The development of a new high- delity methodology for predicting entry  ows with coupled radiation and ablation is described. The prediction methodology consists of an axisymmetric, nonequilibrium, Navier–Stokes  ow solver loosely coupled to a radiation prediction code and a material thermal response code. The methodology is used to simulate the 12.6-km/s Earth atmospheric entry of the Stardust sample return capsule using ablating and nonablating boundary conditions. These  ow simulations are used to size and design the Stardust forebody and afterbody heatshields and develop arcjet test conditions and models. The  ow simulations indicate that the afterbody heating and pressure pro les in time are signi cantly different than the forebody heating and pressure pro les. This result is explained in terms of the pertinent aerothermodynamicsof the  ow eld and the vehicle’s geometry.When applied to the afterbody thermal protection system, these results show that the traditional afterbody heatshield design approach is nonconservative for the Stardust sample return capsule shape and entry conditions.

Aerothermodynamics of the Stardust Sample Return Capsule

Numerical simulations of axisymmetric flows over reentry configurations at hypersonic conditions using a Navier-Stokes solver are presented. The Navier-Stokes equations are modified using Park’s two-temperature model to account for thermochemical nonequilibrium and weak ionization eects. The finite-volume method is used to solve the set of dierential equations. The code has the capability to handle any mixture of hexahedra, tetrahedra, prisms and pyramids in 3D or triangles and quadrilaterals in 2D. The results in this paper only use quadrilaterals. Numerical fluxes between the cells are discretized using a modified Steger-Warming Flux Vector Splitting approach which has low dissipation and is appropriate to calculate boundary layers. A point or line implicit method is used to perform the time integration. Pressure, heat transfer rates and electron number density profiles are compared to available experimental and flight measurements.

/pdf/numerical-simulation-of-weakly-ionized-hypersonic-flow-for-30xt4o6pat.pdf

Numerical Simulation of Weakly Ionized Hypersonic Flow for Reentry Configurations

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

Numerical simulations of a spacecraft at reentry conditions are presented. The fluid at such conditions is modeled as a reacting gas in thermal and chemical nonequilibrium. The reacting gas is modeled using a standard finite rate chemistry model for air. A twotemperature model is used to account for the thermal nonequilibrium eects. The finitevolume method is used to solve the set of dierential equations on unstructured meshes. Numerical fluxes between the cells are discretized using a modified Steger-Warming Flux Vector Splitting (FVS) which has low dissipation and is appropriate to calculate boundary layers. The scheme switches back to the original Steger-Warming FVS near shock waves. A point implicit method is used to perform the time march. The numerical results for heat transfer are compared to available experimental data. The influence of the method used to switch between schemes on the results is assessed.

/pdf/development-of-an-unstructured-navier-stokes-solver-for-4hxo60s5qr.pdf

Development of an Unstructured Navier-Stokes Solver for Hypersonic Nonequilibrium Aerothermodynamics

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.

/pdf/a-review-of-aerothermal-modeling-for-mars-entry-missions-4igddblca7.pdf

A Review of Aerothermal Modeling for Mars Entry Missions

Aerodynamic heating tests were conducted on a 70-deg sphere ‐cone Mars entry vehicle cone guration in a high-enthalpy impulse facility in both carbon dioxide and air test gases. The purpose of these tests was to obtain heat transfer data for comparison with results of Navier ‐Stokes computations. Surface heat transfer rates were determined for both the forebody and afterbody of the test models and for the stings that supported the models in the facility test section. Little difference was observed between normalized heating distributions for the air and carbon dioxide test conditions. For both cases, peak sting heating was on the order of 4 ‐5% of the forebody stagnation-point heating, and it was concluded that the wake e ow remained laminar. The wake e ow establishment process was quantie ed and was found to require approximately 40 ‐70 e ow path lengths, which corresponded to approximately 75% of the available facility test time. The repeatability of facility test conditions was estimated to vary between § 3% and § 10%. The overall experimental uncertainty of the data was estimated to be § 10‐11% for forebody heating and § 17‐22% for wake heating.

High-Enthalpy Aerothermodynamics of a Mars Entry Vehicle Part 1: Experimental Results

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

/pdf/user-s-manual-for-the-one-dimensional-hypersonic-2nyz18wis6.pdf

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

Numerical solutions for hypersonic  ows of carbon dioxide and air around a 70-deg sphere–cone Mars entry vehicle con guration were computed using a laminar, axisymmetric, nonequilibrium Navier–Stokes solver with freestream  ow conditions equivalent to those of aerothermodynamic tests conducted in a high-enthalpy impulse facility The wake  ow eld computations were found to be much more sensitive to both grid resolution and grid adaptationthan the forebody results The wake computations showed the existence of a region of separated, steady, recirculating  ow behind the vehicle Whereas the rapid expansion of the  ow around the corner of the vehicle resulted in a wake that was mostly frozen both chemically and vibrationally, the degree of  ow expansion was not great enough to produce noncontinuum ow behavior Comparisons between computational and experimental surface heating distributionswere within the estimated experimental uncertainty for both cases except around the forebody stagnation point and the free-shear-layer reattachment point for the air case and within a small portion of the wake recirculation vortex for the carbon dioxide case

High-Enthalpy Aerothermodynamics of a Mars Entry Vehicle Part 2: Computational Results

Detailed measurements of aerodynamic heating rates in the wake of a Mars-Pathfinder configuration model have been made. Heating data were obtained in a conventional wind tunnel, the NASA LaRC 31" Mach 10 Air Tunnel, and in a high-enthalpy impulse facility, the NASA HYPULSE expansion tube, in which air and CO2 were employed as test gases. The enthalpy levels were 0.7 MJ/kg in the Mach 10 Tunnel, 12 MJ/kg at Mach 9.8 for HYPULSE CO2 tests and 14 MJ/kg at Mach 7.9 for HYPULSE air tests. Wake heating rates were also measured on three similar parametric configurations, and forebody heating measurements were made in order to facilitate CFD comparisons. The ratio of peak wake heating to forebody stagnation point heating in the Mach 10 Tunnel varied from 7% to 15% depending on the freestream Reynolds number. In HYPULSE, the ratio was ~5% for both air and CO 2. It was observed that an increase in the ratio of forebody corner radius to nose radius resulted in a decrease in peak wake heating, and moved the peak closer to the base of the forebody. The wake flow establishment process in HYPULSE was studied, and a method was developed to determine when the wake has become fully established.

/pdf/hypervelocity-aeroheating-measurements-in-wake-of-mars-3v2vuh1jv2.pdf

Hypervelocity Aeroheating Measurements in Wake of Mars Mission Entry Vehicle

A series of aerodynamic heating tests was conducted on a 70-deg sphere-cone planetary entry vehicle model in a Mach 10 perfect-gas wind tunnel at freestream Reynolds numbers based on diameter of 8.23x104 to 3.15x105. Surface heating distributions were determined from temperature time-histories measured on the model and on its support sting using thin-film resistance gages. The experimental heating data were compared to computations made using an axisymmetric/2D, laminar, perfect-gas Navier-Stokes solver. Agreement between computational and experimental heating distributions to within, or slightly greater than, the experimental uncertainty was obtained on the forebody and afterbody of the entry vehicle as well as on the sting upstream of the free-shear-layer reattachment point. However, the distributions began to diverge near the reattachment point, with the experimental heating becoming increasingly greater than the computed heating with distance downstream from the reattachment point. It was concluded that this divergence was due to transition of the wake free shear layer just upstream of the reattachment point on the sting.

/pdf/transition-effects-on-heating-in-the-wake-of-a-blunt-body-3hbmfqvw1n.pdf

Brian R. Hollis

Papers

High-Enthalpy Aerothermodynamics of a Mars Entry Vehicle Part 1: Experimental Results

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

High-Enthalpy Aerothermodynamics of a Mars Entry Vehicle Part 2: Computational Results

Hypervelocity Aeroheating Measurements in Wake of Mars Mission Entry Vehicle

Transition Effects on Heating in the Wake of a Blunt Body