Validation of Afterbody Aeroheating Predictions for Planetary Probes: Status and Future Work Michael J. Wright,(1) James L. Brown,(1) Krishnendu Sinha,(3) Graham V. Candler,(3) Frank S. Milos,(1) Dinesh K. Prabhu(2) (1) NASA Ames Research Center, MS 230-2, Moffett Field, CA 95050 (2) ELORET Corp., 970 W. Fremont, Suite 8, Sunnyvale, CA 94087 (3) University of Minnesota, 107 Akerman Hall, Minneapolis, MN 55455 ABSTRACT predictions and reviews prior computational analyses of these data. Then, we conduct a brief survey of the state A review of the relevant flight conditions and physical of the art in computing turbulent afterbody flowfields. models for planetary probe afterbody aeroheating Finally, we provide recommendations for areas of calculations is given. Readily available sources of further work, and possible flight data that would aid in afterbody flight data and published attempts to reducing the afterbody aeroheating design uncertainty. computationally simulate those flights are summarized. A current status of the application of turbulence models 2. FLOW REGIMES AND PHYSICAL MODELS to afterbody flows is presented. Finally, recommend- ations for additional analysis and testing that would During entry, a planetary probe will pass from a free- reduce our uncertainties in our ability to accurately molecular (collisionless) to a non-continuum and finally predict base heating levels are given. to a continuum flow regime. The transition between these regimes is usually determined by evaluation of the 1. INTRODUCTION freestream Knudsen number Kn∞ = λ∞ /D, where λ∞ is the mean free path and D is the body diameter. Free Uncertainty levels associated with aeroheating molecular flow is usually defined as the region where predictions for the design of the afterbody of planetary Kn > 100, while continuum flow is usually defined as ∞ € € probes are typically assumed to be in the range of 200- the region where Kn < 0.01. This criterion is not 300%, a level that can have a significant impact on ∞ accurate for separated base flows, because the local Thermal Protection System (TPS) material selection mean free path in the separation region can be much and weight. This conservatism in the afterbody heat € larger than that in the freestream. A more accurate shield design will also shift the center of gravity determination€ can be made by using the density (ρ) aftward, which reduces the stability of the probe and in gradient length local Knudsen number[1] some circumstances may necessitate the addition of ballast in the nose. Current design practice for an λ dρ afterbody heatshield assumes a laminar, fully catalytic, KnGLL = (1) non-ablating surface. The predictions thus obtained are ρ dl max then augmented by a large factor of safety to account for turbulent transition, material response, and where λ and ρ are local values and the derivative is evaluated along the maximum gradient direction. uncertainties in the baseline computations. A primary [1] reason for this uncertainty is a sparsity of data for€ Following the work of Boyd et al., we assume that validation of our computational tools. Ground test data continuum breakdown occurs when KnGLL > 0.1. This are usually complicated by sting interference effects. criterion results in a more useful determination of Little flight data exist, and recent attempts to propose continuum breakdown in a separated flow, because dedicated flight experiments have failed to reach while the local mean free path in the separation region fruition. Therefore, it is important to thoroughly can be quite large, the density gradient is usually small, understand the limited flight data that are available to which delays the onset of non-continuum effects. For improve the design fidelity of the next generation of afterbody flows the highest values of KnGLL are typically Earth and planetary entry vehicles and to assess the observed near the flow separation point due to large need for additional focused flight testing. density gradients. Numerical solutions for free molecular and non-continuum flows are typically This paper will discuss four general topics. First, we obtained using a Direct Simulation Monte Carlo review the relevant flow regimes and physical models (DSMC) methodology. An excellent review on the status of DSMC calculations for non-continuum wake for afterbody flows. Next, the paper surveys the [2] available flight data for validating afterbody-heating flows was presented by Moss and Price. However, for 275 many problems of interest the majority of the aeroheating occurs in continuum flow, where Navier- Stokes based computational fluid dynamics (CFD) methods are applicable. The remainder of this paper will deal with the continuum flow regime. When a probe enters a planetary atmosphere at high velocity, the resulting shock wave will thermally excite, dissociate, and possibly ionize the gas. In order to accurately model the resulting flowfield including the wake of the probe a non-equilibrium model is usually required.[3] Each chemical and thermal relaxation process has an associated characteristic time, and the rapid expansion of the flow into the wake will decrease the collision rate, which freezes the slower processes (such as vibrational relaxation) while the faster Fig. 1. Computed Mach number contours chemical relaxation processes continue at a finite rate. and streamlines in the symmetry plane of the The details of the base flow structure and resulting Mars Pathfinder entry probe. heating rates can be very sensitive to the non- unsteady is near that at which transition to turbulence is equilibrium state of the gas.[4] An excellent review of predicted to begin. For many cases of interest, both the thermodynamic and chemical-kinetic models for a events occur after the peak heating point on the non-equilibrium flowfield is given by Gnoffo et al.[5] trajectory. For these cases much of the heat pulse can be simulated assuming a continuum, laminar, steady flow. The afterbody flowfield will likely transition from a laminar to a turbulent flow during the entry. Wake Computational simulations of axisymmetric base flows transition begins in the far wake and travels upstream with a flat base frequently show a disk shock in the near with increasing freestream Reynolds number (Re) until wake, caused when the reverse flow becomes reaching the neck, where it is (temporarily) stopped by supersonic along the rear stagnation line and a normal the adverse pressure gradient. In the base region shock is required to slow the gas before impacting the transition begins in the separation shear layer. Lees[6] body. The computed pressure and heat transfer on the gives a transition correlation for the free shear layer in a flat base for these cases are much higher than would be two-dimensional or axisymmetric flow that is based on the case if the disk shock were not present. Free flight a local transition Reynolds number, defined as experiments do not appear to show evidence of such a disk shock, although it would be difficult to see such a Retr = ρe ue L /µe (2) weak shock in a conventional Schlieren image. Clearly, since the presence of a disk shock has a significant where L is the running length of the shear layer from the influence on the predicted base heating, it is important separation point and the local density, velocity and to understand whether such a phenomenon is real or € viscosity are evaluated based on fluid properties at the merely a computational artifact. One possibility is that outer edge of the shear layer. The critical transition the disk shock is a neutrally stable solution of the Reynolds number is a function of the edge Mach Navier-Stokes equations, which can occur only for an number, and ranges from about 2×104 at Mach 2 to identically axisymmetric flowfield. Since no real flow is 5×106 at Mach 5. This criterion is based on free-flight ever completely axisymmetric, this solution would data, but does not include effects of upstream ablation rarely (if ever) occur in nature. In order to test this product gas injection, which could have a destabilizing theory, two simulations were performed for Mars effect on the shear layer and separated flow region. Pathfinder (Fig. 1). Freestream velocity is 6.6 km/s and density is 2.8×10-4 kg/m3. The first solution was run Low Re wake flows are steady and dominated by a assuming axisymmetric flow, and clearly shows the small number of large vortices. As the freestream disk shock in the wake. The second was run as a three- Reynolds number increases the extent of separation dimensional flow at α = 1°, and no disk shock is present increases as well and the vortex structure becomes more for this case. In addition, the computed pressure and complex. Eventually the vortices begin to oscillate and heat transfer on the flat base are a factor of three lower the base flow becomes unsteady. Typically, the for the α = 1° solution. This result lends some support Reynolds number at which the flowfield becomes to the present hypothesis; however, the problem of disk 276 shocks in axisymmetric base flows requires further study, including systematic comparison with experimental base heating and pressure data. Finally, wake flows are sensitive to the details of the volume grid used in the CFD analysis. Therefore it is important to generate a grid that is well aligned to anticipated flow features. In particular, it is extremely important that the grid have sufficient points in the shoulder region to capture the rapid expansion and accurately predict the flow separation point and the angle of the resulting shear layer.[7] There must also be sufficient points in the separated flow region to resolve the vortical structure and the wake compression, or Fig. 2. Schematic of Fire reentry vehicle neck. At higher Reynolds numbers the wake will consist showing instrument placement (from [11]).