A compressible turbulence model for the dissipation rate (original) (raw)

Extension of the Launder, Reece and Rodi model on compressible homogeneous shear flow

The European Physical Journal B, 2005

This article describes the second order closure progress that was made to calculate compressible homogeneous shear flow with significant compressibility. Several DNS results show that compressibility has an important effect on the pressure-strain correlation. The term recognized as the principal responsible for the change in the magnitude of Reynolds-stress anisotropies. Thus, the pressure-strain incompressible models do not correctly predict compressible turbulence at high-speed shear flow. A method of including compressibility effects in the pressure-strain correlation is the subject of the present study. The concept of the growth rate of turbulent kinetic energy can be used to construct a compressible correction to the Launder, Reece and Rodi model for the pressure-strain correlation. This correction concerns essentially the C1, C3 and C4 coefficients which become in a compressible turbulence situation a function of the turbulent Mach number. The application of the new model shows good agreement with DNS results of Sarkar for cases A1, A2 and A3. These cases correspond to a moderate mean shear rate, so that nonlinear effects are important.

Compressible Homogeneous Shear: Simulation and Modeling

Turbulent Shear Flows 8, 1993

The present study investigates compressibility effects on turbulence by direct numerical simulation of homogeneous shear flow. A primary observation is that the growth of the turbulent kinetic energy decreases with increasing turbulent Mach number. The sinks provided by compressible dissipation and the pressure-dilatation, along with reduced Reynolds shear stress, are shown to contribute to the reduced growth of kinetic energy. Models are proposed for these dilatational terms and verified by direct comparison with the simulations. The differences between the incompressible and compressible fields are brought out by the examination of spectra, statistical moments, and structure of the rate of strain tensor.

A Reynolds stress model of turbulence and its application to thin shear flows

Journal of Fluid Mechanics, 1972

The paper provides a model of turbulence which effects closure through approximated transport equations for the Reynolds stress tensor overlineuiuj\overline{u_iu_j}overlineuiuj and for the turbulence energy-dissipation rate ε. In its most general form the model thus entails the solution of seven transport equations for turbulence quantities but contains only six constants to be determined by experiment. It is demonstrated that the proposed approximation to the pressure-rate-of-strain correlations leads to satisfactory predictions of the component stress levels in plane homogeneous turbulence, including the non-equality of the lateral and transverse normal-stress components.For boundary-layer flows a simpler version of the model is derived wherein transport equations are solved only for the shear stress −overlineu1u2-\overline{u_1u_2}−overlineu_1u_2 the turbulence energy κ and ε. This model has been incorporated in the numerical solution procedure of Patankar & Spalding (1970) and applied to the prediction of a number of boundary-...

Direct simulation of compressible turbulence in a shear flow

Theoretical and Computational Fluid Dynamics, 1991

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M t2), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.

Explicit algebraic Reynolds stress model for compressible flow turbulence

Journal of Turbulence, 2013

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Reynolds stress transport models in unsteady and non-equilibrium turbulent flows

In this work the predictive capability of a number of Reynolds stress transport (RST) models was first tested in a range of non-equilibrium homogeneous flows, comparisons being drawn with existing direct numerical simulation (DNS) results and physical measurements. The cases considered include both shear and normally strained flows, in some cases with a constant applied strain rate, and in others where this varied with time. Subsequently, the models were also tested in the inhomogeneous case of pulsating channel flow over a wide range of frequencies. Models were generally found to perform well in homogeneous shear at low shear rates, but their performance increasingly deteriorated at higher shear rates. This was attributed mainly to over-predicted shear stress anisotropy at high shear rates. Performance in irrotational homogeneous strains was generally good, and was more consistent over a much wider range of strain rates. In the pulsating channel flows, the most challenging case for the models was found to be the lowest frequency case where, because of the amplitude of oscillation, laminarization and re-transition to turbu- lence were present at certain phases of the cycle.

Development of turbulence models for shear flows by a double expansion technique(Final Report)

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot & Orszag with scale expansions for the Reynolds stress and production of dissipation terms. Th, additional expansion parameter,, (---K/ i) is the ratio of the turbulent to mean strain time scale. While 'low-order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of ;r sufficesterms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent. Aceos2:,a Y-r •~~~~ r aIIon e "' Iji-'ty CcdO8

Development of turbulence models for shear flows by a double expansion technique

Physics of Fluids A: Fluid Dynamics, 1992

A rate-dependent algebraic stress model for turbulence

Applied Mathematical Modelling, 1991

Based on the stress transport model, a rate-dependent algebraic expression for the Reynolds stress tensor is developed. It is shown that the new model includes the normal stress effects and exhibits viscoelastic behavior. Furthermore, it is compatible with recently developed improved models of turbulence. The model is also consistent with the limiting behavior of turbulence in the inertial sublayer and is capable of predicting secondary flows in noncircular ducts. The TEACH code is modified according to the requirements of the rate-dependent model and is used to predict turbulent flow fields in a channel and behind a backward-facing step. The predicted results are compared with the available experimental data and those obtained from the standard k--E and algebraic stress models. It is shown that the predictions of the new model are in better agreements with the experimental data.

Examination of the Shear Stress Transport Assumption with a Low-Reynolds Number k-omega Model for Aerodynamic Flows

37th AIAA Fluid Dynamics Conference and Exhibit, 2007

Using a low-Reynolds number k − ω model and its high-Reynolds number variant as base models, the Shear Stress Transport (SST) concept is examined in computations of flows around the RAE2822 airfoil and the DLR-F6 wind-body configuration. Both flows are characterized by local boundary layer separation. Based on an analysis of the net production for the turbulent kinetic energy, k, and for its specific dissipation rate, ω, the rationale is highlighted behind the SST formulation that enables improved predictions of flow separation. It is shown that the SST formulation may make the modeling contain the growth of the production of k and, consequently, suppress the turbulent diffusion. Incorporating the SST assumption, the model responds more appropriately to the effect of an adverse pressure gradient in the boundary layer and produces more extended flow separation bubble than the original base model. Improvement due to the SST formulation is also observed in predictions of the shock location for the transonic aerodynamic flows considered in this work.

A compressible turbulence model for the dissipation rate (original) (raw)

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