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NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the in- fluence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:1 prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morison, J. H.↗

NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the influence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:l prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morrison, J. H.↗

NASA NTRS2001

A Study of Grid Resolution, Transition and Turbulence Model Using the Transonic Simple Straked Delta Wing

Three-dimensional transonic flow over a delta wing is investigated using several turbulence models. The performance of linear eddy viscosity models and an explicit algebraic stress model is assessed at the start of vortex flow, and the results compared with experimental data. To assess the effect of transition location, computations that either fix transition aft of the leading edge or are fully turbulent are performed. These computations show that grid resolution, transition location and turbulence model significantly affect the 3D flowfield.

Bartels, Robert E.↗

NASA NTRS2013

DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow

The turbulent flows through a plane channel and a channel with a constriction (2-D hill) are numerically simulated using DNS and RANS calculations. The Navier-Stokes equations in the DNS are solved using a higher order kinetic energy preserving central schemes and a fifth order accurate upwind biased WENO scheme for the space discretization. RANS calculations are performed using the NASA code CFL3D with the komega SST two-equation model and a full Reynolds stress model. Using DNS, the magnitudes of different terms that appear in the enstrophy equation are evaluated. The results show that the dissipation and the diffusion terms reach large values at the wall. All the vortex stretching terms have similar magnitudes within the buffer region. Beyond that the triple correlation among the vorticity and strain rate fluctuations becomes the important kinematic term in the enstrophy equation. This term is balanced by the viscous dissipation. In the separated flow, the triple correlation term and the viscous dissipation term peak locally and balance each other near the separated shear layer region. These findings concur with the analysis of Tennekes and Lumley, confirming that the energy transfer terms associated with the small-scale dissipation and the fluctuations of the vortex stretching essentially cancel each other, leaving an equation for the dissipation that is governed by the large-scale motion.

Balakumar, Ponnampalam↗

NASA NTRS1990

A dynamic subgrid-scale eddy viscosity model

One major drawback of the eddy viscosity subgrid-scale stress models used in large-eddy simulations is their inability to represent correctly with a single universal constant different turbulent field in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work, a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity (Germano 1990) between the subgrid-scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid-scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The results of large-eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

Germano, Massimo↗

NASA NTRS1994

A hydrostatic stress-dependent anisotropic model of viscoplasticity

A hydrostatic stress-dependent, anisotropic model of viscoplasticity is formulated as an extension of Bodner's model. This represents a further extension of the isotropic Bodner model over that made to anisotropy by Robinson and MitiKavuma. Account is made of the inelastic deformation that can occur in metallic composites under hydrostatic stress. A procedure for determining the material parameters is identified that is virtually identical to the established characterization procedure for the original Bodner model. Characterization can be achieved using longitudinal/transverse tensile and shear tests and hydrostatic stress tests; alternatively, four off-axis tensile tests can be used. Conditions for a yield stress minimum under off-axis tension are discussed. The model is applied to a W/Cu composite; characterization is made using off-axis tensile data generated at NASA Lewis Research Center (LeRC).

Robinson, D. N.↗

NASA NTRS1992

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

NASA NTRS2003

Computations of Internal and External Axisymmetric Nozzle Aerodynamics at Transonic Speeds

Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles have been completed in support of NASA's Next Generation Launch Technology Program to investigate the effects of high-speed nozzle geometries on the nozzle internal flow and the surrounding boattail regions. These computations span the very difficult transonic flight regime, with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined in Wind, including an Explicit Algebraic Stress model (EASM). Computations on two nozzle geometries have been completed at freestream Mach numbers ranging from 0.6 to 0.9, driven by nozzle pressure ratios (NPR) ranging from 2.9 to 5. Results obtained on converging-only geometry indicate reasonable agreement to experimental data, with the EASM and Shear Stress Transport (SST) turbulence models providing the best agreement. Calculations completed on a converging-diverging geometry involving large-scale internal flow separation did not converge to a true steady-state solution when run with variable timestepping (steady-state). Calculations obtained using constant timestepping (time-accurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was found to be the result of difficulties in using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show fairly good agreement with experimental data. The SST turbulence model demonstrates the best over-all agreement with experimental data.

Dalbello, Teryn↗

NASA NTRS2000

Implementation of Advanced Two Equation Turbulence Models in the USM3D Unstructured Flow Solver

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flow. We have implemented two modified versions of the original Jones and Launder k-epsilon "two-equation" turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for three flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those from direct numerical simulation, empirical formulae, theoretical results, and the existing Spalart-Allmaras one-equation model.

Wang, Qun-Zhen↗

NASA NTRS1999

Solving Navier-Stokes Equations with Advanced Turbulence Models on Three-Dimensional Unstructured Grids

USM3D is a widely-used unstructured flow solver for simulating inviscid and viscous flows over complex geometries. The current version (version 5.0) of USM3D, however, does not have advanced turbulence models to accurately simulate complicated flows. We have implemented two modified versions of the original Jones and Launder k-epsilon two-equation turbulence model and the Girimaji algebraic Reynolds stress model in USM3D. Tests have been conducted for two flat plate boundary layer cases, a RAE2822 airfoil and an ONERA M6 wing. The results are compared with those of empirical formulae, theoretical results and the existing Spalart-Allmaras one-equation model.

Wang, Qun-Zhen↗

NASA NTRS2005

Mimicking Natural Laminar to Turbulent Flow Transition: A Systematic CFD Study Using PAB3D

For applied aerodynamic computations using a general purpose Navier-Stokes code, the common practice of treating laminar to turbulent flow transition over a non-slip surface is somewhat arbitrary by either treating the entire flow as turbulent or forcing the flow to undergo transition at given trip locations in the computational domain. In this study, the possibility of using the PAB3D code, standard k-epsilon turbulence model, and the Girimaji explicit algebraic stresses model to mimic natural laminar to turbulent flow transition was explored. The sensitivity of flow transition with respect to two limiters in the standard k-epsilon turbulence model was examined using a flat plate and a 6:1 aspect ratio prolate spheroid for our computations. For the flat plate, a systematic dependence of transition Reynolds number on background turbulence intensity was found. For the prolate spheroid, the transition patterns in the three-dimensional boundary layer at different flow conditions were sensitive to the free stream turbulence viscosity limit, the reference Reynolds number and the angle of attack, but not to background turbulence intensity below a certain threshold value. The computed results showed encouraging agreements with the experimental measurements at the corresponding geometry and flow conditions.

Pao, S. Paul↗

NASA NTRS2015

Second-Moment RANS Model Verification and Validation Using the Turbulence Modeling Resource Website (Invited)

The implementation of the SSG/LRR-omega differential Reynolds stress model into the NASA flow solvers CFL3D and FUN3D and the DLR flow solver TAU is verified by studying the grid convergence of the solution of three different test cases from the Turbulence Modeling Resource Website. The model's predictive capabilities are assessed based on four basic and four extended validation cases also provided on this website, involving attached and separated boundary layer flows, effects of streamline curvature and secondary flow. Simulation results are compared against experimental data and predictions by the eddy-viscosity models of Spalart-Allmaras (SA) and Menter's Shear Stress Transport (SST).

Eisfeld, Bernhard↗

NASA NTRS1983

Large-area sheet task advanced dendritic web growth development

The thermal stress models were used to test the effect of melt level on stress generation and growth velocity. The results indicate that melt level has only small effects on stresses but significant effects on growth velocity. These results are consistent with experimental growth from measured melt levels. A new low-stress design concept is being evaluated with the models. A width-limiting version of the low-stress J460 configuration was tested experimentally with results consistent with the design goals.

Duncan, C. S.↗

NASA NTRS1991

Computed stress fields in GaAs during vertical Bridgman growth

The thermoelastic stress field of GaAs crystals grown by the vertical Bridgman method has been approximated using a linear elastic, axisymmetric stress model. The model included the effects due to the thermal field and the gravitational field, as well as the interaction with the ampoule, but did not fully account for the elastic anisotropy of the crystal. Realistic thermal fields for different furnace temperatures and insulation zone thicknesses were computed with a similar model. The difference between the Von Mises stress and the critical resolved shear stress (CRSS) was used as a measure of the number of dislocations present. Different sets of growth parameters were examined to determine which produced the lowest amount of stress in the crystal. Results show that the crystal-ampoule interaction is the most important parameter in dislocation generation. In addition, for the same sticking boundary conditions, concave interfaces have lower stress than convex interfaces.

Rosch, William↗

NASA NTRS1992

Comparison of turbulence models for powered-lift flow fields

The development of a practical turbulence model for the complex flows with strong streamline curvature associated with powered-lift aircraft was investigated. The approach was to modify existing models that were compatible with the widely used kappa-epsilon model already available in an existing 3D Navier-Stokes code. The state-of-the-art of current turbulence models was examined. Several models that provide curvature corrections to the kappa-epsilon model were numerically investigated. An algebraic Reynolds stress model, which provides additional physics, was also examined. Test cases including an impinging jet, an impinging jet in a crossflow, and two adjacent impinging jets with the resultant upwash fountain were calculated. The first two test cases could be modeled reasonsbly well with some of the models. The upwash fountain could not be modeled with sufficient accuracy, which is consistent with the findings of other investigators.

Roberts, Donald W.↗

NASA NTRS2001

Evaluation of Turbulence-Model Performance in Jet Flows

The importance of reducing jet noise in both commercial and military aircraft applications has made jet acoustics a significant area of research. A technique for jet noise prediction commonly employed in practice is the MGB approach, based on the Lighthill acoustic analogy. This technique requires as aerodynamic input mean flow quantities and turbulence quantities like the kinetic energy and the dissipation. The purpose of the present paper is to assess existing capabilities for predicting these aerodynamic inputs. Two modern Navier-Stokes flow solvers, coupled with several modern turbulence models, are evaluated by comparison with experiment for their ability to predict mean flow properties in a supersonic jet plume. Potential weaknesses are identified for further investigation. Another comparison with similar intent is discussed by Barber et al. The ultimate goal of this research is to develop a reliable flow solver applicable to the low-noise, propulsion-efficient, nozzle exhaust systems being developed in NASA focused programs. These programs address a broad range of complex nozzle geometries operating in high temperature, compressible, flows. Seiner et al. previously discussed the jet configuration examined here. This convergent-divergent nozzle with an exit diameter of 3.6 inches was designed for an exhaust Mach number of 2.0 and a total temperature of 1680 F. The acoustic and aerodynamic data reported by Seiner et al. covered a range of jet total temperatures from 104 F to 2200 F at the fully-expanded nozzle pressure ratio. The aerodynamic data included centerline mean velocity and total temperature profiles. Computations were performed independently with two computational fluid dynamics (CFD) codes, ISAAC and PAB3D. Turbulence models employed include the k-epsilon model, the Gatski-Speziale algebraic-stress model and the Girimaji model, with and without the Sarkar compressibility correction. Centerline values of mean velocity and mean temperature are compared with experimental data.

Woodruff, S. L.↗

NASA NTRS2001

Turbulence Modeling: A NASA Perspective

This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.

Gatski, T. B.↗

NASA NTRS2003

Computational Study of Axisymmetric Off-Design Nozzle Flows

Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles operating off-design at transonic Mach numbers have been completed. These computations span the very difficult transonic flight regime with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined, including the Explicit Algebraic Stress model. Computations have been completed at freestream Mach numbers of 0.9 and 1.2, and nozzle pressure ratios (NPR) of 4 and 6. Calculations completed with variable time-stepping (steady-state) did not converge to a true steady-state solution. Calculations obtained using constant timestepping (timeaccurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was the result of using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show reasonable agreement with experimental data. The SST turbulence model demonstrates the best overall agreement with experimental data.

DalBello, Teryn↗