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NASA NTRS1992

Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations

By means of either the Roe or the Van Leer flux-splittings for inviscid terms, in conjunction with central differencing for viscous terms in the explicit operator and the Steger-Warming splitting and lower-upper approximate factorization for the implicit operator, the present, robust upwind method for solving the chemical nonequilibrium Navier-Stokes equations yields formulas for finite-volume discretization in general coordinates. Numerical tests in the illustrative cases of a hypersonic blunt body, a ramped duct, divergent nozzle flows, and shock wave/boundary layer interactions, establish the method's efficiency.

Shuen, Jian-Shun↗

NASA NTRS1993

Numerical simulations of three-dimensional laminar flow over a backward facing step; flow near side walls

This paper reports the results of numerical simulations of steady, laminar flow over a backward-facing step. The governing equations used in the simulations are the full 'compressible' Navier-Stokes equations, solutions to which were computed by using a cell-centered, finite volume discretization. The convection terms of the governing equations were discretized by using the Advection Upwind Splitting Method (AUSM), whereas the diffusion terms were discretized using central differencing formulas. The validity and accuracy of the numerical solutions were verified by comparing the results to existing experimental data for flow at identical Reynolds numbers in the same back step geometry. The paper focuses attention on the details of the flow field near the side wall of the geometry.

Steinthorsson, Erlendur↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Two fourth order accurate Osher schemes are presented which maintain higher order accuracy on nonuniform grids. They use either a conservative finite difference or finite volume discretization. Both methods are successfully used for direct numerical simulations of flat plate boundary layer instability at different Mach numbers. Results of growth rates of Tollmien-Schlichting waves compare well with direct simulations of incompressible flow and for compressible flow with results obtained by solving the parabolic stability equations.

Van Der Vegt, J. J. W.↗

NASA NTRS1993

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results are shown a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Steinthorsson, E.↗

NASA NTRS1993

Development of an explicit multiblock/multigrid flow solver for viscous flows in complex geometries

A new computer program is being developed for doing accurate simulations of compressible viscous flows in complex geometries. The code employs the full compressible Navier-Stokes equations. The eddy viscosity model of Baldwin and Lomax is used to model the effects of turbulence on the flow. A cell centered finite volume discretization is used for all terms in the governing equations. The Advection Upwind Splitting Method (AUSM) is used to compute the inviscid fluxes, while central differencing is used for the diffusive fluxes. A four-stage Runge-Kutta time integration scheme is used to march solutions to steady state, while convergence is enhanced by a multigrid scheme, local time-stepping, and implicit residual smoothing. To enable simulations of flows in complex geometries, the code uses composite structured grid systems where all grid lines are continuous at block boundaries (multiblock grids). Example results shown are a flow in a linear cascade, a flow around a circular pin extending between the main walls in a high aspect-ratio channel, and a flow of air in a radial turbine coolant passage.

Steinthorsson, E.↗

NASA NTRS1993

Higher-order accurate Osher schemes with application to compressible boundary layer stability

Vandervegt, J. J. W.↗

NASA NTRS1994

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Whitfield, David L.↗

NASA NTRS1994

Control theory based airfoil design using the Euler equations

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Jameson, Antony↗

NASA NTRS1995

A numerical method for solving the three-dimensional parabolized Navier-Stokes equations

A numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield in a relatively modest CPU time. The present approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme for the evaluation of the inviscid fluxes. Second order accuracy is achieved following the guidelines of the the ENO schemes. The methodology is used to investigate three-dimensional supersonic viscous flows over symmetric corners. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction with shock waves are detected and studied. For purpose of validation, results are compared with experimental data extracted from literature. The agreement is found to be satisfactory. In conclusion, the numerical method proposed seems to be promising as it permits, at a reasonable computational expense, investigation of complex three-dimensional flowfields in great detail.

Dambrosio, Domenic↗

NASA NTRS1995

Shock-Induced Separated Structures in Symmetric Corner Flows

Three-dimensional supersonic viscous laminar flows over symmetric corners are considered in this paper. The characteristic features of such configurations are discussed and an historical survey on the past research work is presented. A new contribution based on a numerical technique that solves the parabolized form of the Navier-Stokes equations is presented. Such a method makes it possible to obtain very detailed descriptions of the flowfield with relatively modest CPU time and memory storage requirements. The numerical approach is based on a space-marching technique, uses a finite volume discretization and an upwind flux-difference splitting scheme (developed for the steady flow equations) for the evaluation of the inviscid fluxes. Second order accuracy is reached following the guidelines of the ENO schemes. Different free-stream conditions and geometrical configurations are considered. Primary and secondary streamwise vortical structures embedded in the boundary layer and originated by the interaction of the latter with shock waves are detected and studied. Computed results are compared with experimental data taken from literature.

DAmbrosio, Domenic↗

NASA NTRS1996

Simulations of Turbine Cooling Flows Using a Multiblock-Multigrid Scheme

Results from numerical simulations of air flow and heat transfer in a 'branched duct' geometry are presented. The geometry contains features, including pins and a partition, as are found in coolant passages of turbine blades. The simulations were performed using a multi-block structured grid system and a finite volume discretization of the governing equations (the compressible Navier-Stokes equations). The effects of turbulence on the mean flow and heat transfer were modeled using the Baldwin-Lomax turbulence model. The computed results are compared to experimental data. It was found that the extent of some regions of high heat transfer was somewhat under predicted. It is conjectured that the underlying reason is the local nature of the turbulence model which cannot account for upstream influence on the turbulence field. In general, however, the comparison with the experimental data is favorable.

Steinthorsson, Erlendur↗

NASA NTRS2008

Direct-View Multi-Point Two-Component Interferometric Rayleigh Scattering Velocimeter

This paper describes an instantaneous velocity measurement system based on the Doppler shift of elastically scattered laser light from gas molecules (Rayleigh scattering) relative to an incident laser. The system uses a pulsed laser as the light source, direct-viewing optics to collect the scattered light, an interferometer to analyze spectrally the scattered light mixed with the incident laser light, and a CCD camera to capture the resulting interferogram. The system is capable of simultaneous, spatially (approximately 0.2 mm(exp 3)) and temporally (approximately 40 ns) resolved, multiple point measurements of two orthogonal components of flow velocity in the presence of background scattered light, acoustic noise and vibrations, and flow particulates. Measurements in a large-scale axi-symmetric Mach 1.6 H2-air combustion-heated jet running at a flow sensible enthalpy specific to Mach 5.5 hypersonic flight are performed to demonstrate the technique. The measurements are compared with CFD calculations using a finite-volume discretization of the Favre-averaged Navier-Stokes equations (VULCAN code).

Bivolaru, Daniel↗

NASA NTRSDate not supplied

Investigation of Improved Wall Heat Flux Behavior Observed When Computing Hypersonic Flow Using a Face-averaged Nodal-gradient Approach On Tetrahedral Grids

We investigate the origin of a significant reduction in computed numerical “noise” in the spatial variation of computed wall heat flux observed when using a node-centered weighted least squares(WLSQ) gradient approach when solving the Reynolds-averaged Navier-Stokes (RANS) equations for hypersonic boundary layer flows on highly stretched tetrahedral grids. This investigation is conducted using a 2nd-order, cell-centered, finite-volume, discretization which we employ to contrast results obtained using two WLSQ gradient approaches: a conventional 3-D, cell-centered, node-neighbor, WLSQ gradient (NN-CCG) approach and a 3-D, face-averaged, node-centered gradient (F-ANG)approach. The F-ANG approach, is shown to produce significantly less “noise” in the spatial variation of wall heat flux, than the NN-CCG approach and we demonstrate the cause of this “noise” via a series of numerical experiments where we compute hypersonic laminar and turbulent boundary layer flows.We further investigate the level of grid resolution required for a tetrahedral grid to approach the fidelity of a grid resolved hexahedral grid solution obtained using an equivalent structured grid method.

Jeffery A. White↗

NASA NTRSDate not supplied

FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

The 1st AIAA Stability and Control Prediction Workshop was created to establish best practices for the prediction of stability & control derivatives using computational fluid dynamics and assess the limitations of these computational methods when those best practices are applied. The inaugural workshop considers the ONERA version of the NASA/Boeing Common Research Model(CRM), which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel tests have been conducted for this configuration with longitudinal tests having been previously published, in addition to unpublished data at small sideslip angles that will serve as ‘blind’ data for workshop data comparisons. Participants were provided a ‘family’ of unstructured grids for the full-span ONERA CRM model with the wind-tunnel sting included. This family of mixed-element grids consists of 5 levels of refinement (tiny, coarse, medium, fine, and extra fine) with surface and volume mesh scaling, resulting in a size range of 14.6 to 53.4 million nodes. In addition, a medium refinement mesh has been provided for the ONERA CRM configuration without a sting to evaluate the sting’s impact on static longitudinal stability characteristics. In addition to these workshop-provided grids, the present work also considers an equivalent ‘family’ of computational grids generated using Heldenmesh™, a rapid grid generation software by Helden Aerospace Corporation for creating high-quality, three-dimensional, mixed-element unstructured meshes. Because of the authors’ familiarity with this software, these additional grids were generated as a comparison to the workshop-provided grids and to better understand the implications of using volume-mirrored grids for stability and control predictions. The present work will contribute to the workshop with test case data generated using the NASA FUN3D code, a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Numerical simulations will be conducted using the Quadratic Constitutive Relationship (QCR) version of the Spalart-Allmaras (SA) turbulence model with negative turbulence variable provisions. Both steady and2nd-order, time-accurate simulation results are to be generated and compared for select test cases, as time permits, to investigate their impact on FUN3D predictions. The present work will consider the three primary workshop test cases: (1) grid convergence study, (2) Mach number effect on static stability, and (3) wind tunnel sting increments. Additionally, data will be provided for the two optional test cases, which include:(1) static stability derivative calculations and (2)sideslip angle sweeps. In each of the test cases, the vehicle is stationary, and the body is assumed to be rigid, where vehicle deformation has been accounted for in the model configuration geometry. For all test cases, longitudinal and lateral force and moment aerodynamic coefficients will be provided for the total configuration, in addition to a component-level breakdown that includes the port wing, starboard wing, fuselage, and tail.

CFD↗

NASA NTRSDate not supplied

NASA Langley FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

This work summarizes the results of FUN3D analyses conducted for the 1st AIAA Stability and Control Workshop on behalf of participants from the NASA Langley Research Center. The workshop was created to establish best practices for the prediction of stability and control derivatives using computational fluid dynamics and assess the limitations of these methods when those best practices are applied. The inaugural workshop considered the ONERA version of the NASA/Boeing Common Research Model, which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel data at small sideslip angles remain unpublished and served as ‘blind’ data for computational comparisons. The present research generated workshop test case data using the NASA FUN3D code, which is a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Steady- state numerical simulations were conducted for workshop test cases investigating the following: grid convergence, Mach number effect on static stability, wind tunnel sting increments, static stability-derivative calculations, and a sideslip angle sweep. Results were generated for two series of unstructured, mixed-element grids, one set provided by the workshop and another set created using the HeldenMesh grid generation software. The results provided include total- and component-level breakdowns of the force and moment coefficients, in addition to sectional pressure distributions for the wing and tail components for comparisons to wind tunnel data.

CFD↗

NASA NTRSDate not supplied

Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes

A node-centered edge-based finite volume discretization of the compressible Navier-Stokes equations is presented with the heat flux reformulated as a first order system. A dissipation vector is derived for the reformulated system, such that the heat flux can be upgraded to O(h^3) on simplex element meshes in the same fashion as the inviscid fluxes. The method of manufactured solutions is used to demonstrate this uniform order property in heat flux. This new system is shown to efficiently produce accurate surface heating predictions on hypersonic hemisphere flow using an anisotropic simplex element mesh, achieving O(h^3) accuracy at relatively low computational cost compared to similar methods.

Computational Fluid Dynamics↗

NASA NTRSDate not supplied

On Computationally Efficient Radiative Transfer Calculations for Three-dimensional Entry Problems

The current work presents an efficient simulation framework for rigorously modeling radiative fields emanating from non-equilibrium planetary entry flows in complex three-dimensional domains. Key to this endeavor is adoption of finite-volume discretization in lieu of brute-force ray tracing. This change in conjunction with mesh sweeping and Lebedev-type quadrature for angular integration allows spatial-angular resolution of radiative transfer to be performed in a computationally tractable manner. Additionally, a new methodology has been established to build standalone reduced-order spectral databases for non-equilibrium radiative properties that can be applied to a broad range of hypersonic planetary entry problems with minimal loss in accuracy. The efficacy of the new framework has been demonstrated on the atomic nitrogen radiative system. The resulting reduced-order model requires three orders-of-magnitude fewer spectral evaluations and results in a 95% decrease in memory footprint. A comparative study for representative forebody and afterbody lines-of-sight from Stardust, FIRE II, and meteor entries into the Earth atmosphere indicates that both total intensity variation and detailed spectra can be retrieved with as few as 625 reduced-order groups (contrasting with the 100,000 frequencies in the original full set model). Similarly, three-dimensional predictions of radiative heating experienced by the Orion forebody are in excellent agreement with legacy radiation solvers while requiring only a sliver (roughly 0.5%) of computing wall time.

3D radiation↗

NASA NTRS2023

Evaluation of Voronoi Meshes for Large Eddy Simulations of High Lift Aerodynamics

Numerical sensitivity to 3 different Voronoi seeding methods is investigated for Large Eddy Simulations (LES). A second order accurate, non-dissipative finite volume discretization is used to systematically investigate the effects of different polyhedral Voronoi mesh types using a sequence of three canonical problems with increasing complexity. First, inviscid isentropic vortex propagation is studied to demonstrate the substantial reduction of errors for rhombic dodecahedron and truncated octahedral cell types over Cartesian hexagonal cells of identical spacing. Furthermore, the reduction of errors induced at cell-size transitions (grid-coarsening interfaces) due to Lloyd smoothing iterations is quantified. It is shown that by utilizing an appropriate viscous flux discretization, a constant coefficient subgrid scale model is sufficient for non-linear stability at the 2:1 cell-size transitions on polyhedral grids, although some further error reduction does occur when smoothing is utilized. Next, forced homogeneous isotropic turbulence at an asymptotically large Reynolds number is studied to demonstrate the non-dissipative character of the inviscid flux discretization, and the non-linear robustness and accuracy offered by the viscous flux discretization using a subgrid scale model for all three Voronoi grid types. Finally,Wall-Modeled Large Eddy Simulations (WMLES) are performed to study the high-lift aerodynamics on the McDonnell Douglas 30P30N multi-element airfoil at two distinct grid levels and for two distinct Voronoi cell types. The formulation is shown to predict the aerodynamic loading with high accuracy at all angles of attack when sufficient resolution is reached, and the hexagonal prism grid topology, while computationally more expensive, has higher effective resolution compared to the Cartesian grid topology with the same spacing.

TTT↗