Radiation Coupling with the FUN3D Unstructured-Grid CFD Code

The HARA radiation code is fully-coupled to the FUN3D unstructured-grid CFD code for the purpose of simulating high-energy hypersonic flows. The radiation energy source terms and surface heat transfer, under the tangent slab approximation, are included within the fluid dynamic ow solver. The Fire II flight test, at the Mach-31 1643-second trajectory point, is used as a demonstration case. Comparisons are made with an existing structured-grid capability, the LAURA/HARA coupling. The radiative surface heat transfer rates from the present approach match the benchmark values within 6%. Although radiation coupling is the focus of the present work, convective surface heat transfer rates are also reported, and are seen to vary depending upon the choice of mesh connectivity and FUN3D ux reconstruction algorithm. On a tetrahedral-element mesh the convective heating matches the benchmark at the stagnation point, but under-predicts by 15% on the Fire II shoulder. Conversely, on a mixed-element mesh the convective heating over-predicts at the stagnation point by 20%, but matches the benchmark away from the stagnation region

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses. Nomenclature Geometric and independent variables i Computational indicie L ref Non-dimensionalizing reference length ` Edge or element length n Normal vector r Distance vector S Generalized volume t Time x Physical coordinate, normalized by L ref \Gamma Perimeter of control volume \Omega Generalized integration volume Dependent variables A Flux Jacobian in conservative variables A Flux Jacobian in auxiliary variables a Sound speed c p Specific heat at constant pressure c v Specific heat at constant volume E Total energy e Internal energy F Flux function f Numerical flux H Tot..

Solution-Adaptive Program for Computing 2D/Axi Viscous Flow

A computer program solves the Navier- Stokes equations governing the flow of a viscous, compressible fluid in an axisymmetric or two-dimensional (2D) setting. To obtain solutions more accurate than those generated by prior such programs that utilize regular and/or fixed computational meshes, this program utilizes unstructured (that is, irregular triangular) computational meshes that are automatically adapted to solutions. The adaptation can refine to regions of high change in gradient or can be driven by a novel residual minimization technique. Starting from an initial mesh and a corresponding data structure, the adaptation of the mesh is controlled by use of minimization functional. Other improvements over prior such programs include the following: (1) Boundary conditions are imposed weakly; that is, following initial specification of solution values at boundary nodes, these values are relaxed in time by means of the same formulations as those used for interior nodes. (2) Eigenvalues are limited in order to suppress expansion shocks. (3) An upwind fluctuation-splitting distribution scheme applied to inviscid flux requires fewer operations and produces less artificial dissipation than does a finite-volume scheme, leading to greater accuracy of solutions

Aerothermodynamic Calculations on X-34 at Mach 6 Wind Tunnel Conditions

The effects of Reynolds number and turbulence on surface heat-transfer rates are numerically investigated for a 0.015 scale X-34 vehicle at wind tunnel conditions. Laminar heating rates, non-dimensionalized by Fay-Riddell stagnation heating, do not change appreciably with an order of magnitude variation in Reynolds number. Modeling a turbulent versus laminar boundary layer at the same Reynolds number increases the windside heating by a factor of four, portions on the leeside by a factor of two, and causes a 30 percent increase in wing leading edge heating. A discrepancy between laminar and turbulent heating trends on the windside centerline is explained by the presence of attached windside vortices in the laminar solutions, structures that are inhibited by the turbulence modeling

Multigrid Approach to Incompressible Viscous Cavity Flows

Two-dimensional incompressible viscous driven-cavity flows are computed for Reynolds numbers on the range 100-20,000 using a loosely coupled, implicit, second-order centrally-different scheme. Mesh sequencing and three-level V-cycle multigrid error smoothing are incorporated into the symmetric Gauss-Seidel time-integration algorithm. Parametrics on the numerical parameters are performed, achieving reductions in solution times by more than 60 percent with the full multigrid approach. Details of the circulation patterns are investigated in cavities of 2-to-1, 1-to-1, and 1-to-2 depth to width ratios

Viscous Driven-Cavity Solver: User's Manual

The viscous driven-cavity problem is solved using a stream-function and vorticity formulation for the incompressible Navier-Stokes equations. This report provides the user's manual and FORTRAN code for the set of governing equations presented in NASA TM-110262

Assessment of CFD Hypersonic Turbulent Heating Rates for Space Shuttle Orbiter

Turbulent CFD codes are assessed for the prediction of convective heat transfer rates at turbulent, hypersonic conditions. Algebraic turbulence models are used within the DPLR and LAURA CFD codes. The benchmark heat transfer rates are derived from thermocouple measurements of the Space Shuttle orbiter Discovery windward tiles during the STS-119 and STS-128 entries. The thermocouples were located underneath the reaction-cured glass coating on the thermal protection tiles. Boundary layer transition flight experiments conducted during both of those entries promoted turbulent flow at unusually high Mach numbers, with the present analysis considering Mach 10{15. Similar prior comparisons of CFD predictions directly to the flight temperature measurements were unsatisfactory, showing diverging trends between prediction and measurement for Mach numbers greater than 11. In the prior work, surface temperatures and convective heat transfer rates had been assumed to be in radiative equilibrium. The present work employs a one-dimensional time-accurate conduction analysis to relate measured temperatures to surface heat transfer rates, removing heat soak lag from the flight data, in order to better assess the predictive accuracy of the numerical models. The turbulent CFD shows good agreement for turbulent fuselage flow up to Mach 13. But on the wing in the wake of the boundary layer trip, the inclusion of tile conduction effects does not explain the prior observed discrepancy in trends between simulation and experiment; the flight heat transfer measurements are roughly constant over Mach 11-15, versus an increasing trend with Mach number from the CFD

CFD: A Castle in the Sand?

The computational simulation community is not routinely publishing independently verifiable tests to accompany new models or algorithms. A survey reveals that only 22% of new models published are accompanied by tests suitable for independently verifying the new model. As the community develops larger codes with increased functionality, and hence increased complexity in terms of the number of building block components and their interactions, it becomes prohibitively expensive for each development group to derive the appropriate tests for each component. Therefore, the computational simulation community is building its collective castle on a very shaky foundation of components with unpublished and unrepeatable verification tests. The computational simulation community needs to begin publishing component level verification tests before the tide of complexity undermines its foundation

Assessment of Turbulent CFD Against STS-128 Hypersonic Flight Data

Turbulent CFD simulations are compared against surface temperature measurements of the space shuttle orbiter windward tiles at reentry flight conditions. Algebraic turbulence models are used within both the LAURA and DPLR CFD codes. The flight data are from temperature measurements obtained by seven thermocouples during the STS-128 mission (September 2009). The flight data indicate boundary layer transition onset over the Mach number range 13.5{15.5, depending upon the location on the vehicle. But the boundary layer flow appeared to be transitional down through Mach 12, based upon the flight data and CFD trends. At Mach 9 the simulations match the flight data on average within 20 F/11 C, where typical surface temperatures were approximately 1600 F/870 C

Re-Entry Aeroheating Analysis of Tile-Repair Augers for the Shuttle Orbiter

Computational re-entry aerothermodynamic analysis of the Space Shuttle Orbiter s tile overlay repair (TOR) sub-assembly is presented. Entry aeroheating analyses are conducted to characterize the aerothermodynamic environment of the TOR and to provide necessary inputs for future TOR thermal and structural analyses. The TOR sub-assembly consists of a thin plate and several augers and spacers that serve as the TOR fasteners. For the computational analysis, the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is used. A 5-species non-equilibrium chemistry model with a finite rate catalytic recombination model and a radiation equilibrium wall condition are used. It is assumed that wall properties are the same as reaction cured glass (RCG) properties with a surface emissivity of epsilon = 0.89. Surface heat transfer rates for the TOR and tile repair augers (TRA) are computed at a STS-107 trajectory point corresponding to Mach 18 free stream conditions. Computational results show that the average heating bump factor (BF), which is a ratio of local heat transfer rate to a design reference point located at the damage site, for the auger head alone is about 1.9. It is also shown that the average BF for the combined auger and washer heads is about 2.0