Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

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Two-equation eddy-viscosity turbulence models for engineering applications

A one-equation turbulence model for aerodynamic flows

A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: 1) conventional A:-e and A>w formulations generally are inaccurate for boundary layers in adverse pressure gradient; 2) using "wall functions'' tends to mask the shortcomings of such models; and 3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows. With no viscous damping of the model's closure coefficients and without the aid of wall functions, the model equations can be integrated through the viscous sublayer. Surface boundary conditions are presented that permit accurate predictions for flow over rough surfaces and for flows with surface mass addition.

Reassessment of the scale-determining equation for advanced turbulence models

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Turbulence models for near-wall and low Reynolds number flows - A review

This paper presents a reformulated version of the author'sk-ω model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-ω model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/ boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.

Formulation of the k-w Turbulence Model Revisited

A model is devised for computing general turbulent flows. The model is an improvement over two-equation turbulence models in a critically important manner, that is, the new model accounts for disalignment of the Reynolds-stress-tensor and the mean-strain-rate-tensor principal axes. The improved representation of the Reynolds-stress tensor has been accomplished through the introduction of a multiscale description of the turbulence, i.e., two energy scales are used corresponding to upper and lower partitions of the turbulence energy spectrum. A novel feature of the formulation is that the differential equation for the Reynolds-stress tensor is of first order, which in effect corresponds to what can be termed an "algebraic stress model" with convective terms. As a consequence of its mathematical simplicity, the model is very efficient and easy to implement computationally. The model is applied to a wide range of turbulent flows including homogeneous turbulence, compressible and incompressible two-dimensional boundary layers, and unsteady boundary layers including periodic separation and reattachment. Comparisons with corresponding experimental data show that the model reproducesall salient features of the flows considered/Perturbation analysis of the viscous sublayer shows that integration through the sublayer can be accomplished with no special viscous modifications to the closure coefficients appearing in the model.

Multiscale model for turbulent flows

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.

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

This paper analyzes dilatation-dissipation based compressibility corrections for advanced turbulence models. Numerical computations verify that the dilatation-dissipation corrections devised by Sarkar and Zeman greatly improve both the k-omega and k-epsilon model predicted effect of Mach number on spreading rate. However, computations with the k-gamma model also show that the Sarkar/Zeman terms cause an undesired reduction in skin friction for the compressible flat-plate boundary layer. A perturbation solution for the compressible wall layer shows that the Sarkar and Zeman terms reduce the effective von Karman constant in the law of the wall. This is the source of the inaccurate k-gamma model skin-friction predictions for the flat-plate boundary layer. The perturbation solution also shows that the k-epsilon model has an inherent flaw for compressible boundary layers that is not compensated for by the dilatation-dissipation corrections. A compressibility modification for k-gamma and k-epsilon models is proposed that is similar to those of Sarkar and Zeman. The new compressibility term permits accurate predictions for the compressible mixing layer, flat-plate boundary layer, and a shock separated flow with the same values for all closure coefficients.

David C. Wilcox

Papers

Reassessment of the scale-determining equation for advanced turbulence models

Formulation of the k-w Turbulence Model Revisited

Multiscale model for turbulent flows

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

Dilatation-dissipation corrections for advanced turbulence models