Turbulence models for gas turbine combustors
This viewgraph presentation covers gas turbine combustor flow physics, turbulence model investigations, turbulent combustion modeling, and present status and future needs.
Brankovic, Andreja↗
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Results for “turbulence modeling”
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Turbulence Model Comparisons and Reynolds Number Effects Over a High-Speed Aircraft at Transonic Speeds
This paper gives the results of a grid study, a turbulence model study, and a Reynolds number effect study for transonic flows over a high-speed aircraft using the thin-layer, upwind, Navier-Stokes CFL3D code. The four turbulence models evaluated are the algebraic Baldwin-Lomax model with the Degani-Schiff modifications, the one-equation Baldwin-Barth model, the one-equation Spalart-Allmaras model, and Menter's two-equation Shear-Stress-Transport (SST) model. The flow conditions, which correspond to tests performed in the NASA Langley National Transonic Facility (NTF), are a Mach number of 0.90 and a Reynolds number of 30 million based on chord for a range of angle-of-attacks (1 degree to 10 degrees). For the Reynolds number effect study, Reynolds numbers of 10 and 80 million based on chord were also evaluated. Computed forces and surface pressures compare reasonably well with the experimental data for all four of the turbulence models. The Baldwin-Lomax model with the Degani-Schiff modifications and the one-equation Baldwin-Barth model show the best agreement with experiment overall. The Reynolds number effects are evaluated using the Baldwin-Lomax with the Degani-Schiff modifications and the Baldwin-Barth turbulence models. Five angles-of-attack were evaluated for the Reynolds number effect study at three different Reynolds numbers. More work is needed to determine the ability of CFL3D to accurately predict Reynolds number effects.
Rivers, Melissa B.↗
Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow
Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.
Wang, Chi R.↗
Turbulence modeling for separated flow
Two projects are described in this report. The first involves assessing turbulence models in separated flow. The second addresses the anomalous behavior of certain turbulence models in stagnation point flow. The primary motivation for developing turbulent transport models is to provide tools for computing non-equilibrium, or complex, turbulent flows. Simple flows can be analyzed using data correlations or algebraic eddy viscosities, but in more complicated flows such as a massively separated boundary layer, a more elaborate level of modeling is required. It is widely believed that at least a two-equation transport model is required in such cases. The transport equations determine the evolution of suitable velocity and time-scales of the turbulence. The present study included assessment of second-moment closures in several separated flows, including sharp edge separation; smooth wall, pressure driven separation; and unsteady vortex shedding. Flows with mean swirl are of interest for their role in enhancing mixing both by turbulent and mean motion. The swirl can have a stabilizing effect on the turbulence. An axi-symmetric extension to the INS-2D computer program was written adding the capability of computing swirling flow. High swirl can produce vortex breakdown on the centerline of the jet and it occurs in various combustors.
Durbin, Paul A.↗
PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows
This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.
Abdol-Hamid, Khaled S.↗
Turbulence modeling
In recent years codes that use the Navier-Stokes equations to compute aerodynamic flows have evolved from computing two-dimensional flows around simple airfoils to computing flows around full scale aircraft configurations. Most flows of engineering interest are turbulent and turbulence models are needed for their prediction. Yet, it is known that present turbulence models are adequate only for simple flows and do poorly in complicated flows such as three-dimensional separation, or large-scale unsteadiness. The same progress that allowed the development of these aerodynamic codes, namely the introduction of supercomputers, has allowed us to compute directly turbulent flows, albeit only for simple flows at moderate Reynolds numbers. These direct turbulence simulations provide us with detailed data that experimentalists were not able to measure. This work is motivated by the fact that data exists for developing better turbulence models and by the need for better models to compute flows of engineering interest. The objective is to develop turbulence models for engineering applications. The model categories that show promise for immediate use are on the two-equation level and the Reynolds-stress level.
Shih, Tsan-Hsing↗
Turbulence modelling for complex shear flows
The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.
Lakshminarayana, B.↗
Multiple-scale turbulence modeling of boundary layer flows for scramjet applications
As part of an investigation into the application of turbulence models to the computation of flows in advanced scramjet combustors, the multiple-scale turbulence model was applied to a variety of flowfield predictions. The model appears to have a potential for improved predictions in a variety of areas relevant to combustor problems. This potential exists because of the partition of the turbulence energy spectrum that is the major feature of the model and which allows the turbulence energy dissipation rate to be out of phase with turbulent energy production. The computations were made using a consistent method of generating experimentally unavailable initial conditions. An appreciable overall improvement in the generality of the predictions is observed, as compared to those of the basic two-equation turbulence model. A Mach number-related correction is found to be necessary to satisfactorily predict the spreading rate of the supersonic jet and mixing layer.
Fabris, G.↗
Evaluation of Full Reynolds Stress Turbulence Models in FUN3D
Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.
reynolds averaging↗
Transition-Sensitized Turbulence Models for Compressible and Incompressible Flows
During the grant period from January 1,2002 to December 31,2002 work was carried out on three projects to extend the range of applicability of advanced turbulence models. First, a new transition-sensitized turbulence model was tested and refined. Second, the influence of compressibility on the pressure-strain rate correlation was studied. Third, the relationship between time-filtered large eddy simulation (TLES) and Reynolds-averaged Navier Stokes (RANS) modeling was investigated leading to submission of the article. The transition-sensitized turbulence model encompasses the early-stage transition and turbulent flow regimes describing the evolution of the ensemble mean disturbance energy and dissipation rate. It is founded on a consistent mathematical description of the laminar regime with its linear disturbances and the fully turbulent regime with its stochastic fluctuations. The unified description is provided by the ensemble viewpoint.
Thacker, William D.↗
Turbulence modelling for unsteady separated flows
The exact transport equations for turbulent (Reynolds) stresses have left-hand sides representing the 'substantial derivatives' of the Reynolds stresses, i.e., the rates of change of stress with respect to time, as seen by an observer following the mean motion of the fluid. Here the 'mean' is a statistical average for the turbulent motion, distinguished from the ordered unsteadiness on which it is superimposed: for a turbomachine blade or a cyclically-pitching airfoil, the mean is a phase average. Written in coordinates fixed with respect to a solid surface, the substantial derivative appears partly as an Eulerian time derivative at given spatial coordinate position and partly as a spatial derivative. Separation presents two specific problems to a turbulence model: (1) prediction of the flow near separation depends critically on the 'near-wall' part of the turbulence model, and (2) downstream of separation, a boundary layer changes gradually to a mixing layer.
Bradshaw, Peter↗
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↗
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↗
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.↗
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.↗
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.↗
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↗
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.↗