A Reynolds stress model of turbulence and its application to thin shear flows (original) (raw)
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Journal of Fluid Mechanics, 1995
Models for the dissipation tensor and (slow) pressure-strain terms of the Reynolds stress transport equations are presented which are applicable near boundaries. These models take into account the large inhomogeneity and anisotropy that can be present near walls and surfaces, and are inspired by the physical insights developed in Part 1 of this paper. The dissipation tensor model represents a fundamentally new approach to dealing with turbulence inhomogeneities. The pressure-strain model shows how the classic return-to-isotropy model of can be adapted to the near-wall region. The closure hypotheses underlying these two models are tested in an a priori fashion using direct numerical simulation (DNS) data.
Progress in the development of a Reynolds-stress turbulence closure
Journal of Fluid Mechanics, 1975
The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate ε. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.
Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence
Journal of Fluid Mechanics, 1976
The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient$\overline{uv^2}/\overline{u^2}\overline{v^2} $is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.
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.
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.
Numerical study of stress-transport turbulence models: Implementation and validation issues
Computers & Fluids, 2007
The primary goal of this work is to implement, validate and compare in shear-free and simple wall-bounded turbulent flows the performance of five stress-transport turbulence models that have recently appeared in the open literature. A secondary goal of this work is to analyze and study the effort and difficulties encountered by programmers when implementing turbulence models developed by other researchers. The need for standardized procedures and for the development of efficient numerical techniques is advocated as a means to reduce the model-variance and code dependency of turbulent models. The second-order models chosen for this study are the Launder-Shima, the Jakirlic-Hanjalic, the elliptic-blending model of Manceau, the Turbulent Potential Model proposed by Perot and an unidentified model. For comparison reasons, Wilcox k-x eddy-viscosity model was included in the study. The validation and the study of the performance of the models were performed through the comparison of the numerical solutions with experimental data and analytical solutions. The five benchmark flowfields considered in this study encompass the shear-free and wall-bounded regimes and are the flat plate without pressure gradient, the flow over a plate with a moderately adverse pressure gradient, and the self-similar flows of the mixing layer, the plane jet and the axi-symmetric jet. The tested stress-transport models produced results in general agreement with the experiments. However, no clear advantage of the stress-transport model over Wilcox k-x model was noticed in these simple flowfields. The Launder-Shima model could not predict accurately the skin friction on a flat plate but it performed well in all the other cases. Although the test cases used were simple, a major difficulty encountered in this effort is the unreliability of the open literature as a resource for turbulence model implementation. A general lack of consistency was observed between model versions published in different journals or at different times. The detrimental effect that such a lack of structure and consistency has on the CFD community is discussed.
A new approach to modelling near-wall turbulence energy and stress dissipation
Journal of Fluid Mechanics, 2002
A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as we...
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.
Critical Evaluation of the Shear-Stress Transport (SST) Κ−ω Turbulence Model
2005
This paper presents a performance analysis of the shear stress transport κ-ω model in the prediction of a flow over a backward facing step. The commercial code CFX, wich is based on the finite volume method, is used to simulate this flow. The results are compared with predictions made by the standard κ-e model and by the κ-ω model and with experimental data, verifying the models capability of representing the recirculation zones and the pressure recuperation after the backward facing step. It has been concluded that the κ-ω SST model is computationally robust and has a better prediction capability than the traditional models.
Symmetry, 2021
The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τ/ρ and the kinetic energy of turbulence (k=q2/2). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τ/ρ=a11−AFRiFq2/2 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. ...