Showing papers on "K-epsilon turbulence model published in 1993"

Turbulence modeling for CFD

Abstract: Keywords: ecoulement : compressible Note: + disquette Reference Record created on 2005-11-18, modified on 2016-08-08

ZONAL TWO EQUATION k-w TURBULENCE MODELS FOR AERODYNAMIC FLOWS

Abstract: Two new versions of the k - w two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k - w model of Wilcox. but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner SOC7£; of the boundary-layer but changes gradually to the standard k - f. model (in a k - w fonnulation) towards the boundary-layer edge. The new model is also virtually identical to the k - f. model for free shear layers. The second version of the model is called Shear-Stress Transport (SSn model. It is a variation of the BSL model with the additional ability to account for the transport of the principal turbulent shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear-stress is pro­ portional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different fiowfields. The results of the BSL model are similar to those of the original k - w model, but without the undesirable free stream dependency. The predictions of the SST model are also independent of the freestrearn values but show better agreement with exper­ imental data for adverse pressure gradient boundary-layer flows.

Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence

Abstract: The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, has been shown to differ from that in still fluid owing to a bias from the particle inertia (Maxey 1987). Previous numerical results for particles in a random flow field, where the flow dynamics were not considered, showed an increase in the average settling velocity. Direct numerical simulations of the motion of heavy particles in isotropic homogeneous turbulence have been performed where the flow dynamics are included. These show that a significant increase in the average settling velocity can occur for particles with inertial response time and still-fluid terminal velocity comparable to the Kolmogorov scales of the turbulence. This increase may be as much as 50% of the terminal velocity, which is much larger than was previously found. The concentration field of the heavy particles, obtained from direct numerical simulations, shows the importance of the inertial bias with particles tending to collect in elongated sheets on the peripheries of local vortical structures. This is coupled then to a preferential sweeping of the particles in downward moving fluid. Again the importance of Kolmogorov scaling to these processes is demonstrated. Finally, some consideration is given to larger particles that are subject to a nonlinear drag force where it is found that the nonlinearity reduces the net increase in settling velocity.

On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification

Abstract: The modification of decaying homogeneous turbulence due to its interaction with dispersed small solid particles (d/η<1), at a volumetric loading ratio φv≤5×10−4, is studied using direct numerical simulation. The results show that the particles increase the fluid turbulence energy at high wave numbers. This increase of energy is accompanied by an increase of the viscous dissipation rate, and, hence, an increase in the rate of energy transfer T(k) from the large‐scale motion. Thus, depending on the conditions at particle injection, the fluid turbulence kinetic energy may increase initially. But, in the absence of external sources (shear or buoyancy), the turbulence energy eventually decays faster than in the particle‐free turbulence. In gravitational environment, particles transfer their momentum to the small‐scale motion but in an anisotropic manner. The pressure‐strain correlation acts to remove this anisotropy by transferring energy from the direction of gravity to the other two directions, but at the sa...

The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence

Abstract: The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Comparison of two-equation turbulence models for boundary layers with pressure gradient

Abstract: This paper compares the performance of eight low Reynolds number k-epsilon and k-omega models for high Reynolds number, incompressible turbulent boundary layers with favorable, zero, and adverse pressure gradients. Results obtained underscore the k-epsilon model's unsuitability for such flows. Even more seriously, the k-epsilon model is demonstrated to be inconsistent with the well-established physical structure of the turbulent boundary layer, and low Reynolds number corrections cannot remove the inconsistency. By contrast, the k-omega model, with and without low Reynolds number modifications, proves to be very accurate for all of the tests conducted. 16 refs.

Mean flow and turbulence fields over two‐dimensional bed forms

Abstract: Detailed laser-Doppler velocity and Reynolds stress measurements over fixed two-dimensional bed forms are used to investigate the coupling between the mean flow and turbulence and to examine effects that play a role in producing the bed form instability and finite amplitude stability. The coupling between the mean flow and the turbulence is explored in both a spatially averaged sense, by determining the structure of spatially averaged velocity and Reynolds stress profiles, and a local sense, through computation of eddy viscosities and length scales. The measurements show that there is significant interaction between the internal boundary layer and the overlying wake turbulence produced by separation at the bed form crest. The interaction produces relatively low correlation coefficients in the internal boundary layer, which suggests that using local bottom stress to predict bed load flux may not only be erroneous, it may also disregard the essence of the bed form instability mechanism. The measurements also indicate that topographically induced acceleration over the bed form stoss slope has a more significant effect in damping the turbulence over bed forms than was previously supposed, which is hypothesized to play a role in the stabilization of fully developed bed forms.

Developments in the gyrofluid approach to Tokamak turbulence simulations

Abstract: A status report is given on developments in the gyrofluid approach to simulating tokamak turbulence. 'Gyrofluid' (r 'gyro-Landau fluid') equations attempt to extend the range of validity of fluid equations to a more collisionless regime typical of tokamaks, by developing fluid models of important kinetic effects such as Landau-damping and gyro-orbit averaging. The fluid moments approach should converge if enough moments are kept, though this may require a large number of moments for some processes. Toroidal gyrofluid equations have been extended from 4 to 6 moments, and to include the mu Del B magnetic mirroring force. An efficient field-line coordinate system for toroidal turbulence simulations (useful for both particle and fluid simulations) is presented. Nonlinear 3-D simulations of toroidal ITG-driven turbulence indicate that turbulence-generated sheared flows play an important role in the development and saturation of the turbulence. There is a strong enhancement of the flows when the electrons are assumed adiabatic on each flux surface, which is partially offset by toroidal drift effects which reduce the flows.

New time scale based k-epsilon model for near-wall turbulence

Abstract: A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data.

Direct numerical simulation of isotropic turbulence interacting with a weak shock wave

Abstract: Direct numerical simulations are used to investigate the interaction of isotropic quasi-incompressible turbulence with a weak shock wave. A linear analysis of the interaction is conducted for comparison with the simulations. Both the simulations and the analysis show that turbulence is enhanced during the interaction. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. It is suggested that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behavior not reproduced by the linear analysis. Analysis of the budget of the turbulent kinetic energy transport equation shows that this behavior can be attributed to the pressure transport term. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.

Turbulence in stratified shear flows: implications for interpreting shear-induced mixing in the ocean

Abstract: Direct numerical simulations of the time evolution of homogeneous stably stratified turbulent sheer flows have been performed for several Richardson numbers Ri and Reynolds numbers Rλ. The results show excellent agreement with length scale models developed from laboratory experiments to characterize oceanic turbulence. When the Richardson number Ri is less than the stationary value Ris, the turbulence intensity grows at all scales; the growth rate is a function of Ri. The size of the vertical density inversions also increases. When Ri ≥ Ri, the largest turbulent eddies become vertically constrained by buoyancy when the Ellison (turbulence) scale LEand the Ozmidov (buoyancy) scale LO are equal. At this point the mixing is most efficient and the flux Richardson number or mixing efficiency is Rf ≈ 0.20 for the stationary Richardson number Ris = 0.21. The vertical mass flux becomes countergradient when ϵ ≈ 19vN2, and vertical density overturns are suppressed in few than half of a Brunt-Vaisala period...

A Realizable Reynolds Stress Algebraic Equation Model

Abstract: The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Origin of turbulence‐producing eddies in a channel flow

Abstract: A principal theoretical problem in understanding wall turbulence is the determination of how turbulence is created and sustained, ie, the explanation of how energy is transferred from the mean flow to the turbulence Flow‐oriented vortical eddies have been associated with large Reynolds stresses and with the production of turbulence in the viscous region close to the wall Their creation and evolution are investigated in a high‐resolution direct numerical simulation of turbulent flow in a channel An important finding is that they regenerate themselves by a process that appears to be weakly dependent on the outer flow This involves the enhancement of streamwise vorticity at the wall, of opposite sign, at a location where a stress‐producing eddy lifts from the wall

Eulerian Prediction of the Fluid/Particle Correlated Motion in Turbulent Two-Phase Flows

Abstract: An approximate equation governing the turbulent fluid velocity encountered along discrete particle path is used to derive the fluid/particle turbulent moments required for dispersed two-phase flows modelling. Then, closure model predictions are compared with results obtained from large-eddy simulation of particle fluctuating motion in forced isotropic fluid turbulence.

Calculation of Vortex Shedding Past a Square Cylinder with Various Turbulence Models

Abstract: The vortex-shedding flow past a square cylinder at Re = 22.000 was calculated with various turbulence models. The 2D periodic shedding motion was resolved in an unsteady calculation, and the superimposed stochastic turbulent fluctuations were simulated both with the k — e eddy-viscocity model and with a Reynolds-stress equation model. For both models, the viscosity-affected near-wall region was either bridged by wall functions or was resolved with a simpler one-equation model using a prescribed length-scale distribution. The k — e model with wall functions does not yield unsteady vortex motion while the other model variants do. The two-layer k —e model underpredicts severely the periodic fluctuations and also the Strouhal number and drag coefficient. The Reynoldsstress-equation models yield considerably better agreement with experiments, but tend to overpredict the periodic fluctuating motion and also miss some other details of the flow behaviour.

Compressibility effects on the growth and structure of homogeneous turbulent shear flow

Abstract: Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure-dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

Effects of Adverse Pressure Gradients on Mean Flows and Turbulence Statistics in a Boundary Layer

Abstract: Measurements in boundary layers with ‘moderate’ to ‘strong’ adverse pressure gradients are presented and discussed. With increasing adverse pressure gradients, the velocity profile in \( {\overline U ^ + } \sim {y^ + }\) coordinates lies below the standard log law, thus indicating a reduction in the thickness of the sublayer. Correspondingly, the turbulence energy components as well as the Reynolds shear stress peak in the outer region of the boundary layer. Higher-order moments of velocity fluctuations are also seriously affected by the adverse pressure gradient. In strong adverse-pressure-gradient flows, the triple products of velocity have completely opposite signs to those in zero-pressure-gradient flows over most of the boundary layer.

Zonal Two Equation Kappa-Omega Turbulence Models for Aerodynamic Flows

Abstract: Two new versions of the kappa-omega two-equation turbulence model will be presented The new Baseline (BSL) model is designed to give results similar to those of the original kappa-omega model of Wilcox, but without its strong dependency on arbitrary freestream values The BSL model is identical to the Wilcox model in the inner 50% of the boundary-layer but changes gradually to the standard kappa-epsilon model (in a kappa- omega formulation) towards the boundary-layer edge The free shear layers The second version of the model is called Shear-Stress Transport (SST) model It is a variation of the BSL model with the additional ability to account for the transport of the principal turbulent shear stress in adverse pressure gradient boundary-layers The model is based on Bradshaw's assumption that the principal shear-stress is proportional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity Both models are tested for a large number of different flowfields The results of the BSL model are similar to those of the original kappa-omega model, but without the undesirable freestream dependency The predictions of the SST model are also independent of the freestream values but show better agreement with experimental data for adverse pressure gradient boundary-layer flows

Large eddy simulation of shock turbulence interaction

Abstract: A nonconservative formulation of the energy equation (solving for internal energy) was used to perform large eddy simulations of compressible turbulence in Moin et al. due to its simplicity in implementing SGS models compared to the conservative formulation (solving for total energy). In problems with shocks in the domain, however, the total energy formulation is preferred due to its conservative nature. A conservative set of equations for the LES were derived from the nonconservative equations derived by Moin et al. Performance of the conservative formulation was compared with the experiment on decaying grid-generated turbulence as well as with the filtered DNS field. Various shock-capturing schemes were tested, and an ENO shock-capturing scheme of Shu and Osher was chosen for the simulation of shock/turbulence interaction. The scheme was tested and validated against the data base generated by DNS of weak shock waves. The results obtained with the essentially nonoscillatory (ENO) scheme were within 5 percent from the DNS results, and used less than 25 percent of the CPU time used in the DNS.

Low-Reynolds-number k-epsilon model for unsteady turbulent boundary-layer flows

Abstract: An assessment of the near-wall and low-Reynolds-number functions used in low-Reynolds-number k-epsilon models suggests that they are not suitable for the near-wall region of unsteady turbulent boundary layers, where the flow is characterized by rapid changes in phase. An improved low-Reynolds-number k-epsilon model is developed in this paper. The near-wall and low-Reynolds-number functions in this model are formulated as functions of the local turbulent Reynolds numbers instead of the inner variable y(+). The present model also has the correct asymptotic behavior in the near-wall region. The turbulence model has been incorporated in an unsteady boundary-layer code and validated for unsteady turbulent boundary layers with and without adverse pressure gradients. The predictions agree well with the experimental data and the theoretical analysis. For the cases tested, the present model correctly predicts the unsteady near-wall flow and the unsteady shin friction at various frequencies.