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NASA NTRS2015

Revisiting Turbulence Model Validation for High-Mach Number Axisymmetric Compression Corner Flows

Two axisymmetric shock-wave/boundary-layer interaction (SWBLI) cases are used to benchmark one- and two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. This validation exercise was executed in the philosophy of the NASA Turbulence Modeling Resource and the AIAA Turbulence Model Benchmarking Working Group. Both SWBLI cases are from the experiments of Kussoy and Horstman for axisymmetric compression corner geometries with SWBLI inducing flares of 20 and 30 degrees, respectively. The freestream Mach number was approximately 7. The RANS closures examined are the Spalart-Allmaras one-equation model and the Menter family of kappa − omega two equation models including the Baseline and Shear Stress Transport formulations. The Wind-US and CFL3D RANS solvers are employed to simulate the SWBLI cases. Comparisons of RANS solutions to experimental data are made for a boundary layer survey plane just upstream of the SWBLI region. In the SWBLI region, comparisons of surface pressure and heat transfer are made. The effects of inflow modeling strategy, grid resolution, grid orthogonality, turbulent Prandtl number, and code-to-code variations are also addressed.

Shock Wave↗

NASA NTRS2021

Solving Two-Equation Turbulence Models With a Perspective on Solving Transport Equations

There are three principal objectives of this report. The first objective is to investigate frequently used two-equation models when solving the RANS equations. In this study, we consider the 2006Wilcox and the 2003 Menter Shear Stress Transport (SST) models. Also, a simple change of the Wilcox model is introduced to improve computational predictions for transonic flows. Computations for flows over two different airfoils are examined to compare these turbulence models. Effects on modeling the physics of each flow due to variations in the models, such as using either strainrate or vorticity in the turbulence production term, are considered and discussed. The second objective of this report is to not only explore but also evaluate the performance of the solution algorithm for the mean flow and the transport equations. The RANS and turbulence modeling equations aresolved in a weakly coupled manner with a diagonal implicit Runge-Kutta (DIRK) solution algorithm. Throughout this report, emphasis is given to reducing the residuals to machine zero in all flow calculations, so as to eliminate the error due to numerical integration of the discrete governing equations. The final objective is to provide a perspective on solving transport equations for turbulence modeling. Aspects of solving such stiff systems of equations, as well as various numerical difficulties and possible techniques to overcome them, are considered. Discussion is also provided concerning what is called ’numerical compatibility’, which is an essential requirement when designing a solution algorithm for solving transport equations.

turbulence modeling↗

NASA NTRS2017

DPW-VI Results Using FUN3D with Focus on k-kL-MEAH2015 (k-kL) Turbulence Model

The Common Research Model wing-body configuration is investigated with the k-kL-MEAH2015 turbulence model implemented in FUN3D. This includes results presented at the Sixth Drag Prediction Workshop and additional results generated after the workshop with a nonlinear Quadratic Constitutive Relation (QCR) variant of the same turbulence model. The workshop provided grids are used, and a uniform grid refinement study is performed at the design condition. A large variation between results with and without a reconstruction limiter is exhibited on "medium" grid sizes, indicating that the medium grid size is too coarse for drawing conclusions in comparison with experiment. This variation is reduced with grid refinement. At a fixed angle of attack near design conditions, the QCR variant yielded decreased lift and drag compared with the linear eddy-viscosity model by an amount that was approximately constant with grid refinement. The k-kL-MEAH2015 turbulence model produced wing root junction flow behavior consistent with wind tunnel observations.

Abdol-Hamid, K. S.↗

NASA NTRS2000

Turbulence Model Predictions of Strongly Curved Flow in a U-Duct

The ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a U-duct is studied. An explicit algebraic stress model performs slightly better than one- or two-equation linear eddy viscosity models, although it is necessary to fully account for the variation of the production-to-dissipation-rate ratio in the algebraic stress model formulation. In their original formulations, none of these turbulence models fully captures the suppressed turbulence near the convex wall, whereas a full Reynolds stress model does. Some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full Reynolds stress model. Through this analysis, the assumption of Reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature. By the accounting for the local variation of the principal axes of the strain rate tensor, the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall.

Rumsey, Christopher L.↗

NASA NTRS1992

Comment on: The current status of turbulence modeling in CFD and its future prospects

Information is given in viewgraph form on computational fluid dynamics (CFD). Topics covered include the fundamental problem with conventional turbulence modeling, the fundamental problems with the state-of-the-art turbulence modeling approach of 'eddy viscosity', major problems with Reynolds stress equation (RSE) closures, RSE challenges that are probably addressable within the context of Reynolds averaging, RSE challenges which may require theoretical/numerical spectral adjuncts for satisfactory solutions, tools available to aid RSE modeling, and a simplex view of the status of turbulence modeling.

Bushnell, D. M.↗

NASA NTRS1991

A two-equation turbulence model for compressible flows

A k-epsilon model of turbulence that accounts for pressure gradients and compressibility effects is presented. To correct the degradation of k-epsilon model performance when pressure gradients are introduced, an extra term is added to the dissipation equation. By including this term and by adding terms to account for compressibility effects, a new k-epsilon model is developed for shear flows. The results show that the new model performs better than the existing k-epsilon models.

Abid, Ridha↗

NASA NTRS1993

Time dependent turbulence modeling and analytical theories of turbulence

By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.

Rubinstein, R.↗

NASA NTRS1990

An abbreviated Reynolds stress turbulence model for airfoil flows

An abbreviated Reynolds stress turbulence model is presented for solving turbulent flow over airfoils. The model consists of two partial differential equations, one for the Reynolds shear stress and the other for the turbulent kinetic energy. The normal stresses and the dissipation rate of turbulent kinetic energy are computed from algebraic relationships having the correct asymptotic near wall behavior. This allows the model to be integrated all the way to the wall without the use of wall functions. Results for a flat plate at zero angle of attack, a NACA 0012 airfoil and a RAE 2822 airfoil are presented.

Gaffney, R. L., Jr.↗

NASA NTRS2009

Consistency, Verification, and Validation of Turbulence Models for Reynolds-Averaged Navier-Stokes Applications

In current practice, it is often difficult to draw firm conclusions about turbulence model accuracy when performing multi-code CFD studies ostensibly using the same model because of inconsistencies in model formulation or implementation in different codes. This paper describes an effort to improve the consistency, verification, and validation of turbulence models within the aerospace community through a website database of verification and validation cases. Some of the variants of two widely-used turbulence models are described, and two independent computer codes (one structured and one unstructured) are used in conjunction with two specific versions of these models to demonstrate consistency with grid refinement for several representative problems. Naming conventions, implementation consistency, and thorough grid resolution studies are key factors necessary for success.

Rumsey, Christopher L.↗

NASA NTRS1992

Turbulence modeling for hypersonic flight

The objective of the present work is to develop, verify, and incorporate two equation turbulence models which account for the effect of compressibility at high speeds into a three dimensional Reynolds averaged Navier-Stokes code and to provide documented model descriptions and numerical procedures so that they can be implemented into the National Aerospace Plane (NASP) codes. A summary of accomplishments is listed: (1) Four codes have been tested and evaluated against a flat plate boundary layer flow and an external supersonic flow; (2) a code named RANS was chosen because of its speed, accuracy, and versatility; (3) the code was extended from thin boundary layer to full Navier-Stokes; (4) the K-omega two equation turbulence model has been implemented into the base code; (5) a 24 degree laminar compression corner flow has been simulated and compared to other numerical simulations; and (6) work is in progress in writing the numerical method of the base code including the turbulence model.

Bardina, Jorge E.↗

NASA NTRS1993

Numerical computation of aerodynamics and heat transfer in a turbine cascade and a turn-around duct using advanced turbulence models

The objective of this research is to develop turbulence models to predict the flow and heat transfer fields dominated by the curvature effect such as those encountered in turbine cascades and turn-around ducts. A Navier-Stokes code has been developed using an explicit Runge-Kutta method with a two layer k-epsilon/ARSM (Algebraic Reynolds Stress Model), Chien's Low Reynolds Number (LRN) k-epsilon model and Coakley's LRN q-omega model. The near wall pressure strain correlation term was included in the ARSM. The formulation is applied to Favre-averaged N-S equations and no thin-layer approximations are made in either the mean flow or turbulence transport equations. Anisotropic scaling of artificial dissipation terms was used. Locally variable timestep was also used to improve convergence. Detailed comparisons were made between computations and data measured in a turbine cascade by Arts et al. at Von Karman Institute. The surface pressure distributions and wake profiles were predicted well by all the models. The blade heat transfer is predicted well by k-epsilon/ARSM model, as well as the k-epsilon model. It's found that the onset of boundary layer transition on both surfaces is highly dependent upon the level of local freestream turbulence intensity, which is strongly influenced by the streamline curvature. Detailed computation of the flow in the turn around duct has been carried out and validated against the data by Monson as well as Sandborn. The computed results at various streamwise locations both on the concave and convex sides are compared with flow and turbulence data including the separation zone on the inner well. The k-epsilon/ARSM model yielded relatively better results than the two-equation turbulence models. A detailed assessment of the turbulence models has been made with regard to their applicability to curved flows.

Lakshminarayana, B.↗

NASA NTRS1998

Evaluation of Turbulence-Model Performance as Applied to Jet-Noise Prediction

The accurate prediction of jet noise is possible only if the jet flow field can be predicted accurately. Predictions for the mean velocity and turbulence quantities in the jet flowfield are typically the product of a Reynolds-averaged Navier-Stokes solver coupled with a turbulence model. To evaluate the effectiveness of solvers and turbulence models in predicting those quantities most important to jet noise prediction, two CFD codes and several turbulence models were applied to a jet configuration over a range of jet temperatures for which experimental data is available.

Woodruff, S. L.↗

NASA NTRS1987

Wall jet analysis for circulation control aerodynamics. Part 1: Fundamental CFD and turbulence modeling concepts

An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented.

Dash, S. M.↗

NASA NTRS2009

Compressibility Considerations for kappa-omega Turbulence Models in Hypersonic Boundary Layer Applications

The ability of kappa-omega models to predict compressible turbulent skin friction in hypersonic boundary layers is investigated. Although uncorrected two-equation models can agree well with correlations for hot-wall cases, they tend to perform progressively worse - particularly for cold walls - as the Mach number is increased in the hypersonic regime. Simple algebraic models such as Baldwin-Lomax perform better compared to experiments and correlations in these circumstances. Many of the compressibility corrections described in the literature are summarized here. These include corrections that have only a small influence for kappa-omega models, or that apply only in specific circumstances. The most widely-used general corrections were designed for use with jet or mixing-layer free shear flows. A less well-known dilatation-dissipation correction intended for boundary layer flows is also tested, and is shown to agree reasonably well with the Baldwin-Lomax model at cold-wall conditions. It exhibits a less dramatic influence than the free shear type of correction. There is clearly a need for improved understanding and better overall physical modeling for turbulence models applied to hypersonic boundary layer flows.

Rumsey, C. L.↗

NASA NTRS1992

Evaluation and application of the Baldwin-Lomax turbulence model in two-dimensional, unsteady, compressible boundary layers with and without separation in engine inlets

The Baldwin-Lomax model is used in many CFD codes because it is quick and easy to implement. In this paper, we discuss implementing the Baldwin-Lomax turbulence model for both steady and unsteady compressible flows. In addition, these flows may be either separated or attached. In order to apply this turbulence model to flows which may be subjected to these conditions, certain modifications should be made to the original Baldwin-Lomax model. We discuss these modifications and determine whether the Baldwin-Lomax model is a viable turbulence model that produces reasonably accurate results for high speed flows that can be found in engine inlets.

Sakowski, Barbara↗

NASA NTRS1992

Evaluation and application of the Baldwin-Lomax turbulence model in two-dimensional, unsteady, compressible boundary layers with and without separation in engine inlets

Sakowski, Barbara↗

NASA NTRS1996

A new approach to turbulence modeling

A new approach to Reynolds averaged turbulence modeling is proposed which has a computational cost comparable to two equation models but a predictive capability approaching that of Reynolds stress transport models. This approach isolates the crucial information contained within the Reynolds stress tensor, and solves transport equations only for a set of 'reduced' variables. In this work, Direct Numerical Simulation (DNS) data is used to analyze the nature of these newly proposed turbulence quantities and the source terms which appear in their respective transport equations. The physical relevance of these quantities is discussed and some initial modeling results for turbulent channel flow are presented.

Perot, B.↗

NASA NTRS1977

Evaluation of subgrid-scale turbulence models using a fully simulated turbulent flow

An exact turbulent flow field was calculated on a three-dimensional grid with 64 points on a side. The flow simulates grid-generated turbulence from wind tunnel experiments. In this simulation, the grid spacing is small enough to include essentially all of the viscous energy dissipation, and the box is large enough to contain the largest eddy in the flow. The method is limited to low-turbulence Reynolds numbers, in our case R sub lambda = 36.6. To complete the calculation using a reasonable amount of computer time with reasonable accuracy, a third-order time-integration scheme was developed which runs at about the same speed as a simple first-order scheme. It obtains this accuracy by saving the velocity field and its first-time derivative at each time step. Fourth-order accurate space-differencing is used.

Clark, R. A.↗