Jeffery A White

NASA · Computational Aerosciences Branch

This is a presentation file for AIAA 2023-4418: In this paper, we report progress in the development of a third-order accurate, second- derivative-free, shock-capturing finite-volume solver for three-dimensional unstructured grids. The method is economical in the sense that the computation and storage of second derivatives are not required for thi...

In this paper, we report progress in the development of a third-order accurate, second- derivative-free, shock-capturing finite-volume solver for three-dimensional unstructured grids. The method is economical in the sense that the computation and storage of second derivatives are not required for third-order accuracy. It is based on point-valued nu...

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed quadratic formula is constructed based on an efficient formula of computing a projected deriva...

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral grids. The proposed quadratic formula is constructed based on an efficient formula of computing a projected deriva...

We describe the extension of a 2-D simplified face-averaged nodal-gradient (F-ANG) method to 3-D and demonstrate that the 3-D simplified FANG method is accomplished by augmenting the node-centered gradient least squares stencil. This augmented stencil FANG method is shown to result in advection and diffusion schemes that are stable for hexahedral,...

We propose a simplification of the face-averaged nodal-gradient (FANG) method for a cell-centered finite-volume Euler/Navier-Stokes solver on arbitrary grids, and compare it with other gradient methods for trouble-prone grids in two dimensions. The implementa- tion of the FANG method is simplified by adding the face-neighbor cells of the cells arou...

View Video Presentation: https://doi.org/10.2514/6.2021-2701.vid Early work is presented for an unstructured grid adaptation workflow with VULCAN and refine. Anisotropic simplex grids are iteratively adapted to match a Riemannian metric tensor field describing desired mesh spacing. The Riemannian metric tensor field is obtained from Hessians of CFD...

We present an overview of recent developments related to the adaptation of structured and unstructured grids to hypersonic flows, as contained within or utilized by the VULCAN-CFD code. We touch briefly on recent improvements to the relatively mature line-by-line 1-D bow shock and boundary layer edge grid adaptation capability developed to compute...

In this paper, a face-averaged nodal-gradient approach is proposed as an efficient gradient method for a second-order cell-centered finite-volume discretization on triangular grids. The gradients needed in the linear reconstruction are computed in two steps: (1) compute gradients at nodes from solutions stored at cells, and (2) compute the gradient...

2-D nodal weighted least-squares gradient method and a related face-averaged nodal gradient approach that were developed for use with triangular grids are extended to 3-D for use with tetrahedral grids. In addition, a method, developed in 2-D, to stabilize the iterative convergence of these methods on quadrilateral cells is described and extended t...

In this paper, the averaged nodal-gradient approach previously developed for triangular grids is extended to mixed triangular-quadrilateral grids. It is shown that the face-averaged approach leads to deteriorated iterative convergence on quadrilateral grids. To develop a convergent solver, we consider cell-averaging instead of face-averaging for qu...

In this paper, a face-averaged nodal-gradient approach is investigated for a second-order cell-centered �nite-volume method. The gradients needed in the linear reconstruction are computed in two steps: compute the gradient at nodes for a given set of solutions at nearby cells, and then compute the gradient at a face by averaging the nodal gradients...

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2 nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use...

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use o...

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2 nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robu...

Boundary-layer transition on axisymmetric bodies at a nonzero angle of attack in Mach 2 supersonic flow was investigated using experimental measurements and linear stability analysis. Transition over four axisymmetric bodies (namely, the Sears-Haack body, the semi-Sears-Haack body, the straight cone, and the flared cone) with different axial pressu...

In this paper, the implementation of two wall function models in the Reynolds averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) code FUN3D is described. FUN3D is a node centered method for solving the three-dimensional Navier-Stokes equations on unstructured computational grids. The first wall function model, based on the work of Kno...

Initial and inflow conditions continue to present a challenge for simulations of turbulent flows via Direct and Large-Eddy Simulations (DNS and LES). The current work utilizes the output of a Sabra [1] shell model of turbulence to synthesize a three-dimensional (3D) homogeneous, isotropic, incompressible, turbulence-in-a-box velocity field. This ap...

Computations are performed to study the boundary layer instability mechanisms pertaining to hypersonic vehicles with significant ablative effects. The process of laminar-turbulent transition over vehicles with ablative heat shields can be influenced by both the out-gassing associated with surface pyrolysis and the resulting modification of surface...

The functional equivalence of the unstructured grid code FUN3D to the the struc- tured grid code LAURA (Langley Aerothermodynamic Upwind Relaxation Algorithm) is documented for applications of interest to the Entry, Descent, and Landing (EDL) com- munity. Examples from an existing suite of regression tests are used to demonstrate the functional equ...

The 2nd-order upwind inviscid flux scheme implemented in the multi-block, structured grid, cell centered, finite volume, high-speed reacting flow code VULCAN has been modified to reduce numerical dissipation. This modification was motivated by the desire to improve the codes ability to perform large eddy simulations. The reduction in dissipation wa...

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight t...

Boundary layer transition along the leeward symmetry plane of axisymmetric bodies at nonzero angle of attack in supersonic flow was investigated experimentally and numerically as part of joint research between the Japan Aerospace Exploration Agency (JAXA) and National Aeronautics and Space Administration (NASA). Transition over four axisymmetric bo...

Computations are performed to study the boundary layer instability mechanisms pertaining to hypersonic flow over blunt capsules. For capsules with ablative heat shields, transition may be influenced both by out-gassing associated with surface pyrolysis and the resulting modification of surface geometry including the formation of micro-roughness. To...

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvat...

Finite-volume discretization schemes for viscous fluxes on general grids are compared using node-centered and cell-centered approaches. The grids range from regular grids to highly irregular grids, including random perturbations of the grid nodes. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered...

Computational challenges in hypersonic flow simulations being addressed by the NASA Fundamental Aeronautics Hypersonics Project are reviewed. The purpose of the project is to conduct foundational research for capsule-based entry vehicles as well as air-breathing launch systems enabling human exploration of the Moon, Mars, and beyond. The challenges...

This work reports improvements to detailed chemistry models, chemistry tabulation techniques, and reduced mechanisms. Pressure-dependent reaction rates for the CO-H2 system improve ignition delay predictions as a function of pressures for CO-H2 mixtures. Previous mechanisms did not even correctly predict the trends according to recent measurements....

This report was developed under SBIR contract for Topic AF05-194. The objective of this work was to develop and demonstrate a means for the efficient integration of detailed numerical analysis into the design-optimization process. An integrated design optimization and engineering analysis tool has been demonstrated. This tool leverages the signific...

An experiment is described that has been conducted to acquire data for the validation of computational fluid dynamics codes used in the design of supersonic combustors. A coaxial nozzle has been designed to produce two uniform, pressure-matched coaxial flows at its exit. The center flow is a 95% He and 5% O-2 mixture at Mach 1.8, and the surroundin...

VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses s...

The wall-matching methodology of Wilcox is modified to include a solid-wall, thermal-conduction model. This coupled fluid-thermal-structure model is derived assuming that the wall thermal-structure behavior is locally one-dimensional and that structural deformations, due to thermally induced stresses, are not significant. The one-dimensional couple...

A computational analysis of Mach 6.2 operation of a hypersonic inlet with rectangular-to-elliptical shape transition has been performed. The results of the computations are compared with experimental data for cases with and without a manually imposed back-pressure. While the no-back-pressure numerical solutions match the general trends of the data,...

A supersonic coaxial jet facility is designed and experimental data are acquired suitable for the validation of CFD codes employed in the analysis of high-speed air-breathing engines. The center jet is of a light gas, the coflow jet is of air, and the mixing layer between them is compressible. The jet flow field is characterized using schlieren ima...

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost a...

Two Mach 2.4 nozzles with square test sections have been designed and analyzed, as part of an effort to develop low-disturbance facilities for laminar-now control for high-speed civil transport, The mean flows have been simulated using a finite volume, central-differencing scheme to solve the thin-layer Navier-Stokes equations, Substantial crossflo...

Assumed Gaussian and β probability density functions (PDFs) for temperature are used with series expansions of the reaction-rate coefficients to compute the mean reaction-rate coefficients in a turbulent, reacting flow. The series-expansion/assumed PDF approach does not require any numerical integration, which substantially reduces computational co...

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rathe...

A flux-difference split explicit finite-difference algorithm is presented for solving the parabolized form of the equations governing three-dimensional nonequilibrium chemically reacting flows. The algorithm is based on an explicit noniterative, upwind space-marching scheme developed by Korte, but differs in that the unsteady Riemann problem, rathe...

The use is considered of a multigrid method with central differencing to solve the Navier-Stokes equations for high speed flows. The time dependent form of the equations is integrated with a Runge-Kutta scheme accelerated by local time stepping and variable coefficient implicit residual smoothing. Of particular importance are the details of the num...

Two assumed probability density functions (pdfs) are employed for computing the effect of temperature fluctuations on chemical reaction. The pdfs assumed for this purpose are the Gaussian and the beta densities of the first kind. The pdfs are first used in a parametric study to determine the influence of temperature fluctuations on the mean reactio...

THREE-DIMENSIONAL effects in a mixed compression inlet typical of supersonic combustion ramjet engine are studied using a full Navier-Stokes analysis method. The solution procedure uses a multistep pressure correction method with an implicit density treatment to establish the pressure and velocity fields. The strong shocks are captured using a smar...

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time-dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process t...

A procedure for the generation of two and quasi-three-dimensional grids with control of orthogonality and spacing with respect to any and/or all boundaries of the domain is described. The elliptic grid generation equations of Thompson are solved implicitly. Control of the grid behavior is achieved through the introduction of forcing functions terms...

The complex viscous shock interaction phenomenon present when an oblique shock impinges on a blunt body bow shock, and the peak heat transfer rates representative of the flow field near the inlet cowl leading edge of a hypersonic vehicle are computed. A pressure based implicit finite volume method is used to solve the steady state Reynolds averaged...

The available two- and three-dimensional codes are used to estimate external heat loads and aerodynamic characteristics of a highly loaded turbine stage in order to demonstrate state-of-the-art methodologies in turbine design. By using data for a low aspect ratio turbine, it is found that a three-dimensional multistage Euler code gives good averall...