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Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

Warfield, M. J.↗

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

Kim, Sang-Wook↗

Application of the algebraic RNG model for transition simulation

The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.

Lund, Thomas S.↗

Performance of Renormalization Group Algebraic Turbulence Model on Boundary Layer Transition Simulation

The RNG-based algebraic turbulence model, with a new method of solving the cubic equation and applying new length scales, is introduced. An analysis is made of the RNG length scale which was previously reported and the resulting eddy viscosity is compared with those from other algebraic turbulence models. Subsequently, a new length scale is introduced which actually uses the two previous RNG length scales in a systematic way to improve the model performance. The performance of the present RNG model is demonstrated by simulating the boundary layer flow over a flat plate and the flow over an airfoil.

Ahn, Kyung H.↗

Survey of Turbulence Models for the Computation of Turbulent Jet Flow and Noise

The report presents an overview of jet noise computation utilizing the computational fluid dynamic solution of the turbulent jet flow field. The jet flow solution obtained with an appropriate turbulence model provides the turbulence characteristics needed for the computation of jet mixing noise. A brief account of turbulence models that are relevant for the jet noise computation is presented. The jet flow solutions that have been directly used to calculate jet noise are first reviewed. Then, the turbulent jet flow studies that compute the turbulence characteristics that may be used for noise calculations are summarized. In particular, flow solutions obtained with the k-e model, algebraic Reynolds stress model, and Reynolds stress transport equation model are reviewed. Since, the small scale jet mixing noise predictions can be improved by utilizing anisotropic turbulence characteristics, turbulence models that can provide the Reynolds stress components must now be considered for jet flow computations. In this regard, algebraic stress models and Reynolds stress transport models are good candidates. Reynolds stress transport models involve more modeling and computational effort and time compared to algebraic stress models. Hence, it is recommended that an algebraic Reynolds stress model (ASM) be implemented in flow solvers to compute the Reynolds stress components.

Nallasamy, N.↗

An algebraic turbulence model for three-dimensional viscous flows

An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

Chima, R. V.↗

An algebraic turbulence model for three-dimensional viscous flows

An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(v) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(v) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

Chima, R. V.↗

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

Georgiadis, N. J.↗

Development of an algebraic turbulence model for analysis of propulsion flows

A simple turbulence model that will be applicable to propulsion flows having both wall bounded and unbounded regions was developed and installed within the PARC Navier-Stokes code by linking two existing algebraic turbulence models. The first is the Modified Mixing Length (MML) model which is optimized for wall bounded flows. The second is the Thomas model, the standard algebraic turbulence model in PARC which has been used to calculate both bounded and unbounded turbulent flows but was optimized for the latter. This paper discusses both models and the method employed to link them into one model (referred to as the MMLT model). The PARC code with the MMLT model was applied to two dimensional turbulent flows over a flat plate and over a backward facing step to validate and optimize the model and to compare its predictions to those obtained with the three turbulence models already available in PARC.

Georgiadis, N. J.↗

The present status and future direction of algebraic Reynolds stress models

The need for algebraic models and deficiencies of linear gradient models are presented. Classical algebraic Reynolds stress models are discussed with nonlinear stress-strain relations. Finally, the models are critiqued and some new developments are shown. All results are in viewgraph format.

Taulbee, Dale B.↗

Nonequilibrium algebraic turbulence modeling considerations for transonic airfoils and wings

The nonequilibrium algebraic turbulence model of Johnson and King has been applied successfully to both airfoils and wings. However, in wing applications a different expression for the outer 'equilibrium' eddy viscosity has been used because of apparent difficulties in determining the boundary-layer thickness. It is shown in this paper, that this expression does not give eddy viscosity levels for two-dimensional flows that are consistent with Clauser's correlation for equilibrium turbulent boundary layers. And as a consequence, results in inferior predictions when used in airfoil calculations. The objective of this paper is to develop a formulation applicable to wing flows which reduces to the proper form in the two-dimensional case. This necessitates, in part, finding a better way of estimating the boundary-layer thickness from the computed flowfield.

Johnson, D. A.↗

Shapes and stability of algebraic nuclear models

A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

Lopez-Moreno, Enrique↗

Turbulence modeling for hypersonic flows

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

Marvin, J. G.↗

Turbulence modeling for hypersonic flows

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

Marvin, J. G.↗

Turbulence modeling for hypersonic flows

Turbulence modeling for high-speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models, and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary-layer flows, shock-wave boundary-layer interactions, and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

Marvin, J. G.↗

Modification of the Two-equation Turbulence Model in NPARC to a Chien Low Reynolds Number K-epsilon Formulation

This report documents the changes that were made to the two-equation k-epsilon turbulence model in the NPARC (National-PARC) code. The previous model based on the low Reynolds number model of Speziale, was replaced with the low Reynolds number k-epsilon model of Chien. The most significant difference was in the turbulent Prandtl numbers appearing in the diffusion terms of the k and epsilon transport equations. A new inflow boundary condition and stability enhancements were also implemented into the turbulence model within NPARC. The report provides the rationale for making the change to the Chien model, code modifications required, and comparisons of the performances of the new model with the previous k-epsilon model and algebraic models used most often in PARC/NPARC. The comparisons show that the Chien k-epsilon model installed here improves the capability of NPARC to calculate turbulent flows.

Georgiadis, Nicholas J.↗

Direct numerical simulations and modeling of a spatially-evolving turbulent wake

Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with appropriate noise. After some adjustment period, the flow downstream of the inlet develops into a fully three-dimensional turbulent wake. Of particular interest in the present study is the far wake spreading rate and the self-similar mean and turbulence profiles. At the time of this writing, grid resolution studies are underway, and a code is being written to calculate turbulence statistics from these wake calculations; the statistics will be compared to those from the ongoing PIV wake measurements, those of previous experiments, and those predicted by the various turbulence models. These calculations will lead to significant long-term benefits for the turbulence modeling effort. In particular, quantities such as the pressure-strain correlation and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. Present turbulence models do a very good job at prediction of the shape of the mean velocity and Reynolds stress profiles in a turbulent wake, but significantly underpredict the magnitude of the stresses and the spreading rate of the wake. Thus, the turbulent wake is an ideal flow for turbulence modeling research. By careful comparison and analysis of each term in the modeled Reynolds stress equations, the DNS data can show where deficiencies in the models exist; improvements to the models can then be attempted.

Cimbala, John M.↗

Improvements to an Explicit Algebraic Stress Model for Turbulent Jet Mixing Predictions

Modifications to key coefficients in a k − E based explicit algebraic stress model (EASM) are examined with the objective of improving the prediction of turbulent jet flows. The pressure strain coefficient, C2 and the turbulent diffusion coefficients, σk and σE were investigated. For a series of benchmark subsonic jets at heated and unheated conditions, lowering C2 from the default value of 0.36 to 0.10 resulted in a significant improvement in the jet mixing, when compared to experimental data. Changing σk and σE from default values of 1.00 and 1.4489, respectively, to 0.50 and 0.7244, respectively, improved the initial mixing rate, while reducing the farfield mixing rate and the peak turbulent kinetic energy along the centerline. A high-speed mixing layer was also investigated for performance of baseline and modified EASM coefficients, with similar results as for the jet cases. A flat plate boundary layer was briefly examined to determine the effects of changing the coefficients on the turbulent skin friction coefficient. The change to the pressure strain coefficient, C2 = 0.10 is recommended for future EASM calculation of jets flow; however, it is also recommended that the diffusion coefficients remain at their default values.

Turbulent Mixing↗