on soft viscoelastic surfaces is influenced by dynamic wettability of these surfaces. Comparing sessile drop oscillation with a damped harmonic oscillator allows us to conclude that surface viscoelasticity affects the damping coefficient and liquid surface tension sets the spring constant of the system.
A LES-based Eulerian-Lagrangian approach to predict the dynamics of bubble plumes
Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.
2016-01-01
An approach for Eulerian-Lagrangian large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian and Lagrangian frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted Eulerian and Lagrangian velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.
Lagrangian study of transport and mixing in a mesoscale eddy street
Prants, S V; Ponomarev, V I; Uleysky, M Yu; 10.1016/j.ocemod.2011.02.008
2012-01-01
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian trajectories are computed for a large number of particles in an interpolated velocity field generated by a numerical regional multi-layer eddy-resolving circulation model. We compute finite-time Lyapunov exponents for a comparatively long period of time by the method developed and plot the Lyapunov synoptic map quantifying surface transport and mixing in that region. This map uncovers the striking flow structures along the coast with a mesoscale eddy street and repelling material lines. We propose new Lagrangian diagnostic tools --- the time of exit of particles off a selected box, the number of changes of the sign of zonal and meridional velocities --- to study transport and mixing by a pair of strongly interacting eddies often visible at sea-surface temperature satellite imag...
A Lagrangian particle method with remeshing for tracer transport on the sphere
Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane
2017-07-01
A Lagrangian particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular Lagrangian panels. Remeshing is applied to control particle disorder and two schemes are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracer integral, and preservation of nonlinear correlation in a pair of tracers. We compare results obtained using LPM and the Lin-Rood finite-volume scheme. An adaptive particle/panel refinement scheme is demonstrated.
Lagrangian theoretical framework of dynamics of nonholonomic systems
无
2007-01-01
@@ By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
Lagrangian theoretical framework of dynamics of nonholonomic systems
LIANG; LiFu
2007-01-01
By the generalized variational principle of two kinds of variables in general mechanics, it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then, one important formula of similar Lagrangian classical relationship called the popularized Lagrangian classical relationship was derived. From Vakonomic model, by two Lagrangian classical relationships and the popularized Lagrangian classical relationship, the result is the same with Chetaev's model, and thus Chetaev's model and Vakonomic model were unified. Simultaneously, the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples, it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right. ……
On Stability of the Mechanical Lagrangian Systems
Valer Niminet
2011-12-01
Full Text Available
We consider MLS (mechanical Lagrangian systems with
external forces. We give some conditions of stability and dissipativity and show that the energy of the system decreases on the integral curves.
Key words: LMS, stability, dissipative system.
Towards effective Lagrangians for adelic strings
Dragovich, Branko
2009-01-01
p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these sca...
A new semi-Lagrangian difference scheme
季仲贞; 陈嘉滨
2001-01-01
A new completely energy-conserving semi-Lagrangian scheme is constructed. The numerical solution of shallow water equation shows that this conservative scheme preserves the total energy in twelve significant digits, while the traditional scheme does only in five significant digits.
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation s
Lagrangian duality and cone convexlike functions
J.B.G. Frenk (Hans); G. Kassay
2005-01-01
textabstractIn this paper we will show that the closely K-convexlike vector-valued functions with K Rm a nonempty convex cone and related classes of vector-valued functions discussed in the literature arise naturally within the theory of biconjugate functions applied to the Lagrangian perturbation
Pollitz, F.; Banerjee, P.; Grijalva, K.; Nagarajan, B.; Burgmann, R.
2008-01-01
The 2004 M=9.2 Sumatra-Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ???1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress-strain relation; an aspherical perturbation in viscoelastic structure; a 'static'mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra-Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation. ?? Journal compilation ?? 2008 RAS.
Classification of Lagrangian Fibrations over a Klein Bottle
Sepe, D
2009-01-01
This paper completes the classification of regular Lagrangian fibratiopns over compact surfaces. \\cite{misha} classifies regular Lagrangian fibrations over $\\mathbb{T}^2$. The main theorem in \\cite{hirsch} is used in order to classify integral affine structures on the Klein bottle $K^2$ and, hence, regular Lagrangian fibrations over this space.
Lagrangian multiplier and massive Yang-Mills fields
Li, Z.P.
1982-09-01
If we give appropriate constraint to the gauge invariant Lagrangian, the variation principle of the action convert to the variational problems with subsidiary condition. The effective Lagrangian which contains Lagrangian multiplier may have the mass term of the mesons. In that case we obtain naturally the massive Yang-Mills fields which was discussed by Nakanishi.
Deformation and relaxation of an incompressible viscoelastic body with surface viscoelasticity
Liu, Liping; Yu, Miao; Lin, Hao; Foty, Ramsey
2017-01-01
Measuring mechanical properties of cells or cell aggregates has proven to be an involved process due to their geometrical and structural complexity. Past measurements are based on material models that completely neglect the elasticity of either the surface membrane or the interior bulk. In this work, we consider general material models to account for both surface and bulk viscoelasticity. The boundary value problems are formulated for deformations and relaxations of a closed viscoelastic surface coupled with viscoelastic media inside and outside of the surface. The linearized surface elasticity models are derived for the constant surface tension model and the Helfrich-Canham bending model for coupling with the bulk viscoelasticity. For quasi-spherical surfaces, explicit solutions are obtained for the deformation, stress-strain and relaxation behaviors under a variety of loading conditions. These solutions can be applied to extract the intrinsic surface and bulk viscoelastic properties of biological cells or cell aggregates in the indentation, electro-deformation and relaxation experiments.
STABILITY ANALYSIS OF MAXWELL VISCOELASTIC PIPES CONVEYING FLUID WITH BOTH ENDS SIMPLY SUPPORTED
赵凤群; 王忠民; 冯振宇; 刘宏昭
2001-01-01
On the basis of some studies of elastic pipe conveying fluid, the dynamic behavior and stability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported, which are gyroscopic conservative system, were investigated by using the finite difference method and the corresponding recurrence formula. The effect of relaxation time of viscoelastic materials on the variation curve between dimensionless flow velocity and the real part and imaginary part of dimensionless complex frequencies in the first-three-order modes were analyzed concretely. It is found that critical flow velocities of divergence instability of Maxwell viscoelastic pipes conveying fluid with both ends simply supported decrease with the decrease of the relaxation time, while after the onset of divergence instability(buckling)critical flow velocities of coupled-mode flutter increase with the decrease of the relaxation time. Particularly, in the case of greater mass ratio, with the decrease of relaxation time,the onset of coupled-mode flutter delays, and even does not take place. When the relaxation time is greater than 103 , stability behavior of viscoelastic pipes conveying fluid is almost similar to the elastic pipes conveying fluid.
Effect of viscoelasticity and RBC migration phenomena in stenotic microvessels
Dimakopoulos, Yiannis; Syrakos, Alexandros; Georgiou, Georgios; Tsamopoulos, John
2014-11-01
This study deals with the numerical simulation of the hemodynamics in stenotic microvessels. The blood flow in microvessels differs significantly from that in large arteries and veins, because the Red Blood Cells (RBCs) are comparable in size with the radius of the microvessels and, consequently, local effects such as cell interaction and migration are more pronounced. In terms of complexity of the flow, viscoelasticity along with stress-gradient induced migration effects have a more dominant role, which exceeds the viscous, inertial and transient effects. Recently, a non-homogeneous viscoelastic model has been proposed by Moyers-Gonzalez et al. (2008), which can accurately predict the Fahraeus effects. We developed a numerical algorithm for the time-integration of the set of differential equations that arise from the coupling of momentum, mass, and population balances for RBCs and aggregates with the constitutive laws for both species. The simulations show that a cell-depleted layer develops along the vessel wall with an almost constant thickness. Along this layer, the shear stresses are almost Newtonian because of the plasma, but the normal stresses that are exerted on the wall are high due to the contribution of the individual RBCs and rouleaux.
阵性泥石流运动与堆积的欧拉-拉格朗日模型——Ⅰ.理论%An Euler-Lagrangian model for non-continuous debris flow:I.Theory
倪晋仁; 廖谦; 曲轶众; 章书成
2000-01-01
自然界中的泥石流具有突发性和非恒定性的特点.为了模拟典型泥石流现象,在流团模型的基础上,进一步完善了基于欧拉-拉格朗日（E-L）观点的PIC(ParcelInCell)算法,细化了流元结构,建立了能够模拟典型阵性泥石流发生、运动和堆积的准结构两相流模型.求解该模型不仅可以模拟泥石流运动过程,而且可以对泥石流的堆积过程、停积形态、冲刷特征及泥石流中多组分颗粒的分选特征进行定量描述.%A new model based on conceptual two-phase flow and PIC numerical solution method is developed to simulate natural debris flow of paroxysmal and unsteady characteristics.By combing the conventional Euler and Lagrange methods,the E-Lmodel can be used for description of the whole process of the typical debris flow in greater details through the elements.The present model is also proper for describing the sediment sorting accompanied with erosion and depositional processes.
Miller, J W; Nestler, F H M; Schrag, J L
2004-12-20
Oscillatory flow birefringence (OFB) properties have been measured for dilute solutions of bovine fibrinogen in 65-68% aqueous glycerol with the Miller-Schrag Thin Fluid Layer (TFL) apparatus employing either titanium or stainless steel surfaces in contact with the solutions. The shearing frequency range was 1 to 2500 Hz, the concentrations ranged from 4 to 8 mg/ml, and measurement temperatures were 9.9, 10.0, and 15.8 degrees C. The data showed evidence of significant amounts of aggregation that apparently is caused by the presence of glycerol; contributions from the various aggregates were readily detected since the staggered half-overlap aggregation in this system results in substantial differences in the rotational relaxation times of the various effectively rigid aggregates. The combination of oscillatory flow birefringence and viscoelasticity (VE) data provided sensitive and precise characterization of aggregation in these example systems; all aggregates exhibited the expected positive optical anisotropy. The length of unaggregated fibrinogen in solution was found to be that obtained via electron microscopy. Addition of guanidine hydrochloride to hopefully reduce aggregation did so but also resulted in formation of a very large (2800 to 3500 A), apparently nearly monodisperse, negatively birefringent aggregate, suggesting that this new species might be formed by lateral aggregation.
A Lagrangian Dynamic Mode Decomposition
Sesterhenn, Jörn
2016-01-01
Temporal or spatial structures are readily extracted from complex data by modal decompositions like POD or DMD. Subspaces of that decompositions serve as reduced order models and define spatial structures in time or temporal structures in space. Convecting phenomena pose a major problem to those decompositions. A structure travelling with a certain group velocity will be perceived as a plethora of modes in time or space respectively. This manifests itself for example in poorly decaying Singular Values when using a POD. The poor decay is very counter-intuitive, since we expect a single structure to be represented by a few modes. The intuition proves to be correct and we show that in a properly chosen reference frame along the characteristic defined by the group velocity, a POD or DMD reduces moving structures to a few modes, as expected. Beyond serving as a reduced model, the re- sulting entity can be used to define a constant or minimally changing structure in turbulent flows. This can be interpreted as an em...
Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane
Bang-Yen CHEN; Johan FASTENAKELS
2007-01-01
One of the most fundamental problems in the study of Lagrangian submanifolds fromRiemannian geometric point of view is to classify Lagrangian immersions of real space forms intocomplex space forms. The main purpose of this paper is thus to classify flat Lagrangian surfaces inthe Lorentzian complex plane C12. Our main result states that there are thirty-eight families of flatLagrangian surfaces in C12. Conversely, every flat Lagrangian surface in C12 is locally congruent to oneof the thirty-eight families.
3D Viscoelastic traction force microscopy.
Toyjanova, Jennet; Hannen, Erin; Bar-Kochba, Eyal; Darling, Eric M; Henann, David L; Franck, Christian
2014-10-28
Native cell-material interactions occur on materials differing in their structural composition, chemistry, and physical compliance. While the last two decades have shown the importance of traction forces during cell-material interactions, they have been almost exclusively presented on purely elastic in vitro materials. Yet, most bodily tissue materials exhibit some level of viscoelasticity, which could play an important role in how cells sense and transduce tractions. To expand the realm of cell traction measurements and to encompass all materials from elastic to viscoelastic, this paper presents a general, and comprehensive approach for quantifying 3D cell tractions in viscoelastic materials. This methodology includes the experimental characterization of the time-dependent material properties for any viscoelastic material with the subsequent mathematical implementation of the determined material model into a 3D traction force microscopy (3D TFM) framework. Utilizing this new 3D viscoelastic TFM (3D VTFM) approach, we quantify the influence of viscosity on the overall material traction calculations and quantify the error associated with omitting time-dependent material effects, as is the case for all other TFM formulations. We anticipate that the 3D VTFM technique will open up new avenues of cell-material investigations on even more physiologically relevant time-dependent materials including collagen and fibrin gels.
Parametric imaging of viscoelasticity using optical coherence elastography
Wijesinghe, Philip; McLaughlin, Robert A.; Sampson, David D.; Kennedy, Brendan F.
2015-03-01
We demonstrate imaging of soft tissue viscoelasticity using optical coherence elastography. Viscoelastic creep deformation is induced in tissue using step-like compressive loading and the resulting time-varying deformation is measured using phase-sensitive optical coherence tomography. From a series of co-located B-scans, we estimate the local strain rate as a function of time, and parameterize it using a four-parameter Kelvin-Voigt model of viscoelastic creep. The estimated viscoelastic strain and time constant are used to visualize viscoelastic creep in 2D, dual-parameter viscoelastograms. We demonstrate our technique on six silicone tissue-simulating phantoms spanning a range of viscoelastic parameters. As an example in soft tissue, we report viscoelastic contrast between muscle and connective tissue in fresh, ex vivo rat gastrocnemius muscle and mouse abdominal transection. Imaging viscoelastic creep deformation has the potential to provide complementary contrast to existing imaging modalities, and may provide greater insight into disease pathology.
Synchronous Lagrangian variational principles in General Relativity
Cremaschini, Claudio
2016-01-01
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in relativistic classical field theory which are either asynchronous or synchronous. The historical Einstein-Hilbert and Palatini variational formulations are found to belong to the first category. Nevertheless, it is shown that an alternative route exists which permits one to cast these principles in terms of equivalent synchronous Lagrangian variational formulations. The advantage is twofold. First, synchronous approaches allow one to overcome the lack of gauge symmetry of the asynchronous principles. Second, the property of manifest covariance of the theory is also restored at all levels, including the symbolic Euler-Lagrange equations, with the variational Lagrangian density being now identified with a $4-$scalar. As an application, a joint synchronous variational principle...
A Lagrangian particle level set method
Hieber, Simone E.; Koumoutsakos, Petros
2005-11-01
We present a novel particle level set method for capturing interfaces. The level set equation is solved in a Lagrangian frame using particles that carry the level set information. A key aspect of the method involves a consistent remeshing procedure for the regularization of the particle locations when the particle map gets distorted by the advection field. The Lagrangian description of the level set method is inherently adaptive and exact in the case of solid body motions. The efficiency and accuracy of the method is demonstrated in several benchmark problems in two and three dimensions involving pure advection and curvature induced motion of the interface. The simplicity of the particle description is shown to be well suited for real time simulations of surfaces involving cutting and reconnection as in virtual surgery environments.
Multiloop Information from the QED Effective Lagrangian
Dunne, G V; Dunne, Gerald V.; Schubert, Christian
2006-01-01
We obtain information on the QED photon amplitudes at high orders in perturbation theory starting from known results on the QED effective Lagrangian in a constant electric field. A closed-form all-order result for the weak field limit of the imaginary part of this Lagrangian has been given years ago by Affleck, Alvarez and Manton (for scalar QED) and by Lebedev and Ritus (for spinor QED). We discuss the evidence for its correctness, and conjecture an analogous formula for the case of a self-dual field. From this extension we then obtain, using Borel analysis, the leading asymptotic growth for large N of the maximally helicity violating component of the L - loop N - photon amplitude in the low energy limit. The result leads us to conjecture that the perturbation series converges for the on-shell renormalized QED N - photon amplitudes in the quenched approximation.
Inertial and viscoelastic forces on rigid colloids in microfluidic channels.
Howard, Michael P; Panagiotopoulos, Athanassios Z; Nikoubashman, Arash
2015-06-14
We perform hybrid molecular dynamics simulations to study the flow behavior of rigid colloids dispersed in a dilute polymer solution. The underlying Newtonian solvent and the ensuing hydrodynamic interactions are incorporated through multiparticle collision dynamics, while the constituent polymers are modeled as bead-spring chains, maintaining a description consistent with the colloidal nature of our system. We study the cross-stream migration of the solute particles in slit-like channels for various polymer lengths and colloid sizes and find a distinct focusing onto the channel center under specific solvent and flow conditions. To better understand this phenomenon, we systematically measure the effective forces exerted on the colloids. We find that the migration originates from a competition between viscoelastic forces from the polymer solution and hydrodynamically induced inertial forces. Our simulations reveal a significantly stronger fluctuation of the lateral colloid position than expected from thermal motion alone, which originates from the complex interplay between the colloid and polymer chains.
Lagrangian Vortices in Developing Tropical Cyclones
2015-06-25
cyclones B. Rutherford,a* T. J. Dunkertona and M. T. Montgomeryb aNorthwest Research Associates, Redmond, WA, USA bNaval Postgraduate School, Monterey...article has been contributed to by a US Government employee and his work is in the public domain in the USA. Tracking pre-genesis tropical cyclones is...season. All of the Lagrangian coherent structures that can be identified by this field are shown for developing disturbances and mature cyclones . The
Equivalent Lagrangians: Generalization, Transformation Maps, and Applications
N. Wilson
2012-01-01
Full Text Available Equivalent Lagrangians are used to find, via transformations, solutions and conservation laws of a given differential equation by exploiting the possible existence of an isomorphic algebra of Lie point symmetries and, more particularly, an isomorphic Noether point symmetry algebra. Applications include ordinary differential equations such as the Kummer equation and the combined gravity-inertial-Rossbywave equation and certain classes of partial differential equations related to multidimensional wave equations.
Ocean Model Assessment with Lagrangian Metrics
2016-06-07
Ocean Model Assessment With Lagrangian Metrics” Pearn P. Niiler Scripps Institution of Oceanography 9500 Gilman Drive MC 0213 La Jolla, CA...project are to aid in the development of accurate modeling of upper ocean circulation by using data on circulation observations to test models . These tests...or metrics, will be statistical measures of model and data comparisons. It is believed that having accurate models of upper ocean currents will
Lagrangian Observations and Modeling of Marine Larvae
Paris, Claire B.; Irisson, Jean-Olivier
2017-04-01
Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a Lagrangian platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed Lagrangian behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source Lagrangian tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive Lagrangian trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.
Random Response of Linear Viscoelastic Systems under Random Excitation
张天舒; 方同
2001-01-01
A method of analyzing random response of linear viscoelastic systems under random excitation has been presented. The covariance matrices of random responses of a single-degree-freedom linear viscoelastic system subjected to stationary white noise and filtered white noise excitations have been obtained in closed form. For illustration, a numerical example has been included. It is observed that viscoelasticity has damping effect on the mean square random responses of the system, the higher is viscoelastic behavior, the higher the damping effect.
Chaotic Lagrangian transport and mixing in the ocean
Prants, S V
2015-01-01
Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows, researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation. This review article gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to monitor spreading of Fukushima-derived radionuclides in the ocean.