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All sourcesNASA NTRSDOE OSTI
NASA NTRS2023

Implementation, Realization and an Effective Solver of Two-Equation Turbulence Models

Currently, when the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using turbulence modeling, most often the one-equation model of Spalart and Allmaras is used. Then, it is only necessary to solve the RANS equations in conjunction with a single transport equation for modeling turbulence. For this model, considerable assessment and analysis has been performed, allowing the possibility of a reliable solution method for an eddy viscosity required to compute the Reynolds stresses in the RANS equations. Such evaluation along with analysis has not been achieved to realize similar performance with two-equation models of the k-w type. The primary objective of this paper is to present and discuss the components of an effective numerical algorithm for solving the RANS equations and the two transport equations of k-w type turbulence models. All the important details of the turbulence model as actually implemented are given, which is sometimes not done in various papers considering such modeling. The viability and effectiveness of this solution algorithm are demonstrated by solving both two-dimensional and three-dimensional aerodynamic flows. In all applications, a linear rate of convergence without oscillations or other evidence of unstable behavior is observed. This behavior is also particularly true when the proposed algorithm is applied to systematically renewed mesh sequences, which is generally not observed with algorithms solving more than one transport equation. Thus, numerical integration errors are systematically reduced, allowing for a significantly more reliable assessment of the effectiveness of the turbulence model. Additionally, in this paper, analysis of the solution algorithm, including linear stability, is also performed for a particular flow problem.

Turbulence↗
NASA NTRS1978

A study of key features of the RAE atmospheric turbulence model

A complex atmospheric turbulence model for use in aircraft simulation is analyzed in terms of its temporal, spectral, and statistical characteristics. First, a direct comparison was made between cases of the RAE model and the more conventional Dryden turbulence model. Next the control parameters of the RAE model were systematically varied and the effects noted. The RAE model was found to possess a high degree of flexibility in its characteristics, but the individual control parameters are cross-coupled in terms of their effect on various measures of intensity, bandwidth, and probability distribution.

Jewell, W. F.↗
NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗
NASA NTRS2010

Description of a Website Resource for Turbulence Modeling Verification and Validation

The activities of the Turbulence Model Benchmarking Working Group - which is a subcommittee of the American Institute of Aeronautics and Astronautics (AIAA) Fluid Dynamics Technical Committee - are described. The group s main purpose is to establish a web-based repository for Reynolds-averaged Navier-Stokes turbulence model documentation, including verification and validation cases. This turbulence modeling resource has been established based on feedback from a survey on what is needed to achieve consistency and repeatability in turbulence model implementation and usage, and to document and disseminate information on new turbulence models or improvements to existing models. The various components of the website are described in detail: description of turbulence models, turbulence model readiness rating system, verification cases, validation cases, validation databases, and turbulence manufactured solutions. An outline of future plans of the working group is also provided.

Rumsey, Christopher L.↗
NASA NTRS1983

A turbulence model for three dimensional turbulent shear flows over curved rotating bodies

There exists currently considerable interest in the development of numerical procedures for solving the equations governing three-dimensional fluid flows. In particular, improved calculations of viscous flows on rotating bodies such a turbomachinery rotors are of great importance. The present investigation is mainly concerned with the analysis of the effect of rotation on the dissipation rate equation and the Reynolds stress equations. Attention is given to governing equations and modelling, algebraic Reynolds stress equations, a procedure for implementing the turbulence closure scheme, results for a model representative of centrifugal turbomachinery, and results for axial turbomachinery. The proposed turbulence model is valid for three-dimensional, rotating, and curved flows. The model has all the essential physics of turbulence, mean flow, rotation, and the curvature.

Galmes, J. M.↗
NASA NTRS1990

Numerical investigation of separated transonic turbulent flows with a multiple-time-scale turbulence model

A numerical investigation of transonic turbulent flows separated by curvature and shock wave - boundary layer interaction is presented. The free stream Mach numbers considered are 0.4, 0.5, 0.6, 0.7, 0.8, 0.825, 0.85, 0.875, 0.90, and 0.925. In the numerical method, the conservation of mass equation is replaced by a pressure correction equation for compressible flows and thus incremental pressure is solved for instead of density. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. The present numerical results show that there exists a reversed flow region at all free stream Mach numbers considered whereas various k-epsilon turbulence models fail to predict such a reversed flow region at low free stream Mach numbers. The numerical results also show that the size of the reversed flow region grows extensively due to the shock wave - turbulent boundary layer interaction as the free stream Mach number is increased. These numerical results show that the turbulence model can resolve the turbulence field subjected to extra strains caused by the curvature and the shock wave - turbulent boundary layer interaction and that the numerical method yields a significantly accurate solution for the complex compressible turbulent flow.

Kim, S.-W.↗
NASA NTRS1990

Turbulence modeling for high speed compressible flows

Turbulence models are necessary in numerical simulations because of the impracticality of computing all scales of turbulent motion. Approximate methods, or turbulence models, are introduced to simplify and make the computations practical. There are several approaches to turbulence modeling: subgrid scale modeling; modeling of all the scales of turbulent motion; eddy viscosity; and Reynolds stress turbulence closure models. In many instances, computations based on turbulence models are compared with available experimental data. The effort is directed at seeking models which have reasonable accuracy over a limited range of flow conditions. Future needs are briefly discussed. Work to date is outlined.

Chandra, Suresh↗
NASA NTRS1982

Assessment of turbulent models for scramjet flowfields

The behavior of several turbulence models applied to the prediction of scramjet combustor flows is described. These models include the basic two equation model, the multiple dissipation length scale variant of the two equation model, and the algebraic stress model (ASM). Predictions were made of planar backward facing step flows and axisymmetric sudden expansion flows using each of these approaches. The formulation of each of these models are discussed, and the application of the different approaches to supersonic flows is described. A modified version of the ASM is found to provide the best prediction of the planar backward facing step flow in the region near the recirculation zone, while the basic ASM provides the best results downstream of the recirculation. Aspects of the interaction of numerica modeling and turbulences modeling as they affect the assessment of turbulence models are discussed.

Sindir, M. M.↗
NASA NTRS1990

Turbulence modeling: Near-wall turbulence and effects of rotation on turbulence

Many Reynolds averaged Navier-Stokes solvers use closure models in conjunction with 'the law of the wall', rather than deal with a thin, viscous sublayer near the wall. This work is motivated by the need for better models to compute near wall turbulent flow. The authors use direct numerical simulation of fully developed channel flow and one of three dimensional turbulent boundary layer flow to develop new models. These direct numerical simulations provide detailed data that experimentalists have not been able to measure directly. Another objective of the work is to examine analytically the effects of rotation on turbulence, using Rapid Distortion Theory (RDT). This work was motivated by the observation that the pressure strain models in all current second order closure models are unable to predict the effects of rotation on turbulence.

Shih, T.-H.↗
NASA NTRS1992

Multigrid acceleration and turbulence models for computations of 3D turbulent jets in crossflow

A multigrid method is presented for the calculation of three-dimensional turbulent jets in crossflow. Turbulence closure is achieved with either the standard k-epsilon model or a Reynolds stress model (RSM). Multigrid acceleration enables convergence rates which are far superior to that for a single grid method to be obtained with both turbulence models. With the k-epsilon model the rate approaches that for laminar flow, but with RSM it is somewhat slower. The increased stiffness of the system of equation in the latter may be responsible. Computed results with both turbulence models are compared to experimental data for a pair of opposed jets in crossflow. Both models yield reasonable agreement for the mean flow velocity, but RSM yields better predictions of the Reynolds stresses.

Demuren, A. O.↗
DOE OSTI2022

Validation of URANS and STRUCT-ε turbulence models for stratified sodium flow

Simulations of a transient stratified sodium experiment are carried out using a classic unsteady RANS model and the second-generation URANS model, STRUCT-ε. Turbulence modeling challenges and their implications to stratified flow prediction are discussed in the context of other sources of error. Input errors are discussed and addressed; discretization error is calculated to be less than 5% of the inlet velocity, for 80% of the domain; and remaining errors in temperature distributions are attributed to the turbulence model. Qualitative flow features from the simulations are presented and discussed. Compared to the experiment, the STRUCT-ε turbulence model provides a more physically accurate prediction of temperature and momentum mixing in key regions of the domain. Quantitative measures such as the L 2 norm of the temperature discrepancy demonstrate the improved performance of the STRUCT-ε approach. In conclusion, the magnitude of the temperature fluctuations is very well-predicted by the STRUCT-ε, while URANS overpredicts them by approximately 50%.

42 ENGINEERING↗
NASA NTRS1991

Examination of various turbulence models for application in liquid rocket thrust chambers

There is a large variety of turbulence models available. These models include direct numerical simulation, large eddy simulation, Reynolds stress/flux model, zero equation model, one equation model, two equation k-epsilon model, multiple-scale model, etc. Each turbulence model contains different physical assumptions and requirements. The natures of turbulence are randomness, irregularity, diffusivity and dissipation. The capabilities of the turbulence models, including physical strength, weakness, limitations, as well as numerical and computational considerations, are reviewed. Recommendations are made for the potential application of a turbulence model in thrust chamber and performance prediction programs. The full Reynolds stress model is recommended. In a workshop, specifically called for the assessment of turbulence models for applications in liquid rocket thrust chambers, most of the experts present were also in favor of the recommendation of the Reynolds stress model.

Hung, R. J.↗
NASA NTRSDate not supplied

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗
NASA NTRSDate not supplied

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗
NASA NTRS1992

Analysis of an RNG based turbulence model for separated flows

A two-equation turbulence model of the K-epsilon type was recently derived by using Renormalization Group (RNG) methods. It was later reported that this RNG based model yields substantially better predictions than the standard K-epsilon model for turbulent flow over a backward facing step - a standard test case used to benchmark the performance of turbulence models in separated flows. The improvements obtained from the RNG K-epsilon model were attributed to the better treatment of near wall turbulence effects. In contrast to these earlier claims, it is shown in this paper that the original version of the RNG K-epsilon model substantially underpredicts the reattachment point in the backstep problem. This is a deficiency that is traced to the modeling of the production of dissipation term. However, with the most recent improvements in the RNG K-epsilon model, excellent results for the backstep problem are now obtained.

Speziale, C. G.↗
NASA NTRS1992

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.↗
NASA NTRS1992

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.↗
NASA NTRS1989

More accurate predictions with transonic Navier-Stokes methods through improved turbulence modeling

Significant improvements in predictive accuracies for off-design conditions are achievable through better turbulence modeling; and, without necessarily adding any significant complication to the numerics. One well established fact about turbulence is it is slow to respond to changes in the mean strain field. With the 'equilibrium' algebraic turbulence models no attempt is made to model this characteristic and as a consequence these turbulence models exaggerate the turbulent boundary layer's ability to produce turbulent Reynolds shear stresses in regions of adverse pressure gradient. As a consequence, too little momentum loss within the boundary layer is predicted in the region of the shock wave and along the aft part of the airfoil where the surface pressure undergoes further increases. Recently, a 'nonequilibrium' algebraic turbulence model was formulated which attempts to capture this important characteristic of turbulence. This 'nonequilibrium' algebraic model employs an ordinary differential equation to model the slow response of the turbulence to changes in local flow conditions. In its original form, there was some question as to whether this 'nonequilibrium' model performed as well as the 'equilibrium' models for weak interaction cases. However, this turbulence model has since been further improved wherein it now appears that this turbulence model performs at least as well as the 'equilibrium' models for weak interaction cases and for strong interaction cases represents a very significant improvement. The performance of this turbulence model relative to popular 'equilibrium' models is illustrated for three airfoil test cases of the 1987 AIAA Viscous Transonic Airfoil Workshop, Reno, Nevada. A form of this 'nonequilibrium' turbulence model is currently being applied to wing flows for which similar improvements in predictive accuracy are being realized.

Johnson, Dennis A.↗