Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation with reference to aeronautical operating systems

Science.gov (United States)

Frost, W.; Harper, W. L.

1975-01-01

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.

A new algebraic turbulence model for accurate description of airfoil flows

Science.gov (United States)

Xiao, Meng-Juan; She, Zhen-Su

2017-11-01

We report a new algebraic turbulence model (SED-SL) based on the SED theory, a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both the streamwise and wall-normal directions, which thus define the eddy viscosity in the RANS equation (e.g. a zero-equation model). After a successful simulation of flat plate flow (APS meeting, 2016), we report here further applications of the model to the flow around airfoil, with significant improvement of the prediction accuracy of the lift (CL) and drag (CD) coefficients compared to other popular models (e.g. BL, SA, etc.). Two airfoils, namely RAE2822 airfoil and NACA0012 airfoil, are computed for over 50 cases. The results are compared to experimental data from AGARD report, which shows deviations of CL bounded within 2%, and CD within 2 counts (10-4) for RAE2822 and 6 counts for NACA0012 respectively (under a systematic adjustment of the flow conditions). In all these calculations, only one parameter (proportional to the Karmen constant) shows slight variation with Mach number. The most remarkable outcome is, for the first time, the accurate prediction of the drag coefficient. The other interesting outcome is the physical interpretation of the multi-layer parameters: they specify the corresponding multi-layer structure of turbulent boundary layer; when used together with simulation data, the SED-SL enables one to extract physical information from empirical data, and to understand the variation of the turbulent boundary layer.

Modeling of Turbulent Swirling Flows

Science.gov (United States)

Shih, Tsan-Hsing; Zhu, Jiang; Liou, William; Chen, Kuo-Huey; Liu, Nan-Suey; Lumley, John L.

1997-01-01

Aircraft engine combustors generally involve turbulent swirling flows in order to enhance fuel-air mixing and flame stabilization. It has long been recognized that eddy viscosity turbulence models are unable to appropriately model swirling flows. Therefore, it has been suggested that, for the modeling of these flows, a second order closure scheme should be considered because of its ability in the modeling of rotational and curvature effects. However, this scheme will require solution of many complicated second moment transport equations (six Reynolds stresses plus other scalar fluxes and variances), which is a difficult task for any CFD implementations. Also, this scheme will require a large amount of computer resources for a general combustor swirling flow. This report is devoted to the development of a cubic Reynolds stress-strain model for turbulent swirling flows, and was inspired by the work of Launder's group at UMIST. Using this type of model, one only needs to solve two turbulence equations, one for the turbulent kinetic energy k and the other for the dissipation rate epsilon. The cubic model developed in this report is based on a general Reynolds stress-strain relationship. Two flows have been chosen for model evaluation. One is a fully developed rotating pipe flow, and the other is a more complex flow with swirl and recirculation.

Analysis of turbulence spectra in gas-liquid two-phase flow

International Nuclear Information System (INIS)

Kataoka, Isao; Besnard, D.C.; Serizawa, Akimi.

1993-01-01

An analysis was made on the turbulence spectra in bubbly flow. Basic equation for turbulence spectrum in bubbly flow was formulated considering the eddy disintegration induced by bubble. Based on the dimensional analysis and modeling of eddy disintegration by bubble, constitutive equations for eddy disintegration were derived. Using these equations, turbulence spectra in bubbly flow (showing -8/3 power) was successfully explained. (author)

Direct test of a nonlinear constitutive equation for simple turbulent shear flows using DNS data

Science.gov (United States)

Schmitt, François G.

2007-10-01

Several nonlinear constitutive equations have been proposed to overcome the limitations of the linear eddy-viscosity models to describe complex turbulent flows. These nonlinear equations have often been compared to experimental data through the outputs of numerical models. Here we perform a priori analysis of nonlinear eddy-viscosity models using direct numerical simulation (DNS) of simple shear flows. In this paper, the constitutive equation is directly checked using a tensor projection which involves several invariants of the flow. This provides a 3 terms development which is exact for 2D flows, and a best approximation for 3D flows. We provide the quadratic nonlinear constitutive equation for the near-wall region of simple shear flows using DNS data, and estimate their coefficients. We show that these coefficients have several common properties for the different simple shear flow databases considered. We also show that in the central region of pipe flows, where the shear rate is very small, the coefficients of the constitutive equation diverge, indicating the failure of this representation for vanishing shears.

Exploiting similarity in turbulent shear flows for turbulence modeling

Science.gov (United States)

Robinson, David F.; Harris, Julius E.; Hassan, H. A.

1992-12-01

It is well known that current k-epsilon models cannot predict the flow over a flat plate and its wake. In an effort to address this issue and other issues associated with turbulence closure, a new approach for turbulence modeling is proposed which exploits similarities in the flow field. Thus, if we consider the flow over a flat plate and its wake, then in addition to taking advantage of the log-law region, we can exploit the fact that the flow becomes self-similar in the far wake. This latter behavior makes it possible to cast the governing equations as a set of total differential equations. Solutions of this set and comparison with measured shear stress and velocity profiles yields the desired set of model constants. Such a set is, in general, different from other sets of model constants. The rational for such an approach is that if we can correctly model the flow over a flat plate and its far wake, then we can have a better chance of predicting the behavior in between. It is to be noted that the approach does not appeal, in any way, to the decay of homogeneous turbulence. This is because the asymptotic behavior of the flow under consideration is not representative of the decay of homogeneous turbulence.

Exploiting similarity in turbulent shear flows for turbulence modeling

Science.gov (United States)

Robinson, David F.; Harris, Julius E.; Hassan, H. A.

1992-01-01

It is well known that current k-epsilon models cannot predict the flow over a flat plate and its wake. In an effort to address this issue and other issues associated with turbulence closure, a new approach for turbulence modeling is proposed which exploits similarities in the flow field. Thus, if we consider the flow over a flat plate and its wake, then in addition to taking advantage of the log-law region, we can exploit the fact that the flow becomes self-similar in the far wake. This latter behavior makes it possible to cast the governing equations as a set of total differential equations. Solutions of this set and comparison with measured shear stress and velocity profiles yields the desired set of model constants. Such a set is, in general, different from other sets of model constants. The rational for such an approach is that if we can correctly model the flow over a flat plate and its far wake, then we can have a better chance of predicting the behavior in between. It is to be noted that the approach does not appeal, in any way, to the decay of homogeneous turbulence. This is because the asymptotic behavior of the flow under consideration is not representative of the decay of homogeneous turbulence.

On the prediction of turbulent secondary flows

Science.gov (United States)

Speziale, C. G.; So, R. M. C.; Younis, B. A.

1992-01-01

The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points.

Compressibility, turbulence and high speed flow

CERN Document Server

Gatski, Thomas B

2013-01-01

Compressibility, Turbulence and High Speed Flow introduces the reader to the field of compressible turbulence and compressible turbulent flows across a broad speed range, through a unique complimentary treatment of both the theoretical foundations and the measurement and analysis tools currently used. The book provides the reader with the necessary background and current trends in the theoretical and experimental aspects of compressible turbulent flows and compressible turbulence. Detailed derivations of the pertinent equations describing the motion of such turbulent flows is provided and an extensive discussion of the various approaches used in predicting both free shear and wall bounded flows is presented. Experimental measurement techniques common to the compressible flow regime are introduced with particular emphasis on the unique challenges presented by high speed flows. Both experimental and numerical simulation work is supplied throughout to provide the reader with an overall perspective of current tre...

Numerical simulation of secondary flow in bubbly turbulent flow in sub-channel

International Nuclear Information System (INIS)

Ikeno, Tsutomu; Kataoka, Isao

2009-01-01

Secondary flow in bubbly turbulent flow in sub-channel was simulated by using an algebraic turbulence stress model. The mass, momentum, turbulence energy and bubble diffusion equations were used as fundamental equation. The basis for these equations was the two-fluid model: the equation of liquid phase was picked up from the equation system theoretically derived for the gas-liquid two-fluid turbulent flow. The fundamental equation was transformed onto a generalized coordinate system fitted to the computational domain in sub-channel. It was discretized for the SIMPLE algorism using the finite-volume method. The shape of sub-channel causes a distortion of the computational mesh, and orthogonal nature of the mesh is sometimes broken. An iterative method to satisfy a requirement for the contra-variant velocity was introduced to represent accurate symmetric boundary condition. Two-phase flow at a steady state was simulated for different magnitude of secondary flow and void fraction. The secondary flow enhanced the momentum transport in sub-channel and accelerated the liquid phase in the rod gap. This effect was slightly mitigated when the void fraction increased. The acceleration can contribute to effective cooling in the rod gap. The numerical result implied a phenomenon of industrial interest. This suggested that experimental approach is necessary to validate the numerical model and to identify the phenomenon. (author)

PDF methods for turbulent reactive flows

Science.gov (United States)

Hsu, Andrew T.

1995-01-01

Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.

Computational Analysis of Multi-Rotor Flows

Science.gov (United States)

Yoon, Seokkwan; Lee, Henry C.; Pulliam, Thomas H.

2016-01-01

Interactional aerodynamics of multi-rotor flows has been studied for a quadcopter representing a generic quad tilt-rotor aircraft in hover. The objective of the present study is to investigate the effects of the separation distances between rotors, and also fuselage and wings on the performance and efficiency of multirotor systems. Three-dimensional unsteady Navier-Stokes equations are solved using a spatially 5th order accurate scheme, dual-time stepping, and the Detached Eddy Simulation turbulence model. The results show that the separation distances as well as the wings have significant effects on the vertical forces of quadroror systems in hover. Understanding interactions in multi-rotor flows would help improve the design of next generation multi-rotor drones.

Self-adaptive Newton-based iteration strategy for the LES of turbulent multi-scale flows

International Nuclear Information System (INIS)

Daude, F.; Mary, I.; Comte, P.

2014-01-01

An improvement of the efficiency of implicit schemes based on Newton-like methods for the simulation of turbulent flows by compressible LES or DNS is proposed. It hinges on a zonal Self-Adaptive Newton method (hereafter denoted SAN), capable of taking advantage of Newton convergence rate heterogeneities in multi-scale flow configurations due to a strong spatial variation of the mesh resolution, such as transitional or turbulent flows controlled by small actuators or passive devices. Thanks to a predictor of the local Newton convergence rate, SAN provides computational savings by allocating resources in regions where they are most needed. The consistency with explicit time integration and the efficiency of the method are checked in three test cases: - The standard test-case of 2-D linear advection of a vortex, on three different two-block grids. - Transition to 3-D turbulence on the lee-side of an airfoil at high angle of attack, which features a challenging laminar separation bubble with a turbulent reattachment. - A passively-controlled turbulent transonic cavity flow, for which the CPU time is reduced by a factor of 10 with respect to the baseline algorithm, illustrates the interest of the proposed algorithm. (authors)

Local measurement and numerical calculation on turbulent two-phase flow in a vertical pipe with sudden expansion

International Nuclear Information System (INIS)

Kondo, Koichi; Yoshida, Kenji; Okawa, Tomio; Kataoka, Isao

2004-01-01

Experiment and numerical calculation were carried out for upward, turbulent bubbly two-phase flow in a vertical pipe with an axisymmetric sudden expansion, which is one of the typical multi-dimensional channel geometries. The void fraction, the liquid velocity and turbulent intensity along the flow direction below and the above the sudden expansion point were measured for various turbulent flow conditions by using a point-electrode resistivity probe and a hot-film anemometry probe. They showed quite complicated behaviors depending upon flow rates of gas and liquid phases and bubble size. In particular, the geometry of sudden expansion affected on the bubble behaviors in multi-dimensional two-phase flow, such as the bubble-stagnation, the bubble-deformation, the enhancement and suppression effects due to the two-phase turbulence etc. Through the measurements, fundamental parameters of the two-phase flow were clarified for the sudden expansion channel. Moreover, a three-dimensional one-way bubble tracking simulation of a single bubble behavior in turbulent flow field along the downstream of the sudden expansion was also demonstrated where equation of motion of bubble was solved by assuming appropriate constitutive models and turbulence model. Based on the trajectories of large number of bubbles, the void fraction distribution was predicted in this calculation. It concretely revealed that the lift force and the two-phase turbulence model were the most important parameters in determining the multi-dimensional void fraction distribution and the calculation should be considered by using the measured experimental data. (author)

Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

Directory of Open Access Journals (Sweden)

M. L. Kavvas

2017-10-01

Full Text Available Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.

Acceleration methods for multi-physics compressible flow

Science.gov (United States)

Peles, Oren; Turkel, Eli

2018-04-01

In this work we investigate the Runge-Kutta (RK)/Implicit smoother scheme as a convergence accelerator for complex multi-physics flow problems including turbulent, reactive and also two-phase flows. The flows considered are subsonic, transonic and supersonic flows in complex geometries, and also can be either steady or unsteady flows. All of these problems are considered to be a very stiff. We then introduce an acceleration method for the compressible Navier-Stokes equations. We start with the multigrid method for pure subsonic flow, including reactive flows. We then add the Rossow-Swanson-Turkel RK/Implicit smoother that enables performing all these complex flow simulations with a reasonable CFL number. We next discuss the RK/Implicit smoother for time dependent problem and also for low Mach numbers. The preconditioner includes an intrinsic low Mach number treatment inside the smoother operator. We also develop a modified Roe scheme with a corresponding flux Jacobian matrix. We then give the extension of the method for real gas and reactive flow. Reactive flows are governed by a system of inhomogeneous Navier-Stokes equations with very stiff source terms. The extension of the RK/Implicit smoother requires an approximation of the source term Jacobian. The properties of the Jacobian are very important for the stability of the method. We discuss what the chemical physics theory of chemical kinetics tells about the mathematical properties of the Jacobian matrix. We focus on the implication of the Le-Chatelier's principle on the sign of the diagonal entries of the Jacobian. We present the implementation of the method for turbulent flow. We use a two RANS turbulent model - one equation model - Spalart-Allmaras and a two-equation model - k-ω SST model. The last extension is for two-phase flows with a gas as a main phase and Eulerian representation of a dispersed particles phase (EDP). We present some examples for such flow computations inside a ballistic evaluation

On the computation of the turbulent flow near rough surface

Science.gov (United States)

Matveev, S. K.; Jaychibekov, N. Zh.; Shalabayeva, B. S.

2018-05-01

One of the problems in constructing mathematical models of turbulence is a description of the flows near a rough surface. An experimental study of such flows is also difficult because of the impossibility of measuring "inside" the roughness. The theoretical calculation is difficult because of the lack of equations describing the flow in this zone. In this paper, a new turbulence model based on the differential equation of turbulent viscosity balance was used to describe a turbulent flow near a rough surface. The difference between the new turbulence model and the previously known consists in the choice of constants and functions that determine the generation, dissipation and diffusion of viscosity.

A computer model for dispersed fluid-solid turbulent flows

International Nuclear Information System (INIS)

Liu, C.H.; Tulig, T.J.

1985-01-01

A computer model is being developed to simulate two-phase turbulent flow phenomena in fluids containing finely dispersed solids. The model is based on a dual-continuum picture of the individual phases and an extension of a two-equation turbulence closure theory. The resulting set of nonlinear partial differential equations are solved using a finite difference procedure with special treatment to promote convergence. The model has been checked against a number of idealized flow problems with known solutions. The authors are currently comparing model predictions with measurements to determine a proper set of turbulence parameters needed for simulating two-phase turbulent flows

Zonal flows and turbulence in fluids and plasmas

Science.gov (United States)

Parker, Jeffrey Bok-Cheung

In geophysical and plasma contexts, zonal flows are well known to arise out of turbulence. We elucidate the transition from statistically homogeneous turbulence without zonal flows to statistically inhomogeneous turbulence with steady zonal flows. Starting from the Hasegawa--Mima equation, we employ both the quasilinear approximation and a statistical average, which retains a great deal of the qualitative behavior of the full system. Within the resulting framework known as CE2, we extend recent understanding of the symmetry-breaking 'zonostrophic instability'. Zonostrophic instability can be understood in a very general way as the instability of some turbulent background spectrum to a zonally symmetric coherent mode. As a special case, the background spectrum can consist of only a single mode. We find that in this case the dispersion relation of zonostrophic instability from the CE2 formalism reduces exactly to that of the 4-mode truncation of generalized modulational instability. We then show that zonal flows constitute pattern formation amid a turbulent bath. Zonostrophic instability is an example of a Type I s instability of pattern-forming systems. The broken symmetry is statistical homogeneity. Near the bifurcation point, the slow dynamics of CE2 are governed by a well-known amplitude equation, the real Ginzburg-Landau equation. The important features of this amplitude equation, and therefore of the CE2 system, are multiple. First, the zonal flow wavelength is not unique. In an idealized, infinite system, there is a continuous band of zonal flow wavelengths that allow a nonlinear equilibrium. Second, of these wavelengths, only those within a smaller subband are stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets. These behaviors are shown numerically to hold in the CE2 system, and we calculate a stability diagram. The stability diagram is in agreement with direct numerical simulations of the quasilinear

Multi-scale-nonlinear interactions among macro-MHD mode, micro-turbulence, and zonal flow

International Nuclear Information System (INIS)

Ishizawa, Akihiro; Nakajima, Noriyoshi

2007-01-01

This is the first numerical simulation demonstrating that macro-magnetohydrodynamic (macro-MHD) mode is exited as a result of multi-scale interaction in a quasi-steady equilibrium formed by a balance between zonal flow and micro-turbulence via reduced-two-fluid simulation. Only after obtaining the equilibrium which includes zonal flow and the turbulence caused by kinetic ballooning mode is this simulation of macro-MHD mode, double tearing mode, accomplished. In the quasi-steady equilibrium a macro-fluctuation which has the same helicity as that of double tearing mode is a part of the turbulence until it grows as a macro-MHD mode finally. When the macro-MHD grows it effectively utilize free energy of equilibrium current density gradient because of positive feedback loop between suppression of zonal flow and growth of the macro-fluctuation causing magnetic reconnection. Thus once the macro-MHD grows from the quasi-equilibrium, it does not go back. This simulation is more comparable with experimental observation of growing macro-fluctuation than traditional MHD simulation of linear instabilities in a static equilibrium. (author)

Numerical simulation of stratified flows with different k-ε turbulence models

International Nuclear Information System (INIS)

Dagestad, S.

1991-01-01

The thesis comprises the numerical simulation of stratified flows with different k-ε models. When using the k-ε model, two equations are solved to describe the turbulence. The k-equation represents the turbulent kinetic energy of the turbulence and the ε-equation is the turbulent dissipation. Different k-ε models predict stratified flows differently. The standard k-ε model leads to higher turbulent mixing than the low-Reynolds model does. For lower Froude numbers, F 0 , this effect becomes enhanced. Buoyancy extension of the k-ε model also leads to less vertical mixing in cases with strong stratification. When the stratification increases, buoyancy-extension becomes larger influence. The turbulent Prandtl number effects have large impact on the transport of heat and the development of the flow. Two different formulae which express the turbulent Prandtl effects have been tested. For unstably stratified flows, the rapid mixing and three-dimensionality of the flow can in fact be computed using a k-ε model when buoyancy-extended is employed. The turbulent heat transfer and thus turbulent production in unstable stratified flows depends strongly upon the turbulent Prandtl number effect. The main conclusions are: Stable stratified flows should be computed with a buoyancy-extended low-Reynolds k-ε model; Unstable stratified flows should be computed with a buoyancy-extended standard k-ε model; The turbulent Prandtl number effects should be included in the computations; Buoyancy-extension has lead to more correct description of the physics for all of the investigated flows. 78 refs., 128 figs., 17 tabs

PDF modeling of turbulent flows on unstructured grids

Science.gov (United States)

Bakosi, Jozsef

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. Because the technique solves a transport equation for the PDF of the velocity and scalars, a mathematically exact treatment of advection, viscous effects and arbitrarily complex chemical reactions is possible; these processes are treated without closure assumptions. A set of algorithms is proposed to provide an efficient solution of the PDF transport equation modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain and to track particles. All three aspects regarding the grid make use of the finite element method. Compared to hybrid methods, the current methodology is stand-alone, therefore it is consistent both numerically and at the level of turbulence closure without the use of consistency conditions. Since both the turbulent velocity and scalar concentration fields are represented in a stochastic way, the method allows for a direct and close interaction between these fields, which is beneficial in computing accurate scalar statistics. Boundary conditions implemented along solid bodies are of the free-slip and no-slip type without the need for ghost elements. Boundary layers at no-slip boundaries are either fully resolved down to the viscous sublayer, explicitly modeling the high anisotropy and inhomogeneity of the low-Reynolds-number wall region without damping or wall-functions or specified via logarithmic wall-functions. As in moment closures and large eddy simulation, these wall-treatments provide the usual trade-off between resolution and computational cost as required by the given application. Particular attention is focused on

Weak and strong turbulence in the CGL equation

International Nuclear Information System (INIS)

Gibbon, J.D.; Bartuccelli, M.V.; Doering, C.R.

1993-01-01

To many fluid dynamicists, the only real turbulence is the fine scale 3-dimensional turbulence which occurs at high Reynolds numbers, with an energy cascade and an inertial subrange. The number of degrees of freedom in 3d strong turbulence is clearly many orders of magnitude greater than in such phenomena as convection in a box where perhaps only a few spatial modes govern the dynamics. Only in 2d are the incompressible Navier Stokes equations understood analytically in the sense that there is a rigorous proof of the existence of a finite dimensional global attractor. Computational methods are generally good enough to resolve the smallest scale in a 2d flow and, for 2d homogeneous decaying turbulence, the vorticity obeys a maximum principle. No such maximum principle is known to exist in 3d and regularity remains to be proved. Numerical resolution of the smallest scale in a fully turbulent 3d flow is still a long way off. In order to attempt to get a better grip on the tantalizing phenomena displayed by the Navier Stokes equations, it is a useful exercise to see whether it is possible to mimic some limited features of the 3d Navier Stokes equations with a different PDE system which displays similar functional properties but in a lower spatial dimension. This exercise, however, must obviously be limited by the fact that simpler models in lower dimensions cannot display the vortex stretching properties displayed by the 3d Navier Stokes equations, although the lowering of the spatial dimension does make it easier to compute the dynamics. One equation which will be shown to have some of the desired properites is a version of the d dimensional complex Ginzburg Landau (CDL) equation on the periodic domain [0,1]. It is not our intention here to treat it in its physical context. Our intention in using it is to try and mimic limited features of the Navier Stokes equations with an equation over which we have more analytical control

Mathematical model for the calculation of internal turbulent flow

International Nuclear Information System (INIS)

Nicolau, V. de P.; Valle Pereira Filho, H. do

1981-01-01

The Navier-Stokes and the turbulent kinetic energy equations for the incompressible, turbulent and fully developed pipe flow, were solved by a finite difference procedure. The distributions of the mean velocity, turbulent shear stress and turbulent kinetic energy were obtained at different Reynolds numbers. Those numerical results were compared with experimental data and the agreement was good in whole cross section of the flow. (Author) [pt

Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

OpenAIRE

M. L. Kavvas; T. Tu; A. Ercan; J. Polsinelli

2017-01-01

Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally...

Notes on Well-Posed, Ensemble Averaged Conservation Equations for Multiphase, Multi-Component, and Multi-Material Flows

International Nuclear Information System (INIS)

Ray A. Berry

2005-01-01

At the INL researchers and engineers routinely encounter multiphase, multi-component, and/or multi-material flows. Some examples include: Reactor coolant flows Molten corium flows Dynamic compaction of metal powders Spray forming and thermal plasma spraying Plasma quench reactor Subsurface flows, particularly in the vadose zone Internal flows within fuel cells Black liquor atomization and combustion Wheat-chaff classification in combine harvesters Generation IV pebble bed, high temperature gas reactor The complexity of these flows dictates that they be examined in an averaged sense. Typically one would begin with known (or at least postulated) microscopic flow relations that hold on the ''small'' scale. These include continuum level conservation of mass, balance of species mass and momentum, conservation of energy, and a statement of the second law of thermodynamics often in the form of an entropy inequality (such as the Clausius-Duhem inequality). The averaged or macroscopic conservation equations and entropy inequalities are then obtained from the microscopic equations through suitable averaging procedures. At this stage a stronger form of the second law may also be postulated for the mixture of phases or materials. To render the evolutionary material flow balance system unique, constitutive equations and phase or material interaction relations are introduced from experimental observation, or by postulation, through strict enforcement of the constraints or restrictions resulting from the averaged entropy inequalities. These averaged equations form the governing equation system for the dynamic evolution of these mixture flows. Most commonly, the averaging technique utilized is either volume or time averaging or a combination of the two. The flow restrictions required for volume and time averaging to be valid can be severe, and violations of these restrictions are often found. A more general, less restrictive (and far less commonly used) type of averaging known as

A turbulent two-phase flow model for nebula flows

International Nuclear Information System (INIS)

Champney, J.M.; Cuzzi, J.N.

1990-01-01

A new and very efficient turbulent two-phase flow numericaly model is described to analyze the environment of a protoplanetary nebula at a stage prior to the formation of planets. Focus is on settling processes of dust particles in flattened gaseous nebulae. The model employs a perturbation technique to improve the accuracy of the numerical simulations of such flows where small variations of physical quantities occur over large distance ranges. The particles are allowed to be diffused by gas turbulence in addition to settling under gravity. Their diffusion coefficients is related to the gas turbulent viscosity by the non-dimensional Schmidt number. The gas turbulent viscosity is determined by the means of the eddy viscosity hypothesis that assumes the Reynolds stress tensor proportional to the mean strain rate tensor. Zero- and two-equation turbulence models are employed. Modeling assumptions are detailed and discussed. The numerical model is shown to reproduce an existing analytical solution for the settling process of particles in an inviscid nebula. Results of nebula flows are presented taking into account turbulence effects of nebula flows. Diffusion processes are found to control the settling of particles. 24 refs

Compressible turbulent flows: aspects of prediction and analysis

Energy Technology Data Exchange (ETDEWEB)

Friedrich, R. [TU Muenchen, Garching (Germany). Fachgebiet Stroemungsmechanik

2007-03-15

Compressible turbulent flows are an important element of high-speed flight. Boundary layers developing along fuselage and wings of an aircraft and along engine compressor and turbine blades are compressible and mostly turbulent. The high-speed flow around rockets and through rocket nozzles involves compressible turbulence and flow separation. Turbulent mixing and combustion in scramjet engines is another example where compressibility dominates the flow physics. Although compressible turbulent flows have attracted researchers since the fifties of the last century, they are not completely understood. Especially interactions between compressible turbulence and combustion lead to challenging, yet unsolved problems. Direct numerical simulation (DNS) and large-eddy simulation (LES) represent modern powerful research tools which allow to mimic such flows in great detail and to analyze underlying physical mechanisms, even those which cannot be accessed by the experiment. The present lecture provides a short description of these tools and some of their numerical characteristics. It then describes DNS and LES results of fully-developed channel and pipe flow and highlights effects of compressibility on the turbulence structure. The analysis of pressure fluctuations in such flows with isothermal cooled walls leads to the conclusion that the pressure-strain correlation tensor decreases in the wall layer and that the turbulence anisotropy increases, since the mean density falls off relative to the incompressible flow case. Similar increases in turbulence anisotropy due to compressibility are observed in inert and reacting temporal mixing layers. The nature of the pressure fluctuations is however two-facetted. While inert compressible mixing layers reveal wave-propagation effects in the pressure and density fluctuations, compressible reacting mixing layers seem to generate pressure fluctuations that are controlled by the time-rate of change of heat release and mean density

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

Science.gov (United States)

Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.

2008-12-01

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

Numerical modeling of buoyancy-driven turbulent flows in enclosures

International Nuclear Information System (INIS)

Hsieh, K.J.; Lien, F.S.

2004-01-01

Modeling turbulent natural convection in enclosures with differentially heated vertical walls is numerically challenging, in particular, when low-Reynolds-number (low-Re) models are adopted. When the turbulence level in the core region of cavity is low, most low-Re models, particular those showing good performance for bypass transitional flows, tend to relaminarize the flow and, as a consequence, significantly underpredict the near-wall turbulence intensities and boundary-layer thickness. Another challenge associated with low-turbulence buoyancy-driven flows in enclosures is its inherent unsteadiness, which can pose convergence problems when a steady Reynolds-averaged Navier-Stokes (RANS) equation is solved. In the present study, an unsteady RANS approach in conjunction with the low-Re k-ε model of Lien and Leschziner [Int. J. Comput. Fluid Dyn. 12 (1999) 1] is initially adopted and the predicted flow field is found effectively relaminarized. To overcome this difficulty, likely caused by the low-Re functions in the ε-equation, the two-layer approach is attempted, in which ε is prescribed algebraically using the one-equation k-l model of Wolfshtein [Int. J. Heat Mass Transfer 12 (1969) 301]. The two-layer approach combined with a quadratic stress-strain relation gives overall the best performance in terms of mean velocities, temperature and turbulence quantities

Macro-scale turbulence modelling for flows in porous media

International Nuclear Information System (INIS)

Pinson, F.

2006-03-01

- This work deals with the macroscopic modeling of turbulence in porous media. It concerns heat exchangers, nuclear reactors as well as urban flows, etc. The objective of this study is to describe in an homogenized way, by the mean of a spatial average operator, turbulent flows in a solid matrix. In addition to this first operator, the use of a statistical average operator permits to handle the pseudo-aleatory character of turbulence. The successive application of both operators allows us to derive the balance equations of the kind of flows under study. Two major issues are then highlighted, the modeling of dispersion induced by the solid matrix and the turbulence modeling at a macroscopic scale (Reynolds tensor and turbulent dispersion). To this aim, we lean on the local modeling of turbulence and more precisely on the k - ε RANS models. The methodology of dispersion study, derived thanks to the volume averaging theory, is extended to turbulent flows. Its application includes the simulation, at a microscopic scale, of turbulent flows within a representative elementary volume of the porous media. Applied to channel flows, this analysis shows that even within the turbulent regime, dispersion remains one of the dominating phenomena within the macro-scale modeling framework. A two-scale analysis of the flow allows us to understand the dominating role of the drag force in the kinetic energy transfers between scales. Transfers between the mean part and the turbulent part of the flow are formally derived. This description significantly improves our understanding of the issue of macroscopic modeling of turbulence and leads us to define the sub-filter production and the wake dissipation. A f - f - w >f model is derived. It is based on three balance equations for the turbulent kinetic energy, the viscous dissipation and the wake dissipation. Furthermore, a dynamical predictor for the friction coefficient is proposed. This model is then successfully applied to the study of

A finite-elements method for turbulent flow analysis

International Nuclear Information System (INIS)

Autret, A.

1986-03-01

The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. In our specific case, we have to deal with monophasic incompressible flow in Boussinesq approximation in the normal operating conditions of a primary circuit of nuclear power plant. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A Law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step [fr

PDF methods for combustion in high-speed turbulent flows

Science.gov (United States)

Pope, Stephen B.

1995-01-01

This report describes the research performed during the second year of this three-year project. The ultimate objective of the project is extend the applicability of probability density function (pdf) methods from incompressible to compressible turbulent reactive flows. As described in subsequent sections, progress has been made on: (1) formulation and modelling of pdf equations for compressible turbulence, in both homogeneous and inhomogeneous inert flows; and (2) implementation of the compressible model in various flow configurations, namely decaying isotropic turbulence, homogeneous shear flow and plane mixing layer.

The lagRST Model: A Turbulence Model for Non-Equilibrium Flows

Science.gov (United States)

Lillard, Randolph P.; Oliver, A. Brandon; Olsen, Michael E.; Blaisdell, Gregory A.; Lyrintzis, Anastasios S.

2011-01-01

This study presents a new class of turbulence model designed for wall bounded, high Reynolds number flows with separation. The model addresses deficiencies seen in the modeling of nonequilibrium turbulent flows. These flows generally have variable adverse pressure gradients which cause the turbulent quantities to react at a finite rate to changes in the mean flow quantities. This "lag" in the response of the turbulent quantities can t be modeled by most standard turbulence models, which are designed to model equilibrium turbulent boundary layers. The model presented uses a standard 2-equation model as the baseline for turbulent equilibrium calculations, but adds transport equations to account directly for non-equilibrium effects in the Reynolds Stress Tensor (RST) that are seen in large pressure gradients involving shock waves and separation. Comparisons are made to several standard turbulence modeling validation cases, including an incompressible boundary layer (both neutral and adverse pressure gradients), an incompressible mixing layer and a transonic bump flow. In addition, a hypersonic Shock Wave Turbulent Boundary Layer Interaction with separation is assessed along with a transonic capsule flow. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWTBLI flows assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

Simulation of turbulent flow over staggered tube bundles using multi-relaxation time lattice Boltzmann method

International Nuclear Information System (INIS)

Park, Jong Woon; Choi, Hyun Gyung

2014-01-01

A turbulent fluid flow over staggered tube bundles is of great interest in many engineering fields including nuclear fuel rods, heat exchangers and especially a gas cooled reactor lower plenum. Computational methods have evolved for the simulation of such flow for decades and lattice Boltzmann method (LBM) is one of the attractive methods due to its sound physical basis and ease of computerization including parallelization. In this study to find computational performance of the LBM in turbulent flows over staggered tubes, a fluid flow analysis code employing multi-relaxation time lattice Boltzmann method (MRT-LBM) is developed based on a 2-dimensional D2Q9 lattice model and classical sub-grid eddy viscosity model of Smagorinsky. As a first step, fundamental performance MRT-LBM is investigated against a standard problem of a flow past a cylinder at low Reynolds number in terms of drag forces. As a major step, benchmarking of the MRT-LBM is performed over a turbulent flow through staggered tube bundles at Reynolds number of 18,000. For a flow past a single cylinder, the accuracy is validated against existing experimental data and previous computations in terms of drag forces on the cylinder. Mainly, the MRT-LBM computation for a flow through staggered tube bundles is performed and compared with experimental data and general purpose computational fluid dynamic (CFD) analyses with standard k-ω turbulence and large eddy simulation (LES) equipped with turbulence closures of Smagrinsky-Lilly and wall-adapting local eddy-viscosity (WALE) model. The agreement between the experimental and the computational results from the present MRT-LBM is found to be reasonably acceptable and even comparable to the LES whereas the computational efficiency is superior. (orig.)

Simulation of turbulent flow over staggered tube bundles using multi-relaxation time lattice Boltzmann method

Energy Technology Data Exchange (ETDEWEB)

Park, Jong Woon; Choi, Hyun Gyung [Dongguk Univ., Gyeongju (Korea, Republic of). Nuclear and Energy Engineering Dept.

2014-02-15

A turbulent fluid flow over staggered tube bundles is of great interest in many engineering fields including nuclear fuel rods, heat exchangers and especially a gas cooled reactor lower plenum. Computational methods have evolved for the simulation of such flow for decades and lattice Boltzmann method (LBM) is one of the attractive methods due to its sound physical basis and ease of computerization including parallelization. In this study to find computational performance of the LBM in turbulent flows over staggered tubes, a fluid flow analysis code employing multi-relaxation time lattice Boltzmann method (MRT-LBM) is developed based on a 2-dimensional D2Q9 lattice model and classical sub-grid eddy viscosity model of Smagorinsky. As a first step, fundamental performance MRT-LBM is investigated against a standard problem of a flow past a cylinder at low Reynolds number in terms of drag forces. As a major step, benchmarking of the MRT-LBM is performed over a turbulent flow through staggered tube bundles at Reynolds number of 18,000. For a flow past a single cylinder, the accuracy is validated against existing experimental data and previous computations in terms of drag forces on the cylinder. Mainly, the MRT-LBM computation for a flow through staggered tube bundles is performed and compared with experimental data and general purpose computational fluid dynamic (CFD) analyses with standard k-ω turbulence and large eddy simulation (LES) equipped with turbulence closures of Smagrinsky-Lilly and wall-adapting local eddy-viscosity (WALE) model. The agreement between the experimental and the computational results from the present MRT-LBM is found to be reasonably acceptable and even comparable to the LES whereas the computational efficiency is superior. (orig.)

Turbulent flow simulation of the NREL S809 airfoil

Energy Technology Data Exchange (ETDEWEB)

Guerri, Ouahiba; Bouhadef, Khadidja; Harhad, Ameziane

2006-05-15

Numerical computations are carried out for the NREL S809 airfoil. The flow is modelled using an unsteady incompressible Reynolds Averaged Navier-Stokes solver. Two turbulence models (SST {kappa}/{omega}of Menter and RNG {kappa}/{epsilon}) are applied to close the RANS equations. All computations are performed assuming fully turbulent flow. The flow field is analyzed at various angles of attack from 0 to 20 degrees. Lift and drag forces are obtained from the computations by integrating the pressure and shear stress over the blade surface. The performance of the two turbulence models is compared and the influence of the free stream turbulence intensity is checked. The results confirm the satisfactory performance of the SST {kappa}/{omega} model of Menter for modelling turbulent flow around airfoils. (author)

DNS of droplet motion in a turbulent flow

Science.gov (United States)

Rosso, Michele; Elghobashi, S.

2013-11-01

The objective of our research is to study the multi-way interactions between turbulence and vaporizing liquid droplets by performing direct numerical simulations (DNS). The freely-moving droplets are fully resolved in 3D space and time and all the relevant scales of the turbulent motion are simultaneously resolved down to the smallest length- and time-scales. Our DNS solve the unsteady three-dimensional Navier-Stokes and continuity equations throughout the whole computational domain, including the interior of the liquid droplets. The droplet surface motion and deformation are captured accurately by using the Level Set method. The pressure jump condition, density and viscosity discontinuities across the interface as well as surface tension are accounted for. Here, we present only the results of the first stage of our research which considers the effects of turbulence on the shape change of an initially spherical liquid droplet, at density ratio (of liquid to carrier fluid) of 1000, moving in isotropic turbulent flow. We validate our results via comparison with available expe. This research has been supported by NSF-CBET Award 0933085 and NSF PRAC (Petascale Computing Resource Allocation) Award.

Application of PDF methods to compressible turbulent flows

Science.gov (United States)

Delarue, B. J.; Pope, S. B.

1997-09-01

A particle method applying the probability density function (PDF) approach to turbulent compressible flows is presented. The method is applied to several turbulent flows, including the compressible mixing layer, and good agreement is obtained with experimental data. The PDF equation is solved using a Lagrangian/Monte Carlo method. To accurately account for the effects of compressibility on the flow, the velocity PDF formulation is extended to include thermodynamic variables such as the pressure and the internal energy. The mean pressure, the determination of which has been the object of active research over the last few years, is obtained directly from the particle properties. It is therefore not necessary to link the PDF solver with a finite-volume type solver. The stochastic differential equations (SDE) which model the evolution of particle properties are based on existing second-order closures for compressible turbulence, limited in application to low turbulent Mach number flows. Tests are conducted in decaying isotropic turbulence to compare the performances of the PDF method with the Reynolds-stress closures from which it is derived, and in homogeneous shear flows, at which stage comparison with direct numerical simulation (DNS) data is conducted. The model is then applied to the plane compressible mixing layer, reproducing the well-known decrease in the spreading rate with increasing compressibility. It must be emphasized that the goal of this paper is not as much to assess the performance of models of compressibility effects, as it is to present an innovative and consistent PDF formulation designed for turbulent inhomogeneous compressible flows, with the aim of extending it further to deal with supersonic reacting flows.

Simulation of Reynolds number influence on heat exchange in turbulent flow of medium slurry

Science.gov (United States)

Bartosik, A.

2016-10-01

The paper deals with the numerical simulation of mass and heat exchange in turbulent flow of solid-liquid mixture in the range of averaged solid particle diameter from 0.10mm to 0.80mm, named further as the medium slurry. Physical model assumes that dispersed phase is fully suspended and a turbulent flow is hydro-dynamically, and thermally developed in a straight horizontal pipeline. Taking into account the aforementioned assumptions the slurry is treated as a single-phase flow with increased density, while viscosity is equals to a carrier liquid viscosity. The mathematical model constitutes time averaged momentum equation in which the turbulent stress tensor was designated using a two-equation turbulence model, which makes use of the Boussinesq eddy-viscosity hypothesis. Turbulence damping function in the turbulence model was especially designed for the medium slurry. In addition, an energy equation has been used in which a convective term was determined from the energy balance acting on a unit pipe length, assuming linear changes of temperature in main flow direction. Finally, the mathematical model of non-isothermal medium slurry flow comprises four partial differential equations, namely momentum and energy equations, equations of kinetic energy of turbulence and its dissipation rate. Four partial differential equations were solved by a finite difference scheme using own computer code. The objective of the paper is to examine the influence of Reynolds number on temperature profiles and Nusselt number in turbulent flow of medium slurry in the range of solids concentration from 0% to 30% by volume. The effect of influential factors on heat transfer between the pipe and slurry is analysed. The paper demonstrates substantial impact of Reynolds number and solids volume fraction on the Nusselt number. The results of numerical simulation are reviewed.

Turbulence modelling for incompressible flows

International Nuclear Information System (INIS)

Rodi, W.

1985-12-01

EUROMECH colloquium 180 was held at Karlsruhe from 4-6 July, 1984, with the aim of bringing together specialists working in the area of turbulence modelling and of reviewing the state-of-the-art in this field. 44 scientists from 12 countries participated and 28 papers were presented. The meeting started with a review of the performance of two-equation turbulence models employing transport equations for both the velocity and the length scale of turbulence. These models are now generally well established, but it was found that their application to certain flow situations remains problematic. The modelling assumptions involved in Reynolds stress-equation models were reviewed next, and new assumptions were proposed. It was generally agreed that, as computing power increases, these more complex models will become more popular also for practical applications. The increase in computing power also allows more and more to resolve the viscous sublayer with low Reynolds numbers models, and the capabilities and problems of these models were discussed. In this connection, special aspects of boundary layer calculations were also discussed, namely those associated with 3D boundary layers, converging and diverging flow and slightly detached boundary layers. The complex physical phenomena prevalent in situations under the influence of buoyancy and rotation were reviewed, and several papers were presented on models for simulating these effects. (orig./HP) [de

Kinetic equation of Lagrange particles and turbulence of an incompressible fluid

International Nuclear Information System (INIS)

Gordienko, S.N.

1999-01-01

Closed equation for the two-point function of the velocity and pressure gradient distribution is obtained. The spectral properties of the turbulent flow are studied on the basis of the analysis of scaling properties of the above equation and the problem on the role of the vorticity distribution in a turbulent flow alternation was considered. It is shown, that alternation is connected with boundary conditions. The geometric picture of the alternation is found. It is established, that distribution of the vorticity and correspondingly the role of alternation in the currents with spirality and without spirality are completely different

On the One-Dimensional Steady and Unsteady Porous Flow Equation

DEFF Research Database (Denmark)

Andersen, O. H.; Burcharth, H. F.

1995-01-01

Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative...... derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow...... resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available....

Particle resuspension from a multi-layer deposit by turbulent flow

International Nuclear Information System (INIS)

Fromentin, A.

1989-09-01

The aim of this work was to contribute to the understanding and quantification of particle resuspension from a bed exposed to a turbulent flow. The PARESS experiment has been set up and conducted. Multi-layer deposits of particles were created by allowing aerosols to settle on steel plates under conditions typical of a nuclear reactor containment following a severe accident. These were then exposed to a controlled turbulent airflow (U ∞ =5-25 m/s) in a wind tunnel and the evolution of the resuspension flux as a function of time was measured. The resuspension flux F r decreased with exposure time to the airflow t, according to a power law F r = a.t -b [kg/m 2 .s]. The parameters a and b depend on the flow velocity and the nature of the deposit. A new semi-empirical model, based on the comparison between the distributions of adhesive forces holding the particles on the deposit and aerodynamic forces tending to remove them, has been developed to simulate the stochastic nature of particle resuspension. This model is able to predict the experimentally observed decrease of the resuspension flux as a function of time and its dependence on flow velocity. Based on the results of the PARESS experiment, an empirical global relationship, which ignores the fine effects due to the nature of the different deposits, has been proposed. It appears that the resuspension flux is approximately proportinal to the cube of the flow velocity, and that a pseudo threshold velocity exists below which virtually no resuspension occurs. (author) 57 figs., 1 tab., 79 refs

Large-eddy simulations of turbulent flows in internal combustion engines

Science.gov (United States)

Banaeizadeh, Araz

The two-phase compressible scalar filtered mass density function (FMDF) model is further developed and employed for large-eddy simulations (LES) of turbulent spray combustion in internal combustion (IC) engines. In this model, the filtered compressible Navier-Stokes equations are solved in a generalized curvilinear coordinate system with high-order, multi-block, compact differencing schemes for the turbulent velocity and pressure. However, turbulent mixing and combustion are computed with a new two-phase compressible scalar FMDF model. The spray and droplet dispersion/evaporation are modeled with a Lagrangian method. A new Lagrangian-Eulerian-Lagrangian computational method is employed for solving the flow, spray and scalar equation. The pressure effect in the energy equation, as needed in compressible flows, is included in the FMDF formulation. The performance of the new compressible LES/FMDF model is assessed by simulating the flow field and scalar mixing in a rapid compression machine (RCM), in a shock tube and in a supersonic co-axial jet. Consistency of temperatures predicted by the Eulerian finite-difference (FD) and Lagrangian Monte Carlo (MC) parts of the LES/FMDF model are established by including the pressure on the FMDF. It is shown that the LES/FMDF model is able to correctly capture the scalar mixing in both compressible subsonic and supersonic flows. Using the new two-phase LES/FMDF model, fluid dynamics, heat transfer, spray and combustion in the RCM with flat and crevice piston are studied. It is shown that the temperature distribution in the RCM with crevice piston is more uniform than the RCM with flat piston. The fuel spray characteristics and the spray parameters affecting the fuel mixing inside the RCM in reacting and non-reacting flows are also studied. The predicted liquid penetration and flame lift-off lengths for respectively non-reacting and reacting sprays are found to compare well with the available experimental data. Temperatures and

Application of turbulence modeling to predict surface heat transfer in stagnation flow region of circular cylinder

Science.gov (United States)

Wang, Chi R.; Yeh, Frederick C.

1987-01-01

A theoretical analysis and numerical calculations for the turbulent flow field and for the effect of free-stream turbulence on the surface heat transfer rate of a stagnation flow are presented. The emphasis is on the modeling of turbulence and its augmentation of surface heat transfer rate. The flow field considered is the region near the forward stagnation point of a circular cylinder in a uniform turbulent mean flow. The free stream is steady and incompressible with a Reynolds number of the order of 10 to the 5th power and turbulence intensity of less than 5 percent. For this analysis, the flow field is divided into three regions: (1) a uniform free-stream region where the turbulence is homogeneous and isotropic; (2) an external viscid flow region where the turbulence is distorted by the variation of the mean flow velocity; and, (3) an anisotropic turbulent boundary layer region over the cylinder surface. The turbulence modeling techniques used are the kappa-epsilon two-equation model in the external flow region and the time-averaged turbulence transport equation in the boundary layer region. The turbulence double correlations, the mean velocity, and the mean temperature within the boundary layer are solved numerically from the transport equations. The surface heat transfer rate is calculated as functions of the free-stream turbulence longitudinal microlength scale, the turbulence intensity, and the Reynolds number.

Large CYBER-205-model of the Euler equations for vortex-stretched turbulent flow around Delta wings

International Nuclear Information System (INIS)

Rizzi, A.; Purcell, C.J.

1985-01-01

The large-scale numerical simulation of fluid flow is described as a discipline within the field of software engineering. As an example of such work, a vortex flow field is analyzed for its essential physical flow features, an appropriate mathematical description is presented (the Euler equations with an artificial viscosity model), a numerical algorithm to solve mathematical equations is described, and the programming methodology which allows us to attain a very high degree of vectorization on the CYBER 205 is discussed. Four simulated flowfields with vorticity shed from wing edges are computed with up to as many as one million grid points and verify the realism of the simulation model. The computed solutions show all of the qualitative features that are expected in these flows. The twisted cranked-and-cropped delta case is one where the leading-edge vortex is highly stretched and unstable, displaying ultimately inviscid large-scale turbulent-like phenomena

A finite-elements method for turbulent flow analysis

International Nuclear Information System (INIS)

Autret, A.

1986-03-01

The work discussed here covers turbulent flow calculations using GALERKIN's finite-element method. Turbulence effects on the mean field are taken into account by the k-epsilon model with two evolution equations: one for the kinetic energy of the turbulence, and one for the energy dissipation rate. The wall zone is covered by wall laws, and by REICHARDT's law in particular. A law is advanced for the epsilon input profile, and a numerical solution is proposed for the physically aberrant values of k and epsilon generated by the model. Single-equation models are reviewed comparatively with the k-epsilon model. A comparison between calculated and analytical solutions or calculated and experimental results is presented for decreasing turbulence behind a grid, for the flow between parallel flat plates with three REYNOLDS numbers, and for backward facing step. This part contains graphs and curves corresponding to results of the calculations presented in part one [fr

Validation of turbulence models for LMFBR outlet plenum flows

International Nuclear Information System (INIS)

Chen, Y.B.; Golay, M.W.

1977-01-01

Small scale experiments involving water flows are used to provide mean flow and turbulence field data for LMFBR outlet plenum flows. Measurements are performed at Reynolds number (Re) values of 33000 and 70000 in a 1/15 - scale FFTF geometry and at Re = 35000 in a 3/80-scale CRBR geometry. The experimental behavior is predicted using two different two-equation turbulence model computer programs, TEACH-T and VARR-II. It is found that the qualitative nature of the flow field within the plenum depends strongly upon the distribution of the mean inlet flow field, importantly also upon the degree of inlet turbulence, and also upon the turbulent momentum exchange model used in the calculations. In the FFTF geometry, the TEACH-T predictions agree well with the experiments. 7 refs

Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds

Science.gov (United States)

Egorov, I. V.; Novikov, A. V.

2016-06-01

A method for direct numerical simulation of a laminar-turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier-Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton-Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of M = 5.37. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar-turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer.

Dynamical eigenfunction decomposition of turbulent channel flow

Science.gov (United States)

Ball, K. S.; Sirovich, L.; Keefe, L. R.

1991-01-01

The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loeve (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number Re(tau) = 80 (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 percent of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions.

Turbulence modulation in dilute particle-laden flow

DEFF Research Database (Denmark)

Mandø, Matthias; Lightstone, M. F.; Rosendahl, Lasse

2009-01-01

augmentation of the carrier phase turbulence is expected, and small particles, for which attenuation is expected. The new model is derived directly from the balance equations of fluid flow and represents a combination of the so-called standard and consistent approaches. The performance of the new model......A new particle source term to account for the effect of particles on the turbulence equations based on the Euler/Lagrange approach is introduced and compared with existing models and experimental data. Three different sizes of particles are considered to cover the range of large particles, where...

Turbulence Modeling of Flows with Extensive Crossflow Separation

Directory of Open Access Journals (Sweden)

Argyris G. Panaras

2015-07-01

Full Text Available The reasons for the difficulty in simulating accurately strong 3-D shock wave/turbulent boundary layer interactions (SBLIs and high-alpha flows with classical turbulence models are investigated. These flows are characterized by the appearance of strong crossflow separation. In view of recent additional evidence, a previously published flow analysis, which attributes the poor performance of classical turbulence models to the observed laminarization of the separation domain, is reexamined. According to this analysis, the longitudinal vortices into which the separated boundary layer rolls up in this type of separated flow, transfer external inviscid air into the part of the separation adjacent to the wall, decreasing its turbulence. It is demonstrated that linear models based on the Boussinesq equation provide solutions of moderate accuracy, while non-linear ones and others that consider the particular structure of the flow are more efficient. Published and new Reynolds Averaged Navier–Stokes (RANS simulations are reviewed, as well as results from a recent Large Eddy Simulation (LES study, which indicate that in calculations characterized by sufficient accuracy the turbulent kinetic energy of the reverse flow inside the separation vortices is very low, i.e., the flow is almost laminar there.

Turbulence spectra, transport, and E × B flows in helical plasmas

International Nuclear Information System (INIS)

Watanabe, T.-H.; Nunami, M.; Sugama, H.; Satake, S.; Matsuoka, S.; Ishizawa, A.; Tanaka, K.; Maeyama, Shinya

2012-11-01

Gyrokinetic simulation of ion temperature gradient turbulence and zonal flows for helical plasmas has been validated against the Large Helical Device experiments with high ion temperature, where a reduced modeling of ion heat transport is also considered. It is confirmed by the entropy transfer analysis that the turbulence spectrum elongated in the radial wavenumber space is associated with successive interactions with zonal flows. A novel multi-scale simulation for turbulence and zonal flows in poloidally-rotating helical plasmas has demonstrated strong zonal flow generation by turbulence, which implies that turbulent transport processes in non-axisymmetric systems are coupled to neoclassical transport through the macroscopic E × B flows determined by the ambipolarty condition for neoclassical particle fluxes. (author)

Statistical Mechanics of Turbulent Flows

International Nuclear Information System (INIS)

Cambon, C

2004-01-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

Subgrid-scale turbulence in shock-boundary layer flows

Science.gov (United States)

Jammalamadaka, Avinash; Jaberi, Farhad

2015-04-01

Data generated by direct numerical simulation (DNS) for a Mach 2.75 zero-pressure gradient turbulent boundary layer interacting with shocks of different intensities are used for a priori analysis of subgrid-scale (SGS) turbulence and various terms in the compressible filtered Navier-Stokes equations. The numerical method used for DNS is based on a hybrid scheme that uses a non-dissipative central scheme in the shock-free turbulent regions and a robust monotonicity-preserving scheme in the shock regions. The behavior of SGS stresses and their components, namely Leonard, Cross and Reynolds components, is examined in various regions of the flow for different shock intensities and filter widths. The backscatter in various regions of the flow is found to be significant only instantaneously, while the ensemble-averaged statistics indicate no significant backscatter. The budgets for the SGS kinetic energy equation are examined for a better understanding of shock-tubulence interactions at the subgrid level and also with the aim of providing useful information for one-equation LES models. A term-by-term analysis of SGS terms in the filtered total energy equation indicate that while each term in this equation is significant by itself, the net contribution by all of them is relatively small. This observation is consistent with our a posteriori analysis.

Numerical investigation on cavitation flow of hydrofoil and its flow noise with emphasis on turbulence models

Directory of Open Access Journals (Sweden)

Sanghyeon Kim

2017-06-01

Full Text Available In this study, cavitation flow of hydrofoils is numerically investigated to characterize the effects of turbulence models on cavitation-flow patterns and the corresponding radiated sound waves. The two distinct flow conditions are considered by varying the mean flow velocity and angle of attack, which are categorized under the experimentally observed unstable or stable cavitation flows. To consider the phase interchanges between the vapor and the liquid, the flow fields around the hydrofoil are analyzed by solving the unsteady compressible Reynolds-averaged Navier–Stokes equations coupled with a mass-transfer model, also referred to as the cavitation model. In the numerical solver, a preconditioning algorithm with dual-time stepping techniques is employed in generalized curvilinear coordinates. The following three types of turbulence models are employed: the laminar-flow model, standard k − ε turbulent model, and filter-based model. Hydro-acoustic field formed by the cavitation flow of the hydrofoil is predicted by applying the Ffowcs Williams and Hawkings equation to the predicted flow field. From the predicted results, the effects of the turbulences on the cavitation flow pattern and radiated flow noise are quantitatively assessed in terms of the void fraction, sound-pressure-propagation directivities, and spectrum.

Interfacial structures in confined cap-turbulent and churn-turbulent flows

International Nuclear Information System (INIS)

Sun Xiaodong; Kim, Seungjin; Cheng Ling; Ishii, Mamoru; Beus, Stephen G.

2004-01-01

The objective of the present work is to study and model the interfacial structure development of air-water two-phase flow in a confined flow passage. Experiments of a total of 13 flow conditions in cap-turbulent and churn-turbulent flow regimes are carried out in a vertical air-water upward two-phase flow experimental loop with a test section of 200 mm in width and 10 mm in gap. Miniaturized four-sensor conductivity probes are used to measure local two-phase parameters at three different elevations for each flow condition. Bubble characteristics captured by the probes are categorized into two groups in view of the two-group interfacial area transport equation, i.e., spherical/distorted bubbles as Group 1 and cap/churn-turbulent bubbles as Group 2. The acquired local parameters are time-averaged void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for each group of bubbles. Also, the line-averaged and area-averaged data are presented and discussed in detail. The comparisons of these parameters at different elevations demonstrate the development of interfacial structures along the flow direction due to bubble interactions and the hydrodynamic effects. Furthermore, these data can serve as one part of the experimental data for investigation of the interfacial area transport in a confined two-phase flow

Statistical theory of turbulent incompressible multimaterial flow

International Nuclear Information System (INIS)

Kashiwa, B.

1987-10-01

Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of κ-ε modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy κ, and the rate of fluctuational energy dissipation ε, for each material. Hence a set of κ and ε equations must be solved, together with mean mass and momentum conservation equations, for each material. Both κ and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe

Comparison of turbulent particle dispersion models in turbulent shear flows

Directory of Open Access Journals (Sweden)

S. Laín

2007-09-01

Full Text Available This work compares the performance of two Lagrangian turbulent particle dispersion models: the standard model (e.g., that presented in Sommerfeld et al. (1993, in which the fluctuating fluid velocity experienced by the particle is composed of two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, and the model proposed by Minier and Peirano (2001, which is based on the PDF approach and performs closure at the level of acceleration of the fluid experienced by the particle. Formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping the mathematical manipulation of the stochastic model simple, thereby avoiding some pitfalls and simplifying the derivation of macroscopic relations. The performance of both dispersion models is tested in the configurations of grid-generated turbulence (Wells and Stock (1983 experiments, simple shear flow (Hyland et al., 1999 and confined axisymmetric jet flow laden with solids (Hishida and Maeda (1987 experiments.

SOMAR-LES: A framework for multi-scale modeling of turbulent stratified oceanic flows

Science.gov (United States)

Chalamalla, Vamsi K.; Santilli, Edward; Scotti, Alberto; Jalali, Masoud; Sarkar, Sutanu

2017-12-01

A new multi-scale modeling technique, SOMAR-LES, is presented in this paper. Localized grid refinement gives SOMAR (the Stratified Ocean Model with Adaptive Resolution) access to small scales of the flow which are normally inaccessible to general circulation models (GCMs). SOMAR-LES drives a LES (Large Eddy Simulation) on SOMAR's finest grids, forced with large scale forcing from the coarser grids. Three-dimensional simulations of internal tide generation, propagation and scattering are performed to demonstrate this multi-scale modeling technique. In the case of internal tide generation at a two-dimensional bathymetry, SOMAR-LES is able to balance the baroclinic energy budget and accurately model turbulence losses at only 10% of the computational cost required by a non-adaptive solver running at SOMAR-LES's fine grid resolution. This relative cost is significantly reduced in situations with intermittent turbulence or where the location of the turbulence is not known a priori because SOMAR-LES does not require persistent, global, high resolution. To illustrate this point, we consider a three-dimensional bathymetry with grids adaptively refined along the tidally generated internal waves to capture remote mixing in regions of wave focusing. The computational cost in this case is found to be nearly 25 times smaller than that of a non-adaptive solver at comparable resolution. In the final test case, we consider the scattering of a mode-1 internal wave at an isolated two-dimensional and three-dimensional topography, and we compare the results with Legg (2014) numerical experiments. We find good agreement with theoretical estimates. SOMAR-LES is less dissipative than the closure scheme employed by Legg (2014) near the bathymetry. Depending on the flow configuration and resolution employed, a reduction of more than an order of magnitude in computational costs is expected, relative to traditional existing solvers.

Modified k-l model and its ability to simulate supersonic axisymmetric turbulent flows

International Nuclear Information System (INIS)

Ahmadikia, H.; Shirani, E.

2001-05-01

The k-l turbulence model is a promising two-equation model. In this paper, the k and l model equations were derived from k-kl incompressible and one-equation turbulent models. Then the model was modified for compressible and transitional flows, and was applied to simulate supersonic axisymmetric flows over Hollow cylinder flare an hyperboloid flare bodies. The results were compared with the results obtained for the same flows experimentally as well as k-ε, k-ω and Baldwin-Lomax models. It was shown that the k-l model produces good results compared with experimental data and numerical data obtained when other turbulence models were used. It gives better results than k-ω and k-ε models in some cases. (author)

Drift-free kinetic equations for turbulent dispersion

Science.gov (United States)

Bragg, A.; Swailes, D. C.; Skartlien, R.

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

Simulation of turbulent flow in a packed bed

Energy Technology Data Exchange (ETDEWEB)

Guo, B.; Yu, A. [Centre for Simulation and Modelling of Particulate Systems and School of Material Science and Engineering, The University of New South Wales, Sydney 2052 (Australia); Wright, B.; Zulli, P. [BlueScope Steel Research Laboratories, P.O. Box 202, Port Kembla, NSW 2505 (Australia)

2006-05-15

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

Basic equations of interfacial area transport in gas-liquid two-phase flow

International Nuclear Information System (INIS)

Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.

2011-01-01

The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)

Equations of motion and conservation laws in a theory of stably stratified turbulence

Energy Technology Data Exchange (ETDEWEB)

L' vov, Victor S; Rudenko, Oleksii [Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: oleksii.rudenko@weizmann.ac.il

2008-12-15

This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of state including both non-ideal gases as well as liquids. The proposed approach is based on a suggested general definition of potential temperature. Special attention is paid to the energy conservation principle: the proposed approximation exactly preserves the total mechanical energy by approximate equations of motion. It is emphasized explicitly the importance for any turbulent boundary layer model to respect the conservation laws.

Simulation analysis of air flow and turbulence statistics in a rib grit roughened duct.

Science.gov (United States)

Vogiatzis, I I; Denizopoulou, A C; Ntinas, G K; Fragos, V P

2014-01-01

The implementation of variable artificial roughness patterns on a surface is an effective technique to enhance the rate of heat transfer to fluid flow in the ducts of solar air heaters. Different geometries of roughness elements investigated have demonstrated the pivotal role that vortices and associated turbulence have on the heat transfer characteristics of solar air heater ducts by increasing the convective heat transfer coefficient. In this paper we investigate the two-dimensional, turbulent, unsteady flow around rectangular ribs of variable aspect ratios by directly solving the transient Navier-Stokes and continuity equations using the finite elements method. Flow characteristics and several aspects of turbulent flow are presented and discussed including velocity components and statistics of turbulence. The results reveal the impact that different rib lengths have on the computed mean quantities and turbulence statistics of the flow. The computed turbulence parameters show a clear tendency to diminish downstream with increasing rib length. Furthermore, the applied numerical method is capable of capturing small-scale flow structures resulting from the direct solution of Navier-Stokes and continuity equations.

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

Science.gov (United States)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Finite element analysis of turbulent flow in fast reactor fuel subassembly elementary flow cell

International Nuclear Information System (INIS)

Muehlbauer, P.

1987-03-01

The method is described of calculating fully developed longitudinal steady-state turbulent flow of an incompressible fluid through an infinite bundle of parallel smooth rods, based on the finite element method and one-equation turbulence model. Theoretical calculation results are compared with experimental results. (author). 5 figs., 3 refs

Multi-scale full-field measurements and near-wall modeling of turbulent subcooled boiling flow using innovative experimental techniques

Energy Technology Data Exchange (ETDEWEB)

Hassan, Yassin A., E-mail: y-hassan@tamu.edu

2016-04-01

Highlights: • Near wall full-field velocity components under subcooled boiling were measured. • Simultaneous shadowgraphy, infrared thermometry wall temperature and particle-tracking velocimetry techniques were combined. • Near wall velocity modifications under subcooling boiling were observed. - Abstract: Multi-phase flows are one of the challenges on which the CFD simulation community has been working extensively with a relatively low success. The phenomena associated behind the momentum and heat transfer mechanisms associated to multi-phase flows are highly complex requiring resolving simultaneously for multiple scales on time and space. Part of the reasons behind the low predictive capability of CFD when studying multi-phase flows, is the scarcity of CFD-grade experimental data for validation. The complexity of the phenomena and its sensitivity to small sources of perturbations makes its measurements a difficult task. Non-intrusive and innovative measuring techniques are required to accurately measure multi-phase flow parameters while at the same time satisfying the high resolution required to validate CFD simulations. In this context, this work explores the feasible implementation of innovative measuring techniques that can provide whole-field and multi-scale measurements of two-phase flow turbulence, heat transfer, and boiling parameters. To this end, three visualization techniques are simultaneously implemented to study subcooled boiling flow through a vertical rectangular channel with a single heated wall. These techniques are listed next and are used as follow: (1) High-speed infrared thermometry (IR-T) is used to study the impact of the boiling level on the heat transfer coefficients at the heated wall, (2) Particle Tracking Velocimetry (PTV) is used to analyze the influence that boiling parameters have on the liquid phase turbulence statistics, (3) High-speed shadowgraphy with LED illumination is used to obtain the gas phase dynamics. To account

Direct numerical simulation of turbulent channel flow with deformed bubbles

International Nuclear Information System (INIS)

Yamamoto, Yoshinobu; Kunugi, Tomoaki

2010-01-01

In this study, the direct numerical simulation of a fully-developed turbulent channel flow with deformed bubbles were conducted by means of the refined MARS method, turbulent Reynolds number 150, and Bubble Reynolds number 120. As the results, large-scale wake motions were observed round the bubbles. At the bubble located region, mean velocity was degreased and turbulent intensities and Reynolds shear stress were increased by the effects of the large-scale wake motions round bubbles. On the other hands, near wall region, bubbles might effect on the flow laminarlize and drag reduction. Two types of drag coefficient of bubble were estimated from the accelerated velocity of bubble and correlation equation as a function of Particle Reynolds number. Empirical correlation equation might be overestimated the drag effects in this Particle Reynolds number range. (author)

Numerical prediction of flow, heat transfer, turbulence and combustion

CERN Document Server

Spalding, D Brian; Pollard, Andrew; Singhal, Ashok K

1983-01-01

Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion: Selected Works of Professor D. Brian Spalding focuses on the many contributions of Professor Spalding on thermodynamics. This compilation of his works is done to honor the professor on the occasion of his 60th birthday. Relatively, the works contained in this book are selected to highlight the genius of Professor Spalding in this field of interest. The book presents various research on combustion, heat transfer, turbulence, and flows. His thinking on separated flows paved the way for the multi-dimensional modeling of turbu

A Novel Multi-scale Simulation Strategy for Turbulent Reacting Flows

Energy Technology Data Exchange (ETDEWEB)

James, Sutherland [University of Utah

2018-04-12

Abstract In this project, a new methodology was proposed to bridge the gap between Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). This novel methodology, titled Lattice-Based Multiscale Simulation (LBMS), creates a lattice structure of One-Dimensional Turbulence (ODT) models. This model has been shown to capture turbulent combustion with high fidelity by fully resolving interactions between turbulence and diffusion. By creating a lattice of ODT models, which are then coupled, LBMS overcomes the shortcomings of ODT, which are its inability to capture large scale three dimensional flow structures. However, by spacing these lattices significantly apart, LBMS can avoid the curse of dimensionality that creates untenable computational costs associated with DNS. This project has shown that LBMS is capable of reproducing statistics of isotropic turbulent flows while coarsening the spacing between lines significantly. It also investigates and resolves issues that arise when coupling ODT lines, such as flux reconstruction perpendicular to a given ODT line, preservation of conserved quantities when eddies cross a course cell volume and boundary condition application. Robust parallelization is also investigated.

Transport equation for the time scale of a turbulent scalar field

International Nuclear Information System (INIS)

Kurbatskij, A.F.

1999-01-01

The two-parametric turbulence models cause serious difficulties by modeling the near-wall flows due to absence of the natural boundary condition on the wall for dissipation of the ε turbulence energy and the ε θ scalar field destruction. This difficulty may be overcome, if instead of the ε and ε θ , as the second parameter of the model, to apply the time scales of the turbulent dynamic and scalar fields. The equation of the scalar field is derived and numerical coefficients included therein, are determined from the simplest problems on the turbulent heat transfer [ru

Comparative study of turbulence model performance for axisymmetric sudden expansion flow

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Young In; Kim, Keung Koo; Yoon, Juhyeon

2013-01-01

In this study, the performance of turbulence models in predicting the turbulent flow in an axisymmetric sudden expansion with an expansion ratio of 4 is assessed for a Reynolds number of 5.6 Χ 10 4 . The comparisons show that the standard k-ε and RSM models provide the best agreement with the experimental data, whereas the standard k-ω model gives poor predictions. Owing to its computational efficiency, the Reynolds Averaged Navier-Stokes (RANS) approach has been widely used for the prediction of turbulent flows and associated pressure losses in a variety of internal flow systems such as a diffuser, orifice, converging nozzle, and pipes with sudden expansion. However, the lack of a general turbulence model often leads to limited applications of a RANS approach, i. e., the accuracy and validity of solutions obtained from RANS equations vary with the turbulence model, flow regime, near-wall treatment, and configuration of the problem. In light of the foregoing, a large amount of turbulence research has been conducted to assess the performance of existing turbulence models for different flow fields. In this paper, the turbulent flow in an axisymmetric sudden expansion is numerically investigated for a Reynolds number of 5.6 Χ 10 4 , with the aim of examining the performance of several turbulence models

Modification of Turbulent Pipe Flow Equations to Estimate the Vertical Velocity Profiles Under Woody Debris Jams

Science.gov (United States)

Cervania, A.; Knack, I. M. W.

2017-12-01

The presence of woody debris (WD) jams in rivers and streams increases the risk of backwater flooding and reduces the navigability of a channel, but adds fish and macroinvertebrate habitat to the stream. When designing river engineering projects engineers use hydraulic models to predict flow behavior around these obstructions. However, the complexities of flow through and beneath WD jams are still poorly understood. By increasing the ability to predict flow behavior around WD jams, landowners and engineers are empowered to develop sustainable practices regarding the removal or placement of WD in rivers and flood plains to balance the desirable and undesirable effects to society and the environment. The objective of this study is to address some of this knowledge gap by developing a method to estimate the vertical velocity profile of flow under WD jams. When flow passes under WD jams, it becomes affected by roughness elements on all sides, similar to turbulent flows in pipe systems. Therefore, the method was developed using equations that define the velocity profiles of turbulent pipe flows: the law of the wall, the logarithmic law, and the velocity defect law. Flume simulations of WD jams were conducted and the vertical velocity profiles were measured along the centerline. A calculated velocity profile was fit to the measured profile through the calibration of eight parameters. An optimal value or range of values have been determined for several of these parameters using cross-validation techniques. The results indicate there may be some promise to using this method in hydraulic models.

Large-eddy simulation of heavy particle dispersion in wall-bounded turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Salvetti, M.V. [DICI, University of Pisa, I-56122 Pisa (Italy)

2015-03-10

Capabilities and accuracy issues in Lagrangian tracking of heavy particles in velocity fields obtained from large-eddy simulations (LES) of wall-bounded turbulent flows are reviewed. In particular, it is shown that, if no subgrid scale (SGS) model is added to the particle motion equations, particle preferential concentration and near-wall accumulation are significantly underestimated. Results obtained with SGS modeling for the particle motion equations based on approximate deconvolution are briefly recalled. Then, the error purely due to filtering in particle tracking in LES flow fields is singled out and analyzed. The statistical properties of filtering errors are characterized in turbulent channel flow both from an Eulerian and a Lagrangian viewpoint. Implications for stochastic SGS modeling in particle motion equations are briefly outlined.

A model for reaction rates in turbulent reacting flows

Science.gov (United States)

Chinitz, W.; Evans, J. S.

1984-01-01

To account for the turbulent temperature and species-concentration fluctuations, a model is presented on the effects of chemical reaction rates in computer analyses of turbulent reacting flows. The model results in two parameters which multiply the terms in the reaction-rate equations. For these two parameters, graphs are presented as functions of the mean values and intensity of the turbulent fluctuations of the temperature and species concentrations. These graphs will facilitate incorporation of the model into existing computer programs which describe turbulent reacting flows. When the model was used in a two-dimensional parabolic-flow computer code to predict the behavior of an experimental, supersonic hydrogen jet burning in air, some improvement in agreement with the experimental data was obtained in the far field in the region near the jet centerline. Recommendations are included for further improvement of the model and for additional comparisons with experimental data.

Langevin equation of a fluid particle in wall-induced turbulence

NARCIS (Netherlands)

Brouwers, J.J.H.

2010-01-01

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-inducedturbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer).The analysis is based on the asymptotic behavior at a large Reynolds number. We use

Rough flows and homogenization in stochastic turbulence

OpenAIRE

Bailleul, I.; Catellier, R.

2016-01-01

We provide in this work a tool-kit for the study of homogenisation of random ordinary differential equations, under the form of a friendly-user black box based on the tehcnology of rough flows. We illustrate the use of this setting on the example of stochastic turbulence.

Scalar statistics in variable property turbulent channel flows

NARCIS (Netherlands)

Patel, A.; Boersma, B.J.; Pecnik, R.

2017-01-01

Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive

Comparative study of turbulence model performance for axisymmetric sudden expansion flow

Energy Technology Data Exchange (ETDEWEB)

Bae, Youngmin; Kim, Young In; Kim, Keung Koo; Yoon, Juhyeon [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

2013-10-15

In this study, the performance of turbulence models in predicting the turbulent flow in an axisymmetric sudden expansion with an expansion ratio of 4 is assessed for a Reynolds number of 5.6 Χ 10{sup 4}. The comparisons show that the standard k-ε and RSM models provide the best agreement with the experimental data, whereas the standard k-ω model gives poor predictions. Owing to its computational efficiency, the Reynolds Averaged Navier-Stokes (RANS) approach has been widely used for the prediction of turbulent flows and associated pressure losses in a variety of internal flow systems such as a diffuser, orifice, converging nozzle, and pipes with sudden expansion. However, the lack of a general turbulence model often leads to limited applications of a RANS approach, i. e., the accuracy and validity of solutions obtained from RANS equations vary with the turbulence model, flow regime, near-wall treatment, and configuration of the problem. In light of the foregoing, a large amount of turbulence research has been conducted to assess the performance of existing turbulence models for different flow fields. In this paper, the turbulent flow in an axisymmetric sudden expansion is numerically investigated for a Reynolds number of 5.6 Χ 10{sup 4}, with the aim of examining the performance of several turbulence models.

Numerical investigation of turbulent fluid flow and heat transfer in complex ducts

Energy Technology Data Exchange (ETDEWEB)

Rokni, M.

1998-01-01

The need for a reliable and reasonable accurate turbulence model without specific convergence problem for calculating duct flows in industrial applications has become more evident. In this study a general computational method has been developed for calculating turbulent quantities in any arbitrary three dimensional duct. Four different turbulence models for predicting the turbulent Reynolds stresses namely; standard k-{epsilon} model, the non-linear-k-{epsilon} model of Speziale, an Explicit Algebraic Stress Model (EASM) and a full Reynolds Stress Model (RSM) are compared with each other. The advantages, disadvantages and accuracy of these models are discussed. The turbulent heat fluxes are modeled by the SED concept, the GGDH and the WET methods. The advantages of GGDH and WET compared to SED are discussed and the limitations of these models are clarified. The two-equation model of temperature invariance and its dissipation rate for calculating turbulent heat fluxes are also discussed. The low Reynolds number version of all the models are considered except for the RSM. At high Reynolds numbers the wall functions for both the temperature field and the flow field are applied. It has been shown that the standard k-{epsilon} model with the curvilinear transformation provides false secondary motions in general non-orthogonal ducts and can not be used for predicting the turbulent secondary motions in ducts. The numerical method is based on the finite volume technique with non-staggered grid arrangement. The SIMPLEC algorithm is used for pressure-velocity coupling. A modified SIP and TDMA solving methods are implemented for solving the equations. The van Leer, QUICK and hybrid schemes are applied for treating the convective terms. However, in order to achieve stability in the k and {epsilon} equations, the hybrid scheme is used for the convective terms in these equations. Periodic boundary conditions are imposed in the main flow direction for decreasing the number of

Equations of motion and conservation laws in a theory of stable stratified turbulence

NARCIS (Netherlands)

L'vov, V.S.; Rudenko, O.

2008-01-01

This paper is part of an invited talk given at the international conference 'Turbulent Mixing and Beyond'. We consider non-isothermal fluid flows and revise simplifications of basic hydrodynamic equations for such flows, arriving eventually at a generalization of the Oberbeck–Boussinesq

Equilibrium-eulerian les model for turbulent poly-dispersed particle-laden flow

KAUST Repository

Icardi, Matteo; Marchisio, Daniele Luca; Chidambaram, Narayanan; Fox, Rodney O.

2013-01-01

An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.

Equilibrium-eulerian les model for turbulent poly-dispersed particle-laden flow

KAUST Repository

Icardi, Matteo

2013-04-01

An efficient Eulerian method for poly-dispersed particles in turbulent flows is implemented, verified and validated for a channel flow. The approach couples a mixture model with a quadrature-based moment method for the particle size distribution in a LES framework, augmented by an approximate deconvolution method to reconstructs the unfiltered velocity. The particle velocity conditioned on particle size is calculated with an equilibrium model, valid for low Stokes numbers. A population balance equation is solved with the direct quadrature method of moments, that efficiently represents the continuous particle size distribution. In this first study particulate processes are not considered and the capability of the model to properly describe particle transport is investigated for a turbulent channel flow. First, single-phase LES are validated through comparison with DNS. Then predictions for the two-phase system, with particles characterised by Stokes numbers ranging from 0.2 to 5, are compared with Lagrangian DNS in terms of particle velocity and accumulation at the walls. Since this phenomenon (turbophoresis) is driven by turbulent fluctuations and depends strongly on the particle Stokes number, the approximation of the particle size distribution, the choice of the sub-grid scale model and the use of an approximate deconvolution method are important to obtain good results. Our method can be considered as a fast and efficient alternative to classical Lagrangian methods or Eulerian multi-fluid models in which poly-dispersity is usually neglected.

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

Science.gov (United States)

Cambon, C.

2004-10-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their

A simple recipe for modeling reaction-rate in flows with turbulent-combustion

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Girimaji, Sharath S.

1991-01-01

A computationally viable scheme to account for chemical reaction in turbulent flows is presented. The multivariate beta-pdf model for multiple scalar mixing forms the basis of this scheme. Using the model scalar joint pdf and a general form of the instantaneous reaction-rate, the unclosed chemical reaction terms are expressed as simple functions of scalar means and the turbulent scalar energy. The calculation procedure requires that the mean scalar equations and only one other transport equation - for the turbulent scalar energy - be solved.

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

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Lee, J.

1994-01-01

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Turbulent mixed buoyancy driven flow and heat transfer in lid driven enclosure

International Nuclear Information System (INIS)

Mishra, Ajay Kumar; Sharma, Anil Kumar

2015-01-01

Turbulent mixed buoyancy driven flow and heat transfer of air in lid driven rectangular enclosure has been investigated for Grashof number in the range of 10 8 to 10 11 and for Richardson number 0.1, 1 and 10. Steady two dimensional Reynolds-Averaged-Navier-Stokes equations and conservation equations of mass and energy, coupled with the Boussinesq approximation, are solved. The spatial derivatives in the equations are discretized using the finite-element method. The SIMPLE algorithm is used to resolve pressure-velocity coupling. Turbulence is modeled with the k-ω closure model with physical boundary conditions along with the Boussinesq approximation, for the flow and heat transfer. The predicted results are validated against benchmark solutions reported in literature. The results include stream lines and temperature fields are presented to understand flow and heat transfer characteristics. There is a marked reduction in mean Nusselt number (about 58%) as the Richardson number increases from 0.1 to 10 for the case of Ra=10 10 signifying the effect of reduction of top lid velocity resulting in reduction of turbulent mixing. (author)

Spectral Cascade-Transport Turbulence Model Development for Two-Phase Flows

Science.gov (United States)

Brown, Cameron Scott

Turbulence modeling remains a challenging problem in nuclear reactor applications, particularly for the turbulent multiphase flow conditions in nuclear reactor subchannels. Understanding the fundamental physics of turbulent multiphase flows is crucial for the improvement and further development of multiphase flow models used in reactor operation and safety calculations. Reactor calculations with Reynolds-averaged Navier-Stokes (RANS) approach continue to become viable tools for reactor analysis. The on-going increase in available computational resources allows for turbulence models that are more complex than the traditional two-equation models to become practical choices for nuclear reactor computational fluid dynamic (CFD) and multiphase computational fluid dynamic (M-CFD) simulations. Similarly, increased computational capabilities continue to allow for higher Reynolds numbers and more complex geometries to be evaluated using direct numerical simulation (DNS), thus providing more validation and verification data for turbulence model development. Spectral turbulence models are a promising approach to M-CFD simulations. These models resolve mean flow parameters as well as the turbulent kinetic energy spectrum, reproducing more physical details of the turbulence than traditional two-equation type models. Previously, work performed by other researchers on a spectral cascade-transport model has shown that the model behaves well for single and bubbly twophase decay of isotropic turbulence, single and two-phase uniform shear flow, and single-phase flow in a channel without resolving the near-wall boundary layer for relatively low Reynolds number. Spectral models are great candidates for multiphase RANS modeling since bubble source terms can be modeled as contributions to specific turbulence scales. This work focuses on the improvement and further development of the spectral cascadetransport model (SCTM) to become a three-dimensional (3D) turbulence model for use in M

Instability of water-ice interface under turbulent flow

Science.gov (United States)

Izumi, Norihiro; Naito, Kensuke; Yokokawa, Miwa

2015-04-01

It is known that plane water-ice interface becomes unstable to evolve into a train of waves. The underside of ice formed on the water surface of rivers are often observed to be covered with ice ripples. Relatively steep channels which discharge melting water from glaciers are characterized by beds covered with a series of steps. Though the flowing agent inducing instability is not water but gas including water vapor, a similar train of steps have been recently observed on the Polar Ice Caps on Mars (Spiral Troughs). They are expected to be caused by the instability of water-ice interface induced by flowing fluid on ice. There have been some studies on this instability in terms of linear stability analysis. Recently, Caporeale and Ridolfi (2012) have proposed a complete linear stability analysis in the case of laminar flow, and found that plane water-ice interface is unstable in the range of sufficiently large Reynolds numbers, and that the important parameters are the Reynolds number, the slope angle, and the water surface temperature. However, the flow inducing instability on water-ice interface in the field should be in the turbulent regime. Extension of the analysis to the case of fully developed turbulent flow with larger Reynolds numbers is needed. We have performed a linear stability analysis on the instability of water-ice interface under turbulent flow conditions with the use of the Reynolds-averaged Navier-Stokes equations with the mixing length turbulent model, the continuity equation of flow, the diffusion/dispersion equation of heat, and the Stefan equation. In order to reproduce the accurate velocity distribution and the heat transfer in the vicinity of smooth walls with the use of the mixing length model, it is important to take into account of the rapid decrease in the mixing length in the viscous sublayer. We employ the Driest model (1956) to the formulation. In addition, as the thermal boundary condition at the water surface, we describe the

Large eddy simulation of bundle turbulent flows

International Nuclear Information System (INIS)

Hassan, Y.A.; Barsamian, H.R.

1995-01-01

Large eddy simulation may be defined as simulation of a turbulent flow in which the large scale motions are explicitly resolved while the small scale motions are modeled. This results into a system of equations that require closure models. The closure models relate the effects of the small scale motions onto the large scale motions. There have been several models developed, the most popular is the Smagorinsky eddy viscosity model. A new model has recently been introduced by Lee that modified the Smagorinsky model. Using both of the above mentioned closure models, two different geometric arrangements were used in the simulation of turbulent cross flow within rigid tube bundles. An inlined array simulations was performed for a deep bundle (10,816 nodes) as well as an inlet/outlet simulation (57,600 nodes). Comparisons were made to available experimental data. Flow visualization enabled the distinction of different characteristics within the flow such as jet switching effects in the wake of the bundle flow for the inlet/outlet simulation case, as well as within tube bundles. The results indicate that the large eddy simulation technique is capable of turbulence prediction and may be used as a viable engineering tool with the careful consideration of the subgrid scale model. (author)

Diffusive separation of particles by diffusion in swirled turbulent flows

International Nuclear Information System (INIS)

Arbuzov, V.N.; Shiliaev, M.I.

1984-01-01

An analysis of the dynamics of turbulent flow and diffusive separation of solid particles in a centrifugal air separator (consisting of two flat disks rotating at the same angular velocity) is presented. A closed set of balances for all the components of the tensor of turbulent stresses, extended to the entire flow region, is employed in the numerical analysis of transition and turbulent air flows between the rotating disks. The analytical relationships obtained for the case of the mixed flow for the various components of the average velocity, energy of fluctuations, and turbulence level in the circumferential direction agreed well with the theoretical and experimental distributions of Bakke, et al. (1973). It is shown that at high Reynolds numbers the flow is isotropic, the dependence of the circumferential component of the average velocity obeys a power law, and the generation of the radial component is controlled by the local centrifugal field. The sharpness of particle separation was calculated by the eddy diffusion equation and was found to depend on the geometry and the operating conditions. 8 references

A new energy transfer model for turbulent free shear flow

Science.gov (United States)

Liou, William W.-W.

1992-01-01

A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

Suppression of turbulent resistivity in turbulent Couette flow

Science.gov (United States)

Si, Jiahe; Colgate, Stirling A.; Sonnenfeld, Richard G.; Nornberg, Mark D.; Li, Hui; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe

2015-07-01

Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations.

Suppression of turbulent resistivity in turbulent Couette flow

Energy Technology Data Exchange (ETDEWEB)

Si, Jiahe, E-mail: jsi@nmt.edu; Sonnenfeld, Richard G.; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe [New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801 (United States); Colgate, Stirling A.; Li, Hui [Los Alamos National Laboratory, Los Alamos, New Mexico 87544 (United States); Nornberg, Mark D. [University of Wisconsin-Madison, Madison, Wisconsin 53706 (United States)

2015-07-15

Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations.

Suppression of turbulent resistivity in turbulent Couette flow

International Nuclear Information System (INIS)

Si, Jiahe; Sonnenfeld, Richard G.; Colgate, Arthur S.; Westpfahl, David J.; Romero, Van D.; Martinic, Joe; Colgate, Stirling A.; Li, Hui; Nornberg, Mark D.

2015-01-01

Turbulent transport in rapidly rotating shear flow very efficiently transports angular momentum, a critical feature of instabilities responsible both for the dynamics of accretion disks and the turbulent power dissipation in a centrifuge. Turbulent mixing can efficiently transport other quantities like heat and even magnetic flux by enhanced diffusion. This enhancement is particularly evident in homogeneous, isotropic turbulent flows of liquid metals. In the New Mexico dynamo experiment, the effective resistivity is measured using both differential rotation and pulsed magnetic field decay to demonstrate that at very high Reynolds number rotating shear flow can be described entirely by mean flow induction with very little contribution from correlated velocity fluctuations

Computation of noise generation and propagation for free and confined turbulent flows

International Nuclear Information System (INIS)

Bailly, C.; Lafon, P.; Candel, S.

1996-09-01

In this paper, a stochastic noise generation and propagation model based on the resolution of the linearized Euler equation is proposed to compute turbulent mixing noise for free and confined flows. Two problems must be solved in the framework of an acoustic analogy. First, a wave operator must be derived for sound waves travelling in any mean flow. An expression of the source term in then deduced by comparing the linearized form and the non linear form of the equations. Secondly, the knowledge of the turbulence velocity field is required to compute this source term. The radiated acoustic field is calculated numerically by solving the inhomogeneous acoustic wave equation. In this study, the wave operator is the system of the linearized Euler equations and the space-time turbulent velocity field is generated by a sum of random Fourier modes. This method is applied to the case of a confined flow in a two dimensional duct obstructed by a diaphragm. Numerical results are compared to experimental ones. For each aperture of the diaphragm, the radiated acoustic power is close to the experimental values and follows the U 4 law. The comparison of numerical and experimental spectrum is satisfactory too. Further investigation is needed in order to characterize precisely the influence of the mean flow on the radiated noise. (authors)

Lattice Boltzmann equation calculation of internal, pressure-driven turbulent flow

International Nuclear Information System (INIS)

Hammond, L A; Halliday, I; Care, C M; Stevens, A

2002-01-01

We describe a mixing-length extension of the lattice Boltzmann approach to the simulation of an incompressible liquid in turbulent flow. The method uses a simple, adaptable, closure algorithm to bound the lattice Boltzmann fluid incorporating a law-of-the-wall. The test application, of an internal, pressure-driven and smooth duct flow, recovers correct velocity profiles for Reynolds number to 1.25 x 10 5 . In addition, the Reynolds number dependence of the friction factor in the smooth-wall branch of the Moody chart is correctly recovered. The method promises a straightforward extension to other curves of the Moody chart and to cylindrical pipe flow

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

Directory of Open Access Journals (Sweden)

V. G. Ferreira

2007-01-01

Full Text Available In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005 is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994 methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000. A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

International Nuclear Information System (INIS)

Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

2015-01-01

This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations

Energy Technology Data Exchange (ETDEWEB)

B. A. Kashiwa; W. B. VanderHeyden

2000-12-01

A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.

PEVC-FMDF for Large Eddy Simulation of Compressible Turbulent Flows

Science.gov (United States)

Nouri Gheimassi, Arash; Nik, Mehdi; Givi, Peyman; Livescu, Daniel; Pope, Stephen

2017-11-01

The filtered density function (FDF) closure is extended to a ``self-contained'' format to include the subgrid scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint ``pressure-energy-velocity-composition filtered mass density function (PEVC-FMDF).'' In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation (SDE) for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

Density based topology optimization of turbulent flow heat transfer systems

DEFF Research Database (Denmark)

Dilgen, Sümer Bartug; Dilgen, Cetin Batur; Fuhrman, David R.

2018-01-01

The focus of this article is on topology optimization of heat sinks with turbulent forced convection. The goal is to demonstrate the extendibility, and the scalability of a previously developed fluid solver to coupled multi-physics and large 3D problems. The gradients of the objective and the con...... in the optimization process, while also demonstrating extension of the methodology to include coupling of heat transfer with turbulent flows.......The focus of this article is on topology optimization of heat sinks with turbulent forced convection. The goal is to demonstrate the extendibility, and the scalability of a previously developed fluid solver to coupled multi-physics and large 3D problems. The gradients of the objective...

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

Science.gov (United States)

Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.

2014-01-01

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

On the freestream matching condition for stagnation point turbulent flows

Science.gov (United States)

Speziale, C. G.

1989-01-01

The problem of plane stagnation point flow with freestream turbulence is examined from a basic theoretical standpoint. It is argued that the singularity which arises from the standard kappa-epsilon model is not due to a defect in the model but results from the use of an inconsistent freestream boundary condition. The inconsistency lies in the implementation of a production equals dissipation equilibrium hypothesis in conjunction with a freestream mean velocity field that corresponds to homogeneous plane strain - a turbulent flow which does not reach such a simple equilibrium. Consequently, the adjustment that has been made in the constants of the epsilon-transport equation to eliminate this singularity is not self-consistent since it is tantamount to artificially imposing an equilibrium structure on a turbulent flow which is known not to have one.

Transfer equations for spectral densities of inhomogeneous MHD turbulence

International Nuclear Information System (INIS)

Tu, C.-Y.; Marsch, E.

1990-01-01

On the basis of the dynamic equations governing the evolution of magnetohydrodynamic fluctuations expressed in terms of Elsaesser variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented describing the evolutions of the energy spectrum e ± and of the residual energy spectra e R and e S of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e ± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for e R the triple correlations do not correspond to an 'energy' conserving process, but also represent a nonlinear source term for e R . If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations. (author)

Development of Interfacial Structure in a Confined Air-Water Cap-Turbulent and Churn-Turbulent Flow

International Nuclear Information System (INIS)

Sun, X.; Kim, S.; Cheng, L.; Ishii, M.; Beus, S.G.

2001-01-01

The objective of the present work is to study and model the interfacial structure development of air-water two-phase flow in a confined test section. Experiments of a total of 9 flow conditions in a cap-turbulent and churn-turbulent flow regimes are carried out in a vertical air-water upward two-phase flow experimental loop with a test section of 20-cm in width and 1-cm in gap. The miniaturized four-sensor conductivity probes are used to measure local two-phase parameters at three different elevations for each flow condition. The bubbles captured by the probes are categorized into two groups in view of the two-group interfacial area transport equation, i.e., spherical/distorted bubbles as Group 1 and cap/churn-turbulent bubbles as Group 2. The acquired parameters are time-averaged local void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for both groups of bubbles. Also, the line-averaged and area-averaged data are presented and discussed. The comparisons of these parameters at different elevations demonstrate the development of interfacial structure along the flow direction due to bubble interactions

Development of Interfacial Structure in a Confined Air-Water Cap-Turbulent and Churn-Turbulent Flow

International Nuclear Information System (INIS)

Xiaodong Sun; Seungjin Kim; Ling Cheng; Mamoru Ishii; Beus, Stephen G.

2002-01-01

The objective of the present work is to study and model the interfacial structure development of air-water two-phase flow in a confined test section. Experiments of a total of 9 flow conditions in cap-turbulent and churn-turbulent flow regimes are carried out in a vertical air-water upward two-phase flow experimental loop with a test section of 200-mm in width and 10-mm in gap. Miniaturized four-sensor conductivity probes are used to measure local two-phase parameters at three different elevations for each flow condition. The bubbles captured by the probes are categorized into two groups in view of the two-group interfacial area transport equation, i.e., spherical/distorted bubbles as Group 1 and cap/churn-turbulent bubbles as Group 2. The acquired parameters are time-averaged local void fraction, interfacial velocity, bubble number frequency, interfacial area concentration, and bubble Sauter mean diameter for both groups of bubbles. Also, the line-averaged and area-averaged data are presented and discussed. The comparisons of these parameters at different elevations demonstrate the development of interfacial structure along the flow direction due to bubble interactions. (authors)

An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

Science.gov (United States)

Subramanian, Ramanathan Vishnampet Ganapathi

, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited only by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Though the gradient from our fully discrete adjoint is formally exact, it does include sensitivity to numerical solutions that are only an artifact of the discretization. These are typically saw-tooth type features, such as seen in under-resolved numerical simulations. Since these have no physical analog, for physical analysis or design of realistic actuators, such solutions are in a sense spurious. This has been addressed without sacrificing accuracy by redesigning the basic discretization to be dual-consistent, for which the discrete-adjoint is consistent with the adjoint of the continuous system, and thus, free from spurious numerical sensitivity modes. We extend our exact discrete-adjoint to a spatially dual-consistent discretization of the compressible flow equations and demonstrate its practical application for aeroacoustic control of a Mach 1.3 turbulent jet. The formulation admits a broad class of finite-difference schemes that satisfy a summation by-parts rule, and extends to multi-block curvilinear grids for efficient handling of complex geometries. The formulation is developed for several boundary conditions commonly used in simulation of free-shear and wall-bounded flows. In addition, the proposed discretization leads to superconvergent approximations of functionals

TO THE QUESTION ABOUT THE SIMULATION OF TURBULENT THERMAL FLOWS

Directory of Open Access Journals (Sweden)

2016-01-01

Full Text Available The main purpose of this work was the simulation of turbulent thermal flows, which is aimed at improving the visualization and the modeling of the flow fields of wind flows, which are necessary for aviation. The physical-mathematical model of gas flow in thermal is proposed on the basis of thermodynamic model and dynamic model under the assumption that the condensation energy, when the movement of the thermal is upward, becomes the turbulent fluctuations. A thermal is an air mass, which goes up and is capable to intermix with ambient air. In the work the thermodynamic model of thermal is presented, the equations and the system of equations are derived, that describe the main characteristics of wind flow, which are required for the modeling of airflows. The generation of vertical turbulent gust with von Karman spectrum is shown. The basic assumption in the construction of the dynamic model of generation was that the energy, which is stood out in the thermal due to the condensation of steam, is converted into the energy of turbulent pulsations. Some examples of numerical simulation are given in the article. The visualizations of the generation of the vertical velocity of random wind gust are given depending on the size of the considered space and depending on the pitch of cell partition. The analysis and comparison of the obtained results of the calculation are presented. The conducted studies are aimed at the simulation of the atmospheric background and atmospheric processes and, in the final result, at the increasing of flight safety.

Prediction of stably stratified homogeneous shear flows with second-order turbulence models

International Nuclear Information System (INIS)

Pereira, J C F; Rocha, J M P

2010-01-01

The present study investigated the role of pressure-correlation second-order turbulence modelling schemes on the predicted behaviour of stably stratified homogeneous vertical-sheared turbulence. The pressure-correlation terms were modelled with a nonlinear formulation (Craft 1991), which was compared with a linear pressure-strain model and the 'isotropization of production' model for the pressure-scalar correlation. Two additional modelling issues were investigated: the influence of the buoyancy term in the kinetic energy dissipation rate equation and the time scale in the thermal production term in the scalar variance dissipation equation. The predicted effects of increasing the Richardson number on turbulence characteristics were compared against a comprehensive set of direct numerical simulation databases. The linear models provide a broadly satisfactory description of the major effects of the Richardson number on stratified shear flow. The buoyancy term in the dissipation equation of the turbulent kinetic energy generates excessively low levels of dissipation. For moderate and large Richardson numbers, the term yields unrealistic linear oscillations in the shear and buoyancy production terms, and therefore should be dropped in this flow (or at least their coefficient c ε3 should be substantially reduced from its standard value). The mechanical dissipation time scale provides marginal improvements in comparison to the scalar time scale in the production. The observed inaccuracy of the linear model in predicting the magnitude of the effects on the velocity anisotropy was demonstrated to be attributed mainly to the defective behaviour of the pressure-correlation model, especially for stronger stratification. The turbulence closure embodying a nonlinear formulation for the pressure-correlations and specific versions of the dissipation equations failed to predict the tendency of the flow to anisotropy with increasing stratification. By isolating the effects of the

Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

Science.gov (United States)

Liou, Tong-Miin; Wang, Chun-Sheng

2018-01-01

Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

Redistribution of Kinetic Energy in Turbulent Flows

Directory of Open Access Journals (Sweden)

Alain Pumir

2014-10-01

Full Text Available In statistically homogeneous turbulent flows, pressure forces provide the main mechanism to redistribute kinetic energy among fluid elements, without net contribution to the overall energy budget. This holds true in both two-dimensional (2D and three-dimensional (3D flows, which show fundamentally different physics. As we demonstrate here, pressure forces act on fluid elements very differently in these two cases. We find in numerical simulations that in 3D pressure forces strongly accelerate the fastest fluid elements, and that in 2D this effect is absent. In 3D turbulence, our findings put forward a mechanism for a possibly singular buildup of energy, and thus may shed new light on the smoothness problem of the solution of the Navier-Stokes equation in 3D.

An algebraic stress/flux model for two-phase turbulent flow

International Nuclear Information System (INIS)

Kumar, R.

1995-12-01

An algebraic stress model (ASM) for turbulent Reynolds stress and a flux model for turbulent heat flux are proposed for two-phase bubbly and slug flows. These mathematical models are derived from the two-phase transport equations for Reynolds stress and turbulent heat flux, and provide C μ , a turbulent constant which defines the level of eddy viscosity, as a function of the interfacial terms. These models also include the effect of heat transfer. When the interfacial drag terms and the interfacial momentum transfer terms are absent, the model reduces to a single-phase model used in the literature

Turbulent flow computation in a circular U-Bend

Directory of Open Access Journals (Sweden)

Miloud Abdelkrim

2014-03-01

Full Text Available Turbulent flows through a circular 180° curved bend with a curvature ratio of 3.375, defined as the the bend mean radius to pipe diameter is investigated numerically for a Reynolds number of 4.45×104. The computation is performed for a U-Bend with full long pipes at the entrance and at the exit. The commercial ANSYS FLUENT is used to solve the steady Reynolds–Averaged Navier–Stokes (RANS equations. The performances of standard k-ε and the second moment closure RSM models are evaluated by comparing their numerical results against experimental data and testing their capabilities to capture the formation and extend this turbulence driven vortex. It is found that the secondary flows occur in the cross-stream half-plane of such configurations and primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend.

Turbulent flow computation in a circular U-Bend

Science.gov (United States)

Miloud, Abdelkrim; Aounallah, Mohammed; Belkadi, Mustapha; Adjlout, Lahouari; Imine, Omar; Imine, Bachir

2014-03-01

Turbulent flows through a circular 180° curved bend with a curvature ratio of 3.375, defined as the the bend mean radius to pipe diameter is investigated numerically for a Reynolds number of 4.45×104. The computation is performed for a U-Bend with full long pipes at the entrance and at the exit. The commercial ANSYS FLUENT is used to solve the steady Reynolds-Averaged Navier-Stokes (RANS) equations. The performances of standard k-ɛ and the second moment closure RSM models are evaluated by comparing their numerical results against experimental data and testing their capabilities to capture the formation and extend this turbulence driven vortex. It is found that the secondary flows occur in the cross-stream half-plane of such configurations and primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend.

Combustion characteristics and turbulence modeling of swirling reacting flow in solid fuel ramjet

Science.gov (United States)

Musa, Omer; Xiong, Chen; Changsheng, Zhou

2017-10-01

This paper reviews the historical studies have been done on the solid-fuel ramjet engine and difficulties associated with numerical modeling of swirling flow with combustible gases. A literature survey about works related to numerical and experimental investigations on solid-fuel ramjet as well as using swirling flow and different numerical approaches has been provided. An overview of turbulence modeling of swirling flow and the behavior of turbulence at streamline curvature and system rotation are presented. A new and simple curvature/correction factor is proposed in order to reduce the programming complexity of SST-CC turbulence model. Finally, numerical and experimental investigations on the impact of swirling flow on SFRJ have been carried out. For that regard, a multi-physics coupling code is developed to solve the problems of multi-physics coupling of fluid mechanics, solid pyrolysis, heat transfer, thermodynamics, and chemical kinetics. The connected-pipe test facility is used to carry out the experiments. The results showed a positive impact of swirling flow on SFRJ along with, three correlations are proposed.

Development and assessment of Multi-dimensional flow models in the thermal-hydraulic system analysis code MARS

Energy Technology Data Exchange (ETDEWEB)

Chung, B. D.; Bae, S. W.; Jeong, J. J.; Lee, S. M

2005-04-15

A new multi-dimensional component has been developed to allow for more flexible 3D capabilities in the system code, MARS. This component can be applied in the Cartesian and cylindrical coordinates. For the development of this model, the 3D convection and diffusion terms are implemented in the momentum and energy equation. And a simple Prandtl's mixing length model is applied for the turbulent viscosity. The developed multi-dimensional component was assessed against five conceptual problems with analytic solution. And some SETs are calculated and compared with experimental data. With this newly developed multi-dimensional flow module, the MARS code can realistic calculate the flow fields in pools such as those occurring in the core, steam generators and IRWST.

Development and assessment of Multi-dimensional flow models in the thermal-hydraulic system analysis code MARS

International Nuclear Information System (INIS)

Chung, B. D.; Bae, S. W.; Jeong, J. J.; Lee, S. M.

2005-04-01

A new multi-dimensional component has been developed to allow for more flexible 3D capabilities in the system code, MARS. This component can be applied in the Cartesian and cylindrical coordinates. For the development of this model, the 3D convection and diffusion terms are implemented in the momentum and energy equation. And a simple Prandtl's mixing length model is applied for the turbulent viscosity. The developed multi-dimensional component was assessed against five conceptual problems with analytic solution. And some SETs are calculated and compared with experimental data. With this newly developed multi-dimensional flow module, the MARS code can realistic calculate the flow fields in pools such as those occurring in the core, steam generators and IRWST

Mixing in 3D Sparse Multi-Scale Grid Generated Turbulence

Science.gov (United States)

Usama, Syed; Kopec, Jacek; Tellez, Jackson; Kwiatkowski, Kamil; Redondo, Jose; Malik, Nadeem

2017-04-01

Flat 2D fractal grids are known to alter turbulence characteristics downstream of the grid as compared to the regular grids with the same blockage ratio and the same mass inflow rates [1]. This has excited interest in the turbulence community for possible exploitation for enhanced mixing and related applications. Recently, a new 3D multi-scale grid design has been proposed [2] such that each generation of length scale of turbulence grid elements is held in its own frame, the overall effect is a 3D co-planar arrangement of grid elements. This produces a 'sparse' grid system whereby each generation of grid elements produces a turbulent wake pattern that interacts with the other wake patterns downstream. A critical motivation here is that the effective blockage ratio in the 3D Sparse Grid Turbulence (3DSGT) design is significantly lower than in the flat 2D counterpart - typically the blockage ratio could be reduced from say 20% in 2D down to 4% in the 3DSGT. If this idea can be realized in practice, it could potentially greatly enhance the efficiency of turbulent mixing and transfer processes clearly having many possible applications. Work has begun on the 3DSGT experimentally using Surface Flow Image Velocimetry (SFIV) [3] at the European facility in the Max Planck Institute for Dynamics and Self-Organization located in Gottingen, Germany and also at the Technical University of Catalonia (UPC) in Spain, and numerically using Direct Numerical Simulation (DNS) at King Fahd University of Petroleum & Minerals (KFUPM) in Saudi Arabia and in University of Warsaw in Poland. DNS is the most useful method to compare the experimental results with, and we are studying different types of codes such as Imcompact3d, and OpenFoam. Many variables will eventually be investigated for optimal mixing conditions. For example, the number of scale generations, the spacing between frames, the size ratio of grid elements, inflow conditions, etc. We will report upon the first set of findings

An implicit turbulence model for low-Mach Roe scheme using truncated Navier-Stokes equations

Science.gov (United States)

Li, Chung-Gang; Tsubokura, Makoto

2017-09-01

The original Roe scheme is well-known to be unsuitable in simulations of turbulence because the dissipation that develops is unsatisfactory. Simulations of turbulent channel flow for Reτ = 180 show that, with the 'low-Mach-fix for Roe' (LMRoe) proposed by Rieper [J. Comput. Phys. 230 (2011) 5263-5287], the Roe dissipation term potentially equates the simulation to an implicit large eddy simulation (ILES) at low Mach number. Thus inspired, a new implicit turbulence model for low Mach numbers is proposed that controls the Roe dissipation term appropriately. Referred to as the automatic dissipation adjustment (ADA) model, the method of solution follows procedures developed previously for the truncated Navier-Stokes (TNS) equations and, without tuning of parameters, uses the energy ratio as a criterion to automatically adjust the upwind dissipation. Turbulent channel flow at two different Reynold numbers and the Taylor-Green vortex were performed to validate the ADA model. In simulations of turbulent channel flow for Reτ = 180 at Mach number of 0.05 using the ADA model, the mean velocity and turbulence intensities are in excellent agreement with DNS results. With Reτ = 950 at Mach number of 0.1, the result is also consistent with DNS results, indicating that the ADA model is also reliable at higher Reynolds numbers. In simulations of the Taylor-Green vortex at Re = 3000, the kinetic energy is consistent with the power law of decaying turbulence with -1.2 exponents for both LMRoe with and without the ADA model. However, with the ADA model, the dissipation rate can be significantly improved near the dissipation peak region and the peak duration can be also more accurately captured. With a firm basis in TNS theory, applicability at higher Reynolds number, and ease in implementation as no extra terms are needed, the ADA model offers to become a promising tool for turbulence modeling.

Analysis of turbulent boundary layers

CERN Document Server

Cebeci, Tuncer

1974-01-01

Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculati

Theoretical study of turbulent channel flow - Bulk properties, pressure fluctuations, and propagation of electromagnetic waves

Science.gov (United States)

Canuto, V. M.; Hartke, G. J.; Battaglia, A.; Chasnov, J.; Albrecht, G. F.

1990-01-01

In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr-Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O-S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend strongly on the structure of the turbulence spectrum at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel.

Adaptive LES Methodology for Turbulent Flow Simulations

Energy Technology Data Exchange (ETDEWEB)

Oleg V. Vasilyev

2008-06-12

Although turbulent flows are common in the world around us, a solution to the fundamental equations that govern turbulence still eludes the scientific community. Turbulence has often been called one of the last unsolved problem in classical physics, yet it is clear that the need to accurately predict the effect of turbulent flows impacts virtually every field of science and engineering. As an example, a critical step in making modern computational tools useful in designing aircraft is to be able to accurately predict the lift, drag, and other aerodynamic characteristics in numerical simulations in a reasonable amount of time. Simulations that take months to years to complete are much less useful to the design cycle. Much work has been done toward this goal (Lee-Rausch et al. 2003, Jameson 2003) and as cost effective accurate tools for simulating turbulent flows evolve, we will all benefit from new scientific and engineering breakthroughs. The problem of simulating high Reynolds number (Re) turbulent flows of engineering and scientific interest would have been solved with the advent of Direct Numerical Simulation (DNS) techniques if unlimited computing power, memory, and time could be applied to each particular problem. Yet, given the current and near future computational resources that exist and a reasonable limit on the amount of time an engineer or scientist can wait for a result, the DNS technique will not be useful for more than 'unit' problems for the foreseeable future (Moin & Kim 1997, Jimenez & Moin 1991). The high computational cost for the DNS of three dimensional turbulent flows results from the fact that they have eddies of significant energy in a range of scales from the characteristic length scale of the flow all the way down to the Kolmogorov length scale. The actual cost of doing a three dimensional DNS scales as Re{sup 9/4} due to the large disparity in scales that need to be fully resolved. State-of-the-art DNS calculations of isotropic

RANS-based simulation of turbulent wave boundary layer and sheet-flow sediment transport processes

DEFF Research Database (Denmark)

Fuhrman, David R.; Schløer, Signe; Sterner, Johanna

2013-01-01

A numerical model coupling the horizontal component of the incompressible Reynolds-averaged Navier–Stokes (RANS) equationswith two-equation k−ω turbulence closure is presented and used to simulate a variety of turbulent wave boundary layer processes. The hydrodynamic model is additionally coupled...... with bed and suspended load descriptions, the latter based on an unsteady turbulent-diffusion equation, for simulation of sheet-flow sediment transport processes. In addition to standard features common within such RANS-based approaches, the present model includes: (1) hindered settling velocities at high...

Macro-scale turbulence modelling for flows in porous media; Modelisation a l'echelle macroscopique d'un ecoulement turbulent au sein d'un milieu poreux

Energy Technology Data Exchange (ETDEWEB)

Pinson, F

2006-03-15

- This work deals with the macroscopic modeling of turbulence in porous media. It concerns heat exchangers, nuclear reactors as well as urban flows, etc. The objective of this study is to describe in an homogenized way, by the mean of a spatial average operator, turbulent flows in a solid matrix. In addition to this first operator, the use of a statistical average operator permits to handle the pseudo-aleatory character of turbulence. The successive application of both operators allows us to derive the balance equations of the kind of flows under study. Two major issues are then highlighted, the modeling of dispersion induced by the solid matrix and the turbulence modeling at a macroscopic scale (Reynolds tensor and turbulent dispersion). To this aim, we lean on the local modeling of turbulence and more precisely on the k - {epsilon} RANS models. The methodology of dispersion study, derived thanks to the volume averaging theory, is extended to turbulent flows. Its application includes the simulation, at a microscopic scale, of turbulent flows within a representative elementary volume of the porous media. Applied to channel flows, this analysis shows that even within the turbulent regime, dispersion remains one of the dominating phenomena within the macro-scale modeling framework. A two-scale analysis of the flow allows us to understand the dominating role of the drag force in the kinetic energy transfers between scales. Transfers between the mean part and the turbulent part of the flow are formally derived. This description significantly improves our understanding of the issue of macroscopic modeling of turbulence and leads us to define the sub-filter production and the wake dissipation. A f - <{epsilon}>f - <{epsilon}{sub w}>f model is derived. It is based on three balance equations for the turbulent kinetic energy, the viscous dissipation and the wake dissipation. Furthermore, a dynamical predictor for the friction coefficient is proposed. This model is then

Low-dimensional representations of exact coherent states of the Navier-Stokes equations from the resolvent model of wall turbulence.

Science.gov (United States)

Sharma, Ati S; Moarref, Rashad; McKeon, Beverley J; Park, Jae Sung; Graham, Michael D; Willis, Ashley P

2016-02-01

We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just a few modes of the model of McKeon and Sharma [J. Fluid Mech. 658, 336 (2010)]. This model provides modes that act as a basis to decompose the velocity field, ordered by their amplitude of response to forcing arising from the interaction between scales. The model was originally derived from the Navier-Stokes equations to represent turbulent flows and has been used to explain coherent structure and to predict turbulent statistics. This establishes a surprising new link between the two distinct approaches to understanding turbulence.

Large eddy simulation of turbulent premixed combustion flows over backward facing step

Energy Technology Data Exchange (ETDEWEB)

Park, Nam Seob [Yuhan University, Bucheon (Korea, Republic of); Ko, Sang Cheol [Jeju National University, Jeju (Korea, Republic of)

2011-03-15

Large eddy simulation (LES) of turbulent premixed combustion flows over backward facing step has been performed using a dynamic sub-grid G-equation flamelet model. A flamelet model for the premixed flame is combined with a dynamic sub-grid combustion model for the filtered propagation of flame speed. The objective of this study is to investigate the validity of the dynamic sub-grid G-equation model in a complex turbulent premixed combustion flow. For the purpose of validating the LES combustion model, the LES of isothermal and reacting shear layer formed at a backward facing step is carried out. The calculated results are compared with the experimental results, and a good agreement is obtained.

Large eddy simulation of turbulent premixed combustion flows over backward facing step

International Nuclear Information System (INIS)

Park, Nam Seob; Ko, Sang Cheol

2011-01-01

Large eddy simulation (LES) of turbulent premixed combustion flows over backward facing step has been performed using a dynamic sub-grid G-equation flamelet model. A flamelet model for the premixed flame is combined with a dynamic sub-grid combustion model for the filtered propagation of flame speed. The objective of this study is to investigate the validity of the dynamic sub-grid G-equation model in a complex turbulent premixed combustion flow. For the purpose of validating the LES combustion model, the LES of isothermal and reacting shear layer formed at a backward facing step is carried out. The calculated results are compared with the experimental results, and a good agreement is obtained

VNAP2: a computer program for computation of two-dimensional, time-dependent, compressible, turbulent flow

Energy Technology Data Exchange (ETDEWEB)

Cline, M.C.

1981-08-01

VNAP2 is a computer program for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow. VNAP2 solves the two-dimensional, time-dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing-length model, a one-equation model, or the Jones-Launder two-equation model. The geometry may be a single- or a dual-flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference-plane-characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free-jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet-powered afterbodies, airfoils, and free-jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

Simulations of Turbulent Flows with Strong Shocks and Density Variations: Final Report

Energy Technology Data Exchange (ETDEWEB)

Sanjiva Lele

2012-10-01

The target of this SciDAC Science Application was to develop a new capability based on high-order and high-resolution schemes to simulate shock-turbulence interactions and multi-material mixing in planar and spherical geometries, and to study Rayleigh-Taylor and Richtmyer-Meshkov turbulent mixing. These fundamental problems have direct application in high-speed engineering flows, such as inertial confinement fusion (ICF) capsule implosions and scramjet combustion, and also in the natural occurrence of supernovae explosions. Another component of this project was the development of subgrid-scale (SGS) models for large-eddy simulations of flows involving shock-turbulence interaction and multi-material mixing, that were to be validated with the DNS databases generated during the program. The numerical codes developed are designed for massively-parallel computer architectures, ensuring good scaling performance. Their algorithms were validated by means of a sequence of benchmark problems. The original multi-stage plan for this five-year project included the following milestones: 1) refinement of numerical algorithms for application to the shock-turbulence interaction problem and multi-material mixing (years 1-2); 2) direct numerical simulations (DNS) of canonical shock-turbulence interaction (years 2-3), targeted at improving our understanding of the physics behind the combined two phenomena and also at guiding the development of SGS models; 3) large-eddy simulations (LES) of shock-turbulence interaction (years 3-5), improving SGS models based on the DNS obtained in the previous phase; 4) DNS of planar/spherical RM multi-material mixing (years 3-5), also with the two-fold objective of gaining insight into the relevant physics of this instability and aiding in devising new modeling strategies for multi-material mixing; 5) LES of planar/spherical RM mixing (years 4-5), integrating the improved SGS and multi-material models developed in stages 3 and 5. This final report is

Bounded energy states in homogeneous turbulent shear flow - An alternative view

Science.gov (United States)

Bernard, P. S.; Speziale, C. G.

1992-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if a residual vortex stretching term is maintained in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are presented for a k-epsilon model modified to account for net vortex stretching.

Bounded energy states in homogeneous turbulent shear flow: An alternative view

Science.gov (United States)

Bernard, Peter S.; Speziale, Charles G.

1990-01-01

The equilibrium structure of homogeneous turbulent shear flow is investigated from a theoretical standpoint. Existing turbulence models, in apparent agreement with physical and numerical experiments, predict an unbounded exponential time growth of the turbulent kinetic energy and dissipation rate; only the anisotropy tensor and turbulent time scale reach a structural equilibrium. It is shown that if vortex stretching is accounted for in the dissipation rate transport equation, then there can exist equilibrium solutions, with bounded energy states, where the turbulence production is balanced by its dissipation. Illustrative calculations are present for a k-epsilon model modified to account for vortex stretching. The calculations indicate an initial exponential time growth of the turbulent kinetic energy and dissipation rate for elapsed times that are as large as those considered in any of the previously conducted physical or numerical experiments on homogeneous shear flow. However, vortex stretching eventually takes over and forces a production-equals-dissipation equilibrium with bounded energy states. The validity of this result is further supported by an independent theoretical argument. It is concluded that the generally accepted structural equilibrium for homogeneous shear flow with unbounded component energies is in need of re-examination.

Mathematics of large eddy simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Berselli, L.C. [Pisa Univ. (Italy). Dept. of Applied Mathematics ' ' U. Dini' ' ; Iliescu, T. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Mathematics; Layton, W.J. [Pittsburgh Univ., PA (United States). Dept. of Mathematics

2006-07-01

Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive development and has matured into a highly-developed computational technology. It uses the tools of turbulence theory and the experience gained from practical computation. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations. The authors give a mathematically informed and detailed treatment of an interesting selection of models, focusing on issues connected with understanding and expanding the correctness and universality of LES. This volume offers a useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations. Non-mathematicians will appreciate it as a reference that introduces them to current tools and advances in the mathematical theory of LES. (orig.)

Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

Science.gov (United States)

Williams, Z. R.; Pueschel, M. J.; Terry, P. W.; Hauff, T.

2017-12-01

The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

Flow and Heat Transfer Characteristics of Turbulent Gas Flow in Microtube with Constant Heat Flux

International Nuclear Information System (INIS)

Hong, Chungpyo; Matsushita, Shinichi; Ueno, Ichiro; Asako, Yutaka

2012-01-01

Local friction factors for turbulent gas flows in circular microtubes with constant wall heat flux were obtained numerically. The numerical methodology is based on arbitrary-Lagrangian-Eulerian method to solve two-dimensional compressible momentum and energy equations. The Lam-Bremhorst's Low-Reynolds number turbulence model was employed to calculate eddy viscosity coefficient and turbulence energy. The simulations were performed for a wide flow range of Reynolds numbers and Mach numbers with different constant wall heat fluxes. The stagnation pressure was chosen in such a way that the outlet Mach number ranged from 0.07 to 1.0. Both Darcy friction factor and Fanning friction factor were locally obtained. The result shows that the obtained both friction factors were evaluated as a function of Reynolds number on the Moody chart. The values of Darcy friction factor differ from Blasius correlation due to the compressibility effects but the values of Fanning friction factor almost coincide with Blasius correlation. The wall heat flux varied from 100 to 10000 W/m 2 . The wall and bulk temperatures with positive heat flux are compared with those of incompressible flow. The result shows that the Nusselt number of turbulent gas flow is different from that of incompressible flow.

Incipient motion in gravel bed rivers due to energetic turbulent flow events

Science.gov (United States)

Valyrakis, Manousos

2013-04-01

This contribution reviews recent developments and contributions in the field of incipient motion and entrainment of coarse sediment grains due to the action of near bed turbulent flows. Specifically, traditional shear based spatio-temporally averaged concepts and instantaneous stress tensor criteria are contrasted to the newly proposed flow event based impulse and energy criteria. The energy criterion, suggests that only sufficiently energetic turbulent events can remove a particle from its resting position on the bed surface and result on its entrainment downstream. While the impulse and energy criteria are interconnected through the energy-impulse equation, the later appears to be more versatile and appropriate for generalising to sediment transport. These flow event based criteria have a sound physical basis for describing the intermittent character of particle entrainment as inherited by near boundary turbulence at near threshold conditions. These criteria can be derived from fundamental laws of physics such as Newtonian classical mechanics and the Lagrange equations respectively. The energetic events that are capable of performing geomorphic work at the scale of individual particles are shown to follow a power law, meaning that more energetic events (capable of removing larger stones) are expected to occur less frequently. In addition, this paper discusses the role of the coefficient of energy transfer efficiency introduced in the energy equation for particle entrainment. A preliminary investigation from analysis of a series of mobile grain flume experiments illustrates that different signatures of turbulence or sequence of flow structures may have different effectiveness towards particle transport. Characteristic cases of specific energetic flow events and the associated particle response are shown and classified with regard to the time required for complete entrainment. Finally these findings are commented with respect to the implications for sediment

Framework for simulating droplet vaporization in turbulent flows

Science.gov (United States)

Palmore, John; Desjardins, Olivier

2017-11-01

A framework for performing direct numerical simulations of droplet vaporization is presented. The work is motivated by spray combustion in engines wherein fuel droplets vaporize in a turbulent gas flow. The framework is built into a conservative finite volume code for simulating low Mach number turbulent multiphase flows. Phase tracking is performed using a discretely conservative geometric volume of fluid method, while the transport of mass fraction and temperature is performed using the BQUICK scheme. Special attention is given to the implementation of transport equations near the interface to ensure the consistency between fluxes of mass, momentum, and scalars. The effect of evaporation on the flow appears as a system of coupled source terms which depend on the local thermodynamic equilibrium between the phases. The sources are implemented implicitly using an unconditionally stable, monotone scheme. Two methodologies for resolving the system's thermodynamic equilibrium are compared for their accuracy, robustness, and computational expense. Verification is performed by comparing results to known solutions in one and three dimensions. Finally, simulations of droplets vaporizing in turbulence are demonstrated, and trends for mass fraction and temperature fields are discussed.

Numerical modeling of turbulent swirling flow in a multi-inlet vortex nanoprecipitation reactor using dynamic DDES

Science.gov (United States)

Hill, James C.; Liu, Zhenping; Fox, Rodney O.; Passalacqua, Alberto; Olsen, Michael G.

2015-11-01

The multi-inlet vortex reactor (MIVR) has been developed to provide a platform for rapid mixing in the application of flash nanoprecipitation (FNP) for manufacturing functional nanoparticles. Unfortunately, commonly used RANS methods are unable to accurately model this complex swirling flow. Large eddy simulations have also been problematic, as expensive fine grids to accurately model the flow are required. These dilemmas led to the strategy of applying a Delayed Detached Eddy Simulation (DDES) method to the vortex reactor. In the current work, the turbulent swirling flow inside a scaled-up MIVR has been investigated by using a dynamic DDES model. In the DDES model, the eddy viscosity has a form similar to the Smagorinsky sub-grid viscosity in LES and allows the implementation of a dynamic procedure to determine its coefficient. The complex recirculating back flow near the reactor center has been successfully captured by using this dynamic DDES model. Moreover, the simulation results are found to agree with experimental data for mean velocity and Reynolds stresses.

Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

Science.gov (United States)

Ruprecht, A.

A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

Numerical simulation of flow in fluidized beds

Czech Academy of Sciences Publication Activity Database

Bauer, Petr; Beneš, M.; Fučík, R.; Dieu, H.H.; Klement, V.; Máca, R.; Mach, J.; Oberhuber, T.; Strachota, P.; Žabka, V.; Havlena, V.

2015-01-01

Roč. 8, č. 5 (2015), s. 833-846 ISSN 1937-1632 Institutional support: RVO:61388998 Keywords : Navier-Stokes equations * multi- phase flow * combustion * turbulence * reactive flow s Subject RIV: BK - Fluid Dynamics Impact factor: 0.737, year: 2015

Mass transfer from smooth alabaster surfaces in turbulent flows

Science.gov (United States)

Opdyke, Bradley N.; Gust, Giselher; Ledwell, James R.

1987-11-01

The mass transfer velocity for alabaster plates in smooth-wall turbulent flow is found to vary with the friction velocity according to an analytic solution of the advective diffusion equation. Deployment of alabaster plates on the sea floor can perhaps be used to estimate the viscous stress, and transfer velocities for other species.

Turbulent flow with suction in smooth and rough pipes

International Nuclear Information System (INIS)

Verdier, Andre.

1977-11-01

It concerns an experimental study of turbulent flow inside a pipe with rough and porous wall and suction applied through it. The first part recall the basic knowledge concerning the turbulent flow with roughness. In second part statistical equations of fluid wall stress are written in the case of a permeable rough wall, in order to underline the respective role played by viscosity and pressure terms. In the third part the dynamic equilibrium of the flow is experimentally undertaken in the smooth and rough range with and without wall suction. Some empirical formulae are proposed for the mean velocity profiles in the inertial range and for friction velocity with suction. In the case of the sand roughness used, it does not seem that critical Reynolds number of transition from smooth to rough range is varied [fr

Study of compressible turbulent flows in supersonic environment by large-eddy simulation

Science.gov (United States)

Genin, Franklin

The numerical resolution of turbulent flows in high-speed environment is of fundamental importance but remains a very challenging problem. First, the capture of strong discontinuities, typical of high-speed flows, requires the use of shock-capturing schemes, which are not adapted to the resolution of turbulent structures due to their intrinsic dissipation. On the other hand, low-dissipation schemes are unable to resolve shock fronts and other sharp gradients without creating high amplitude numerical oscillations. Second, the nature of turbulence in high-speed flows differs from its incompressible behavior, and, in the context of Large-Eddy Simulation, the subgrid closure must be adapted to the modeling of compressibility effects and shock waves on turbulent flows. The developments described in this thesis are two-fold. First, a state of the art closure approach for LES is extended to model subgrid turbulence in compressible flows. The energy transfers due to compressible turbulence and the diffusion of turbulent kinetic energy by pressure fluctuations are assessed and integrated in the Localized Dynamic ksgs model. Second, a hybrid numerical scheme is developed for the resolution of the LES equations and of the model transport equation, which combines a central scheme for turbulent resolutions to a shock-capturing method. A smoothness parameter is defined and used to switch from the base smooth solver to the upwind scheme in regions of discontinuities. It is shown that the developed hybrid methodology permits a capture of shock/turbulence interactions in direct simulations that agrees well with other reference simulations, and that the LES methodology effectively reproduces the turbulence evolution and physical phenomena involved in the interaction. This numerical approach is then employed to study a problem of practical importance in high-speed mixing. The interaction of two shock waves with a high-speed turbulent shear layer as a mixing augmentation technique is

Stochastic transport models for mixing in variable-density turbulence

Science.gov (United States)

Bakosi, J.; Ristorcelli, J. R.

2011-11-01

In variable-density (VD) turbulent mixing, where very-different- density materials coexist, the density fluctuations can be an order of magnitude larger than their mean. Density fluctuations are non-negligible in the inertia terms of the Navier-Stokes equation which has both quadratic and cubic nonlinearities. Very different mixing rates of different materials give rise to large differential accelerations and some fundamentally new physics that is not seen in constant-density turbulence. In VD flows material mixing is active in a sense far stronger than that applied in the Boussinesq approximation of buoyantly-driven flows: the mass fraction fluctuations are coupled to each other and to the fluid momentum. Statistical modeling of VD mixing requires accounting for basic constraints that are not important in the small-density-fluctuation passive-scalar-mixing approximation: the unit-sum of mass fractions, bounded sample space, and the highly skewed nature of the probability densities become essential. We derive a transport equation for the joint probability of mass fractions, equivalent to a system of stochastic differential equations, that is consistent with VD mixing in multi-component turbulence and consistently reduces to passive scalar mixing in constant-density flows.

Comparison of superhydrophobic drag reduction between turbulent pipe and channel flows

Science.gov (United States)

Im, Hyung Jae; Lee, Jae Hwa

2017-09-01

It has been known over several decades that canonical wall-bounded internal flows of a pipe and channel share flow similarities, in particular, close to the wall due to the negligible curvature effect. In the present study, direct numerical simulations of fully developed turbulent pipe and channel flows are performed to investigate the influence of the superhydrophobic surfaces (SHSs) on the turbulence dynamics and the resultant drag reduction (DR) of the flows under similar conditions. SHSs at the wall are modeled in spanwise-alternating longitudinal regions with a boundary with no-slip and shear-free conditions, and the two parameters of the spanwise periodicity (P/δ) and SHS fraction (GF) within a pitch are considered. It is shown, in agreement with previous investigations in channels, that the turbulent drag for the pipe and channel flows over SHSs is continuously decreased with increases in P/δ and GF. However, the DR rate in the pipe flows is greater than that in the channel flows with an accompanying reduction of the Reynolds stress. The enhanced performance of the DR for the pipe flow is attributed to the increased streamwise slip and weakened Reynolds shear stress contributions. In addition, a mathematical analysis of the spanwise mean vorticity equation suggests that the presence of a strong secondary flow due to the increased spanwise slip of the pipe flows makes a greater negative contribution of advective vorticity transport than the channel flows, resulting in a higher DR value. Finally, an inspection of the origin of the mean secondary flow in turbulent flows over SHSs based on the spatial gradients of the turbulent kinetic energy demonstrates that the secondary flow is both driven and sustained by spatial gradients in the Reynolds stress components, i.e., Prandtl's secondary flow of the second kind.

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

International Nuclear Information System (INIS)

Inagaki, Masahide; Abe, Ken-ichi

2017-01-01

Highlights: • An anisotropy-resolving subgrid-scale model, covering a wide range of grid resolutions, is improved. • The new model enhances its applicability to flows in the laminar-turbulent transition region. • A mixed-timescale subgrid-scale model is used as the eddy viscosity model. • The proposed model successfully predicts the channel flows at transitional Reynolds numbers. • The influence of the definition of the grid-filter width is also investigated. - Abstract: Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k SGS , containing a production term proportional to the square root of k SGS , its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k SGS . To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k SGS transport equation. In the MTS model, the SGS turbulence energy, k es , estimated by

Direct Numerical Simulations of turbulent flow in a driven cavity

NARCIS (Netherlands)

Verstappen, R.; Wissink, J.G.; Cazemier, W.; Veldman, A.E.P.

Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large

Numerical study on turbulent flow inside a channel with an extended chamber

International Nuclear Information System (INIS)

Lee, Young Tae; Lim, Hee Chang

2009-01-01

The paper presents a LES numerical simulation of turbulent flow around an extended chamber. The simulations are carried out on a series of 3-dimensional cavities placed in a turbulent boundary layer at a Reynolds number of 1.0x10 5 based on U and h, which are the velocity at the upper top of the cavity and the depth height, respectively. In order to get an appropriate solution in the Filtered Navier-Stokes equation for the incompressible flow, the computational mesh is densely attracted to the cavity surface and coarsely far-field, as this aids saving the computation cost and rapid convergence. The Boussinesq hypothesis is employed in the subgrid-scale turbulence model. In order to obtain the subgrid-scale turbulent viscosity, the Smagorinsky-Lilly SGS model is applied and the CFL number for time marching is 1.0. The results include the flow variations inside a cavity with the different sizes and shapes.

Numerical Study on Turbulent Flow Inside a Channel with an Extended Chamber

International Nuclear Information System (INIS)

Lee, Young Tae; Lim, Hee Chang

2010-01-01

The paper describes a Large Eddy Simulation (LES) study of turbulent flow around a cavity. A series of three-dimensional cavities placed in a turbulent boundary layer are simulated at a Reynolds number of 1.0 x 10 5 by considering U and h, which represent the velocity at the top and the depth of the cavity, respectively. In order to obtain the appropriate solution for the filtered Navier-Stokes equation for incompressible flow, the computational mesh forms dense close to the wall of the cavity but relatively coarse away from the wall; this helps reduce computation cost and ensure rapid convergence. The Boussinesq hypothesis is employed in the subgrid-scale turbulence model. In order to determine the subgrid-scale turbulent viscosity, the Smagorinsky-Lilly SGS model is applied and the CFL number for time marching is set as 1.0. The results show the flow variations inside cavities of different sizes and shapes

Near-Wall Turbulence Modelling of Rotating and Curved Shear Flows

Energy Technology Data Exchange (ETDEWEB)

Pettersson, Bjoern Anders

1997-12-31

This thesis deals with verification and refinement of turbulence models within the framework of the Reynolds-averaged approach. It pays special attention to modelling the near-wall region, where the turbulence is strongly non-homogeneous and anisotropic. It also studies in detail the effects associated with an imposed rotation of the reference frame or streamline curvature. The objective with near-wall turbulence closure modelling is to formulate a set of equations governing single point turbulence statistics, which can be solved in the region of the flow which extends to the wall. This is in contrast to the commonly adopted wall-function approach in which the wall-boundary conditions are replaced by matching conditions in the logarithmic region. The near-wall models allow more flexibility by not requiring any such universal behaviour. Assessment of the novel elliptic relaxation approach to model the proximity of a solid boundary reveals an encouraging potential used in conjunction with second-moment and eddy-viscosity closures. The most natural level of closure modelling to predict flows affected by streamline curvatures or an imposed rotation of the reference frame is at the second-moment closure (SMC) level. Although SMCs naturally accounts for the effects of system rotation, the usual application of a scalar dissipation rate equation is shown to require ad hoc corrections in some cases in order to give good results. The elliptic relaxation approach is also used in conjunction with non-linear pressure-strain models and very encouraging results are obtained for rotating flows. Rotational induced secondary motions are vital to predicting the effects of system rotation. Some severe weaknesses of non-linear pressure-strain models are also indicated. Finally, a modelling methodology for anisotropic dissipation in nearly homogeneous turbulence are proposed. 84 refs., 56 figs., 16 tabs.

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

Science.gov (United States)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Turbulence in two-phase flows

International Nuclear Information System (INIS)

Sullivan, J.P.; Houze, R.N.; Buenger, D.E.; Theofanous, T.G.

1981-01-01

Hot film Anemometry and Laser Doppler Velocimetry have been employed in this work to study the turbulence characteristics of Bubbly and Stratified two-phase flows, respectively. Extensive consistency checks were made to establish the reliability and hence the utility of these experimental techniques for the measurement of turbulence in two-phase flows. Buoyancy-driven turbulence in vertical bubbly flows has been identified experimentally and correlated in terms of a shear velocity superposition approach. This approach provides a criterion for the demarcation of the buoyancy-driven turbulence region from the wall shear-generated turbulence region. Our data confirm the roughly isotropic behavior expected for buoyancy-driven turbulence. Upgrading of our experimental system will permit investigations of the wall-shear dominated regime (i.e., isotropy, superposition approach, etc.). The stratified flow data demonstrate clearly that the maximum in the mean velocity profile does not coincide with the zero shear plane, indicating the existence of a negative eddy viscosity region. Previous studies do not take into account this difference and thus they yield incorrect friction factor data in addition to certain puzzling behavior in the upper wall region. The conditioned turbulence data in the wavy region indicate interesting trends and that an appropriate normalization of intensities must take into account the shear velocity at the interfacial (wavy) region

Multi-fidelity uncertainty quantification in large-scale predictive simulations of turbulent flow

Science.gov (United States)

Geraci, Gianluca; Jofre-Cruanyes, Lluis; Iaccarino, Gianluca

2017-11-01

The performance characterization of complex engineering systems often relies on accurate, but computationally intensive numerical simulations. It is also well recognized that in order to obtain a reliable numerical prediction the propagation of uncertainties needs to be included. Therefore, Uncertainty Quantification (UQ) plays a fundamental role in building confidence in predictive science. Despite the great improvement in recent years, even the more advanced UQ algorithms are still limited to fairly simplified applications and only moderate parameter dimensionality. Moreover, in the case of extremely large dimensionality, sampling methods, i.e. Monte Carlo (MC) based approaches, appear to be the only viable alternative. In this talk we describe and compare a family of approaches which aim to accelerate the convergence of standard MC simulations. These methods are based on hierarchies of generalized numerical resolutions (multi-level) or model fidelities (multi-fidelity), and attempt to leverage the correlation between Low- and High-Fidelity (HF) models to obtain a more accurate statistical estimator without introducing additional HF realizations. The performance of these methods are assessed on an irradiated particle laden turbulent flow (PSAAP II solar energy receiver). This investigation was funded by the United States Department of Energy's (DoE) National Nuclear Security Administration (NNSA) under the Predicitive Science Academic Alliance Program (PSAAP) II at Stanford University.

Studies on turbulence structure and liquid film behavior in annular two-phase flow flowing in a throat section

International Nuclear Information System (INIS)

Yoshida, Kenji; Miyabe, Masaya; Matsumoto, Tadayoshi; Kataoka, Isao; Ohmori, Shuichi; Mori, Michitsugu

2004-01-01

Experimental studies on turbulence structure and liquid film behavior in annular two-phase flow were carried out concerned with the steam injector systems for a next-generation nuclear reactor. In the steam injector, steam/water annular two-phase flow is formed at the mixing nozzle. To make an appropriate design for high-performance steam injector system, it is very important to accumulate the fundamental data of thermo-hydro dynamic characteristics of annular flow in the steam injector. Especially, the turbulence modification in multi-phase flow due to the phase interaction is one of the most important phenomena and has attracted research attention. In this study, the liquid film behavior and the resultant turbulence modification due to the phase interaction were investigated. The behavior of the interfacial waves on liquid film flow such as the ripple or disturbance waves were observed to make clear the interfacial velocity and the special structure of the interfacial waves by using the high-speed video camera and the digital camera. The measurements for gas-phase velocity profiles and turbulent intensity in annular flow passing through the throat section were precisely performed to investigate quantitatively the turbulent modification in annular flow by using the constant temperature hot-wire anemometer. The measurements for liquid film thickness by the electrode needle method were also carried out. (author)

Large eddy simulations of turbulent flows with heat transfer

International Nuclear Information System (INIS)

Chatelain, Alexandre

2004-01-01

LES of turbulent flows with heat transfer was used within the framework of conjugate heat transfer problems. The objective of this work lies not only in identifying the various elements likely to impair temperature fluctuations estimations at the fluid/solid interface but also to introduce adequate wall modeling. The choice of a proper convection scheme for the transport of passive scalars led to the adoption of a high order upwind scheme with slope limiter. The use of classical wall models having shown some weaknesses as for the estimation of parietal temperature fluctuations, two new approaches are proposed and tested. The first one relies on a complete resolution of the Navier-Stokes equations on a refined grid close to the wall making it possible to rebuild the temperature fluctuations near the wall. The second one relies on the simultaneous and one dimensional resolution of a turbulent boundary layer equation and a variance transport equation near the wall. (author) [fr

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

Science.gov (United States)

Nielsen, Eric J.; Diskin, Boris; Yamaleev, Nail K.

2009-01-01

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

The effect of mixing-vane arrangements in a subchannel turbulent flow

International Nuclear Information System (INIS)

Ikeno, Tsutomu; Murata, Tamotsu; Kajishima, Takeo

2006-01-01

Large eddy simulation (LES) of developed turbulent flows in a rod bundle was carried out for four spacer designs. The mixing-vanes attached at the spacer were inclined at 30degC or 20deg; they were arranged to promote the swirling or convective flow. These arrangements are possible elements to compose an actual rod bundle. Our LES technique with a consistent higher-order immersed boundary method and a one-equation dynamic sub-grid scale model contributed to an efficient treatment of the complex wall configurations of rods and spacers. The computational results reasonably reproduced experimental results for the drag coefficient and the decay rate of swirling flow. The profiles of the axial velocities and the turbulence intensities indicated reasonable trend for the turbulent flow in the rod bundle. The effect of mixing-vane arrangement on the lateral flows was successfully clarified: the cross flow took the longer way on the rod surface than the swirling flow and then was more significantly influenced by momentum diffusion at the no-slip wall. Therefore, the largely inclined mixing-vanes promoted the cross flow only in the neighborhood of the spacer, the swirling flow inside a subchannel could reach farther downstream than the cross flow. (author)

Modelling of structural effects on chemical reactions in turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Gammelsaeter, H.R.

1997-12-31

Turbulence-chemistry interactions are analysed using algebraic moment closure for the chemical reaction term. The coupling between turbulence and chemical length and time scales generate a complex interaction process. This interaction process is called structural effects in this work. The structural effects are shown to take place on all scales between the largest scale of turbulence and the scales of the molecular motions. The set of equations describing turbulent correlations involved in turbulent reacting flows are derived. Interactions are shown schematically using interaction charts. Algebraic equations for the turbulent correlations in the reaction rate are given using the interaction charts to include the most significant couplings. In the frame of fundamental combustion physics, the structural effects appearing on the small scales of turbulence are proposed modelled using a discrete spectrum of turbulent scales. The well-known problem of averaging the Arrhenius law, the specific reaction rate, is proposed solved using a presumed single variable probability density function and a sub scale model for the reaction volume. Although some uncertainties are expected, the principles are addressed. Fast chemistry modelling is shown to be consistent in the frame of algebraic moment closure when the turbulence-chemistry interaction is accounted for in the turbulent diffusion. The modelling proposed in this thesis is compared with experimental data for an laboratory methane flame and advanced probability density function modelling. The results show promising features. Finally it is shown a comparison with full scale measurements for an industrial burner. All features of the burner are captured with the model. 41 refs., 33 figs.

The dimension of attractors underlying periodic turbulent Poiseuille flow

Science.gov (United States)

Keefe, Laurence; Moin, Parviz; Kim, John

1992-01-01

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Numerical prediction of local transitional features of turbulent forced gas flows in circular tubes with strong heating

International Nuclear Information System (INIS)

Ezato, Koichiro; Kunugi, Tomoaki; Shehata, A.M.; McEligot, D.M.

1997-03-01

Previous numerical simulation for the laminarization due to heating of the turbulent flow in pipe were assessed by comparison with only macroscopic characteristics such as heat transfer coefficient and pressure drop, since no experimental data on the local distributions of the velocity and temperature in such flow situation was available. Recently, Shehata and McEligot reported the first measurements of local distributions of velocity and temperature for turbulent forced air flow in a vertical circular tube with strongly heating. They carried out the experiments in three situations from turbulent flow to laminarizing flow according to the heating rate. In the present study, we analyzed numerically the local transitional features of turbulent flow evolving laminarizing due to strong heating in their experiments by using the advanced low-Re two-equation turbulence model. As the result, we successfully predicted the local distributions of velocity and temperature as well as macroscopic characteristics in three turbulent flow conditions. By the present study, a numerical procedure has been established to predict the local characteristics such as velocity distribution of the turbulent flow with large thermal-property variation and laminarizing flow due to strong heating with enough accuracy. (author). 60 refs

Modeling of turbulent bubbly flows; Modelisation des ecoulements turbulents a bulles

Energy Technology Data Exchange (ETDEWEB)

Bellakhal, Ghazi

2005-03-15

The two-phase flows involve interfacial interactions which modify significantly the structure of the mean and fluctuating flow fields. The design of the two-fluid models adapted to industrial flows requires the taking into account of the effect of these interactions in the closure relations adopted. The work developed in this thesis concerns the development of first order two-fluid models deduced by reduction of second order closures. The adopted reasoning, based on the principle of decomposition of the Reynolds stress tensor into two statistically independent contributions turbulent and pseudo-turbulent parts, allows to preserve the physical contents of the second order relations closure. Analysis of the turbulence structure in two basic flows: homogeneous bubbly flows uniform and with a constant shear allows to deduce a formulation of the two-phase turbulent viscosity involving the characteristic scales of bubbly turbulence, as well as an analytical description of modification of the homogeneous turbulence structure induced by the bubbles presence. The Eulerian two-fluid model was then generalized with the case of the inhomogeneous flows with low void fractions. The numerical results obtained by the application of this model integrated in the computer code MELODIF in the case of free sheared turbulent bubbly flow of wake showed a satisfactory agreement with the experimental data and made it possible to analyze the modification of the characteristic scales of such flow by the interfacial interactions. The two-fluid first order model is generalized finally with the case of high void fractions bubbly flows where the hydrodynamic interactions between the bubbles are not negligible any more. (author)

Modeling of turbulent flows in porous media and at the interface with a free fluid medium

International Nuclear Information System (INIS)

Chandesris, M.

2006-12-01

This work deals with the numerical simulation of turbulent flows in the whole nuclear reactor core, using multi-scale approaches. First, a macroscopic turbulence model is built, based on a porous media approach, to describe the flow in the fuel assemblies part of the nuclear core. Then, we study the jump conditions that have to be applied at a free fluid/porous interface. A thorough analytical study is carried out for laminar flows. This study allows to answer some fundamental questions about the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface. Using these results, jump conditions for turbulent flows are proposed. The model is then applied to the simulation of a turbulent flow in a simplified model of a reactor core. (author)

Development of two-group interfacial area transport equation for confined flow-1. Modeling of bubble interactions

International Nuclear Information System (INIS)

Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

2003-01-01

This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)

Molecular-Level Simulations of the Turbulent Taylor-Green Flow

Science.gov (United States)

Gallis, M. A.; Bitter, N. P.; Koehler, T. P.; Plimpton, S. J.; Torczynski, J. R.; Papadakis, G.

2017-11-01

The Direct Simulation Monte Carlo (DSMC) method, a statistical, molecular-level technique that provides accurate solutions to the Boltzmann equation, is applied to the turbulent Taylor-Green vortex flow. The goal of this work is to investigate whether DSMC can accurately simulate energy decay in a turbulent flow. If so, then simulating turbulent flows at the molecular level can provide new insights because the energy decay can be examined in detail from molecular to macroscopic length scales, thereby directly linking molecular relaxation processes to macroscopic transport processes. The DSMC simulations are performed on half a million cores of Sequoia, the 17 Pflop platform at Lawrence Livermore National Laboratory, and the kinetic-energy dissipation rate and the energy spectrum are computed directly from the molecular velocities. The DSMC simulations are found to reproduce the Kolmogorov -5/3 law and to agree with corresponding Navier-Stokes simulations obtained using a spectral method. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.

Analysis of Influence of the Thermal Dependence of Air Thermophysical Properties on the Accuracy of Simulation of Heat Transfer in a Turbulent Flow in Case of Applying Different Methods of Averaging Navier-Stokes Equations

Directory of Open Access Journals (Sweden)

A. D. Kliukvin

2014-01-01

Full Text Available There is theoretically investigated the influence of thermal dependence of air thermophysical properties on accuracy of heat transfer problems solution in a turbulent flow when using different methods of averaging the Navier-Stokes equations.There is analyzed the practicability of using particular method of averaging the NavierStokes equations when it’s necessary to clarify the solution of heat transfer problem taking into account the variability of air thermophysical properties.It’s shown that Reynolds and Favre averaging (the most common methods of averaging the Navier-Stokes equations are not effective in this case because these methods inaccurately describe behavior of large scale turbulent structures which strongly depends on geometry of particular flow. Thus it’s necessary to use more universal methods of turbulent flow simulation which are not based on averaging of all turbulent scales.In the article it’s shown that instead of Reynold and Favre averaging it’s possible to use large eddy simulation whereby turbulent structures are divided into small-scale and large-scale ones with subsequent modelling of small-scale ones only. But this approach leads to the necessarity of increasing the computational power by 2-3 orders.For different methods of averaging the form of additional terms of averaged Navier-Stokes equations in case of accounting pulsation of thermophysical properties of the air is obtained.On the example of a submerged heated air jet the errors (which occur when neglecting the thermal dependence of air thermophysical properties on averaged flow temperature in determination of convectional and conductive components of heat flux and viscous stresses are evaluated. It’s shown that the greatest increase of solution accuracy can be obtained in case of the flows with high temperature gradients.Finally using infinite Teylor series it’s found that underestimation of convective and conductive components of heat flux and

Assessment of turbulence models for pulsatile flow inside a heart pump.

Science.gov (United States)

Al-Azawy, Mohammed G; Turan, A; Revell, A

2016-02-01

Computational fluid dynamics (CFD) is applied to study the unsteady flow inside a pulsatile pump left ventricular assist device, in order to assess the sensitivity to a range of commonly used turbulence models. Levels of strain and wall shear stress are directly relevant to the evaluation of risk from haemolysis and thrombosis, and thus understanding the sensitivity to these turbulence models is important in the assessment of uncertainty in CFD predictions. The study focuses on a positive displacement or pulsatile pump, and the CFD model includes valves and moving pusher plate. An unstructured dynamic layering method was employed to capture this cyclic motion, and valves were simulated in their fully open position to mimic the natural scenario, with in/outflow triggered at control planes away from the valves. Six turbulence models have been used, comprising three relevant to the low Reynolds number nature of this flow and three more intended to investigate different transport effects. In the first group, we consider the shear stress transport (SST) [Formula: see text] model in both its standard and transition-sensitive forms, and the 'laminar' model in which no turbulence model is used. In the second group, we compare the one equation Spalart-Almaras model, the standard two equation [Formula: see text] and the full Reynolds stress model (RSM). Following evaluation of spatial and temporal resolution requirements, results are compared with available experimental data. The model was operated at a systolic duration of 40% of the pumping cycle and a pumping rate of 86 BPM (beats per minute). Contrary to reasonable preconception, the 'transition' model, calibrated to incorporate additional physical modelling specifically for these flow conditions, was not noticeably superior to the standard form of the model. Indeed, observations of turbulent viscosity ratio reveal that the transition model initiates a premature increase of turbulence in this flow, when compared with

Advancements in engineering turbulence modeling

Science.gov (United States)

Shih, T.-H.

1991-01-01

Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

Large-Eddy-Simulation of turbulent magnetohydrodynamic flows

Directory of Open Access Journals (Sweden)

Woelck Johannes

2017-01-01

Full Text Available A magnetohydrodynamic turbulent channel flow under the influence of a wallnormal magnetic field is investigated using the Large-Eddy-Simulation technique and k-equation subgrid-scale-model. Therefore, the new solver MHDpisoFoam is implemented in the OpenFOAM CFD-Code. The temporal decay of an initial turbulent field for different magnetic parameters is investigated. The rms values of the averaged velocity fluctuations show a similar, trend for each coordinate direction. 80% of the fluctuations are damped out in the range between 0 < Ha < < 75 at Re = 6675. The trend can be approximated via an exponential of the form exp(−a·Ha, where a is a scaling parameter. At higher Hartmann numbers the fluctuations decrease in an almost linear way. Therefore, the results of this study show that it may be possible to construct a general law for the turbulence damping due to action of magnetic fields.

Preliminary study of the effect of the turbulent flow field around complex surfaces on their acoustic characteristics

Science.gov (United States)

Olsen, W. A.; Boldman, D.

1978-01-01

Fairly extensive measurements have been conducted of the turbulent flow around various surfaces as a basis for a study of the acoustic characteristics involved. In the experiments the flow from a nozzle was directed upon various two-dimensional surface configurations such as the three-flap model. A turbulent flow field description is given and an estimate of the acoustic characteristics is provided. The developed equations are based upon fundamental theories for simple configurations having simple flows. Qualitative estimates are obtained regarding the radiation pattern and the velocity power law. The effect of geometry and turbulent flow distribution on the acoustic emission from simple configurations are discussed.

A New Eulerian Model for Turbulent Evaporating Sprays in Recirculating Flows

NARCIS (Netherlands)

Wittig, S.; Hallmann, M.; Scheurlen, M.; Schmehl, R.

1993-01-01

A new Eulerian model for the computation of turbulent evaporating sprays in recirculating flows is derived. It comprises droplet heating and evaporation processes by solving separate transport equations for the droplet's temperature and diameter. Full coupling of the droplet and the gaseous phase is

Effects of solid inertial particles on the velocity and temperature statistics of wall bounded turbulent flow

DEFF Research Database (Denmark)

Nakhaei, Mohammadhadi; Lessani, B.

2016-01-01

and particles, and the scatter plotsof fluid-particle temperature differences are presented. In addition, the variations of different budgetterms for the turbulent kinetic energy equation and fluctuating temperature variance equation in thepresence of particles are reported. The fluid turbulent heat flux...... is reduced by the presence of particles,and in spite of the additional heat exchange between the carrier fluid and the particles, the total heattransfer rate stays always lower for particle-laden flows. To further clarify this issue, the total Nusseltnumber is split into a turbulence contribution...... and a particle contribution, and the effects of particles inertiaon fluid turbulent heat flux and fluid-particle heat transfer are examined in detail...

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

Science.gov (United States)

Foti, Daniel; Duraisamy, Karthik

2017-11-01

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.

Turbulence

CERN Document Server

Bailly, Christophe

2015-01-01

This book covers the major problems of turbulence and turbulent processes, including  physical phenomena, their modeling and their simulation. After a general introduction in Chapter 1 illustrating many aspects dealing with turbulent flows, averaged equations and kinetic energy budgets are provided in Chapter 2. The concept of turbulent viscosity as a closure of the Reynolds stress is also introduced. Wall-bounded flows are presented in Chapter 3, and aspects specific to boundary layers and channel or pipe flows are also pointed out. Free shear flows, namely free jets and wakes, are considered in Chapter 4. Chapter 5 deals with vortex dynamics. Homogeneous turbulence, isotropy, and dynamics of isotropic turbulence are presented in Chapters 6 and 7. Turbulence is then described both in the physical space and in the wave number space. Time dependent numerical simulations are presented in Chapter 8, where an introduction to large eddy simulation is offered. The last three chapters of the book summarize remarka...

Numerical Simulation of Polymer Injection in Turbulent Flow Past a Circular Cylinder

KAUST Repository

Richter, David; Shaqfeh, Eric S. G.; Iaccarino, Gianluca

2011-01-01

Using a code developed to compute high Reynolds number viscoelastic flows, polymer injection from the upstream stagnation point of a circular cylinder is modeled at Re = 3900. Polymer stresses are represented using the FENE-P constitutive equations. By increasing polymer injection rates within realistic ranges, significant near wake stabilization is observed. Rather than a turbulent detached shear layer giving way to a chaotic primary vortex (as seen in Newtonian flows at high Re), a much more coherent primary vortex is shed, which possesses an increased core pressure as well as a reduced level of turbulent energy. © 2011 American Society of Mechanical Engineers.

Analysis of the Numerical Modelling of Turbulence in the Conical Reverse-Flow Cyclone

Directory of Open Access Journals (Sweden)

Inga Jakštonienė

2011-02-01

Full Text Available The paper describes the numerical modelling of the swirling fluid flow in the Stairmand cyclone (conical reverse-flow – CRF with tangential inlet (equipment for separating solid particles from the gaseous fluid flow. A review of experimental and theoretical papers is conducted introducing three-dimen­sional differential equations for transfer processes. The numerical modelling of the Stairmand cyclone the height of which is 0.75 m, diameter – 0.17 m, the height of a cylindrical part – 0.290 m, a conical part – 0,39 m and an inlet area is 0,085×0,032 m is presented. When governing three-dimensional fluid flow, transfer equations Navje-Stokes and Reynolds are solved using the finite volume method in a body-fitted co-ordinate system using standard k– e and RNG k– e model of turbulence. Modelling is realised for inlet velocity 4.64, 9.0 and 14.8 m/s (flow rate was 0.0112, 0.0245 and 0.0388 m3/s. The results obtained from the numerical tests have demonstrated that the RNG k– e model of turbulence yields a reasonably good prediction for highly swirling flows in cyclones: the presented numerical results (tangential and radial velocity profiles are compared with numerical and experimental data obtained by other authors. The mean relative error of ± 7,5% is found. Keywords: cyclone, solid particles, numerical modelling, turbulence, one-phase flow.DOI: 10.3846/mla.2010.085

On the Values for the Turbulent Schmidt Number in Environmental Flows

Directory of Open Access Journals (Sweden)

Carlo Gualtieri

2017-04-01

Full Text Available Computational Fluid Dynamics (CFD has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH, which requires the definition of the turbulent Schmidt number, Sct (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow. However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sct in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1 transverse mixing in a shallow water flow; (2 tracer transport in a contact tank; and (3 sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper.

Stochastic models for turbulent reacting flows

Energy Technology Data Exchange (ETDEWEB)

Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)

1993-12-01

The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.

Prediction of free turbulent mixing using a turbulent kinetic energy method

Science.gov (United States)

Harsha, P. T.

1973-01-01

Free turbulent mixing of two-dimensional and axisymmetric one- and two-stream flows is analyzed by a relatively simple turbulent kinetic energy method. This method incorporates a linear relationship between the turbulent shear and the turbulent kinetic energy and an algebraic relationship for the length scale appearing in the turbulent kinetic energy equation. Good results are obtained for a wide variety of flows. The technique is shown to be especially applicable to flows with heat and mass transfer, for which nonunity Prandtl and Schmidt numbers may be assumed.

Dynamics of fibres in a turbulent flow field - A particle-level simulation technique

International Nuclear Information System (INIS)

Sasic, Srdjan; Almstedt, Alf-Erik

2010-01-01

A particle-level simulation technique has been developed for modelling the flow of fibres in a turbulent flow field. A single fibre is conceived here as a chain of segments, thus enabling the model fibre to have all the degrees of freedom (translation, rotation, bending and twisting) needed to realistically reproduce the dynamics of real fibres. Equations of motion are solved for each segment, accounting for the interaction forces with the fluid, the contact forces with other fibres and the forces that maintain integrity of the fibre. The motion of the fluid is resolved as a combination of 3D mean flow velocities obtained from a CFD code and fluctuating turbulent velocities derived from the Langevin equation. A case of homogeneous turbulence is treated in this paper. The results obtained show that fibre flocs in air-fibre flows can be created even when attractive forces are not present. In such a case, contacts between fibres, properties of an individual fibre (such as flexibility and equilibrium shapes) and properties of the flow of the carrying fluid are shown to govern the physics behind formation and breaking up of fibre flocs. Highly irregular fibre shapes and stiff fibres lead to strong flocculation. The modelling framework applied in this work aims at making possible a numerical model applicable for designing processes involving transport of fibres by air at industrial scale.

SIMULATION OF TURBULENT FLOW AND HEAT TRANSFER OVER A BACKWARD -FACING STEP WITH RIBS TURBULATORS

Directory of Open Access Journals (Sweden)

Khudheyer S Mushatet

2011-01-01

Full Text Available Simulation is presented for a backward facing step flow and heat transfer inside a channel with ribs turbulators. The problem was investigated for Reynolds numbers up to 32000. The effect of a step height, the number of ribs and the rib thickness on the flow and thermal field were investigated. The computed results are presented as streamlines counters, velocity vectors and graphs of Nusselt number and turbulent kinetic energy variation. A control volume method employing a staggered grid techniques was imposed to discretize the governing continuity, full Navier Stockes and energy equations. A computer program using a SIMPLE algorithm was developed to handle the considered problem. The effect of turbulence was modeled by using a k-є model with its wall function formulas. The obtained results show that the strength and size of the re-circulation zones behind the step are increased with the increase of contraction ratio(i.e. with the increase of a step height. The size of recirculation regions and the reattachment length after the ribs are decreased with increasing of the contraction ratio. Also the results show that the Reynolds number and contraction ratio have a significant effect on the variation of turbulent kinetic energy and Nusselt number

Approximate solution of oil film load-carrying capacity of turbulent journal bearing with couple stress flow

Science.gov (United States)

Zhang, Yongfang; Wu, Peng; Guo, Bo; Lü, Yanjun; Liu, Fuxi; Yu, Yingtian

2015-01-01

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.

Turbulence modeling of transverse flow on ship hulls in shallow water

Energy Technology Data Exchange (ETDEWEB)

Jakobsen, Ken-Robert Gjelstad

2010-09-15

The hydrodynamic forces acting on a ship that travels in restricted water vary greatly with water depth and the geometry of the ship hull. This will affect the ship maneuverability in terms of various flow effects like for instance squat, when the ship is sucked down towards the seabed due to a pressure drop on the hull at forward speed. It is, thus, important to gain detailed knowledge on these aspects of marine engineering. The problem is in the present work addressed through a numerical investigation of turbulent transverse flow on two-dimensional ship sections in shallow water. The numerical code is validated against traditional flow problems in the literature. Namely, the Backward-facing step (BFS) and the Smoothly-contoured ramp (SCR). 2D and 3D laminar flows and 2D low Reynolds number turbulent flows are calculated, and the results are found to be in good agreement with the previous numerical and experimental comparison data. The turbulence model used in the calculations is the one-equation Spalart-Allmaras model. The overall goal of achieving more efficient and accurate numerical schemes will always be in focus of code development. Adaptive mesh refinement (AMR) is then a very helpful tool to save both time for grid generation prior to the calculations in question and the CPU hours needed to solve the governing equations. The latter is even more evident in a parallel environment. These aspects are included in the present investigation as part of the process to adapt and investigate a CFD tool suitable to handle turbulent flows on a ship hull in shallow water. Several physical and numerical parameters are included in the present study and the Plackett-Burman screening design is utilized to efficiently analyze the results. With the latter method, a simple function for calculating the drag force on a two-dimensional ship section as function of the given parameters has been obtained. (Author)

Two-phase wall function for modeling of turbulent boundary layer in subcooled boiling flow

International Nuclear Information System (INIS)

Bostjan Koncar; Borut Mavko; Yassin A Hassan

2005-01-01

flow experiments from the literature. A sensitivity analysis of the influence of the 'two-phase' wall function will be performed. Reference: A.A. Troshko, Y.A. Hassan, A two-equation turbulence model of turbulent bubbly flows. Int. J. Multiphase Flow, Vol. 27 (2001), 1965-2000. (authors)

Destabilizing turbulence in pipe flow

Science.gov (United States)

Kühnen, Jakob; Song, Baofang; Scarselli, Davide; Budanur, Nazmi Burak; Riedl, Michael; Willis, Ashley P.; Avila, Marc; Hof, Björn

2018-04-01

Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities1-3, so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 90%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. Since neither the Reynolds number nor the shear stresses decrease (the latter often increase), these measures are not indicative of turbulence collapse. Instead, an amplification mechanism4,5 measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.

Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method

Science.gov (United States)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2018-03-01

In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ = 180 are compared systematically with both published experimental and other DNS results based on solving the Navier-Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.

Direct Numerical Simulation of Turbulent Flow Over Complex Bathymetry

Science.gov (United States)

Yue, L.; Hsu, T. J.

2017-12-01

Direct numerical simulation (DNS) is regarded as a powerful tool in the investigation of turbulent flow featured with a wide range of time and spatial scales. With the application of coordinate transformation in a pseudo-spectral scheme, a parallelized numerical modeling system was created aiming at simulating flow over complex bathymetry with high numerical accuracy and efficiency. The transformed governing equations were integrated in time using a third-order low-storage Runge-Kutta method. For spatial discretization, the discrete Fourier expansion was adopted in the streamwise and spanwise direction, enforcing the periodic boundary condition in both directions. The Chebyshev expansion on Chebyshev-Gauss-Lobatto points was used in the wall-normal direction, assuming there is no-slip on top and bottom walls. The diffusion terms were discretized with a Crank-Nicolson scheme, while the advection terms dealiased with the 2/3 rule were discretized with an Adams-Bashforth scheme. In the prediction step, the velocity was calculated in physical domain by solving the resulting linear equation directly. However, the extra terms introduced by coordinate transformation impose a strict limitation to time step and an iteration method was applied to overcome this restriction in the correction step for pressure by solving the Helmholtz equation. The numerical solver is written in object-oriented C++ programing language utilizing Armadillo linear algebra library for matrix computation. Several benchmarking cases in laminar and turbulent flow were carried out to verify/validate the numerical model and very good agreements are achieved. Ongoing work focuses on implementing sediment transport capability for multiple sediment classes and parameterizations for flocculation processes.

One-equation near-wall turbulence modeling with the aid of direct simulation data

Science.gov (United States)

Rodi, W.; Mansour, N. N.; Michelassi, V.

1993-01-01

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

An explicit multi-time-stepping algorithm for aerodynamic flows

OpenAIRE

Niemann-Tuitman, B.E.; Veldman, A.E.P.

1997-01-01

An explicit multi-time-stepping algorithm with applications to aerodynamic flows is presented. In the algorithm, in different parts of the computational domain different time steps are taken, and the flow is synchronized at the so-called synchronization levels. The algorithm is validated for aerodynamic turbulent flows. For two-dimensional flows speedups in the order of five with respect to single time stepping are obtained.

A sparse-mode spectral method for the simulation of turbulent flows

International Nuclear Information System (INIS)

Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.

1996-01-01

We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows

Measurements of turbulence in a microscale multi-inlet vortex nanoprecipitation reactor

International Nuclear Information System (INIS)

Shi, Yanxiang; Cheng, Janine Chungyin; Fox, Rodney O; Olsen, Michael G

2013-01-01

The microscale multi-inlet vortex reactor (MIVR) is designed for use in Flash NanoPrecipitation (FNP), a promising technique for producing nanoparticles within small particle size distribution. Fluid mixing is crucial in the FNP process, and due to mixing’s strong dependence upon fluid kinematics, investigating velocity and turbulence within the reactor is crucial to optimizing reactor design. To this end, microscopic particle image velocimetry has been used to investigate flow within the MIVR. Three Reynolds numbers are studied, namely, Re j = 53, 93 and 240. At Re j = 53, the flow is laminar and steady. Due to the strong viscous effects at this Reynolds number, distinct flow patterns are observed at different distances from the reactor top and bottom walls. The viscous effects also retard the tangential motions within the reactor, resulting in a weaker vortex than appears at the higher Reynolds numbers. As the Reynolds number is increased to 93, the flow becomes more homogeneous over the depth of the reactor due to weaker viscous effects, yet the flow is still steady. The diminishing effects of viscosity also result in a stronger vortex. At the highest Reynolds number investigated, the flow is turbulent. Turbulent statistics including tangential and radial velocity fluctuations and Reynolds shear stresses are analyzed for this case in addition to the mean velocity field. The tangential motions of the flow are strongest at Re j = 240. Both the tangential and radial velocity fluctuations increase as the flow spirals toward the center of the reactor. The magnitudes of the tangential and radial velocity fluctuations are similar, suggesting that the turbulence is locally isotropic. (paper)

Creating Turbulent Flow Realizations with Generative Adversarial Networks

Science.gov (United States)

King, Ryan; Graf, Peter; Chertkov, Michael

2017-11-01

Generating valid inflow conditions is a crucial, yet computationally expensive, step in unsteady turbulent flow simulations. We demonstrate a new technique for rapid generation of turbulent inflow realizations that leverages recent advances in machine learning for image generation using a deep convolutional generative adversarial network (DCGAN). The DCGAN is an unsupervised machine learning technique consisting of two competing neural networks that are trained against each other using backpropagation. One network, the generator, tries to produce samples from the true distribution of states, while the discriminator tries to distinguish between true and synthetic samples. We present results from a fully-trained DCGAN that is able to rapidly draw random samples from the full distribution of possible inflow states without needing to solve the Navier-Stokes equations, eliminating the costly process of spinning up inflow turbulence. This suggests a new paradigm in physics informed machine learning where the turbulence physics can be encoded in either the discriminator or generator. Finally, we also propose additional applications such as feature identification and subgrid scale modeling.

On turbulence models for rod bundle flow computations

International Nuclear Information System (INIS)

Hazi, Gabor

2005-01-01

In commercial computational fluid dynamics codes there is more than one turbulence model built in. It is the user responsibility to choose one of those models, suitable for the problem studied. In the last decade, several computations were presented using computational fluid dynamics for the simulation of various problems of the nuclear industry. A common feature in a number of those simulations is that they were performed using the standard k-ε turbulence model without justifying the choice of the model. The simulation results were rarely satisfactory. In this paper, we shall consider the flow in a fuel rod bundle as a case study and discuss why the application of the standard k-ε model fails to give reasonable results in this situation. We also show that a turbulence model based on the Reynolds stress transport equations can provide qualitatively correct results. Generally, our aim is pedagogical, we would like to call the readers attention to the fact that turbulence models have to be selected based on theoretical considerations and/or adequate information obtained from measurements

Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

Science.gov (United States)

Lu, Xiaoyi; Pantano, Carlos

2017-11-01

In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.

Effects of Schmidt number on near-wall turbulent mass transfer in pipe flow

Energy Technology Data Exchange (ETDEWEB)

Kang, Chang Woo; Yang, Kyung Soo [Inha University, Incheon (Korea, Republic of)

2014-12-15

Large Eddy simulation (LES) of turbulent mass transfer in circular-pipe flow has been performed to investigate the characteristics of turbulent mass transfer in the near-wall region. We consider a fully-developed turbulent pipe flow with a constant wall concentration. The Reynolds number under consideration is Re{sub r} = 500 based on the friction velocity and the pipe radius, and the selected Schmidt numbers (Sc) are 0.71, 5, 10, 20 and 100. Dynamic subgrid-scale (SGS) models for the turbulent SGS stresses and turbulent mass fluxes were employed to close the governing equations. The current paper reports a comprehensive characterization of turbulent mass transfer in circular-pipe flow, focusing on its near-wall characteristics and Sc dependency. We start with mean fields by presenting mean velocity and concentration profiles, mean Sherwood numbers and mean mass transfer coefficients for the selected values of the parameters. After that, we present the characteristics of fluctuations including root-mean-square (rms) profiles of velocity, concentration, and mass transfer coefficient fluctuations. Turbulent mass fluxes and correlations between velocity and concentration fluctuations are also discussed. The near-wall behaviour of turbulent diffusivity and turbulent Schmidt number is shown, and other authors' correlations on their limiting behaviour towards the pipe wall are evaluated based on our LES results. The intermittent characteristics of turbulent mass transfer in pipe flow are depicted by probability density functions (pdf) of velocity and concentration fluctuations; joint pdfs between them are also presented. Instantaneous snapshots of velocity and concentration fluctuations are shown to supplement our discussion on the turbulence statistics. Finally, we report the results of octant analysis and budget calculation of concentration variance to clarify Sc-dependency of the correlation between near-wall turbulence structures and concentration fluctuation in

Effects of Schmidt number on near-wall turbulent mass transfer in pipe flow

International Nuclear Information System (INIS)

Kang, Chang Woo; Yang, Kyung Soo

2014-01-01

Large Eddy simulation (LES) of turbulent mass transfer in circular-pipe flow has been performed to investigate the characteristics of turbulent mass transfer in the near-wall region. We consider a fully-developed turbulent pipe flow with a constant wall concentration. The Reynolds number under consideration is Re r = 500 based on the friction velocity and the pipe radius, and the selected Schmidt numbers (Sc) are 0.71, 5, 10, 20 and 100. Dynamic subgrid-scale (SGS) models for the turbulent SGS stresses and turbulent mass fluxes were employed to close the governing equations. The current paper reports a comprehensive characterization of turbulent mass transfer in circular-pipe flow, focusing on its near-wall characteristics and Sc dependency. We start with mean fields by presenting mean velocity and concentration profiles, mean Sherwood numbers and mean mass transfer coefficients for the selected values of the parameters. After that, we present the characteristics of fluctuations including root-mean-square (rms) profiles of velocity, concentration, and mass transfer coefficient fluctuations. Turbulent mass fluxes and correlations between velocity and concentration fluctuations are also discussed. The near-wall behaviour of turbulent diffusivity and turbulent Schmidt number is shown, and other authors' correlations on their limiting behaviour towards the pipe wall are evaluated based on our LES results. The intermittent characteristics of turbulent mass transfer in pipe flow are depicted by probability density functions (pdf) of velocity and concentration fluctuations; joint pdfs between them are also presented. Instantaneous snapshots of velocity and concentration fluctuations are shown to supplement our discussion on the turbulence statistics. Finally, we report the results of octant analysis and budget calculation of concentration variance to clarify Sc-dependency of the correlation between near-wall turbulence structures and concentration fluctuation in the

Description and detection of burst events in turbulent flows

Science.gov (United States)

Schmid, P. J.; García-Gutierrez, A.; Jiménez, J.

2018-04-01

A mathematical and computational framework is developed for the detection and identification of coherent structures in turbulent wall-bounded shear flows. In a first step, this data-based technique will use an embedding methodology to formulate the fluid motion as a phase-space trajectory, from which state-transition probabilities can be computed. Within this formalism, a second step then applies repeated clustering and graph-community techniques to determine a hierarchy of coherent structures ranked by their persistencies. This latter information will be used to detect highly transitory states that act as precursors to violent and intermittent events in turbulent fluid motion (e.g., bursts). Used as an analysis tool, this technique allows the objective identification of intermittent (but important) events in turbulent fluid motion; however, it also lays the foundation for advanced control strategies for their manipulation. The techniques are applied to low-dimensional model equations for turbulent transport, such as the self-sustaining process (SSP), for varying levels of complexity.

On soft stability loss in rotating turbulent MHD flows

International Nuclear Information System (INIS)

Kapusta, Arkady; Mikhailovich, Boris

2014-01-01

The problem of the stability of turbulent flows of liquid metal in a cylindrical cavity against small velocity disturbances under the action of a rotating magnetic field (RMF) has been studied. The flow is considered in the induction-free approximation using the ‘external’ friction model. A system of dimensionless equations is examined in cylindrical coordinates. The results of computations performed on the basis of this mathematical model using the exchange of stabilities principle have shown a good consistency between the critical values of computed and experimental Reynolds numbers. (paper)

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

Science.gov (United States)

Kou, Jisheng; Sun, Shuyu

2016-08-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

KAUST Repository

Kou, Jisheng

2016-05-10

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests

Large Eddy Simulations of Two-phase Turbulent Reactive Flows in IC Engines

Science.gov (United States)

Banaeizadeh, Araz; Schock, Harold; Jaberi, Farhad

2008-11-01

The two-phase filtered mass density function (FMDF) subgrid-scale (SGS) model is used for large-eddy simulation (LES) of turbulent spray combustion in internal combustion (IC) engines. The LES/FMDF is implemented via an efficient, hybrid numerical method. In this method, the filtered compressible Navier-Stokes equations in curvilinear coordinate systems are solved with a generalized, high-order, multi-block, compact differencing scheme. The spray and the FMDF are implemented with Lagrangian methods. The reliability and the consistency of the numerical methods are established for different IC engines and the complex interactions among mean and turbulent velocity fields, fuel droplets and combustion are shown to be well captured with the LES/FMDF. In both spark-ignition/direct-injection and diesel engines, the droplet size and velocity distributions are found to be modified by the unsteady, vortical motions generated by the incoming air during the intake stroke. In turn, the droplets are found to change the in-cylinder flow structure. In the spark-ignition engine, flame propagation is similar to the experiment. In the diesel engine, the maximum evaporated fuel concentration is near the cylinder wall where the flame starts, which is again consistent with the experiment.

Roughness topographical effects on mean momentum and stress budgets in developed turbulent channel flows

Science.gov (United States)

Aghaei Jouybari, Mostafa; Yuan, Junlin

2017-11-01

Direct numerical simulations of turbulent channel flows are carried out over two surfaces: a synthesized sand-grain surface and a realistic turbine roughness that is characterized by more prominent large-scale surface features. To separate the effects of wall-normal variation of the roughness area fraction from the (true) variation of flow statistics, the governing equations are area-averaged using intrinsic averaging, contrary to the usually practice based on the total area (i.e., superficial averaging). Additional terms appear in the mean-momentum equation resulted from the wall-normal variation of the solid fraction and play a role in the near-wall balance. Results from surfaces with a step solidity function (e.g., cubes) will also be discussed. Compared to the sand grains, the turbine surface generates stronger form-induced fluctuations, despite weaker dispersive shear stress. This is associated with more significant form-induced productions (comparable to shear production) in Reynolds stress budgets, weaker pressure work, and, consequently, more anisotropic redistribution of turbulent kinetic energy in the roughness sublayer, which potentially leads to different turbulent responses between the two surfaces in non-equilibrium flows.

PSI-BOIL, a building block towards the multi-scale modeling of flow boiling phenomena

International Nuclear Information System (INIS)

Niceno, Bojan; Andreani, Michele; Prasser, Horst-Michael

2008-01-01

Full text of publication follows: In these work we report the current status of the Swiss project Multi-scale Modeling Analysis (MSMA), jointly financed by PSI and Swissnuclear. The project aims at addressing the multi-scale (down to nano-scale) modelling of convective boiling phenomena, and the development of physically-based closure laws for the physical scales appropriate to the problem considered, to be used within Computational Fluid Dynamics (CFD) codes. The final goal is to construct a new computational tool, called Parallel Simulator of Boiling phenomena (PSI-BOIL) for the direct simulation of processes all the way down to the small-scales of interest and an improved CFD code for the mechanistic prediction of two-phase flow and heat transfer in the fuel rod bundle of a nuclear reactor. An improved understanding of the physics of boiling will be gained from the theoretical work as well as from novel small- and medium scale experiments targeted to assist the development of closure laws. PSI-BOIL is a computer program designed for efficient simulation of turbulent fluid flow and heat transfer phenomena in simple geometries. Turbulence is simulated directly (DNS) and its efficiency plays a vital role in a successful simulation. Having high performance as one of the main prerequisites, PSIBOIL is tailored in such a way to be as efficient a tool as possible, relying on well-established numerical techniques and sacrificing all the features which are not essential for the success of this project and which might slow down the solution procedure. The governing equations are discretized in space with orthogonal staggered finite volume method. Time discretization is performed with projection method, the most obvious a the most widely used choice for DNS. Systems of linearized equation, stemming from the discretization of governing equations, are solved with the Additive Correction Multigrid (ACM). methods. Two distinguished features of PSI-BOIL are the possibility to

Spectrally-consistent regularization modeling of turbulent natural convection flows

International Nuclear Information System (INIS)

Trias, F Xavier; Gorobets, Andrey; Oliva, Assensi; Verstappen, Roel

2012-01-01

The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.

Behaviour of turbulence models near a turbulent/non-turbulent interface revisited

International Nuclear Information System (INIS)

Ferrey, P.; Aupoix, B.

2006-01-01

The behaviour of turbulence models near a turbulent/non-turbulent interface is investigated. The analysis holds as well for two-equation as for Reynolds stress turbulence models using Daly and Harlow diffusion model. The behaviour near the interface is shown not to be a power law, as usually considered, but a more complex parametric solution. Why previous works seemed to numerically confirm the power law solution is explained. Constraints for turbulence modelling, i.e., for ensuring that models have a good behaviour near a turbulent/non-turbulent interface so that the solution is not sensitive to small turbulence levels imposed in the irrotational flow, are drawn

Turbulence introduction to theory and applications of turbulent flows

CERN Document Server

Westerweel, Jerry; Nieuwstadt, Frans T M

2016-01-01

This book provides a general introduction to the topic of turbulent flows. Apart from classical topics in turbulence, attention is also paid to modern topics. After studying this work, the reader will have the basic knowledge to follow current topics on turbulence in scientific literature. The theory is illustrated with a number of examples of applications, such as closure models, numerical simulations and turbulent diffusion, and experimental findings. The work also contains a number of illustrative exercises.

Modelling turbulent fluid flows in nuclear and fossil-fired power plants

International Nuclear Information System (INIS)

Viollet, P.L.

1995-06-01

The turbulent flows encountered in nuclear reactor thermal hydraulic studies or fossil-fired plant thermo-aerodynamic analyses feature widely varying characteristics, frequently entailing heat transfers and two-phase flows so that modelling these phenomena tends more and more to involve coupling between several branches of engineering. Multi-scale geometries are often encountered, with complex wall shapes, such as a PWR vessel, a reactor coolant pump impeller or a circulating fluidized bed combustion chamber. When it comes to validating physical models of these flows, the analytical process highlights the main descriptive parameters of local flow conditions: tensor characterizing the turbulence anisotropy, characteristic time scales for turbulent flow particle dynamics. Cooperative procedures implemented between national or international working parties can accelerate validation by sharing and exchanging results obtained by the various organizations involved. With this principle accepted, we still have to validate the products themselves, i.e. the software used for the studies. In this context, the ESTET, ASTRID and N3S codes have been subjected to a battery of test cases covering their respective fields of application. These test cases are re-run for each new version, so that the sets of test cases systematically benefit from the gradually upgraded functionalities of the codes. (author). refs., 3 figs., 6 tabs

A multi-phase ferrofluid flow model with equation of state for thermomagnetic pumping and heat transfer

Energy Technology Data Exchange (ETDEWEB)

Aursand, Eskil, E-mail: eskil.aursand@sintef.no; Gjennestad, Magnus Aa.; Yngve Lervåg, Karl; Lund, Halvor

2016-03-15

A one-dimensional multi-phase flow model for thermomagnetically pumped ferrofluid with heat transfer is proposed. The thermodynamic model is a combination of a simplified particle model and thermodynamic equations of state for the base fluid. The magnetization model is based on statistical mechanics, taking into account non-uniform particle size distributions. An implementation of the proposed model is validated against experiments from the literature, and found to give good predictions for the thermomagnetic pumping performance. However, the results reveal a very large sensitivity to uncertainties in heat transfer coefficient predictions. - Highlights: • A multi-phase flow model for thermomagnetically pumped ferrofluid is proposed. • An implementation is validated against experiments from the literature. • Predicted thermomagnetic pumping effect agrees with experiments. • However, a very large sensitivity to heat transfer coefficient is revealed.

Tendency to occupy a statistically dominant spatial state of the flow as a driving force for turbulent transition.

Science.gov (United States)

Chekmarev, Sergei F

2013-03-01

The transition from laminar to turbulent fluid motion occurring at large Reynolds numbers is generally associated with the instability of the laminar flow. On the other hand, since the turbulent flow characteristically appears in the form of spatially localized structures (e.g., eddies) filling the flow field, a tendency to occupy such a structured state of the flow cannot be ruled out as a driving force for turbulent transition. To examine this possibility, we propose a simple analytical model that treats the flow as a collection of localized spatial structures, each of which consists of elementary cells in which the behavior of the particles (atoms or molecules) is uncorrelated. This allows us to introduce the Reynolds number, associating it with the ratio between the total phase volume for the system and that for the elementary cell. Using the principle of maximum entropy to calculate the most probable size distribution of the localized structures, we show that as the Reynolds number increases, the elementary cells group into the localized structures, which successfully explains turbulent transition and some other general properties of turbulent flows. An important feature of the present model is that a bridge between the spatial-statistical description of the flow and hydrodynamic equations is established. We show that the basic assumptions underlying the model, i.e., that the particles are indistinguishable and elementary volumes of phase space exist in which the state of the particles is uncertain, are involved in the derivation of the Navier-Stokes equation. Taking into account that the model captures essential features of turbulent flows, this suggests that the driving force for the turbulent transition is basically the same as in the present model, i.e., the tendency of the system to occupy a statistically dominant state plays a key role. The instability of the flow at high Reynolds numbers can then be a mechanism to initiate structural rearrangement of

Experimental and numerical studies of turbulent flow in an in-line tube bundles

Directory of Open Access Journals (Sweden)

Aounalah Mohamed

2012-04-01

Full Text Available In the present paper an experimental and a numerical simulation of the turbulent flow in an in-line tube bundles have been performed. The experiments were carried out using a subsonic wind tunnel. The pressure distributions along the tubes (22 circumferential pressure taping were determined for a variation of the azimuthal angle from 0 to 360deg. The drag and lift forces are measured using the TE 44 balance. The Navier-Stokes equations of the turbulent flow are solved using Reynolds Stress and K-ε, turbulence models (RANS provided by Fluent CFD code. An adapted grid using static pressure, pressure coefficient and velocity gradient, furthermore, a second order upwind scheme were used. The obtained results from the experimental and numerical studies show a satisfactory agreement.

MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow

International Nuclear Information System (INIS)

Jirkovsky, L.; Bo-ot, L. Ma.; Chiang, C. M.

2010-01-01

We derive higher order magneto-hydrodynamic (MHD) equations from a microscopic picture using projection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number. (physics of gases, plasmas, and electric discharges)

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

Directory of Open Access Journals (Sweden)

Saluto Lidia

2016-06-01

Full Text Available We investigate the evolution equation for the average vortex length per unit volume L of superfluid turbulence in inhomogeneous flows. Inhomogeneities in line density L andincounterflowvelocity V may contribute to vortex diffusion, vortex formation and vortex destruction. We explore two different families of contributions: those arising from asecondorder expansionofthe Vinenequationitself, andthose whichare notrelated to the original Vinen equation but must be stated by adding to it second-order terms obtained from dimensional analysis or other physical arguments.

A Generalized turbulent dispersion model for bubbly flow numerical simulation in NEPTUNE-CFD

Energy Technology Data Exchange (ETDEWEB)

Laviéville, Jérôme, E-mail: Jerome-marcel.lavieville@edf.fr; Mérigoux, Nicolas, E-mail: nicolas.merigoux@edf.fr; Guingo, Mathieu, E-mail: mathieu.guingo@edf.fr; Baudry, Cyril, E-mail: Cyril.baudry@edf.fr; Mimouni, Stéphane, E-mail: stephane.mimouni@edf.fr

2017-02-15

The NEPTUNE-CFD code, based upon an Eulerian multi-fluid model, is developed within the framework of the NEPTUNE project, financially supported by EDF (Electricité de France), CEA (Commissariat à l’Energie Atomique et aux Energies Alternatives), IRSN (Institut de Radioprotection et de Sûreté Nucléaire) and AREVA-NP. NEPTUNE-CFD is mainly focused on Nuclear Safety applications involving two-phase water-steam flows, like two-phase Pressurized Shock (PTS) and Departure from Nucleate Boiling (DNB). Many of these applications involve bubbly flows, particularly, for application to flows in PWR fuel assemblies, including studies related to DNB. Considering a very usual model for interfacial forces acting on bubbles, including drag, virtual mass and lift forces, the turbulent dispersion force is often added to moderate the lift effect in orthogonal directions to the main flow and get the right dispersion shape. This paper presents a formal derivation of this force, considering on the one hand, the fluctuating part of drag and virtual mass, and on the other hand, Turbulent Pressure derivation obtained by comparison between Lagrangian and Eulerian description of bubbles motion. An extension of the Tchen’s theory is used to express the turbulent kinetic energy of bubbles and the two-fluid turbulent covariance tensor in terms of liquid turbulent velocities and time scale. The model obtained by this way, called Generalized Turbulent Dispersion Model (GTD), does not require any user parameter. The model is validated against Liu & Bankoff air-water experiment, Arizona State University (ASU) experiment, DEBORA experiment and Texas A&M University (TAMU) boiling flow experiments.

Computer investigations of the turbulent flow around a NACA2415 airfoil wind turbine

Science.gov (United States)

Driss, Zied; Chelbi, Tarek; Abid, Mohamed Salah

2015-12-01

In this work, computer investigations are carried out to study the flow field developing around a NACA2415 airfoil wind turbine. The Navier-Stokes equations in conjunction with the standard k-ɛ turbulence model are considered. These equations are solved numerically to determine the local characteristics of the flow. The models tested are implemented in the software "SolidWorks Flow Simulation" which uses a finite volume scheme. The numerical results are compared with experiments conducted on an open wind tunnel to validate the numerical results. This will help improving the aerodynamic efficiency in the design of packaged installations of the NACA2415 airfoil type wind turbine.

Procedure for the direct numerical simulation of turbulent flows in plane channels and annuli and its application in the development of turbulence models

Energy Technology Data Exchange (ETDEWEB)

Schumann, U

1973-10-01

Thesis. Submitted to Technische Hochschule, Karlsruhe (West Germany). A numerical difference scheme is described to simulate threedimensional, time- dependent, turbulent flows of incompressible fluids at high Reynolds numbers in a plane channel and in concertric annuli. Starting from the results of Deardorff, the NavierStokes equations, averaged over grid volumes, are integrated. For description of the subgrid scale motion a novel model has been developed which takes into account strongly inhomogeneous turbulence and grid volumes of unequal side lengths. The premises used in the model are described and discussed. Stability criteria are established for this method and for similar difference schemes. For computation of the pressure field the appropriate Poisson's equation is solved accurately, except for rounding errors, by Fast Fourier Transform. The procedure implemented in the TURBIT-1 program is used to simulate turbulent flows in a plane channel and an annulus of 5: 1 ratio of radii. For both types of flow, different cases are realized with a maximum number of grid volumes of 65536. For rather small grid volume numbers the numerical results are in good agreement with experimental values. Especially the velocity profile and the mean velocity fluctuations are computed with significantly better accuracy than in earlier, direct simulations. The energy --length-scale model and the pressurestrain correlation are used as examples to show that the method may be used successfully to evaluate the parameters of turbulence models. Earlier results are reviewed and proposals for future research are made. (auth)

Impact of large scale flows on turbulent transport

Energy Technology Data Exchange (ETDEWEB)

Sarazin, Y [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Grandgirard, V [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Dif-Pradalier, G [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Fleurence, E [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Garbet, X [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Ghendrih, Ph [Association Euratom-CEA, CEA/DSM/DRFC centre de Cadarache, 13108 St-Paul-Lez-Durance (France); Bertrand, P [LPMIA-Universite Henri Poincare Nancy I, Boulevard des Aiguillettes BP239, 54506 Vandoe uvre-les-Nancy (France); Besse, N [LPMIA-Universite Henri Poincare Nancy I, Boulevard des Aiguillettes BP239, 54506 Vandoe uvre-les-Nancy (France); Crouseilles, N [IRMA, UMR 7501 CNRS/Universite Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg (France); Sonnendruecker, E [IRMA, UMR 7501 CNRS/Universite Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg (France); Latu, G [LSIIT, UMR 7005 CNRS/Universite Louis Pasteur, Bd Sebastien Brant BP10413, 67412 Illkirch (France); Violard, E [LSIIT, UMR 7005 CNRS/Universite Louis Pasteur, Bd Sebastien Brant BP10413, 67412 Illkirch (France)

2006-12-15

The impact of large scale flows on turbulent transport in magnetized plasmas is explored by means of various kinetic models. Zonal flows are found to lead to a non-linear upshift of turbulent transport in a 3D kinetic model for interchange turbulence. Such a transition is absent from fluid simulations, performed with the same numerical tool, which also predict a much larger transport. The discrepancy cannot be explained by zonal flows only, despite they being overdamped in fluids. Indeed, some difference remains, although reduced, when they are artificially suppressed. Zonal flows are also reported to trigger transport barriers in a 4D drift-kinetic model for slab ion temperature gradient (ITG) turbulence. The density gradient acts as a source drive for zonal flows, while their curvature back stabilizes the turbulence. Finally, 5D simulations of toroidal ITG modes with the global and full-f GYSELA code require the equilibrium density function to depend on the motion invariants only. If not, the generated strong mean flows can completely quench turbulent transport.

Impact of large scale flows on turbulent transport

International Nuclear Information System (INIS)

Sarazin, Y; Grandgirard, V; Dif-Pradalier, G; Fleurence, E; Garbet, X; Ghendrih, Ph; Bertrand, P; Besse, N; Crouseilles, N; Sonnendruecker, E; Latu, G; Violard, E

2006-01-01

The impact of large scale flows on turbulent transport in magnetized plasmas is explored by means of various kinetic models. Zonal flows are found to lead to a non-linear upshift of turbulent transport in a 3D kinetic model for interchange turbulence. Such a transition is absent from fluid simulations, performed with the same numerical tool, which also predict a much larger transport. The discrepancy cannot be explained by zonal flows only, despite they being overdamped in fluids. Indeed, some difference remains, although reduced, when they are artificially suppressed. Zonal flows are also reported to trigger transport barriers in a 4D drift-kinetic model for slab ion temperature gradient (ITG) turbulence. The density gradient acts as a source drive for zonal flows, while their curvature back stabilizes the turbulence. Finally, 5D simulations of toroidal ITG modes with the global and full-f GYSELA code require the equilibrium density function to depend on the motion invariants only. If not, the generated strong mean flows can completely quench turbulent transport

Inner-outer predictive wall model for wall-bounded turbulence in hypersonic flow

Science.gov (United States)

Martin, M. Pino; Helm, Clara M.

2017-11-01

The inner-outer predictive wall model of Mathis et al. is modified for hypersonic turbulent boundary layers. The model is based on a modulation of the energized motions in the inner layer by large scale momentum fluctuations in the logarithmic layer. Using direct numerical simulation (DNS) data of turbulent boundary layers with free stream Mach number 3 to 10, it is shown that the variation of the fluid properties in the compressible flows leads to large Reynolds number (Re) effects in the outer layer and facilitate the modulation observed in high Re incompressible flows. The modulation effect by the large scale increases with increasing free-stream Mach number. The model is extended to include spanwise and wall-normal velocity fluctuations and is generalized through Morkovin scaling. Temperature fluctuations are modeled using an appropriate Reynolds Analogy. Density fluctuations are calculated using an equation of state and a scaling with Mach number. DNS data are used to obtain the universal signal and parameters. The model is tested by using the universal signal to reproduce the flow conditions of Mach 3 and Mach 7 turbulent boundary layer DNS data and comparing turbulence statistics between the modeled flow and the DNS data. This work is supported by the Air Force Office of Scientific Research under Grant FA9550-17-1-0104.

Explicit formulas for the computation of friction factors in turbulent pipe flow

International Nuclear Information System (INIS)

Selander, W.N.

1978-11-01

For fully developed turbulent flow in smooth or rough circular pipe, the friction factor depends on the Reynolds number and on the roughness parameter through an implicit equation, which must usually be solved by an iterative numerical method. In this report we derive several approximate methods for the explicit evaluation of friction factors, with specific reference to the Colebrook-White equation. The accuracy and convenience of each method is discussed and formulas for practical use are recommended. (author)

Electromotive force and large-scale magnetic dynamo in a turbulent flow with a mean shear.

Science.gov (United States)

Rogachevskii, Igor; Kleeorin, Nathan

2003-09-01

An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a "shear-current" effect. A mean velocity shear results in an anisotropy of turbulent magnetic diffusion. A contribution to the electromotive force related to the symmetric parts of the gradient tensor of the mean magnetic field (the kappa effect) is found in nonrotating turbulent flows with a mean shear. The kappa effect and turbulent magnetic diffusion reduce the growth rate of the mean magnetic field. It is shown that a mean magnetic field can be generated when the exponent of the energy spectrum of the background turbulence (without the mean velocity shear) is less than 2. The shear-current effect was studied using two different methods: the tau approximation (the Orszag third-order closure procedure) and the stochastic calculus (the path integral representation of the solution of the induction equation, Feynman-Kac formula, and Cameron-Martin-Girsanov theorem). Astrophysical applications of the obtained results are discussed.

Wall modeled large eddy simulations of complex high Reynolds number flows with synthetic inlet turbulence

International Nuclear Information System (INIS)

Patil, Sunil; Tafti, Danesh

2012-01-01

Highlights: ► Large eddy simulation. ► Wall layer modeling. ► Synthetic inlet turbulence. ► Swirl flows. - Abstract: Large eddy simulations of complex high Reynolds number flows are carried out with the near wall region being modeled with a zonal two layer model. A novel formulation for solving the turbulent boundary layer equation for the effective tangential velocity in a generalized co-ordinate system is presented and applied in the near wall zonal treatment. This formulation reduces the computational time in the inner layer significantly compared to the conventional two layer formulations present in the literature and is most suitable for complex geometries involving body fitted structured and unstructured meshes. The cost effectiveness and accuracy of the proposed wall model, used with the synthetic eddy method (SEM) to generate inlet turbulence, is investigated in turbulent channel flow, flow over a backward facing step, and confined swirling flows at moderately high Reynolds numbers. Predictions are compared with available DNS, experimental LDV data, as well as wall resolved LES. In all cases, there is at least an order of magnitude reduction in computational cost with no significant loss in prediction accuracy.

Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent

International Nuclear Information System (INIS)

Bettencourt, João H; López, Cristóbal; Hernández-García, Emilio

2013-01-01

In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Experimental characterization of extreme events of inertial dissipation in a turbulent swirling flow

Science.gov (United States)

Saw, E. -W.; Kuzzay, D.; Faranda, D.; Guittonneau, A.; Daviaud, F.; Wiertel-Gasquet, C.; Padilla, V.; Dubrulle, B.

2016-01-01

The three-dimensional incompressible Navier–Stokes equations, which describe the motion of many fluids, are the cornerstones of many physical and engineering sciences. However, it is still unclear whether they are mathematically well posed, that is, whether their solutions remain regular over time or develop singularities. Even though it was shown that singularities, if exist, could only be rare events, they may induce additional energy dissipation by inertial means. Here, using measurements at the dissipative scale of an axisymmetric turbulent flow, we report estimates of such inertial energy dissipation and identify local events of extreme values. We characterize the topology of these extreme events and identify several main types. Most of them appear as fronts separating regions of distinct velocities, whereas events corresponding to focusing spirals, jets and cusps are also found. Our results highlight the non-triviality of turbulent flows at sub-Kolmogorov scales as possible footprints of singularities of the Navier–Stokes equation. PMID:27578459

Inception of supraglacial channelization under turbulent flow conditions

Science.gov (United States)

Mantelli, E.; Camporeale, C.; Ridolfi, L.

2013-12-01

Glacier surfaces exhibit an amazing variety of meltwater-induced morphologies, ranging from small scale ripples and dunes on the bed of supraglacial channels to meandering patterns, till to large scale drainage networks. Even though the structure and geometry of these morphologies play a key role in the glacier melting processes, the physical-based modeling of such spatial patterns have attracted less attention than englacial and subglacial channels. In order to partially fill this gap, our work concerns the large scale channelization occurring on the ice slopes and focuses on the role of turbulence on the wavelength selection processes during the channelization inception. In a recent study[1], two of us showed that the morphological instability induced by a laminar film flowing over an ice bed is characterized by transversal length scales of order of centimeters. Being these scales much smaller than the spacing observed in the channelization of supraglacial drainage networks (that are of order of meters) and considering that the water films flowing on glaciers can exhibit Reynolds numbers larger than 104, we investigated the role of turbulence in the inception of channelization. The flow-field is modeled by means of two-dimensional shallow water equations, where Reynolds stresses are also considered. In the depth-averaged heat balance equation an incoming heat flux from air is assumed and forced convection heat exchange with the wall is taken into account, in addition to convection and diffusion in the liquid. The temperature profile in the ice is finally coupled to the liquid through Stefan equation. We then perform a linear stability analysis and, under the assumption of small Stefan number, we solve the differential eigenvalue problem analytically. As main outcome of such an analysis, the morphological instability of the ice-water interface is detected and investigated in a wide range of the independent parameters: longitudinal and transversal wavenumbers

Homogeneous purely buoyancy driven turbulent flow

Science.gov (United States)

Arakeri, Jaywant; Cholemari, Murali; Pawar, Shashikant

2010-11-01

An unstable density difference across a long vertical tube open at both ends leads to convection that is axially homogeneous with a linear density gradient. We report results from such tube convection experiments, with driving density caused by salt concentration difference or temperature difference. At high enough Rayleigh numbers (Ra) the convection is turbulent with zero mean flow and zero mean Reynolds shear stresses; thus turbulent production is purely by buoyancy. We observe different regimes of turbulent convection. At very high Ra the Nusselt number scales as the square root of the Rayleigh number, giving the so-called "ultimate regime" of convection predicted for Rayleigh-Benard convection in limit of infinite Ra. Turbulent convection at intermediate Ra, the Nusselt number scales as Ra^0.3. In both regimes, the flux and the Taylor scale Reynolds number are more than order of magnitude larger than those obtained in Rayleigh-Benard convection. Absence of a mean flow makes this an ideal flow to study shear free turbulence near a wall.

Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence

Science.gov (United States)

Grebenev, V. N.; Wacławczyk, M.; Oberlack, M.

2017-10-01

We study the statistical properties of the vorticity field in two-dimensional turbulence. The field is described in terms of the infinite Lundgren-Monin-Novikov (LMN) chain of equations for multi-point probability density functions (pdf’s) of vorticity. We perform a Lie group analysis of the first equation in this chain using the direct method based on the canonical Lie-Bäcklund transformations devised for integro-differential equations. We analytically show that the conformal group is broken for the first LMN equation i.e. for the 1-point pdf at least for the inviscid case but the equation is still conformally invariant on the associated characteristic with zero-vorticity. Then, we demonstrate that this characteristic is conformally transformed. We find this outcome coincides with the numerical results about the conformal invariance of the statistics of zero-vorticity isolines, see e.g. Falkovich (2007 Russian Math. Surv. 63 497-510). The conformal symmetry can be understood as a ‘local scaling’ and its traces in two-dimensional turbulence were already discussed in the literature, i.e. it was conjectured more than twenty years ago in Polyakov (1993 Nucl. Phys. B 396 367-85) and clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124-8).

Advances in engineering turbulence modeling. [computational fluid dynamics

Science.gov (United States)

Shih, T.-H.

1992-01-01

Some new developments in two equation models and second order closure models are presented. In this paper, modified two equation models are proposed to remove shortcomings such as computing flows over complex geometries and the ad hoc treatment near the separation and reattachment points. The calculations using various two equation models are compared with direct numerical solutions of channel flows and flat plate boundary layers. Development of second order closure models will also be discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All existing models poorly predict the normal stresses near the wall and fail to predict the three dimensional effect of mean flow on the turbulence. The newly developed second order near-wall turbulence model to be described in this paper is capable of capturing the near-wall behavior of turbulence as well as the effect of three dimension mean flow on the turbulence.

Analysis of zonal flow bifurcations in 3D drift wave turbulence simulations

International Nuclear Information System (INIS)

Kammel, Andreas

2012-01-01

The main issue of experimental magnetic fusion devices lies with their inherently high turbulent transport, preventing long-term plasma confinement. A deeper understanding of the underlying transport processes is therefore desirable, especially in the high-gradient tokamak edge which marks the location of the drift wave regime as well as the outer boundary of the still badly understood high confinement mode. One of the most promising plasma features possibly connected to a complete bifurcation theory for the transition to this H-mode is found in large-scale phenomena capable of regulating radial transport through vortex shearing - i.e. zonal flows, linearly stable large-scale poloidal vector E x vector B-modes based on radial flux surface averages of the potential gradient generated through turbulent self-organization. Despite their relevance, few detailed turbulence studies of drift wave-based zonal flows have been undertaken, and none of them have explicitly targeted bifurcations - or, within a resistive sheared-slab environment, observed zonal flows at all. In this work, both analytical means and the two-fluid code NLET are used to analyze a reduced set of Hasegawa-Wakatani equations, describing a sheared collisional drift wave system without curvature. The characteristics of the drift waves themselves, as well as those of the drift wave-based zonal flows and their retroaction on the drift wave turbulence are examined. The single dimensionless parameter ρ s proposed in previous analytical models is examined numerically and shown to divide the drift wave scale into two transport regimes, the behavioral characteristics of which agree perfectly with theoretical expectations. This transport transition correlates with a transition from pure drift wave turbulence at low ρ s into the high-ρ s zonal flow regime. The associated threshold has been more clearly identified by tracing it back to a tipping of the ratio between a newly proposed frequency gradient length at

Turbulence modeling for flows around convex features giving rapid eddy distortion

International Nuclear Information System (INIS)

Tucker, P.G.; Liu, Y.

2007-01-01

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, Re W ≤ 2.5 x 10 3 . The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's ν t -92; Secundov et al.'s two equation ν t -L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with Re W ∼ 2.5 x 10 3 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov ν t -92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from Re W = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for Re W W = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results

Momentum and scalar transport in a localised synthetic turbulence in a channel flow with a short contraction

Energy Technology Data Exchange (ETDEWEB)

Lefeuvre, N; Djenidi, L [University of Newcastle, NSW Australia (Australia); Tardu, S, E-mail: nathan.lefeuvre@uon.edu.au [Laboratoire des Ecoulements Geophysiques et Industriels (LEGI), Grenoble (France)

2011-12-22

A numerical simulation is undertaken to investigate the transport of momentum and a passive scalar in a localised turbulence in a channel with a contraction. The simulation is carried out using a hybrid method which combines the lattice Boltzmann method (LBM, for the velocity field) and the energy equation (for the temperature field). The localised turbulence is generated through pulsed jets issued in the Poiseuille flow developing in the channel at a Reynolds number of about 1000. The aim of the study is twofold : i) determine effect of the contraction on the localised turbulence, and ii) study how the passive scalar behaves in such contracted localised turbulence. The contraction increase the averaged vorticity in the channel flow, which is accompanied by an increase in the averaged kinetic energy. The contraction also tends to reduce the Reynolds stresses. These results are similar those obtained in turbulent pipe flow with an axisymmetric contraction and in a turbulent boundary layer subjected to a favourable pressure gradient. However, it is found that the heat transport in the normal to the wall direction is more dramatically affected (reduced) than that in the direction of the flow.

Flowing and heat transfer characteristics of turbulent flow in typical rod bundles at rolling motion

International Nuclear Information System (INIS)

Yan Binghuo; Yu Lei; Gu Hanyang

2011-01-01

The influence mechanism of rolling motion on the flowing and heat transfer characteristics of turbulent flow in typical four rod bundles was investigated with Fluent code. The flowing and heat transfer characteristics of turbulent flow in rod bundles can be affected by rolling motion. But the flowing similarity of turbulent flow in adiabatic and non-adiabatic can not be affected. If the rolling period is small, the radial additional force can make the parameter profiles, the turbulent flowing and heat transfer change greatly. At rolling motion, as the pitch to diameter ratio decreases, especially if it is less than 1.1, the flowing and heat transfer of turbulent flow at rolling motion change significantly. The variation of pitch to diameter ratio can change the profiles of secondary flow and turbulent kinetic energy in cross-section greatly. (authors)

On the turbulent flow in piston engines: Coupling of statistical theory quantities and instantaneous turbulence

Energy Technology Data Exchange (ETDEWEB)

Zentgraf, Florian; Baum, Elias; Dreizler, Andreas [Fachgebiet Reaktive Strömungen und Messtechnik (RSM), Center of Smart Interfaces (CSI), Technische Universität Darmstadt, Jovanka-Bontschits-Straße 2, 64287 Darmstadt (Germany); Böhm, Benjamin [Fachgebiet Energie und Kraftwerkstechnik (EKT), Technische Universität Darmstadt, Jovanka-Bontschits-Straße 2, 64287 Darmstadt (Germany); Peterson, Brian, E-mail: brian.peterson@ed.ac.uk [Department of Mechanical Engineering, School of Engineering, Institute for Energy Systems, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, Scotland (United Kingdom)

2016-04-15

Planar particle image velocimetry (PIV) and tomographic PIV (TPIV) measurements are utilized to analyze turbulent statistical theory quantities and the instantaneous turbulence within a single-cylinder optical engine. Measurements are performed during the intake and mid-compression stroke at 800 and 1500 RPM. TPIV facilitates the evaluation of spatially resolved Reynolds stress tensor (RST) distributions, anisotropic Reynolds stress invariants, and instantaneous turbulent vortical structures. The RST analysis describes distributions of individual velocity fluctuation components that arise from unsteady turbulent flow behavior as well as cycle-to-cycle variability (CCV). A conditional analysis, for which instantaneous PIV images are sampled by their tumble center location, reveals that CCV and turbulence have similar contributions to RST distributions at the mean tumble center, but turbulence is dominant in regions peripheral to the tumble center. Analysis of the anisotropic Reynolds stress invariants reveals the spatial distribution of axisymmetric expansion, axisymmetric contraction, and 3D isotropy within the cylinder. Findings indicate that the mid-compression flow exhibits a higher tendency toward 3D isotropy than the intake flow. A novel post-processing algorithm is utilized to classify the geometry of instantaneous turbulent vortical structures and evaluate their frequency of occurrence within the cylinder. Findings are coupled with statistical theory quantities to provide a comprehensive understanding of the distribution of turbulent velocity components, the distribution of anisotropic states of turbulence, and compare the turbulent vortical flow distribution that is theoretically expected to what is experimentally observed. The analyses reveal requisites of important turbulent flow quantities and discern their sensitivity to the local flow topography and engine operation.

Turbulence models in supersonic flows

International Nuclear Information System (INIS)

Shirani, E.; Ahmadikia, H.; Talebi, S.

2001-05-01

The aim of this paper is to evaluate five different turbulence models when used in rather complicated two-dimensional and axisymmetric supersonic flows. They are Baldwin-Lomax, k-l, k-ε, k-ω and k-ζ turbulence models. The compressibility effects, axisymmetric correction terms and some modifications for transition region are used and tested in the models. Two computer codes based on the control volume approach and two flux-splitting methods. Roe and Van Leer, are developed. The codes are used to simulate supersonic mixing layers, flow behind axisymmetric body, under expanded jet, and flow over hollow cylinder flare. The results are compared with experimental data and behavior of the turbulence models is examined. It is shown that both k-l and k-ζ models produce very good results. It is also shown that the compressibility correction in the model is required to obtain more accurate results. (author)

Aggregate formation in 3D turbulent-like flows

NARCIS (Netherlands)

Dominguez, A.; Clercx, H.J.H.

2006-01-01

Aggregate formation is an important process in industrial and environmental turbulent flows. In oceans turbulence play an important role on Marine Snow (aggregate) formation. For a proper description, the study of aggregate formation in turbulent flows requires a particle based model i.e. following

Unsteady motion and transition to turbulence in developing curved duct flow

International Nuclear Information System (INIS)

Arnal, M.; Firmino, F.; Humphrey, J.A.C.

1987-01-01

An experiment was performed to further the understanding of developing flows in curved ducts of square cross-section. Unlike most earlier works, attention was paid to investigating the time-dependent character of the motion. Mean and unsteady flow characteristics were determined using flow visualization and a laser-Doppler velocimeter. Only one velocity component, that aligned in the longitudinal (streamwise) coordinate direction, was measured. Notwithstanding, the time histories, autocorrelations and spectra derived reveal a time-periodic motion that becomes turbulent with increasing Reynolds number. The results are of intrinsic fundamental value and also illustrate the danger of imposing symmetry of the conservation equations on numerical solutions of this flow. 24 references

A computational technique for turbulent flow of wastewater sludge.

Science.gov (United States)

Bechtel, Tom B

2005-01-01

A computational fluid dynamics (CFD) technique applied to the turbulent flow of wastewater sludge in horizontal, smooth-wall, circular pipes is presented. The technique uses the Crank-Nicolson finite difference method in conjunction with the variable secant method, an algorithm for determining the pressure gradient of the flow. A simple algebraic turbulence model is used. A Bingham-plastic rheological model is used to describe the shear stress/shear rate relationship for the wastewater sludge. The method computes velocity gradient and head loss, given a fixed volumetric flow, pipe size, and solids concentration. Solids concentrations ranging from 3 to 10% (by weight) and nominal pipe sizes from 0.15 m (6 in.) to 0.36 m (14 in.) are studied. Comparison of the CFD results for water to established values serves to validate the numerical method. The head loss results are presented in terms of a head loss ratio, R(hl), which is the ratio of sludge head loss to water head loss. An empirical equation relating R(hl) to pipe velocity and solids concentration, derived from the results of the CFD calculations, is presented. The results are compared with published values of Rhl for solids concentrations of 3 and 6%. A new expression for the Fanning friction factor for wastewater sludge flow is also presented.

CISM-IUTAM School on Advanced Turbulent Flow Computations

CERN Document Server

Krause, Egon

2000-01-01

This book collects the lecture notes concerning the IUTAM School on Advanced Turbulent Flow Computations held at CISM in Udine September 7–11, 1998. The course was intended for scientists, engineers and post-graduate students interested in the application of advanced numerical techniques for simulating turbulent flows. The topic comprises two closely connected main subjects: modelling and computation, mesh pionts necessary to simulate complex turbulent flow.

Modeling of turbulent flows in porous media and at the interface with a free fluid medium; Modelisation des ecoulements turbulents dans les milieux poreux et a l'interface avec un milieu libre

Energy Technology Data Exchange (ETDEWEB)

Chandesris, M

2006-12-15

This work deals with the numerical simulation of turbulent flows in the whole nuclear reactor core, using multi-scale approaches. First, a macroscopic turbulence model is built, based on a porous media approach, to describe the flow in the fuel assemblies part of the nuclear core. Then, we study the jump conditions that have to be applied at a free fluid/porous interface. A thorough analytical study is carried out for laminar flows. This study allows to answer some fundamental questions about the physical meaning of the jump conditions, the values of the jump parameters and the location of the interface. Using these results, jump conditions for turbulent flows are proposed. The model is then applied to the simulation of a turbulent flow in a simplified model of a reactor core. (author)

Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis

KAUST Repository

Wacks, Daniel H.

2016-12-02

The distributions of flow topologies within the flames representing the corrugated flamelets, thin reaction zones, and broken reaction zone regimes of premixed turbulent combustion are investigated using direct numerical simulation data of statistically planar turbulent H-2-air flames with an equivalence ratio phi = 0.7. It was found that the diminishing influence of dilatation rate with increasing Karlovitz number has significant influences on the statistical behaviors of the first, second, and third invariants (i.e., P, Q, and R) of the velocity gradient tensor. These differences are reflected in the distributions of the flow topologies within the flames considered in this analysis. This has important consequences for those topologies that make dominant contributions to the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively. Detailed physical explanations are provided for the observed regime dependences of the flow topologies and their implications on the scalar dissipation rate and enstrophy transport.

Flow topologies in different regimes of premixed turbulent combustion: A direct numerical simulation analysis

KAUST Repository

Wacks, Daniel H.; Chakraborty, Nilanjan; Klein, Markus; Arias, Paul G.; Im, Hong G.

2016-01-01

The distributions of flow topologies within the flames representing the corrugated flamelets, thin reaction zones, and broken reaction zone regimes of premixed turbulent combustion are investigated using direct numerical simulation data of statistically planar turbulent H-2-air flames with an equivalence ratio phi = 0.7. It was found that the diminishing influence of dilatation rate with increasing Karlovitz number has significant influences on the statistical behaviors of the first, second, and third invariants (i.e., P, Q, and R) of the velocity gradient tensor. These differences are reflected in the distributions of the flow topologies within the flames considered in this analysis. This has important consequences for those topologies that make dominant contributions to the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively. Detailed physical explanations are provided for the observed regime dependences of the flow topologies and their implications on the scalar dissipation rate and enstrophy transport.

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

Science.gov (United States)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

Science.gov (United States)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Numerical prediction of forces for turbulent flow around a ship rudder

International Nuclear Information System (INIS)

Rafi, H.; Raza, A.; Bilal, S.; Zahir, S.; Khan, M.A.

2004-01-01

The three dimensional Navier Stokes equations with the standard k-epsilon turbulence model are solved for incompressible turbulent flows around the ship rudder placed in a uniform flow. The solution was obtained using second order high-resolution advection scheme on an unstructured grid. A wall function is used for realizing the no slip condition at walls. Computations were performed on a rudder at two different Reynolds numbers with angle of attack ranging from 0 to 26 degrees. The present results are compared as CFD-Experimental and CFD-CFD in the form of lift and drag coefficients for different degrees of deflection and are in good agreement with the experimental measurements and with the other author's computational results. The calculated stall angles and maximum lift at stall angles are slightly smaller as compared to experimental results. (author)

Evaluation of turbulence models for turbomachinery unsteady three-dimensional flows simulation; Evaluation de modeles de turbulence pour la simulation d'ecoulements tridimensionnels instationnaires en turbomachines

Energy Technology Data Exchange (ETDEWEB)

Dano, C.

2003-01-15

The objective of this thesis is to evaluate k-e, k-l and k-w low Reynolds two equation turbulence models for. A quadratic nonlinear k-l model is also implemented in this study. We analyze the two equation turbulence models capacity to predict the turbomachinery flows and the wakes. We are interested more particularly in the unsteady three dimensional configuration with rotor-stator interactions. A Gaussian distribution reproduces the upstream wake. This analysis is carried out in term of prediction quality but also in term of numerical behavior. Turbines and compressors configurations are tested. (author)

Viscous-inviscid method for the simulation of turbulent unsteady wind turbine airfoil flow

Energy Technology Data Exchange (ETDEWEB)

Bermudez, L.; Velazquez, A.; Matesanz, A. [Thermal Engineering Area, Carlos III University of Madrid, Avd. Universidad 30, 28911 Leganes, Madrid (Spain)

2002-06-01

A Viscous-inviscid interaction method is presented that allows for the simulation of unsteady airfoil flow in the context of wind turbine applications. The method couples a 2-D external unsteady potential flow to a 2-D unsteady turbulent boundary layer. The separation point on the airfoil leeward side is determined in a self-consistent way from the boundary-layer equations, and the separated flow region is modelled independently. Wake shape and motion are also determined in a self-consistent way, while an unsteady Kutta condition is implemented. The method is able to deal with attached flow and light stall situations characterised by unsteady turbulent boundary-layer separation size up to 50% of the airfoil chord length. The results of the validation campaign show that the method could be used for industrial design purposes because of its numerical robustness, reasonable accuracy, and limited computational time demands.

EFFECT OF ION ∇ B DRIFT DIRECTION ON TURBULENCE FLOW AND FLOW SHEAR

International Nuclear Information System (INIS)

FENZI, C; McKEE, G.R; BURRELL, K.H; CARLSTROM, T.N; FONCK, R.J; GROEBNER, R.J

2003-01-01

The divertor magnetic geometry has a significant effect on the poloidal flow and resulting flow shear of turbulence in the outer region of L-mode tokamak plasmas, as determined via two-dimensional measurements of density fluctuations with Beam Emission Spectroscopy on DIII-D. Plasmas with similar parameters, except that in one case the ion (del)B drift points towards the divertor X-point (lower single-null, LSN), and in the other case, the ion (del)B drift points away from the divertor X-point (upper single-null, USN), are compared. Inside of r/a=0.9, the turbulence characteristics (amplitude, flow direction, correlation lengths) are similar in both cases, while near r/a=0.92, a dramatic reversal of the poloidal flow of turbulence relative to the core flow direction is observed in plasmas with the ion (del)B drift pointing towards the divertor X-point. No such flow reversal is observed in plasmas with the ion (del)B drift pointing away from the divertor X-point. This poloidal flow reversal results in a significantly larger local shear in the poloidal turbulence flow velocity in plasmas with the ion (del)B drift pointing towards the divertor X-point. Additionally, these plasmas locally exhibit significant dispersion, with two distinct and counter-propagating turbulence modes. Likewise, the radial correlation length of the turbulence is reduced in these plasmas, consistent with biorthogonal decomposition measurements of dominant turbulence structures. The naturally occurring turbulence flow shear in these LSN plasmas may facilitate the LH transition that occurs at an input power of roughly one-half to one-third that of corresponding plasmas with the ion (del)B drift pointing away from the X-point

Turbulence modeling of the Von Karman flow: Viscous and inertial stirrings

International Nuclear Information System (INIS)

Poncet, Sebastien; Schiestel, Roland; Monchaux, Romain

2008-01-01

The present work considers the turbulent Von Karman flow generated by two counter-rotating smooth flat (viscous stirring) or bladed (inertial stirring) disks. Numerical predictions based on one-point statistical modeling using a low-Reynolds number second-order full stress transport closure (RSM model) are compared to velocity measurements performed at CEA (Commissariat a l'Energie Atomique, France). The main and significant novelty of this paper is the use of a drag force in the momentum equations to reproduce the effects of inertial stirring instead of modeling the blades themselves. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of both the dynamics and the turbulence properties in the Von Karman configuration. In particular, we highlighted the transition between the merged and separated boundary layer regimes and the one between the Batchelor [Batchelor, G.K., 1951. Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quat. J. Mech. Appl. Math. 4 (1), 29-41] and the Stewartson [Stewartson, K., 1953. On the flow between two rotating coaxial disks. Proc. Camb. Philos. Soc. 49, 333-341] flow structures in the smooth disk case. We determined also the transition between the one cell and the two cell regimes for both viscous and inertial stirrings

Direct numerical simulation of the passive scalar field in a two-dimensional turbulent channel flow

International Nuclear Information System (INIS)

Kasagi, N.; Tomita, Y.; Kuroda, A.

1991-01-01

This paper reports on a direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air that was carried out. The iso-flux condition is imposed on the walls so that the local mean temperature linearly increases in the streamwise direction. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained include rms velocity and temperature fluctuations, Reynolds stresses, turbulent heat fluxes and other higher order correlations. They are compared mainly with the DNS data obtained by Kim and Moin (1987) and Kim (1987) in a higher Reynolds number flow with isothermal walls. Agreement between these two results is generally good. Each term in the budget equations of temperature variance, its dissipation rate and turbulent heat fluxes is also calculated in order to establish a data base of convective heat transfer for thermal turbulence modeling

A structure-based model for the transport of passive scalars in homogeneous turbulent flows

International Nuclear Information System (INIS)

Panagiotou, C.F.; Kassinos, S.C.

2016-01-01

Highlights: • The Interacting Particle Representation Model (IPRM) is extended for passive scalar transport. • We develop a structure-based set of scale equations for the scalar field and couple them to the IPRM. • The complete model is evaluated for several cases of homogeneous deformation with good results. • We outline steps for coupling the new scalar scales to the Algebraic Structure-Based Model (ASBM). - Abstract: A structure-based model has been constructed, for the first time, for the study of passive scalar transport in turbulent flows. The scalar variance and the large-scale scalar gradient variance are proposed as the two turbulence scales needed for closure of the scalar equations in the framework of the Interacting Particle Representation Model (IPRM). The scalar dissipation rate is modeled in terms of the scalar variance and the large-scale enstrophy of the velocity field. Model parameters are defined by matching the decay rates in freely isotropic turbulence. The model is validated for a large number of cases of deformation in both fixed and rotating frames, showing encouraging results. The model shows good agreement with DNS results for the case of pure shear flow in the presence of either transverse or streamwise mean scalar gradient, while it correctly predicts the presence of direct cascade for the passive scalar variance in two dimensional isotropic turbulence.

Simulation of Turbulent Wake at Mixing of Two Confined Horizontal Flows

Directory of Open Access Journals (Sweden)

Rok Krpan

2018-01-01

Full Text Available The development of a turbulent mixing layer at mixing of two horizontal water streams with slightly different densities is studied by the means of numerical simulation. The mixing of such flows can be modelled as the flow of two components, where the concentration of one component in the mixing region is described as a passive scalar. The velocity field remains common over the entire computational domain, where the density and viscosity difference due to the concentration mainly affects the turbulent fluctuations in the mixing region. The numerical simulations are performed with the open source code OpenFOAM using two different approaches for turbulence modelling, Reynolds Averaged Navier Stokes equations (RANS and Large Eddy Simulation (LES. The simulation results are discussed and compared with the benchmark experiment obtained within the frame of OECD/NEA benchmark test. A good agreement with experimental results is obtained in the case of the single liquid experiment. A high discrepancy between the simulated and the experimental velocity fluctuations in the case of mixing of the flows with the slightly different densities and viscosities triggered a systematic investigation of the modelling approaches that helped us to find out and interpret the main reasons for the disagreement.

Plane waves and structures in turbulent channel flow

Science.gov (United States)

Sirovich, L.; Ball, K. S.; Keefe, L. R.

1990-01-01

A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

On turbulence structure in vertical pipe flow of fiber suspensions [refractivity, flow measurement, turbulent flow, glass fibers, fluid flow

International Nuclear Information System (INIS)

Steen, M.

1989-01-01

A suspension of glass fibers in alcohol has been used to investigate a upward vertical developing pipe flow. The refractive index of the alcohol was matched to that of the glass fibers, making the whole suspension transparent. Laser Doppler Anemometry (LDA) was applied, and fluid velocities could then be measured for consistencies up to c = 12 g/l. Radial profiles of axial U-velocity and turbulence spectra have been recorded at various positions (z/D = 2, 5, 36) downstream of an orifice (step) with 64% open area. Measurements were taken for different consistencies (c = 1.2, 12 g/l), fiber lengths (l = 1, 3 mm) and Reynolds numbers (R e = 8.5 ⋅ 10 3 , 6.5 ⋅ 10 4 ). The fiber crowding factor (n f ) has been used to discuss the observed effects of the present fibers on momentum transfer and turbulence structure. The results show both an increase (l= 1 mm, c= 1.2 g/l) and decrease (l=3 mm, c = 12 g/l) in turbulence levels in the presence of fibers. Suspensions with long fibers at the highest consistency show plug flow in parts of the core. This causes damping of the turbulence mainly at smaller length scales. For short fibers at low consistency, the increased turbulent energy was mainly observed at small length scales in the spectrum. (author)

Non-Equilibrium Turbulence and Two-Equation Modeling

Science.gov (United States)

Rubinstein, Robert

2011-01-01

Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

Science.gov (United States)

Chang, Chau-Lyan; Venkatachari, Balaji; Cheng, Gary C.

2015-01-01

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the

Large Eddy Simulations of turbulent flows with heat transfer; Simulation des grandes echelles d'ecoulements turbulents avec transferts de chaleur

Energy Technology Data Exchange (ETDEWEB)

Chatelain, A.

2004-09-15

LES of turbulent flows with heat transfer was used within the framework of conjugate heat transfer problems. The objective of this work lies not only in identifying the various elements likely to impair temperature fluctuations estimations at the fluid/solid interface but also to introduce adequate wall modeling. The choice of a proper convection scheme for the transport of passive scalars led to the adoption of a high order upwind scheme with slope limiter. The use of classical wall models having shown some weaknesses as for the estimation of parietal temperature fluctuations, two new approaches are proposed and tested. The first one relies on a complete resolution of the Navier-Stokes equations on a refined grid close to the wall making it possible to rebuild the temperature fluctuations near the wall. The second one relies on the simultaneous and one dimensional resolution of a turbulent boundary layer equation and a variance transport equation near the wall. (author)

Simulation of turbulent flows containing strong shocks

International Nuclear Information System (INIS)

Fryxell, Bruce; Menon, Suresh

2008-01-01

Simulation of turbulent flows with strong shocks is a computationally challenging problem. The requirements for a method to produce accurate results for turbulence are orthogonal to those needed to treat shocks properly. In order to prevent an unphysical rate of decay of turbulent structures, it is necessary to use a method with very low numerical dissipation. Because of this, central difference schemes are widely used. However, computing strong shocks with a central difference scheme can produce unphysical post-shock oscillations that corrupt the entire flow unless additional dissipation is added. This dissipation can be difficult to localize to the area near the shock and can lead to inaccurate treatment of the turbulence. Modern high-resolution shock-capturing methods usually use upwind algorithms to provide the dissipation necessary to stabilize shocks. However, this upwind dissipation can also lead to an unphysical rate of decay of the turbulence. This paper discusses a hybrid method for simulating turbulent flows with strong shocks that couples a high-order central difference scheme with a high-resolution shock-capturing method. The shock-capturing method is used only in the vicinity of discontinuities in the flow, whereas the central difference scheme is used in the remainder of the computational domain. Results of this new method will be shown for a variety of test problems. Preliminary results for a realistic application involving detonation in gas-particle flows will also be presented.

Local Entropy Production in Turbulent Shear Flows: A Tool for Evaluating Heat Transfer Performance

Institute of Scientific and Technical Information of China (English)

H. HERWIG; F. KOCK

2006-01-01

Performance evaluation of heat transfer devices can be based on the overall entropy production in these devices.In our study we therefore provide equations for the systematic and detailed determination of local entropy production due to dissipation of mechanical energy and due to heat conduction, both in turbulent flows. After turbulence modeling has been incorporated for the fluctuating parts the overall entropy production can be determined by integration with respect to the whole flow domain. Since, however, entropy production rates show very steep gradients close to the wall, numerical solutions are far more effective with wall functions for the entropy production terms. These wall functions are mandatory when high Reynolds number turbulence models are used. For turbulent flow in a pipe with an inserted twisted tape as heat transfer promoter it is shown that based on the overall entropy production rate a clear statement from a thermodynamic point of view is possible. For a certain range of twist strength there is a decrease in overall entropy production compared to the case without insert. Also, the optimum twist strength can be determined. This information is unavailable when only pressure drop and heat transfer data are given.

Turbulent Heat Transfer in Curved Pipe Flow

Science.gov (United States)

Kang, Changwoo; Yang, Kyung-Soo

2013-11-01

In the present investigation, turbulent heat transfer in fully-developed curved pipe flow with axially uniform wall heat flux has been numerically studied. The Reynolds numbers under consideration are Reτ = 210 (DNS) and 1,000 (LES) based on the mean friction velocity and the pipe radius, and the Prandtl number (Pr) is 0.71. For Reτ = 210 , the pipe curvature (κ) was fixed as 1/18.2, whereas three cases of κ (0.01, 0.05, 0.1) were computed in the case of Reτ = 1,000. The mean velocity, turbulent intensities and heat transfer rates obtained from the present calculations are in good agreement with the previous numerical and experimental results. To elucidate the secondary flow structures due to the pipe curvature, the mean quantities and rms fluctuations of the flow and temperature fields are presented on the pipe cross-sections, and compared with those of the straight pipe flow. To study turbulence structures and their influence on turbulent heat transfer, turbulence statistics including but not limited to skewness and flatness of velocity fluctuations, cross-correlation coefficients, an Octant analysis, and turbulence budgets are presented and discussed. Based on our results, we attempt to clarify the effects of Reynolds number and the pipe curvature on turbulent heat transfer. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0008457).

Progress in turbulence research

International Nuclear Information System (INIS)

Bradshaw, P.

1990-01-01

Recent developments in experiments and eddy simulations, as an introduction to a discussion of turbulence modeling for engineers is reviewed. The most important advances in the last decade rely on computers: microcomputers to control laboratory experiments, especially for multidimensional imaging, and supercomputers to simulate turbulence. These basic studies in turbulence research are leading to genuine breakthroughs in prediction methods for engineers and earth scientists. The three main branches of turbulence research: experiments, simulations (numerically-accurate three-dimensional, time-dependent solutions of the Navier-Stokes equations, with any empiricism confined to the smallest eddies), and modeling (empirical closure of time-averaged equations for turbulent flow) are discussed. 33 refs

BHR equations re-derived with immiscible particle effects

Energy Technology Data Exchange (ETDEWEB)

Schwarzkopf, John Dennis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Horwitz, Jeremy A. [Stanford Univ., CA (United States)

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.

Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

Science.gov (United States)

Saveliev, V L; Gorokhovski, M A

2005-07-01

On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I

Science.gov (United States)

Zhou, Ye

2017-12-01

Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities play an important role in a wide range of engineering, geophysical, and astrophysical flows. They represent a triggering event that, in many cases, leads to large-scale turbulent mixing. Much effort has been expended over the past 140 years, beginning with the seminal work of Lord Rayleigh, to predict the evolution of the instabilities and of the instability-induced mixing layers. The objective of Part I of this review is to provide the basic properties of the flow, turbulence, and mixing induced by RT, RM, and Kelvin-Helmholtz (KH) instabilities. Historical efforts to study these instabilities are briefly reviewed, and the significance of these instabilities is discussed for a variety of flows, particularly for astrophysical flows and for the case of inertial confinement fusion. Early experimental efforts are described, and analytical attempts to model the linear, and nonlinear regimes of these mixing layers are examined. These analytical efforts include models for both single-mode and multi-mode initial conditions, as well as multi-scale models to describe the evolution. Comparisons of these models and theories to experimental and simulation studies are then presented. Next, attention is paid to the issue of the influence of stabilizing mechanisms (e.g., viscosity, surface tension, and diffuse interface) on the evolution of these instabilities, as well as the limitations and successes of numerical methods. Efforts to study these instabilities and mixing layers using group-theoretic ideas, as well as more formal notions of turbulence cascade processes during the later stages of the induced mixing layers, are inspected. A key element of the review is the discussion of the late-time self-similar scaling for the RT and RM growth factors, α and θ. These parameters are influenced by the initial conditions and much of the observed variation can be explained by this. In some cases, these instabilities

Improvements on digital inline holographic PTV for 3D wall-bounded turbulent flow measurements

International Nuclear Information System (INIS)

Toloui, Mostafa; Mallery, Kevin; Hong, Jiarong

2017-01-01

Three-dimensional (3D) particle image velocimetry (PIV) and particle tracking velocimetry (PTV) provide the most comprehensive flow information for unraveling the physical phenomena in a wide range of fluid problems, from microfluidics to wall-bounded turbulent flows. Compared with other 3D PIV techniques, such as tomographic PIV and defocusing PIV, the digital inline holographic PTV (DIH-PTV) provides 3D flow measurement solution with high spatial resolution, low cost optical setup, and easy alignment and calibration. Despite these advantages, DIH-PTV suffers from major limitations including poor longitudinal resolution, human intervention (i.e. requirement for manually determined tuning parameters during tracer field reconstruction and extraction), limited tracer concentration, small sampling volume and expensive computations, limiting its broad use for 3D flow measurements. In this study, we present our latest developments on minimizing these challenges, which enables high-fidelity DIH-PTV implementation to larger sampling volumes with significantly higher particle seeding densities suitable for wall-bounded turbulent flow measurements. The improvements include: (1) adjustable window thresholding; (2) multi-pass 3D tracking; (3) automatic wall localization; and (4) continuity-based out-of-plane velocity component computation. The accuracy of the proposed DIH-PTV method is validated with conventional 2D PIV and double-view holographic PTV measurements in smooth-wall turbulent channel flow experiments. The capability of the technique in characterization of wall-bounded turbulence is further demonstrated through its application to flow measurements for smooth- and rough-wall turbulent channel flows. In these experiments, 3D velocity fields are measured within sampling volumes of 14.7  ×  50.0  ×  14.4 mm 3 (covering the entire depth of the channel) with a velocity resolution of  <1.1 mm/vector. Overall, the presented DIH-PTV method and

Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

Directory of Open Access Journals (Sweden)

H. Z. Baumert

2009-03-01

Full Text Available This paper extends a turbulence closure-like model for stably stratified flows into a new dynamic domain in which turbulence is generated by internal gravity waves rather than mean shear. The model turbulent kinetic energy (TKE, K balance, its first equation, incorporates a term for the energy transfer from internal waves to turbulence. This energy source is in addition to the traditional shear production. The second variable of the new two-equation model is the turbulent enstrophy (Ω. Compared to the traditional shear-only case, the Ω-equation is modified to account for the effect of the waves on the turbulence time and space scales. This modification is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean shear when turbulence is produced exclusively by internal waves. This paper is part 1 of a continuing theoretical development. It accounts for mean shear- and internal wave-driven mixing only in the two limits of mean shear and no waves and waves but no mean shear, respectively.

The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000b. At small energy density E of the internal wave field, the turbulent dissipation rate (ε scales like ε~E². This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E¹. This is observed, for example, in the highly energetic tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

Tokamak fluidlike equations, with applications to turbulence and transport in H mode discharges

International Nuclear Information System (INIS)

Kim, Y.B.; Biglari, H.; Carreras, B.A.; Diamond, P.H.; Groebner, R.J.; Kwon, O.J.; Spong, D.A.; Callen, J.D.; Chang, Z.; Hollenberg, J.B.; Sundaram, A.K.; Terry, P.W.; Wang, J.F.

1990-01-01

Significant progress has been made in developing tokamak fluidlike equations which are valid in all collisionality regimes in toroidal devices, and their applications to turbulence and transport in tokamaks. The areas highlighted in this paper include: the rigorous derivation of tokamak fluidlike equations via a generalized Chapman-Enskog procedure in various collisionality regimes and on various time scales; their application to collisionless and collisional drift wave models in a sheared slab geometry; applications to neoclassical drift wave turbulence; i.e. neoclassical ion-temperature-gradient-driven turbulence and neoclassical electron-drift-wave turbulence; applications to neoclassical bootstrap-current-driven turbulence; numerical simulation of nonlinear bootstrap-current-driven turbulence and tearing mode turbulence; transport in Hot-Ion H mode discharges. 20 refs., 3 figs

Description of turbulent velocity and temperature fields of single phase flow through tight rod bundles

International Nuclear Information System (INIS)

Monir, C.

1991-02-01

A two-dimensional procedure, VANTACY-II, describing the turbulent velocity and temperature fields for single phase flow in tight lattices is presented and validated. The flow is assumed to be steady, incrompressible and hydraulic and thermal fully developed. First, the state of art of turbulent momentum and heat transport in tight lattices is documented. It is shown that there is a necessity for experimental investigations in the field of turbulent heat transport. The presented new procedure is based on the turbulence model VELASCO-TUBS by NEELEN. The numerical solution of the balance equations is done by the finite element method code VANTACY by KAISER. The validation of the new procedure VANTACY-II is done by comparing the numerically calculated data for the velocity and temperature fields and for natural mixing with the experimental data of SEALE. The comparison shows a good agreement of experimental and numerically computed data. The observed differences can be mainly attributed to the model of the turbulent PRANDTL number used in the new procedure. (orig.) [de

Prediction of velocity distributions in rod bundle axial flow, with a statistical model (K-epsilon) of turbulence

International Nuclear Information System (INIS)

Silva Junior, H.C. da.

1978-12-01

Reactor fuel elements generally consist of rod bundles with the coolant flowing axially through the region between the rods. The confiability of the thermohydraulic design of such elements is related to a detailed description of the velocity field. A two-equation statistical model (K-epsilon) of turbulence is applied to compute main and secondary flow fields, wall shear stress distributions and friction factors of steady, fully developed turbulent flows, with incompressible, temperature independent fluid flowing axially through triangular or square arrays of rod bundles. The numerical procedure uses the vorticity and the stream function to describe the velocity field. Comparison with experimental and analytical data of several investigators is presented. Results are in good agreement. (Author) [pt

Effects of polymer stresses on analogy between momentum and heat transfer in drag-reduced turbulent channel flow

Science.gov (United States)

Kim, Kyoungyoun; Sureshkumar, Radhakrishna

2018-03-01

The effects of polymer stresses on the analogy between momentum and heat transfer are examined by using a direct numerical simulation (DNS) of viscoelastic turbulent channel flows using a constant heat flux boundary condition. The Reynolds number based on the friction velocity and channel half height is 125, and the Prandtl number is 5. The polymer stress is modeled using the finitely extensible nonlinear elastic-Peterlin constitutive model, and low (15%), intermediate (34%), and high drag reduction (DR) (52%) cases are examined. The Colburn analogy is found to be inapplicable for viscoelastic turbulent flows, suggesting dissimilarity between the momentum and heat transfer at the macroscopic coefficient level. The mean temperature profile also shows behaviour different from the mean velocity profile in drag-reduced flows. In contrast to the dissimilarity in the mean profiles, the turbulent Prandtl number Prt predicted by the DNS is near unity. This implies that turbulent heat transfer is still analogous to turbulent momentum transfer in drag-reduced flows, as in Newtonian flow. An increase in DR is accompanied by an increase in the correlation coefficient ρuθ between the instantaneous fluctuations in the streamwise velocity u and temperature θ. The correlation coefficient between u' and wall-normal velocity fluctuations v', ρ-u v, exhibits a profile similar to that of ρ-θ v in drag-reduced and Newtonian flows. Finally, the budget analysis of the transport equations of turbulent heat flux shows a strong similarity between the turbulent momentum and heat transfer, which is consistent with the predictions of Prt near unity.

A Numerically and Experimentally Investigated Structure of the Turbulent Flow Past a Trench with a Separation

Directory of Open Access Journals (Sweden)

V. N. Afanasiev

2017-01-01

Full Text Available The paper studies the convective heat exchange intensification due to two-dimensional depressions formed on the initially flat surface. This problem is of interest for engineering applications because many different convective surfaces have cavities and depressions of constructive or random occurrence. During flow around a depression the boundary layer separation and its reattachment result in occurring specific phenomena, which have a significant impact on drag and heat exchange.The work involved an experimental study of hydrodynamic and heat characteristics of the turbulent boundary layer formed when there was an external airflow of the flat surface with a single transversal separation trench.The experimental part used an open subsonic low-turbulence wind tunnel operating in suction mode. A numerical simulation involves hydrodynamics and heat exchange parameters analysis via solution of the system of differential equations, which describe momentum and heat transport processes using ANSYS Fluent solver.The experimental data of this study are compared with numerical simulation results obtained by solving the steady Reynolds-averaged Navier-Stokes equations (RANS with a two-parametrical Menter k-ω (MSST turbulence model.The comparison shows that simulation results are in good agreement with experimental data, heat exchange surface profiling by a transversal trench system with or without flow separation does not lead to increasing surface drag and, moreover, at the certain ratios of geometrical parameters (cylindrical trenches with h/S£ 0.5 it can decrease the surface drag. Surface conjugations in these depressions should be smooth without any sharp curves and transitions, which can lead to forming stagnation regions.The reason for raising heat exchange is a spatial non-uniformity of the generated turbulence field. During flow analysis there were two sources of turbulence generation found out, namely a wall (heat exchange surface and a mixing

Surface roughness effects on turbulent Couette flow

Science.gov (United States)

Lee, Young Mo; Lee, Jae Hwa

2017-11-01

Direct numerical simulation of a turbulent Couette flow with two-dimensional (2-D) rod roughness is performed to examine the effects of the surface roughness. The Reynolds number based on the channel centerline laminar velocity (Uco) and channel half height (h) is Re =7200. The 2-D rods are periodically arranged with a streamwise pitch of λ = 8 k on the bottom wall, and the roughness height is k = 0.12 h. It is shown that the wall-normal extent for the logarithmic layer is significantly shortened in the rough-wall turbulent Couette flow, compared to a turbulent Couette flow with smooth wall. Although the Reynolds stresses are increased in a turbulent channel flow with surface roughness in the outer layer due to large-scale ejection motions produced by the 2-D rods, those of the rough-wall Couette flow are decreased. Isosurfaces of the u-structures averaged in time suggest that the decrease of the turbulent activity near the centerline is associated with weakened large-scale counter-rotating roll modes by the surface roughness. This research was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2017R1D1A1A09000537) and the Ministry of Science, ICT & Future Planning (NRF-2017R1A5A1015311).

Numerical Solutions of Mechanical Turbulent Filtration Equation Used in Mechatronics and Micro Mechanic

OpenAIRE

Hassan Fathabadi

2013-01-01

In this study, several novel numerical solutions are presented to solve the turbulent filtration equation and its special case called “Non-Newtonian mechanical filtration equation”. The turbulent filtration equation in porous media is a very important equation which has many applications to solve the problems appearing especially in mechatronics, micro mechanic and fluid mechanic. Many applied mechanical problems can be solved using this equation. For example, non-Newtonian mechanical filtrat...

Aerodynamics, heat and mass transfer in steam-aerosol turbulent flows in containment

Energy Technology Data Exchange (ETDEWEB)

Nigmatulin, B.I.; Pershukov, V.A.; Ris, V.V. [Research & Engineering Centre of Nuclear Plants Safety, Moscow (Russian Federation)] [and others

1995-09-01

In this report an analysis of aerodynamic and heat transfer processes at the blowdown of gas-dispersed mixture into the containment volume is presented. A few models for description of the volume averaged and local characteristics are analyzed. The mathematical model for description of the local characteristics of the turbulent gas-dispersed flows was developed. The calculation of aerodynamic, heat and mass transfer characteristics was based on the Navier-Stokes, energy and gas mass fractions conservation equations. For calculation of dynamics and deposition of the aerosols the original diffusion-inertia model is developed. The pulsating characteristics of the gaseous phase were calculated on the base (k-{xi}) model of turbulence with modification to account thermogravitational force action and influence of particle mass loading. The appropriate boundary conditions using the {open_quotes}near-wall function{close_quotes} approach was obtained. Testing of the mathematical models and boundary conditions has shown a good agreement between computation and data of comparison. The described mathematical models were applied to two- and three dimensional calculations of the turbulent flow in containment at the various stages of the accident.

Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

Science.gov (United States)

Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

2017-11-01

In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

Advection diffusion model for particles deposition in Rayleigh-Benard turbulent flows

International Nuclear Information System (INIS)

Oresta, P.; Lippolis, A.; Verzicco, R.; Soldati, A.

2005-01-01

In this paper, Direct Numerical Simulation (DNS) and Lagrangian Particle Tracking are used to precisely investigate the turbulent thermally driven flow and particles dispersion in a closed, slender cylindrical domain. The numerical simulations are carried out for Rayleigh (Ra) and Prandtl numbers (Pr) equal to Ra = 2X10 8 and Pr = 0.7, considering three sets of particles with Stokes numbers, based on Kolmogorov scale, equal to St k 1.3, St k 0.65 and St k = 0.13. This data are used to calculate a priori the drift velocity and the turbulent diffusion coefficient for the Advection Diffusion model. These quantities are function of the Stokes, Froude, Rayleigh and Prandtl numbers only. One dimensional, time dependent, Advection- Diffusion Equation (ADE) is presented to predict particles deposition in Rayleigh-Benard flow in the cylindrical domain. This archetype configuration models flow and aerosol dynamics, produced in case of accident in the passive containment cooling system (PCCS) of a nuclear reactor. ADE results show a good agreement with DNS data for all the sets of particles investigated. (author)

Introduction to turbulence modelling: Applications of Reynolds Averaged Navier Stokes Equations (RANSE) to engineering problems

International Nuclear Information System (INIS)

Laurence, D.

1997-01-01

The k-ε model and Reynolds stress transport model are set out in a few words. Limitations of models are shown, particularly for turbulence generation in the turbulent viscosity context, and, more generally, the uncertainties and miscellaneous changes made to the dissipation equation. The performances of models are then compared, using results of the three latest ERCOFTA/IAHR workshops. It is shown that algebraic constraints which can be derived exactly by assuming asymptotic limits (rapid distortion, homogeneous shear at infinite time, 2D turbulence) have inhibited a better tuning of the models for real life flow where these limits are not encountered. A more pragmatic approach could be taken by allowing the constants to be functions of invariant parameters. But these functions, making the models non-linear, can lead to bifurcations or instability. One essential parameter is the distance to the wall, which recent models have tried to eliminate, although this parameter appears indirectly through the Poisson equation for the fluctuating pressure. A possible indirect model is the elliptic relaxation. Progress was recently achieved in near-wall low Re modelling, but these advances do not always result in benefits to industry since only the 'wall function' approaches can be used in the high Re, 3D flows that we need to study. With the knowledge gained from near-wall modelling, it might be profitable to revisit the 'wall functions' devised 20 years ago. (author)

Characteristic analysis of turbulent heat diffusion in a multi-compartment structure; Takukakuka kukan kozo ni okeru ranryunetsu kakusan gensho no kaiseki

Energy Technology Data Exchange (ETDEWEB)

Hu, C; Fukuchi, N [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1997-10-01

An analysis was made on turbulent heat diffusion in a multi-compartment structure necessary for designing calorific power and environment for functional systems used in marine vessels and off-shore structures. In a multi-compartment structure, the diffusion phenomenon is complex because of movement of air flow in turbulence and buoyancy resulted from non-isothermal condition. The phenomenon is largely affected by space shapes and walls, and the conditions in heat diffusion field is governed also by shapes of opening connecting the compartments. An analysis was made by using the SIMPLE method on turbulent heat diffusion in a multi-compartment space with high Raleigh number in which natural convection is dominant. If the opening is small, the Coanda effect appears, in which air flow passing through the opening rises along the wall, wherein a high-temperature layer is formed near the ceiling, making the heat diffusion inactive. If the opening is large, a jetting flow from the opening and a large circulating flow are created, which cause active advection mixture, making temperature gradient smaller in the upper layer. Heat transfer intensity in an opening on a partition wall decays in proportion with 1/4th power of the opening ratio. 7 refs., 11 figs.

MEASUREMENTS AND COMPUTATIONS OF FUEL DROPLET TRANSPORT IN TURBULENT FLOWS

Energy Technology Data Exchange (ETDEWEB)

Joseph Katz and Omar Knio

2007-01-10

The objective of this project is to study the dynamics of fuel droplets in turbulent water flows. The results are essential for development of models capable of predicting the dispersion of slightly light/heavy droplets in isotropic turbulence. Since we presently do not have any experimental data on turbulent diffusion of droplets, existing mixing models have no physical foundations. Such fundamental knowledge is essential for understanding/modeling the environmental problems associated with water-fuel mixing, and/or industrial processes involving mixing of immiscible fluids. The project has had experimental and numerical components: 1. The experimental part of the project has had two components. The first involves measurements of the lift and drag forces acting on a droplet being entrained by a vortex. The experiments and data analysis associated with this phase are still in progress, and the facility, constructed specifically for this project is described in Section 3. In the second and main part, measurements of fuel droplet dispersion rates have been performed in a special facility with controlled isotropic turbulence. As discussed in detail in Section 2, quantifying and modeling the of droplet dispersion rate requires measurements of their three dimensional trajectories in turbulent flows. To obtain the required data, we have introduced a new technique - high-speed, digital Holographic Particle Image Velocimetry (HPIV). The technique, experimental setup and results are presented in Section 2. Further information is available in Gopalan et al. (2005, 2006). 2. The objectives of the numerical part are: (1) to develop a computational code that combines DNS of isotropic turbulence with Lagrangian tracking of particles based on integration of a dynamical equation of motion that accounts for pressure, added mass, lift and drag forces, (2) to perform extensive computations of both buoyant (bubbles) and slightly buoyant (droplets) particles in turbulence conditions

Large-eddy-simulation approach in understanding flow structures of 2D turbulent density currents over sloping surfaces

Science.gov (United States)

Nayamatullah, M.; Rao Pillalamarri, Narasimha; Bhaganagar, Kiran

2018-04-01

A numerical investigation was performed to understand the flow dynamics of 2D density currents over sloping surfaces. Large eddy simulation was conducted for lock-exchange (L-E) release currents and overflows. 2D Navier-Stokes equations were solved using the Boussinesq approximation. The effects of the lock aspect-ratio (height/length of lock), slope, and Reynolds number on the flow structures and turbulence mixing have been analyzed. Results have confirmed buoyancy within the head of the two-dimensional currents is not conserved which contradicts the classical thermal theory. The lock aspect-ratio dictates the fraction of initial buoyancy which is carried by the head of the current at the beginning of the slumping (horizontal) and accelerating phase (over a slope), which has important implications on turbulence kinetic energy production, and hence mixing in the current. For L-E flows over a slope, increasing slope angle enhances the turbulence production. Increasing slope results in shear reversal within the density current resulting in shear-instabilities. Differences in turbulence production mechanisms and flow structures exist between the L-E and constant-flux release currents resulting in significant differences in the flow characteristics between different releases.

Turbulent flows over sparse canopies

Science.gov (United States)

Sharma, Akshath; García-Mayoral, Ricardo

2018-04-01

Turbulent flows over sparse and dense canopies exerting a similar drag force on the flow are investigated using Direct Numerical Simulations. The dense canopies are modelled using a homogeneous drag force, while for the sparse canopy, the geometry of the canopy elements is represented. It is found that on using the friction velocity based on the local shear at each height, the streamwise velocity fluctuations and the Reynolds stress within the sparse canopy are similar to those from a comparable smooth-wall case. In addition, when scaled with the local friction velocity, the intensity of the off-wall peak in the streamwise vorticity for sparse canopies also recovers a value similar to a smooth-wall. This indicates that the sparse canopy does not significantly disturb the near-wall turbulence cycle, but causes its rescaling to an intensity consistent with a lower friction velocity within the canopy. In comparison, the dense canopy is found to have a higher damping effect on the turbulent fluctuations. For the case of the sparse canopy, a peak in the spectral energy density of the wall-normal velocity, and Reynolds stress is observed, which may indicate the formation of Kelvin-Helmholtz-like instabilities. It is also found that a sparse canopy is better modelled by a homogeneous drag applied on the mean flow alone, and not the turbulent fluctuations.

Richardson effects in turbulent buoyant flows

Science.gov (United States)

Biggi, Renaud; Blanquart, Guillaume

2010-11-01

Rayleigh Taylor instabilities are found in a wide range of scientific fields from supernova explosions to underwater hot plumes. The turbulent flow is affected by the presence of buoyancy forces and may not follow the Kolmogorov theory anymore. The objective of the present work is to analyze the complex interactions between turbulence and buoyancy. Towards that goal, simulations have been performed with a high order, conservative, low Mach number code [Desjardins et. al. JCP 2010]. The configuration corresponds to a cubic box initially filled with homogeneous isotropic turbulence with heavy fluid on top and light gas at the bottom. The initial turbulent field was forced using linear forcing up to a Reynolds number of Reλ=55 [Meneveau & Rosales, POF 2005]. The Richardson number based on the rms velocity and the integral length scale was varied from 0.1 to 10 to investigate cases with weak and strong buoyancy. Cases with gravity as a stabilizer of turbulence (gravity pointing up) were also considered. The evolution of the turbulent kinetic energy and the total kinetic energy was analyzed and a simple phenomenological model was proposed. Finally, the energy spectra and the isotropy of the flow were also investigated.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

KAUST Repository

Kou, Jisheng; Sun, Shuyu

2016-01-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic

Mach Number effects on turbulent superstructures in wall bounded flows

Science.gov (United States)

Kaehler, Christian J.; Bross, Matthew; Scharnowski, Sven

2017-11-01

Planer and three-dimensional flow field measurements along a flat plat boundary layer in the Trisonic Wind Tunnel Munich (TWM) are examined with the aim to characterize the scaling, spatial organization, and topology of large scale turbulent superstructures in compressible flow. This facility is ideal for this investigation as the ratio of boundary layer thickness to test section spanwise extent ratio is around 1/25, ensuring minimal sidewall and corner effects on turbulent structures in the center of the test section. A major difficulty in the experimental investigation of large scale features is the mutual size of the superstructures which can extend over many boundary layer thicknesses. Using multiple PIV systems, it was possible to capture the full spatial extent of large-scale structures over a range of Mach numbers from Ma = 0.3 - 3. To calculate the average large-scale structure length and spacing, the acquired vector fields were analyzed by statistical multi-point methods that show large scale structures with a correlation length of around 10 boundary layer thicknesses over the range of Mach numbers investigated. Furthermore, the average spacing between high and low momentum structures is on the order of a boundary layer thicknesses. This work is supported by the Priority Programme SPP 1881 Turbulent Superstructures of the Deutsche Forschungsgemeinschaft.

Experimental studies of occupation times in turbulent flows

DEFF Research Database (Denmark)

Mann, J.; Ott, Søren; Pécseli, H.L.

2003-01-01

The motion of passively convected particles in turbulent flows is studied experimentally in approximately homogeneous and isotropic turbulent flows, generated in water by two moving grids. The simultaneous trajectories of many small passively convected, neutrally buoyant, polystyrene particles...

Regulation of ETG turbulence by TEM driven zonal flows

Science.gov (United States)

Asahi, Yuuichi; Ishizawa, Akihiro; Watanabe, Tomohiko; Tsutsui, Hiroaki; Tsuji-Iio, Shunji

2013-10-01

Anomalous heat transport driven by electron temperature gradient (ETG) turbulence is investigated by means of gyrokinetic simulations. It is found that the ETG turbulence can be suppressed by zonal flows driven by trapped electron modes (TEMs). The TEMs appear in a statistically steady state of ETG turbulence and generate zonal flows, while its growth rate is much smaller than those of ETGs. The TEM-driven zonal flows with lower radial wave numbers are more strongly generated than those driven by ETG modes, because of the higher zonal flow response to a density source term. An ExB shearing rate of the TEM-driven zonal flows is strong enough to suppress the long-wavelength ETG modes which make the main contribution to the turbulent transport.

Simulations of Turbulence in Tokamak Edge and Effects of Self-Consistent Zonal Flows

Science.gov (United States)

Cohen, Bruce; Umansky, Maxim

2013-10-01

Progress is reported on simulations of electromagnetic drift-resistive ballooning turbulence in the tokamak edge. This extends previous work to include self-consistent zonal flows and their effects. The previous work addressed simulation of L-mode tokamak edge turbulence using the turbulence code BOUT that solves Braginskii-based plasma fluid equations in tokamak edge domain. The calculations use realistic single-null geometry and plasma parameters of the DIII-D tokamak and produce fluctuation amplitudes, fluctuation spectra, and particle and thermal fluxes that compare favorably to experimental data. In the effect of sheared ExB poloidal rotation is included with an imposed static radial electric field fitted to experimental data. In the new work here we include the radial electric field self-consistently driven by the microturbulence, which contributes to the sheared ExB poloidal rotation (zonal flow generation). We present simulations with/without zonal flows for both cylindrical geometry, as in the UCLA Large Plasma Device, and for the DIII-D tokamak L-mode cases in to quantify the influence of self-consistent zonal flows on the microturbulence and the concomitant transport. This work was performed under the auspices of the U.S. Department of Energy under contract DE-AC52-07NA27344 at the Lawrence Livermore National Laboratory.

Prediction of adiabatic bubbly flows in TRACE using the interfacial area transport equation

International Nuclear Information System (INIS)

Talley, J.; Worosz, T.; Kim, S.; Mahaffy, J.; Bajorek, S.; Tien, K.

2011-01-01

The conventional thermal-hydraulic reactor system analysis codes utilize a two-field, two-fluid formulation to model two-phase flows. To close this model, static flow regime transition criteria and algebraic relations are utilized to estimate the interfacial area concentration (a i ). To better reflect the continuous evolution of two-phase flow, an experimental version of TRACE is being developed which implements the interfacial area transport equation (IATE) to replace the flow regime based approach. Dynamic estimation of a i is provided through the use of mechanistic models for bubble coalescence and disintegration. To account for the differences in bubble interactions and drag forces, two-group bubble transport is sought. As such, Group 1 accounts for the transport of spherical and distorted bubbles, while Group 2 accounts for the cap, slug, and churn-turbulent bubbles. Based on this categorization, a two-group IATE applicable to the range of dispersed two-phase flows has been previously developed. Recently, a one-group, one-dimensional, adiabatic IATE has been implemented into the TRACE code with mechanistic models accounting for: (1) bubble breakup due to turbulent impact of an eddy on a bubble, (2) bubble coalescence due to random collision driven by turbulent eddies, and (3) bubble coalescence due to the acceleration of a bubble in the wake region of a preceding bubble. To demonstrate the enhancement of the code's capability using the IATE, experimental data for a i , void fraction, and bubble velocity measured by a multi-sensor conductivity probe are compared to both the IATE and flow regime based predictions. In total, 50 air-water vertical co-current upward and downward bubbly flow conditions in pipes with diameters ranging from 2.54 to 20.32 cm are evaluated. It is found that TRACE, using the conventional flow regime relation, always underestimates a i . Moreover, the axial trend of the a i prediction is always quasi-linear because a i in the

Development of two-group interfacial area transport equation for confined flow-2. Model evaluation

International Nuclear Information System (INIS)

Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

2003-01-01

The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flow. The two-group IATE is evaluated in steady state, one-dimensional form. Also, since the experiments were performed under adiabatic, air-water two-phase flow conditions, the phase change effect is omitted in the evaluation. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes. (author)

Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow

Science.gov (United States)

Farrell, Brian F.; Ioannou, Petros J.

2017-08-01

This paper describes a study of the self-sustaining process in wall turbulence. The study is based on a second order statistical state dynamics model of Couette flow in which the state variables are the streamwise mean flow (first cumulant) and perturbation covariance (second cumulant). This statistical state dynamics model is closed by either setting the third cumulant to zero or by replacing it with a stochastic parametrization. Statistical state dynamics models with this form are referred to as S3T models. S3T models have been shown to self-sustain turbulence with a mean flow and second order perturbation structure similar to that obtained by direct numerical simulation of the equations of motion. The use of a statistical state dynamics model to study the physical mechanisms underlying turbulence has important advantages over the traditional approach of studying the dynamics of individual realizations of turbulence. One advantage is that the analytical structure of S3T statistical state dynamics models isolates the interaction between the mean flow and the perturbation components of the turbulence. Isolation of the interaction between these components reveals how this interaction underlies both the maintenance of the turbulence variance by transfer of energy from the externally driven flow to the perturbation components as well as the enforcement of the observed statistical mean turbulent state by feedback regulation between the mean and perturbation fields. Another advantage of studying turbulence using statistical state dynamics models of S3T form is that the analytical structure of S3T turbulence can be completely characterized. For example, the perturbation component of turbulence in the S3T system is demonstrably maintained by a parametric perturbation growth mechanism in which fluctuation of the mean flow maintains the perturbation field which in turn maintains the mean flow fluctuations in a synergistic interaction. Furthermore, the equilibrium

Experimental study of turbulent flows through pipe bends

OpenAIRE

Kalpakli, Athanasia

2012-01-01

This thesis deals with turbulent flows in 90 degree curved pipes of circular cross-section. The flow cases investigated experimentally are turbulent flow with and without an additional motion, swirling or pulsating, superposed on the primary flow. The aim is to investigate these complex flows in detail both in terms of statistical quantities as well as vortical structures that are apparent when curvature is present. Such a flow field can contain strong secondary flow in a plane normal to the ...

Nonlinear Flow Generation By Electrostatic Turbulence In Tokamaks

International Nuclear Information System (INIS)

Wang, W.X.; Diamond, P.H.; Hahm, T.S.; Ethier, S.; Rewoldt, G.; Tang, W.M.

2010-01-01

Global gyrokinetic simulations have revealed an important nonlinear flow generation process due to the residual stress produced by electrostatic turbulence of ion temperature gradient (ITG) modes and trapped electron modes (TEM). In collisionless TEM (CTEM) turbulence, nonlinear residual stress generation by both the fluctuation intensity and the intensity gradient in the presence of broken symmetry in the parallel wave number spectrum is identified for the first time. Concerning the origin of the symmetry breaking, turbulence self-generated low frequency zonal flow shear has been identified to be a key, universal mechanism in various turbulence regimes. Simulations reported here also indicate the existence of other mechanisms beyond E - B shear. The ITG turbulence driven 'intrinsic' torque associated with residual stress is shown to increase close to linearly with the ion temperature gradient, in qualitative agreement with experimental observations in various devices. In CTEM dominated regimes, a net toroidal rotation is driven in the cocurrent direction by 'intrinsic' torque, consistent with the experimental trend of observed intrinsic rotation. The finding of a 'flow pinch' in CTEM turbulence may offer an interesting new insight into the underlying dynamics governing the radial penetration of modulated flows in perturbation experiments. Finally, simulations also reveal highly distinct phase space structures between CTEM and ITG turbulence driven momentum, energy and particle fluxes, elucidating the roles of resonant and non-resonant particles.

The computation of turbulent recirculating flow using curvilinear finite differences. Application of the k - epsilon model to the flow in dredged trenches

International Nuclear Information System (INIS)

Alfrink, B.J.

1981-08-01

The report treats the computation of turbulent recirculating flow in dredged trenches. The mathematical model consists of the full two-dimensional unsteady Reynolds equations, formulated in primitive variables. Turbulence closure is obtained by means of a two-equation (k - epsilon) model. The numerical technique is based on the use of curvilinear finite differences in space and of fractional steps in time. A procedure is proposed to apply the model for varying roughness circumstances. The value of the Von Karman constant can be determined from geometric information. Afterwards, only the c 1 -constant is adapted by means of a degenerated epsilon-equation. The report describes an extensive sensitivity study for the inlet conditions and the empirical constants. Ultimately, the results of the mathematical model are very satisfactory. Compared with laboratory experiments, the recirculation length is only underpredicted with 10%

Experiments in turbulent pipe flow

Energy Technology Data Exchange (ETDEWEB)

Torbergsen, Lars Even

1998-12-31

This thesis reports experimental results for the mean velocity and turbulence statistics in two straight pipe sections for bulk Reynolds numbers in the range 22000 to 75000. The flow was found consistent with a fully developed state. Detailed turbulence spectra were obtained for low and moderate turbulent Reynolds number. For the pipe centre line location at R{sub {lambda}} = 112, a narrow range in the streamwise power spectrum applied to the -5/3 inertial subrange. However this range was influenced both by turbulence production and viscous dissipation, and therefore did not reflect a true inertial range. The result indicates how the intermediate range between the production and dissipative scales can be misinterpreted as an inertial range for low and moderate R{sub {lambda}}. To examine the universal behaviour of the inertial range, the inertial scaling of the streamwise power spectrum is compared to the inertial scaling of the second order longitudinal velocity structure function, which relate directly by a Fourier transform. Increasing agreement between the Kolmogorov constant C{sub K} and the second order structure function scaling constant C{sub 2} was observed with increasing R{sub {lambda}}. The result indicates that a true inertial range requires several decades of separation between the energy containing and dissipative scales. A method for examining spectral anisotropy is reported and applied to turbulence spectra in fully developed pipe flow. It is found that the spectral redistribution from the streamwise to the two lateral spectra goes primarily to the circumferential component. Experimental results are reported for an axisymmetric contraction of a fully developed pipe flow. 67 refs., 75 figs., 9 tabs.

Statistical descriptions of polydisperse turbulent two-phase flows

Energy Technology Data Exchange (ETDEWEB)

Minier, Jean-Pierre, E-mail: jean-pierre.minier@edf.fr

2016-12-15

Disperse two-phase flows are flows containing two non-miscible phases where one phase is present as a set of discrete elements dispersed in the second one. These discrete elements, or ‘particles’, can be droplets, bubbles or solid particles having different sizes. This situation encompasses a wide range of phenomena, from nano-particles and colloids sensitive to the molecular fluctuations of the carrier fluid to inertia particles transported by the large-scale motions of turbulent flows and, depending on the phenomenon studied, a broad spectrum of approaches have been developed. The aim of the present article is to analyze statistical models of particles in turbulent flows by addressing this issue as the extension of the classical formulations operating at a molecular or meso-molecular level of description. It has a three-fold purpose: (1) to bring out the thread of continuity between models for discrete particles in turbulent flows (above the hydrodynamical level of description) and classical mesoscopic formulations of statistical physics (below the hydrodynamical level); (2) to reveal the specific challenges met by statistical models in turbulence; (3) to establish a methodology for modeling particle dynamics in random media with non-zero space and time correlations. The presentation is therefore centered on organizing the different approaches, establishing links and clarifying physical foundations. The analysis of disperse two-phase flow models is developed by discussing: first, approaches of classical statistical physics; then, by considering models for single-phase turbulent flows; and, finally, by addressing current formulations for discrete particles in turbulent flows. This brings out that particle-based models do not cease to exist above the hydrodynamical level and offer great interest when combined with proper stochastic formulations to account for the lack of equilibrium distributions and scale separation. In the course of this study, general

Implicit gas-kinetic unified algorithm based on multi-block docking grid for multi-body reentry flows covering all flow regimes

Science.gov (United States)

Peng, Ao-Ping; Li, Zhi-Hui; Wu, Jun-Lin; Jiang, Xin-Yu

2016-12-01

Based on the previous researches of the Gas-Kinetic Unified Algorithm (GKUA) for flows from highly rarefied free-molecule transition to continuum, a new implicit scheme of cell-centered finite volume method is presented for directly solving the unified Boltzmann model equation covering various flow regimes. In view of the difficulty in generating the single-block grid system with high quality for complex irregular bodies, a multi-block docking grid generation method is designed on the basis of data transmission between blocks, and the data structure is constructed for processing arbitrary connection relations between blocks with high efficiency and reliability. As a result, the gas-kinetic unified algorithm with the implicit scheme and multi-block docking grid has been firstly established and used to solve the reentry flow problems around the multi-bodies covering all flow regimes with the whole range of Knudsen numbers from 10 to 3.7E-6. The implicit and explicit schemes are applied to computing and analyzing the supersonic flows in near-continuum and continuum regimes around a circular cylinder with careful comparison each other. It is shown that the present algorithm and modelling possess much higher computational efficiency and faster converging properties. The flow problems including two and three side-by-side cylinders are simulated from highly rarefied to near-continuum flow regimes, and the present computed results are found in good agreement with the related DSMC simulation and theoretical analysis solutions, which verify the good accuracy and reliability of the present method. It is observed that the spacing of the multi-body is smaller, the cylindrical throat obstruction is greater with the flow field of single-body asymmetrical more obviously and the normal force coefficient bigger. While in the near-continuum transitional flow regime of near-space flying surroundings, the spacing of the multi-body increases to six times of the diameter of the single

Part I. Inviscid, swirling flows and vortex breakdown. Part II. A numerical investigation of the Lundgren turbulence model

International Nuclear Information System (INIS)

Buntine, J.D.

1994-01-01

Part I. A study of the behaviour of an inviscid, swirling fluid is performed. This flow can be described by the Squire-Long equation if the constraints of time-independence and axisymmetry are invoked. The particular case of flow through a diverging pipe is selected and a study is conducted to determine over what range of parameters does a solution exist. The work is performed with a view to understanding how the phenomenon of vortex breakdown develops. Experiments and previous numerical studies have indicated that the flow is sensitive to boundary conditions particularly at the pipe inlet. A open-quotes quasi-cylindricalclose quotes amplification of the Squire-Long equation is compared with the more complete model and shown to be able to account for most of its behaviour. An advantage of this latter representation is the relatively undetailed description of the flow geometry it requires in order to calculate a solution. open-quotes Criticalityclose quotes or the ability of small disturbances to propagate upstream is related to results of the quasi-cylindrical and axisymmetric flow models. This leads to an examination of claims made by researchers such as Benjamin and Hall concerning the interrelationship between open-quotes failureclose quotes of the quasi-cylindrical model and the occurrence of a open-quotes criticalclose quotes flow state. Lundgren developed an analytical model for homogeneous turbulence based on a collection of contracting spiral vortices each embedded in an axisymmetric strain field. Using asymptotic approximations he was able to deduce the Kolmogorov k -5/3 behaviour for inertial scales in the turbulence energy spectrum. Pullin ampersand Saffman have enlarged upon his work to make a number of predictions about the behaviour of turbulence described by the model. This work investigates the model numerically. The first part considers how the flow description compares with numerical simulations using the Navier-Stokes equations

Statistical properties of turbulence: An overview

Indian Academy of Sciences (India)

the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer ... However, it is not easy to state what would consti- tute a solution of the turbulence ...... flow with Lagrangian tracers and use a cubic spline interpolation method to calculate their ...

Autonomic Closure for Turbulent Flows Using Approximate Bayesian Computation

Science.gov (United States)

Doronina, Olga; Christopher, Jason; Hamlington, Peter; Dahm, Werner

2017-11-01

Autonomic closure is a new technique for achieving fully adaptive and physically accurate closure of coarse-grained turbulent flow governing equations, such as those solved in large eddy simulations (LES). Although autonomic closure has been shown in recent a priori tests to more accurately represent unclosed terms than do dynamic versions of traditional LES models, the computational cost of the approach makes it challenging to implement for simulations of practical turbulent flows at realistically high Reynolds numbers. The optimization step used in the approach introduces large matrices that must be inverted and is highly memory intensive. In order to reduce memory requirements, here we propose to use approximate Bayesian computation (ABC) in place of the optimization step, thereby yielding a computationally-efficient implementation of autonomic closure that trades memory-intensive for processor-intensive computations. The latter challenge can be overcome as co-processors such as general purpose graphical processing units become increasingly available on current generation petascale and exascale supercomputers. In this work, we outline the formulation of ABC-enabled autonomic closure and present initial results demonstrating the accuracy and computational cost of the approach.

Flow-induced vibration test of an advanced water reactor model. Pt. 1. Turbulence-induced forcing function

International Nuclear Information System (INIS)

Au-Yang, M.K.; Brenneman, B.; Raj, D.

1995-01-01

A 1:9 scale model of a proposed advanced water reactor was tested for flow-induced vibration. The main objectives of this test were: (1) to derive an empirical equation for the turbulence forcing function which can be applied to the full-sized prototype; (2) to study the effect of viscosity on the turbulence; (3) to verify the ''superposition'' assumption widely used in dynamic analysis of weakly coupled fluid-shell systems; and (4) to measure the shell responses to verify methods and computer programs used in the flow-induced vibration analysis of the prototype. This paper describes objectives (1), (2), and (3); objective (4) will be discussed in a companion paper.The turbulence-induced fluctuating pressure was measured at 49 locations over the surface of a thick-walled, non-responsive scale model of the reactor vessel/core support cylinders. An empirical equation relating the fluctuating pressure, the frequency, and the distance from the inlet nozzle center line was derived to fit the test data. This equation involves only non-dimensional, fluid mechanical parameters that are postulated to represent the full-sized, geometrically similar prototype. While this postulate cannot be verified until similar measurements are taken on the full-sized unit, a similar approach using a 1:6 scale model of a commercial pressurized water reactor was verified in the mid-1970s by field measurements on the full-sized reactor. (orig.)

Fundamentals of Turbulent and Multi-Phase Combustion

CERN Document Server

Kuo, Kenneth Kuan-yun

2012-01-01

Detailed coverage of advanced combustion topics from the author of Principles of Combustion, Second Edition Turbulence, turbulent combustion, and multiphase reacting flows have become major research topics in recent decades due to their application across diverse fields, including energy, environment, propulsion, transportation, industrial safety, and nanotechnology. Most of the knowledge accumulated from this research has never been published in book form-until now. Fundamentals of Turbulent and Multiphase Combustion presents up-to-date, integrated coverage of the fundamentals of turbulence

Final accepted paper. Effects of turbulence near a free surface on the dynamics of two-phase flow

International Nuclear Information System (INIS)

Uzawa, Ken; Watanabe, Tadashi

2011-01-01

The effect of turbulence on the dynamics of three-dimensional dam break flow is numerically investigated based on the incompressible Reynolds-averaged Navier- Stokes (RANS) equations with the Volume Of Fluid (VOF) function. It is found that the tip velocity over the ground and the impact pressure against the vertical wall in the Launder- Gibson (LG) model are in good agreement with experimental results. The dynamics of the dam break flow is subject to the viscous dissipation during the collapse of the flow, which is underestimated in the laminar model and overestimated in the realizable k - ε (RKE) model. The turbulent viscous dissipation near the free surface is comparable to that inside the water in the LG model. (author)

Turbulence modelling; Modelisation de la turbulence isotherme

Energy Technology Data Exchange (ETDEWEB)

Laurence, D. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

This paper is an introduction course in modelling turbulent thermohydraulics, aimed at computational fluid dynamics users. No specific knowledge other than the Navier Stokes equations is required beforehand. Chapter I (which those who are not beginners can skip) provides basic ideas on turbulence physics and is taken up in a textbook prepared by the teaching team of the ENPC (Benque, Viollet). Chapter II describes turbulent viscosity type modelling and the 2k-{epsilon} two equations model. It provides details of the channel flow case and the boundary conditions. Chapter III describes the `standard` (R{sub ij}-{epsilon}) Reynolds tensions transport model and introduces more recent models called `feasible`. A second paper deals with heat transfer and the effects of gravity, and returns to the Reynolds stress transport model. (author). 37 refs.

The Slug and Churn Turbulence Characteristics of Oil-Gas-Water Flows in a Vertical Small Pipe

Science.gov (United States)

Liu, Weixin; Han, Yunfeng; Wang, Dayang; Zhao, An; Jin, Ningde

2017-08-01

The intention of the present study was to investigate the slug and churn turbulence characteristics of a vertical upward oil-gas-water three-phase flow. We firstly carried out a vertical upward oil-gas-water three-phase flow experiment in a 20-mm inner diameter (ID) pipe to measure the fluctuating signals of a rotating electric field conductance sensor under different flow patterns. Afterwards, typical flow patterns were identified with the aid of the texture structures in a cross recurrence plot. Recurrence quantitative analysis and multi-scale cross entropy (MSCE) algorithms were applied to investigate the turbulence characteristics of slug and churn flows with the varying flow parameters. The results suggest that with cross nonlinear analysis, the underlying dynamic characteristics in the evolution from slug to churn flow can be well understood. The present study provides a novel perspective for the analysis of the spatial-temporal evolution instability and complexity in oil-gas-water three-phase flow.

Turbulent momentum transport due to neoclassical flows

International Nuclear Information System (INIS)

Lee, Jungpyo; Barnes, Michael; Parra, Felix I; Belli, Emily; Candy, Jeff

2015-01-01

Intrinsic toroidal rotation in a tokamak can be driven by turbulent momentum transport due to neoclassical flow effects breaking a symmetry of turbulence. In this paper we categorize the contributions due to neoclassical effects to the turbulent momentum transport, and evaluate each contribution using gyrokinetic simulations. We find that the relative importance of each contribution changes with collisionality. For low collisionality, the dominant contributions come from neoclassical particle and parallel flows. For moderate collisionality, there are non-negligible contributions due to neoclassical poloidal electric field and poloidal gradients of density and temperature, which are not important for low collisionality. (paper)

Computation of a turbulent channel flow using PDF method

International Nuclear Information System (INIS)

Minier, J.P.; Pozorski, J.

1997-05-01

The purpose of the present paper is to present an analysis of a PDF model (Probability Density Function) and an illustration of the possibilities offered by such a method for a high-Reynolds turbulent channel flow. The first part presents the principles of the PDF approach and the introduction of stochastic processes along with a Lagrangian point of view. The model retained is the one put forward by Pope (1991) and includes evolution equations for location, velocity and dissipation of a large number of particles. Wall boundary conditions are then developed for particles. These conditions allow statistical results of the logarithmic region to be correctly reproduced. Simulation of non-homogeneous flows require a pressure-gradient algorithm which is briefly described. Developments are validated by analysing numerical predictions with respect to Comte Bellot experimental data (1965) on a channel flow. This example illustrates the ability of the approach to simulate wall-bounded flows and to provide detailed information such as skewness and flatness factors. (author)

Turbulent water flow over rough bed - part I

Energy Technology Data Exchange (ETDEWEB)

Ksiazek, Leszek; Bartnik, Wojciech; Rumian, Jacek; Zagorowski, Pawel, E-mail: rmksiaze@cyf-kr.edu.pl [Department of Hydraulic Engineering and Geotechnics, University of Agriculture in Krakow, Mickiewicza Avenue 24/28, 30-059 Krakow (Poland)

2011-12-22

Restitution of diadromic fish requires restoration of ecological continuity of watercourses, e.g. by building fish ladders. Directions for fish ladders require that ichthyofauna is granted accurate conditions of water flow. To describe them, average values are used, that do not convey e.g. turbulence intensity or its spatial differentiation. The paper presents results of research on the turbulent water flow over the rough bed. The measurements were carried out with high sampling frequency probe for three velocity components. Bed configuration, distribution of average velocities and turbulence intensity were defined. The range of bed influence for the discussed water flow conditions was ascertained to reach the maximum of about 0.25 of height and decline at 0.35. The lowest turbulence and relatively lowest velocities near the bed may promote successive stages of ichthyofauna development.

Iterative and non-iterative solutions of engine flows using ASM and k-ε turbulence models

International Nuclear Information System (INIS)

Khaleghi, H.; Fallah, E.

2003-01-01

Various turbulent models are widely developed in order to make a good prediction of turbulence phenomena in different applications. The standard k-ε model shows a poor prediction for some applications. The Reynolds Stress Model (RSM) is expected to give a better prediction of turbulent characteristics, because a separate differential equation for each Reynolds stress component is solved in this model. In order to save both time and memory in this calculation a new Algebraic Stress Model (ASM) which was developed by Lumly et al in 1995 is used for calculations of flow characteristics in the internal combustion engine chamber. With using turbulent realizability principles, this model becomes a powerful and reliable turbulence model. In this paper the abilities of the model is examined in internal combustion engine flows. The results of ASM and k-ε models are compared with the experimental data. It is shown that the poor predictions of k-ε model are modified by ASM model. Also in this paper non-iterative PISO and iterative SIMPLE solution algorithms are compared. The results show that the PISO solution algorithm is the preferred and more efficient procedure in the calculation of internal combustion engine. (author)

SGS Modeling of the Internal Energy Equation in LES of Supersonic Channel Flow

Science.gov (United States)

Raghunath, Sriram; Brereton, Giles

2011-11-01

DNS of fully-developed turbulent supersonic channel flows (Reτ = 190) at up to Mach 3 indicate that the turbulent heat fluxes depend only weakly on Mach number, while the viscous dissipation and pressure dilatation do so strongly. Moreover, pressure dilatation makes a significant contribution to the internal energy budget at Mach 3 and higher. The balance between these terms is critical to determining the temperature (and so molecular viscosity) from the internal energy equation and so, in LES of these flows, it is essential to use accurate SGS models for the viscous dissipation and the pressure dilatation. In this talk, we present LES results for supersonic channel flow, using SGS models for these terms that are based on the resolved-scale dilatation, an inverse timescale, and SGS momentum fluxes, which intrinsically represent this Mach number effect.

Scaling Properties of Particle Density Fields Formed in Simulated Turbulent Flows

Science.gov (United States)

Hogan, Robert C.; Cuzzi, Jeffrey N.; Dobrovolskis, Anthony R.; DeVincenzi, Donald (Technical Monitor)

1998-01-01

Direct numerical simulations (DNS) of particle concentrations in fully developed 3D turbulence were carried out in order to study the nonuniform structure of the particle density field. Three steady-state turbulent fluid fields with Taylor microscale Reynolds numbers (Re(sub lambda)) of 40, 80 and 140 were generated by solving the Navier-Stokes equations with pseudospectral methods. Large scale forcing was used to drive the turbulence and maintain temporal stationarity. The response of the particles to the fluid was parameterized by the particle Stokes number St, defined as the ratio of the particle's stopping time to the mean period of eddies on the Kolmogorov scale (eta). In this paper, we consider only passive particles optimally coupled to these eddies (St approx. = 1) because of their tendency to concentrate more than particles with lesser or greater St values. The trajectories of up to 70 million particles were tracked in the equilibrated turbulent flows until the particle concentration field reached a statistically stationary state. The nonuniform structure of the concentration fields was characterized by the multifractal singularity spectrum, f(alpha), derived from measures obtained after binning particles into cells ranging from 2(eta) to 15(eta) in size. We observed strong systematic variations of f(alpha) across this scale range in all three simulations and conclude that the particle concentration field is not statistically self similar across the scale range explored. However, spectra obtained at the 2(eta), 4(eta), and 8(eta) scales of each flow case were found to be qualitatively similar. This result suggests that the local structure of the particle concentration field may be flow-Independent. The singularity spectra found for 2n-sized cells were used to predict concentration distributions in good agreement with those obtained directly from the particle data. This Singularity spectrum has a shape similar to the analogous spectrum derived for the

The role of zonal flows in disc gravito-turbulence

Science.gov (United States)

Vanon, R.

2018-04-01

The work presented here focuses on the role of zonal flows in the self-sustenance of gravito-turbulence in accretion discs. The numerical analysis is conducted using a bespoke pseudo-spectral code in fully compressible, non-linear conditions. The disc in question, which is modelled using the shearing sheet approximation, is assumed to be self-gravitating, viscous, and thermally diffusive; a constant cooling timescale is also considered. Zonal flows are found to emerge at the onset of gravito-turbulence and they remain closely linked to the turbulent state. A cycle of zonal flow formation and destruction is established, mediated by a slow mode instability (which allows zonal flows to grow) and a non-axisymmetric instability (which disrupts the zonal flow), which is found to repeat numerous times. It is in fact the disruptive action of the non-axisymmetric instability to form new leading and trailing shearing waves, allowing energy to be extracted from the background flow and ensuring the self-sustenance of the gravito-turbulent regime.

The role of zonal flows in disc gravito-turbulence

Science.gov (United States)

Vanon, R.

2018-07-01

The work presented here focuses on the role of zonal flows in the self-sustenance of gravito-turbulence in accretion discs. The numerical analysis is conducted using a bespoke pseudo-spectral code in fully compressible, non-linear conditions. The disc in question, which is modelled using the shearing sheet approximation, is assumed to be self-gravitating, viscous, and thermally diffusive; a constant cooling time-scale is also considered. Zonal flows are found to emerge at the onset of gravito-turbulence and they remain closely linked to the turbulent state. A cycle of zonal flow formation and destruction is established, mediated by a slow mode instability (which allows zonal flows to grow) and a non-axisymmetric instability (which disrupts the zonal flow), which is found to repeat numerous times. It is in fact the disruptive action of the non-axisymmetric instability to form new leading and trailing shearing waves, allowing energy to be extracted from the background flow and ensuring the self-sustenance of the gravito-turbulent regime.

Vortex forcing model for turbulent flow over spanwise-heterogeneous topogrpahies: scaling arguments and similarity solution

Science.gov (United States)

Anderson, William; Yang, Jianzhi

2017-11-01

Spanwise surface heterogeneity beneath high-Reynolds number, fully-rough wall turbulence is known to induce mean secondary flows in the form of counter-rotating streamwise vortices. The secondary flows are a manifestation of Prandtl's secondary flow of the second kind - driven and sustained by spatial heterogeneity of components of the turbulent (Reynolds averaged) stress tensor. The spacing between adjacent surface heterogeneities serves as a control on the spatial extent of the counter-rotating cells, while their intensity is controlled by the spanwise gradient in imposed drag (where larger gradients associated with more dramatic transitions in roughness induce stronger cells). In this work, we have performed an order of magnitude analysis of the mean (Reynolds averaged) streamwise vorticity transport equation, revealing the scaling dependence of circulation upon spanwise spacing. The scaling arguments are supported by simulation data. Then, we demonstrate that mean streamwise velocity can be predicted a priori via a similarity solution to the mean streamwise vorticity transport equation. A vortex forcing term was used to represent the affects of spanwise topographic heterogeneity within the flow. Efficacy of the vortex forcing term was established with large-eddy simulation cases, wherein vortex forcing model parameters were altered to capture different values of spanwise spacing.

Mechanics of dense suspensions in turbulent channel flows

NARCIS (Netherlands)

Picano, F.; Costa, P.; Breugem, W.P.; Brandt, L.

2015-01-01

Dense suspensions are usually investigated in the laminar limit where inertial effects are insignificant. When the flow rate is high enough, i.e. at high Reynolds number, the flow may become turbulent and the interaction between solid and liquid phases modifies the turbulence we know in single-phase

Effects of Particles Collision on Separating Gas–Particle Two-Phase Turbulent Flows

KAUST Repository

Sihao, L. V.

2013-10-10

A second-order moment two-phase turbulence model incorporating a particle temperature model based on the kinetic theory of granular flow is applied to investigate the effects of particles collision on separating gas–particle two-phase turbulent flows. In this model, the anisotropy of gas and solid phase two-phase Reynolds stresses and their correlation of velocity fluctuation are fully considered using a presented Reynolds stress model and the transport equation of two-phase stress correlation. Experimental measurements (Xu and Zhou in ASME-FED Summer Meeting, San Francisco, Paper FEDSM99-7909, 1999) are used to validate this model, source codes and prediction results. It showed that the particles collision leads to decrease in the intensity of gas and particle vortices and takes a larger effect on particle turbulent fluctuations. The time-averaged velocity, the fluctuation velocity of gas and particle phase considering particles colli-sion are in good agreement with experimental measurements. Particle kinetic energy is always smaller than gas phase due to energy dissipation from particle collision. Moreover, axial– axial and radial–radial fluctuation velocity correlations have stronger anisotropic behaviors. © King Fahd University of Petroleum and Minerals 2013

A new nonlinear turbulence model based on Partially-Averaged Navier-Stokes Equations

International Nuclear Information System (INIS)

Liu, J T; Wu, Y L; Cai, C; Liu, S H; Wang, L Q

2013-01-01

Partially-averaged Navier-Stokes (PANS) Model was recognized as a Reynolds-averaged Navier-Stokes (RANS) to direct numerical simulation (DNS) bridging method. PANS model was purported for any filter width-from RANS to DNS. PANS method also shared some similarities with the currently popular URANS (unsteady RANS) method. In this paper, a new PANS model was proposed, which was based on RNG k-ε turbulence model. The Standard and RNG k-ε turbulence model were both isotropic models, as well as PANS models. The sheer stress in those PANS models was solved by linear equation. The linear hypothesis was not accurate in the simulation of complex flow, such as stall phenomenon. The sheer stress here was solved by nonlinear method proposed by Ehrhard. Then, the nonlinear PANS model was set up. The pressure coefficient of the suction side of the NACA0015 hydrofoil was predicted. The result of pressure coefficient agrees well with experimental result, which proves that the nonlinear PANS model can capture the high pressure gradient flow. A low specific centrifugal pump was used to verify the capacity of the nonlinear PANS model. The comparison between the simulation results of the centrifugal pump and Particle Image Velocimetry (PIV) results proves that the nonlinear PANS model can be used in the prediction of complex flow field

Kinetic and dynamic probability-density-function descriptions of disperse turbulent two-phase flows

Science.gov (United States)

Minier, Jean-Pierre; Profeta, Christophe

2015-11-01

This article analyzes the status of two classical one-particle probability density function (PDF) descriptions of the dynamics of discrete particles dispersed in turbulent flows. The first PDF formulation considers only the process made up by particle position and velocity Zp=(xp,Up) and is represented by its PDF p (t ;yp,Vp) which is the solution of a kinetic PDF equation obtained through a flux closure based on the Furutsu-Novikov theorem. The second PDF formulation includes fluid variables into the particle state vector, for example, the fluid velocity seen by particles Zp=(xp,Up,Us) , and, consequently, handles an extended PDF p (t ;yp,Vp,Vs) which is the solution of a dynamic PDF equation. For high-Reynolds-number fluid flows, a typical formulation of the latter category relies on a Langevin model for the trajectories of the fluid seen or, conversely, on a Fokker-Planck equation for the extended PDF. In the present work, a new derivation of the kinetic PDF equation is worked out and new physical expressions of the dispersion tensors entering the kinetic PDF equation are obtained by starting from the extended PDF and integrating over the fluid seen. This demonstrates that, under the same assumption of a Gaussian colored noise and irrespective of the specific stochastic model chosen for the fluid seen, the kinetic PDF description is the marginal of a dynamic PDF one. However, a detailed analysis reveals that kinetic PDF models of particle dynamics in turbulent flows described by statistical correlations constitute incomplete stand-alone PDF descriptions and, moreover, that present kinetic-PDF equations are mathematically ill posed. This is shown to be the consequence of the non-Markovian characteristic of the stochastic process retained to describe the system and the use of an external colored noise. Furthermore, developments bring out that well-posed PDF descriptions are essentially due to a proper choice of the variables selected to describe physical systems

A numerical method to calculate flow-induced vibrations in a turbulent flow

International Nuclear Information System (INIS)

Sadaoka, Noriyuki; Umegaki, Kikuo

1993-01-01

An unsteady fluid force on structures in a turbulent flow can cause their vibration. The phenomenon is the most important among various flow-induced vibrations and it is an important subject in design nuclear plant components such as heat exchangers. A new approach to simulate flow-induced vibrations is introduced. A fully coupled analysis of fluid-structure interaction has been realized in a turbulent flow field by integrating the following calculational steps: (a) solving turbulent flow by a direct simulation method where the ALE (arbitrary Lagrangian Eulerian) type approximation is adopted to take account of structure displacements; (b) estimating fluid force on structures by integrating fluid pressure and shear stress; (c) calculating dynamic response of structures and determining the amount of displacement; (d) regenerate curvilinear grids for new geometry using the boundary-fitted coordinate transformation method. Forced vibration of a circular cylinder in a cross flow were successfully simulated and the synchronization phenomena between Karman-vortices and cylinder vibrations were clearly seen

Assessment of intermittency transport equations for modeling transition in boundary layers subjected to freestream turbulence

International Nuclear Information System (INIS)

Suluksna, Keerati; Juntasaro, Ekachai

2008-01-01

The γ-Re θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. ERCOFTAC International Symposium Engineering Turbulence Modelling and Measurements] is a highly generalized transport equation model in which it has been developed based on the concept of local variables compatible with modern CFD methods where the unstructured grid and the parallel computing technique are usually integrated in. To perform the prediction with this model, two essential parameters, F length which is used to control the length of the transition region and Re θc which is used to control the onset of the transition location, must be specified to close the model. At present, both parameters are proprietary and their formulations are unpublished. For the first time here, the relations for both parameters are formulated by means of numerical experiments and analysis under the assumption of Re θc = Re θt corresponding with the bypass transition behavior. Based on this analysis, the optimized values of the parameters are found and their relations can be constructed as follows: Re θc = 803.73(Tu ∞ , le + 0.6067) -1.027 and F length = 163 ln(Tu ∞ , le ) + 3.625. The performance of this transition model is assessed by testing with the experimental cases of T3AM, T3A, and T3B. Detailed comparisons with the predicted results by the transition models of Suzen and Huang [Suzen, Y.B., Huang, P.G., 2000. Modeling of flow transition using an intermittency transport equation. J. Fluids Eng. 122, 273-284] and Lodefier et al. [Lodefier, K., Merci, B., De Langhe, C., Dick, E., 2003. Transition modelling with the SST turbulence model and intermittency transport equation. ASME Turbo Expo, Atlanta, GA, USA, June 16-19], and also with the predicted results by the k-ε model of Launder and Sharma [Launder, B.E., Sharma, B., 1974. Application of the energy dissipation model of turbulence to the calculation of

Formation of hybrid gold nanoparticle network aggregates by specific host-guest interactions in a turbulent flow reactor

NARCIS (Netherlands)

Weinhart-Mejia, R.; Huskens, Jurriaan

2014-01-01

A multi-inlet vortex mixer (MIVM) was used to investigate the formation of hybrid gold nanoparticle network aggregates under highly turbulent flow conditions. To form aggregates, gold nanoparticles were functionalized with β-cyclodextrin (CD) and mixed with adamantyl (Ad)-terminated

A numerical study of a turbulent axisymmetric jet emerging in a co-flowing stream

Energy Technology Data Exchange (ETDEWEB)

Mahmoud, Houda, E-mail: mahhouda2003@yahoo.f [Unite de thermique et thermodynamique des procedes industriels, Ecole Nationale d' Ingenieurs de Monastir, route de Ouardanine, 5020 Monastir (Tunisia); Kriaa, Wassim; Mhiri, Hatem [Unite de thermique et thermodynamique des procedes industriels, Ecole Nationale d' Ingenieurs de Monastir, route de Ouardanine, 5020 Monastir (Tunisia); Palec, Georges Le; Bournot, Philippe [IUSTI, UMR CNRS 6595, 5 Rue Enrico Fermi, Technopole de Chateau-Gombert, 13013 Marseille (France)

2010-11-15

In this work, we propose a numerical study of an axisymmetric turbulent jet discharging into co-flowing stream with different velocities ratios ranging between 0 and {infinity}. The standard k-{epsilon} model and the RSM model were applied in this study. The numerical resolution of the governing equations was carried out using two computed codes: the first is a personal code and the second is a commercial CFD code FLUENT 6.2. These two codes are based on a finite volume method. The present predictions are compared with the experimental data. The results show that the two turbulence models are valid to predict the average and turbulent flow sizes. Also, the effect of the velocities ratios on the flow structure was examined. For R{sub u} > 1, it is noted the appearance of the fall velocity zone due to the presence of a trough low pressure. This fall velocity becomes increasingly intense according to R{sub u} and changes into a recirculation zone for R{sub u} {>=} 4.5. This zone is larger and approaches more the nozzle injection when R{sub u} increases.

Simplified computational simulation of liquid metal behaviour in turbulent flow with heat transfer

International Nuclear Information System (INIS)

Costa, E.B. da.

1992-09-01

The present work selected the available bibliography equations and empirical relationships to the development of a computer code to obtain the turbulent velocity and temperature profiles in liquid metal tube flow with heat generation. The computer code is applied to a standard problem and the results are considered satisfactory, at least from the viewpoint of qualitative behaviour. (author). 50 refs, 21 figs, 3 tabs

Effect of mean flow on the interaction between turbulence and zonal flow

International Nuclear Information System (INIS)

Uzawa, Ken; Kishimoto, Yasuaki; Li Jiquan

2006-01-01

The effects of an external mean flow on the generation of zonal flow in drift wave turbulence are theoretically studied in terms of a modulational instability analysis. A dispersion relation for the zonal flow instability having complex frequency ω q =Ω q +iγ q is derived, which depends on the external mean flow's amplitude |φ f | and radial wave number k f . As an example, we chose an ion temperature gradient (ITG) turbulence-driven zonal flow as the mean flow acting on an electron temperature gradient (ETG) turbulence-zonal flow system. The growth rate of the zonal flow γ q is found to be suppressed, showing a relation γ q =γ q0 (1 - α|φ f | 2 k f 2 ), where γ q0 is the growth rate in the absence of mean flow and α is a positive numerical constant. This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized at α|φ f 2 |k f 2 ≅ 1. Meanwhile, the suppression is accompanied by an increase of the real frequency |Ω q |. The underlying physical mechanism of the suppression is discussed. (author)

On the application of the method of turbulent flow to transient and quasi-stationary flow calculations in high temperature reactors with spherical fuel elements

International Nuclear Information System (INIS)

Hoefer, I.

1980-12-01

For the calculation of flows in high-temperature reactors and of their temperature behavior the equations of the method of turbulent flow in the primitive form are derived for inhomogeneous regions. This system of equations is appropriate for the investigation of transient and quasi-stationary phenomena in pebble beds. By modification of the flow function in parallel arranged reflector channels a parallel flow can be simulated. For simplification the flow in region with a smaller pressure loss is assumed to be a potential flow. For the numerical solution of the time-dependent convective parts of the system of equations a number of explicit and implicit difference methods are compared. If the method using UP-WIND differences is taken to be an interpolation method the introduction of an extension becomes possible, which together with preliminary integration of the fictional terms allows to apply larger time steps. The algebraic system of equations for numerical calculation of a steady flow field also is established by formation of UP-WIND differences for the convective terms. By mathematical verification of some examples the applicability of the mathematical model for flow problems in pebble beds with forced or natural convection is shown. (orig.) [de

Turbulence modeling and surface heat transfer in a stagnation flow region

Science.gov (United States)

Wang, C. R.; Yeh, F. C.

1987-01-01

Analysis for the turbulent flow field and the effect of freestream turbulence on the surface heat transfer rate of a stagnation flow is presented. The emphasis is on modeling and its augmentation of surface heat transfer rate. The flow field considered is the region near the forward stagnation point of a circular cylinder in a uniform turbulent mean flow.

STAR FORMATION IN TURBULENT MOLECULAR CLOUDS WITH COLLIDING FLOW

International Nuclear Information System (INIS)

Matsumoto, Tomoaki; Dobashi, Kazuhito; Shimoikura, Tomomi

2015-01-01

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence is weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of –1.35 when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow, the velocity dispersion of gas tends to be larger than the stellar velocity dispersion. The signatures of colliding flows and turbulence appear in channel maps reconstructed from the simulation data. Clouds without colliding flow exhibit a cloud-scale velocity shear due to the turbulence. In contrast, clouds with colliding flow show a prominent anti-correlated distribution of thin filaments between the different velocity channels, suggesting collisions between the filamentary clouds

STAR FORMATION IN TURBULENT MOLECULAR CLOUDS WITH COLLIDING FLOW

Energy Technology Data Exchange (ETDEWEB)

Matsumoto, Tomoaki [Faculty of Humanity and Environment, Hosei University, Fujimi, Chiyoda-ku, Tokyo 102-8160 (Japan); Dobashi, Kazuhito; Shimoikura, Tomomi, E-mail: matsu@hosei.ac.jp [Department of Astronomy and Earth Sciences, Tokyo Gakugei University, Koganei, Tokyo 184-8501 (Japan)

2015-03-10

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence is weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of –1.35 when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow, the velocity dispersion of gas tends to be larger than the stellar velocity dispersion. The signatures of colliding flows and turbulence appear in channel maps reconstructed from the simulation data. Clouds without colliding flow exhibit a cloud-scale velocity shear due to the turbulence. In contrast, clouds with colliding flow show a prominent anti-correlated distribution of thin filaments between the different velocity channels, suggesting collisions between the filamentary clouds.

Comparison of Turbulence Models in Simulation of Flow in Small-Size Centrifugal Compressor

Directory of Open Access Journals (Sweden)

B. B. Novickii

2015-01-01

Full Text Available The aim of the work is the choice of turbulence model for the closure of the Reynoldsaveraged Navier-Stokes equations for calculation of the characteristics of small-size centrifugal compressor. To this were built three-dimensional sectors (as the compressor axisymmetric blade impeller and the diffuser of the centrifugal compressor on the basis of which they were created two grid models. The dimension of the grid model for the calculation models of turbulence komega and SST was 1.4 million. Elements and the dimensionless parameter y + does not exceed 2. turbulence model family k-epsilon model grid was also 1.4 million. Elements, and the dimensionless parameter y + was greater than 20, which corresponds to recommended values. The next part of the work was the task of boundary conditions required for the correct ca lculation. When the impeller inlet pawned pressure working fluid and the total temperature at the outlet and the gas flow rate through the stage. On the side faces sectors pawned boundary cond ition «Periodic», allowing everything except the wheel, but only axisymmetric part, which significantly reduces the required computational time and resources. Accounting clearance in addition to the meridional geometry construction additionally taken into account boundary condition «Counter Rotating Wall», which allows you to leave the domain in the rotating disc fixed coa ting.The next step was to analyze the results of these calculations, which showed that the turbulence model k-epsilon and RNG does not show the velocity vectors in the boundary layer, and "pushes" the flow from the blade using wall functions. At the core of the flow turbulence model k-omega shown for the undisturbed flow, which is not typical for the compressor working on predpompazhnom mode. For viscous gas diffuser vane for turbulence models SST, k-omega, RNG k-epsilon and has a similar character.The paper compares the characteristics of pressure centrifugal compressor

Experimental study of drop breakup in a turbulent flow; Etude experimentale de la rupture de gouttes dans un ecoulement turbulent

Energy Technology Data Exchange (ETDEWEB)

Galinat, S.

2005-04-15

This work presents the drop breakup phenomenon in a turbulent flow induced by a cross-section restriction in a pipe. A global analysis of single-drop breakup, in a finite volume downstream of the orifice, has allowed deriving statistical quantities such as the break-up probability and the daughter-drop distribution. These parameters are function of a global Weber number based on the maximal pressure drop through the orifice. At a local scale, the locations of breakup events are distributed heterogeneously and depend on the flow Reynolds number. The local hydrodynamic study in downstream of the orifice, which has been done by using Particle Image Velocimetry, reveals the specific breakup zones. Otherwise, this analysis has proved that the turbulence is the predominant external stress at the drop scale. The relation between drop deformation and the external stress along the trajectory has been simulated numerically by the response of a damped oscillator to the locally measured instantaneous turbulence forcing. The results of statistical analysis have allowed to introduce a breakup criterion, based on a unique deformation threshold value for all experiments. This multi-scale approach has been conducted to study drop breakup mechanisms in a concentrated dispersion. The breakup probability decrease with the increase of dispersed phase concentration, which influences the turbulent Weber number distribution in downstream of the orifice. (author)