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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1995

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗
NASA NTRS1990

Comparison of experiment with calculations using curvature-corrected zero and two equation turbulence models for a two-dimensional U-duct

In this paper experimental measurements are compared with Navier-Stokes calculations using seven different turbulence models for the internal flow in a two-dimensional U-duct. The configuration is representative of many internal flows of engineering interst that experience strong curvature. In an effort to improve agreement, this paper tests several versions of the two-equation k-epsilon turbulence model including the standard version, an extended version with a production range time scale, and a version that includes curvature time scales. Each is tested in its high and low Reynolds number formulations. Calculations using these new models and the original mixing length model are compared here with measurements of mean and turbulence velocities, static pressure and skin friction in the U-duct at two Reynolds numbers. The comparisons show that only the low Reynolds number version of the extended k-epsilon model does a reasonable job of predicting the important features of this flow at both Reynolds numbers tested.

Monson, D. J.↗
NASA NTRS2018

kL-based Linear and Nonlinear Two-Equation Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) two-equation turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important differences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The present report documents the formulation of two model levels of turbulence models as implemented in the computational fluid dynamics FUN3D code. The levels are the two-equation linear k-kL and the two-equation algebraic Reynolds stress model (ARSM). Free shear, separated and corner flow cases are documented and compared with experimental, and other turbulence model data. The results show generally very good comparisons with experimental data. The results from this formulation are similar or better than results using the SST two-equation turbulence model. ARSM shows great promise with similar level of computational resources as basic two-equation turbulence models.

Abdol-Hamid, K. S.↗
NASA NTRS1994

Computation of oscillating airfoil flows with one- and two-equation turbulence models

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.

Ekaterinaris, J. A.↗
NASA NTRS1994

Investigation of supersonic jet plumes using an improved two-equation turbulence model

Supersonic jet plumes were studied using a two-equation turbulence model employing corrections for compressible dissipation and pressure-dilatation. A space-marching procedure based on an upwind numerical scheme was used to solve the governing equations and turbulence transport equations. The computed results indicate that two-equation models employing corrections for compressible dissipation and pressure-dilatation yield improved agreement with the experimental data. In addition, the numerical study demonstrates that the computed results are sensitive to the effect of grid refinement and insensitive to the type of velocity profiles used at the inflow boundary for the cases considered in the present study.

Lakshmanan, B.↗
NASA NTRS1991

Analysis of two-equation turbulence models for recirculating flows

The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.

Thangam, S.↗
NASA NTRS1992

Advances in engineering turbulence modeling

Some new developments in two equation models and second order closure models are presented. In this paper, modified two equation models are proposed to remove shortcomings such as computing flows over complex geometries and the ad hoc treatment near the separation and reattachment points. The calculations using various two equation models are compared with direct numerical solutions of channel flows and flat plate boundary layers. Development of second order closure models will also be discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All existing models poorly predict the normal stresses near the wall and fail to predict the three dimensional effect of mean flow on the turbulence. The newly developed second order near-wall turbulence model to be described in this paper is capable of capturing the near-wall behavior of turbulence as well as the effect of three dimension mean flow on the turbulence.

Shih, T.-H.↗
NASA NTRS1991

A two-equation turbulence model for compressible reacting flows

A two-equation turbulence model (k-epsilon) has been modified to model compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. Computations are carried out using the Navier-Stokes solver SPARK which includes a finite rate chemistry model for hydrogen-air combustion. Initially, planar compressible mixing layers are simulated. Comparisons of the predictions with available experimental data and the predictions of a compressible Reynolds stress closure indicate that the model is well suited for the study of such flows. The decrease in the growth rate of the mixing layer with increasing convective Mach number is well predicted. The model is then tested on a three-dimensional supersonic flow problem where solid boundaries are present. An axisymmetric nonreacting mixing layer flow involving dissimilar gases is evaluated next using the model and the predictions are compared with available experimental data. Finally, two reacting turbulent flow configurations have been studied and comparison of predictions and experimental data has been done. The comparisons indicate that the model predicts the overall features of the test cases very well.

Narayan, J. R.↗
NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗
NASA NTRS1989

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of thier predictions.

Speziale, Charles G.↗
NASA NTRS1990

A critical comparison of turbulence models for homogeneous shear flows in a rotating frame

A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of their predictions.

Speziale, Charles G.↗
NASA NTRS1997

Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades

A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely, the VKI rotor with six rows of cooling holes, including three rows on the shower head and the C3X vane with nine rows of holes, including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence model specifically, Coakley's q-omega model, Chien's k-epsilon model and Wilcox's k-omega model with Menter's modifications, have been compared with the experimental data of Camci and Arts for the VKI rotor, and of Hylton et al. for the C3X vane along with predictions using the Baldwin-Lomar (B-L) model taken from Garg and Gaugler. It is found that for the cases considered here the two equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooled holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-omega and k-epsilon models need 40% more computer time than the B-L model the k-omega model requires at least 65% more time because of the slower rate of convergence. It is found that the heat transfer coefficient exhibit a strong spanwise as well as streamwise variation for both blades and all turbulence models.

Garg, Vijay K.↗
NASA NTRS2020

On Boundary-Value Problems for RANS Equations and Two-Equation Turbulence Models

Currently, in engineering computations for high Reynolds number turbulent flows, turbulence modeling continues to be the most frequently used approach to represent the effects of turbulence. Such models generally rely on solving either one or two transport equations along with the Reynolds-Averaged Navier–Stokes (RANS) equations. The solution of the boundary-value problem of any system of partial differential equations requires the complete delineation of the equations and the boundary conditions, including any special restrictions and conditions. In the literature, such a description is often incomplete, neglecting important details related to the boundary conditions and possible restrictive conditions, such as how to ensure satisfying prescribed values of the dependent variables of the transport equations in the far field of a finite domain. In this article, we discuss the possible influence of boundary values, as well as near-field and far-field behavior, on the solution of the RANS equations coupled with transport equations for turbulence modeling. In so doing, we defne the concept of a welldefined boundary-value problem. Additionally, a three-dimensional, rather than a simpler one-dimensional analysis is performed to analyze the near-wall and far-field behavior of the turbulence model variables. This allows an assessment of the decay rate of these variables required to realize the boundary conditions in the far field. This paper also addresses the impact of various transformations of two-equation models (e.g., the model of Wilcox) to remove the singular behavior of the dissipation rate (ω) at the surface boundary. Finally, the issue of well-posedness regarding the governing equations is considered. A compelling argument (although not a proof) for ill-posedness is made for both direct and inverse problems.

Navier–Stokes equations↗
NASA NTRS1992

A comparative study of two codes with an improved two-equation turbulence model for predicting jet plumes

Compressible jet plumes were studied using a two-equation turbulence model. A space marching procedure based on an upwind numerical scheme was used to solve the governing equations and turbulence transport equations. The computed results indicate that extending the space marching procedure for solving supersonic/subsonic mixing problems can be stable, efficient and accurate. Moreover, a newly developed correction for compressible dissipation has been verified in fully expanded and underexpanded jet plumes. For a sonic jet plume, no improvement in results over the standard two-equation model was seen. However for a supersonic jet plume, the correction due to compressible dissipation successfully predicted the reduced spreading rate of the jet compared to the sonic case. The computed results were generally in good agreement with the experimental data.

Balakrishnan, L.↗
NASA NTRS1995

Experiences with two-equation turbulence models

This viewgraph presentation discusses the following: introduction to CFD Research Corporation; experiences with two-equation models - models used, numerical difficulties, validation and applications, and strengths and weaknesses; and answers to three questions posed by the workshop organizing committee - what are your customers telling you, what are you doing in-house, and how can NASA-CMOTT (Center for Modeling of Turbulence and Transition) help.

Singhal, Ashok K.↗
NASA NTRS1995

The applicability of turbulence models to aerodynamic and propulsion flowfields at McDonnell-Douglas Aerospace

The objective of this viewgraph presentation is to evaluate turbulence models for integrated aircraft components such as the forebody, wing, inlet, diffuser, nozzle, and afterbody. The one-equation models have replaced the algebraic models as the baseline turbulence models. The Spalart-Allmaras one-equation model consistently performs better than the Baldwin-Barth model, particularly in the log-layer and free shear layers. Also, the Sparlart-Allmaras model is not grid dependent like the Baldwin-Barth model. No general turbulence model exists for all engineering applications. The Spalart-Allmaras one-equation model and the Chien k-epsilon models are the preferred turbulence models. Although the two-equation models often better predict the flow field, they may take from two to five times the CPU time. Future directions are in further benchmarking the Menter blended k-w/k-epsilon and algorithmic improvements to reduce CPU time of the two-equation model.

Kral, Linda D.↗
NASA NTRS1993

Two-equation turbulence model for compressible reacting flows

A two-equation k-epsilon turbulence model is presently modified for applicability to compressible flows by adapting a compressibility correction model. Compressible mixing layer computations show that the reduced growth rate of the mixing layer with increasing convective Mach number is accurately predicted by these means. Preliminary studies of reacting mixing problems involving dissimilar gases show the model's suitability for application to such flows.

Narayan, J. R.↗
NASA NTRS1989

Modeling of turbulence for compression corner flows and internal flows

A compressible Reynolds averaged Navier-Stokes code is applied to examine the performances of basic turbulence models for unseparated and separated flows. The turbulence models considered are a zero-equation model and several two-equation models, including a new k-epsilon model with an eddy viscosity damping function depending upon the Reynolds number and the distance from the wall. The turbulence models are assessed using the following experimental flows: a channel flow, a backward facing step, and a two-dimensional compression corner at Mach 2.8. Discussions and comparisons of the experimental and numerical results are given. Mesh refinement is shown to have a significant beneficial effect on free shear layer flow results obtained with two-equation turbulence models. The results illustrate the usefulness of several turbulence models as a design tool for fluid engineering systems.

Champney, J. M.↗