Michael J. Wright

Data-Parallel Line Relaxation Method for the Navier -Stokes Equations

The Gauss‐Seidel line relaxation method is modie ed for the simulation of viscous e ows on massively parallel computers. The resulting data-parallel line relaxation method is shown to have good convergence properties for a seriesoftestcases.Thenewmethodrequiressignie cantlymorememorythanthepreviouslydevelopeddata-parallel relaxation methods, but it reaches a steady-state solution in much less time for all cases tested to date. In addition, the data-parallel line relaxation method shows good convergence properties even on the high-cell-aspect-ratio grids required to simulate high-Reynolds-number e ows. The new method is implemented using message passing on the Cray T3E, and the parallel performance of the method on this machine is discussed. The data-parallel line relaxation method combines the fast convergence of the Gauss ‐Seidel line relaxation method with a high parallel efe ciency and thus shows promise for large-scale simulation of viscous e ows.

Recommended Collision Integrals for Transport Property Computations, Part 1: Air Species

Ar eview of the best-available data for calculating a complete set of binary collision integral data for the computation of the mixture transport properties (viscosity, thermal conductivity, and ordinary and thermal diffusion) of 13-species weakly ionized air is presented. Although the fidelity of the data varies, all collision integrals presented herein, except for electron-neutral interactions, are estimated to be accurate to within 25% over the temperature range of interest (300‐15,000 K) for reentry and laboratory plasmas. In addition, most of the dominant atom‐atom and atom‐ion interactions for dissociated weakly ionized air were derived from ab initio methods that are estimated to be accurate to within 10%. The accuracy and valid temperature range for electron-neutral interactions vary because of scarcity of the required cross-sectional data.

Data-parallel lower-upper relaxation method for the navier-stokes equations

The lower-upper symmetric Gauss-Seidel method is modified for the simulation of viscous flows on massively parallel computers. The resulting diagonal data-parallel lower-upper relaxation (DP-LUR) method is shown to have good convergence properties on many problems. However, the convergence rate decreases on the high cell aspect ratio grids required to simulate high Reynolds number flows. Therefore, the diagonal approximation is relaxed, and a full matrix version of the DP-LUR method is derived. The full matrix method retains the data-parallel properties of the original and reduces the sensitivity of the convergence rate to the aspect ratio of the computational grid. Both methods are implemented on the Thinking Machines CM-5, and a large fraction of the peak theoretical performance of the machine is obtained. The low memory use and high parallel efficiency of the methods make them attractive for large-scale simulation of viscous flows.

Recommended collision integrals for transport property computations. Part 2 Mars and Venus entries

A review of the best-available data for calculating a complete set of binary collision integrals for the computation of the mixture transport properties (viscosity, thermal conductivity, ordinary and thermal diffusion) of 17-species weakly ionized CO 2 -N 2 mixtures is presented. The fidelity of the data varies considerably, but most of the atom-atom interactions are derived from ab initio methods that are estimated to be accurate to within 5%. The remaining important interactions between neutral species are estimated to be accurate to within about 30% over the temperature range of interest (300-20,000 K) to Mars and Venus reentry plasmas. Collision integrals for important ion-neutral interactions are computed using a modified Tang-Toennies potential and have an estimated accuracy of ±25%, whereas those between trace species are approximated via the polarization (Langevin) potential model. The accuracy and valid temperature range for electron-neutral interactions vary considerably due to scarcity of the required cross section data.

Comparison of Methods to Compute High-Temperature Gas Viscosity

A review of the basic equations for computing the viscosity of neutral and ionized species is presented. Four commonly used methods for determining viscosity of a gas mixture are discussed. The performance and accuracy of these methods are tested for 11-species air and hydrogen-helium gas mixtures for temperatures ranging from 200 to 20,000 K. The Gupta-Yos mixing rule gives acceptable results for weakly or nonionized flows and requires half the computer time of solving the full multicomponent equations. The Armaly-Sutton mixing rule is applicable to higher temperature, more strongly ionized flows as long as the tuning parameters for the method are appropriately set. The Wilke mixing rule is the least-accurate method, is actually slower than the Gupta-Yos mixing rules, and should be used only as a method of last resort

Uncertainty Analysis of Laminar Aeroheating Predictions for Mars Entries

A Monte Carlo sensitivity and uncertainty analysis is performed for a laminar convective heating prediction in a moderate Mars atmospheric entry condition using a nonequilibrium reacting Navier-Stokes computational fluid dynamics code. The objectives are to isolate the rate limiting mechanisms and identify the chief sources of aeroheating uncertainty. A flux-based wall catalysis formulation is developed and used to define four different catalytic regimes that are then individually analyzed at three different trajectory points. A total of 130 input parameters are statistically varied to short list a handful of parameters that essentially control the heat flux prediction. The uncertainties in these key input parameters are estimated, and a full Monte Carlo uncertainty analysis is performed. The results obtained provide the quantitative contribution of uncertainties in key modeling parameters, such as collision integrals, wall catalysis, and reaction rates to the final heat flux uncertainty. It is found that in high and low catalytic regimes, the collision integrals (which govern the transport properties of the mixture) contribute a large portion of the uncertainty, whereas in the moderately catalytic regime the catalytic properties of the surface contribute almost all of the uncertainty.

Aerothermodynamic Design of the Mars Science Laboratory Heatshield

Aerothermodynamic design environments are presented for the Mars Science Laboratory entry capsule heatshield. The design conditions are based on Navier-Stokes oweld simulations on shallow (maximum total heat load) and steep (maximum heat ux, shear stress, and pressure) entry trajectories from a 2009 launch. Boundary layer transition is expected prior to peak heat ux, a rst for Mars entry, and the heatshield environments were dened for a fully-turbulent heat pulse. The eects of distributed surface roughness on turbulent heat ux and shear stress peaks are included using empirical correlations. Additional biases and uncertainties are based on computational model comparisons with experimental data and sensitivity studies. The peak design conditions are 197 W=cm 2 for heat ux, 471 Pa for shear stress, 0.371 Earth atm for pressure, and 5477 J=cm 2 for total heat load. Time-varying conditions at xed heatshield locations were generated for thermal protection system analysis and ight instrumentation development. Finally, the aerothermodynamic eects of delaying launch until 2011 are previewed.

Impact of Flowfield-Radiation Coupling on Aeroheating for Titan Aerocapture

A methodology is developed that enables fully coupled computation of three-dimensional flow fields including radiation, assuming an optically thin shock layer. The method can easily be incorporated into existing computational fluid dynamics codes and does not appreciably increase the cost or affect the robustness of the resulting simulations. Further improvements in the accuracy of radiative heating predictions in an optically thin gas can be achieved by using a view-factor method rather than the standard tangent slab approach. These techniques are applied to the Titan aerocapture aeroheating problem, which is dominated by strong radiative heating. For this application, neglecting the nonadiabatic effects caused by radiation coupling results in an overprediction of radiative heating levels by about a factor of 2. Radiative coupling effects also significantly lower predicted convective heating by reducing boundary-layer edge temperatures. In addition, it is shown that the tangent slab approximation overpredicts radiative heating levels by a minimum of 20% in the stagnation region for this application. Over an entire design trajectory, correctly modeling radiative heat transfer results in a more than a factor of 2 reduction in total stagnation-region heat load over an uncoupled analysis.

A Review of Aerothermal Modeling for Mars Entry Missions

The current status of aerothermal analysis for Mars entry missions is reviewed. The aeroheating environment of all Mars missions to date has been dominated by convective heating. Two primary uncertainties in our ability to predict forebody convective heating are turbulence on a blunt lifting cone and surface catalysis in a predominantly CO2 environment. Future missions, particularly crewed vehicles, will encounter additional heating from shock-layer radiation due to a combination of larger size and faster entry velocity. Localized heating due to penetrations or other singularities on the aeroshell must also be taken into account. The physical models employed to predict these phenomena are reviewed, and key uncertainties or deficiencies inherent in these models are explored. Capabilities of existing ground test facilities to support aeroheating validation are also summarized. Engineering flight data from the Viking and Pathfinder missions, which may be useful for aerothermal model validation, are discussed, and an argument is presented for obtaining additional flight data. Examples are taken from past, present, and future Mars entry missions, including the twin Mars Exploration Rovers and the Mars Science Laboratory, scheduled for launch by NASA in 2011.

Data-Parallel Lower-Upper Relaxation Method for Reacting Flows

The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method of Yoon and Jameson is modified for use on massively parallel computers. The method has been implemented on the Thinking Machines CM-S and the MasPar MP-1 and MP-2, where large percentages of the theoretical peak floating point performance are obtained. It is shown that the new data-parallel LU relaxation method has better convergence properties than the original method for two different inviscid compressible flow simulations. The convergence is also improved for five-species reacting air computations. The performance of the method on various partitions of the CM-S and on the MasPar computers is discussed. The new method shows promise for the efficient simulation of very large perfect gas and reacting flows