Aerodynamics of Stardust Sample Return Capsule

R. A. Mitcheltree: R. G. Wilmotht F. M. Cheatwood) G. J. Brauckmannf F. A. Greene? NASA Langley Research Center, Hampton, Virginia

Successful return of interstellar dust and cometary material by the Stardust Sample Return Capsule requires an accurate description of the Earth entry vehicle’s aerodynamics. This description must span the hypersonic-rarefied, hypersonic-continuum, supersonic, transonic, and subsonic flow regimes. Data from numerous sources are compiled to accomplish this objective. These include Direct Simulation Monte Carlo analyses, thermochemical nonequilibrium computational fluid dynamics, transonic computational fluid dynamics, existing wind tunnel data, and new wind tunnel data. Four observations are highlighted: 1) a static instability is revealed in the free-molecular and early transitional- flow regime due to aft location of the vehicle’s center-of-gravity, 2) the aerodynamics across the hypersonic regime are compared with the Newtonian flow approximation and a correlation between the accuracy of the Newtonian flow assumption and the sonic line position is noted, 3) the primary effect of shape change due to ablation is shown to be a reduction in drag, and 4) a subsonic dynamic instability is revealed which will necessitate either a change in the vehicle’s center-of-gravity location or the use of a stabilizing drogue parachute.

Introduction continuum, supersonic, transonic, and subsonic flow TARDUST‘, the fourth Discovery class mission, regimes. The passive capsule, once released from its Sis scheduled for launch in February of 1999. In host bus, will rely solely on the predetermined balance addition to collecting interstellar dust, the robotic between aerodynamic forces and gravity to guide it spacecraft will fly within 100 km of the comet Wild-2 through those regimes to a parachute landing, within a nucleus and collect pre-solar cometary material from 75 km ellipse, in the Utah Test Landing Range. High- the coma parent-molecular zone. These materials will fidelity aerodynamic knowledge is essential for mission be returned to Earth for submicron level analysis. success. The drag coefficient must be accurately de- To accomplish the mission’s objective, a capsule con- scribed within each flight regime so the cumulative taining the collected particles must safely transit an effect of the deceleration results in a landing within intense Earth entry, descent, and landing. This paper the targeted Utah site. In addition, the capsule should focuses on the aerodynamics of the Stardust Sample possess sufficient aerodynamic stability to minimize Return Capsule (SRC) during that entry. The results angle-of-attack excursions during the severe heating also have relevance to other proposed sample return portion of the trajectory. This stability must persist missions. through the transonic and subsonic regimes to main- The entry of the Stardust SRC at 12.6 km/s will tain a controlled attitude at parachute deployment. be the fastest Earth entry ever attempted. Its tra- The objective of this paper is to describe the aero- jectory traverses the hypersonic-rarefied, hypersonic- dynamics of the Stardust SRC and assess if the re- quirements cited above are met. The description must *Aerospace Engineer, Aerothermodynamics Branch, Aero- be constructed with sufficient breadth and detail to and Gas-Dynamics Division, NASA Langley Research Center, populate an aerodynamic database suitable for six Senior Member AIAA. degree-of-freedom trajectory simulations. Data from Aerospace Engineer, Aerothermodynamics Branch, Aero- numerous sources are compiled. These include Direct and Gas-Dynamics Division, NASA Langley Research Center, Senior Member AIAA. Simulation Monte Carlo (DSMC) analysis to describe *Aerospace Engineer, Vehicle Analysis Branch, Space Sys- the rarefied flow in the transitional regime, thermo- tems and Concepts Division, NASA Langley Research Center, chemical nonequilibrium computational fluid dynam- Member AIAA. ics (CFD) for the hypersonic regime, CFD and exist- §Aerospace Engineer, Aerothermodynamics Branch, Aero- and Gas-Dynamics Division, NASA Langley Research Center, ing wind tunnel data in the supersonic and transonic Senior Member AIAA. regime, and finally, new subsonic static and dynamic llAerospace Engineer, Aerothermodynamics Branch, Aero- wind tunnel test data. and Gas-Dynamics Division, NASA Langley Research Center, Senior Member AIAA. A description of the entry capsule’s geometry is Copyright 01997 by the American Institute of Aeronautics presented first. Discussion of the approach taken to and Astronautics, Inc. No copyright is asserted in the United describe the static aerodynamics in each flight regime States under Title 17, U.S. Code. The U.S. Government has a royalty-free license to exercise all rights under the copyright is next, followed by comments on the dynamics. De- claimed herein for governmental purposes. All other rights are tailed description of the aerodynamics through each of reserved by the copyright owner. the flight regimes requires knowledge of the expected Irajectory. Three degree-of-freedom (3-DOF) simulations were computed to satisfy this need. From this Table 1 Axisymmetric Results from DSMC (Ref. estimated trajectory, discrete points are chosen for the 3 method). high-fidelity analysis. t(s) Alt(km) M V(m/s) C,t Sample Return Capsule Geometry 0 134.7 - 12597 2.019 120.5 The forebody geometry of the SRC is a 60-degree 8 - 12608 1.974 20 100.9 - 12620 1.822 half-angle sphere-cone with nose radius equal to 0.2286 26 92.0 44.1 12618 1.640 m, shoulder radius of 0.01905 m, and overall diame- 32 83.7 42.7 12592 1.543 ter of 0.8128 m. The afterbody shape is a 30-degree 42.2 12487 1.525 cone which terminates with a flat stern whose radius 38 76.0 - is 0.2116 m. The geometry is shown in Figure 1. The forebody heat shield is made of PICA (Phenolic Im- pregnated Carbon Ablator). Surface recession at the Table 2 3-D Results from DSMC (Ref. 4 method). nose due to heating rates as high as 1200 W/cm2 is estimated to be 0.01194 m (0.47 in) and 0.006858 m (0.27 in) at the shoulder. For aerodynamic considerations, this shape change due to ablation is assumed to result in a forebody which remains a 60-degree sphere cone 20 100.9 10 1.80815 0.219899 -0.07736 except the nose radius increases to 0.2405 m, shoulder 32 83.7 o 1.60761 0. 0. radius increases to 0.02591 m, and overall diameter de- 32 83.7 10 1.52884 0.138041 -0.03952 creases to 0.7991 m. The ablative shape change impact on the aerodynamics is presented. As the capsule continues its descent to altitudes Low-Density Aerodynamics at or below 130 km, ICn drops below 10 and colli- The Stardust SRC is released from the host space- sions between molecules become important and must craft 3 to 4 hours prior to atmospheric interface. When be included in aerodynamic predictions. This is the the spin-stabilized capsule arrives at the outer reaches transitional flow regime. of the atmosphere, it will encounter widely spaced For a given Iin, the transitional-regime aerody- molecules, Surface impacts of these molecules will namics can be described by Direct Simulation Monte exert the first aerodynamic forces on the entry ve- Carlo (DSMC) methods2-6. Three separate efforts are hicle. Knudsen number, Kn, is defined as the ratio used to compute the transitional-regime aerodynamics of the quiescent gas’s mean free path to the vehicle’s for the Stardust SRC. First, six zero-degree angle-of- diameter. At the outer reaches of the atmosphere, attack cases are computed using the method of Ref. 3. long the associated Iin is large. As as Kn > 10, The predictions of CA are presented in Table 1. The aerodynamic forces can be accurately computed by a three-dimensional DSMC methods of Rault et. al.4 free-molecular-flow method. Free-molecular flow as- and Wilmoth et. aL5 are applied at points within the sumes there are no collisions between gas molecules in transitional portion of the trajectory. The results are the flow field. The surface is impacted by free-stream presented in Table 2 and Table 3. In general, there is particles which are diffusely reflected after full thermal good agreement between the different DSMC methods. accommodation. Unlike hypersonic-continuum aero- The scatter in the results for moment coefficient at 83 dynamics, where forces exerted on the blunt body are km is indicative of the uncertainty DSMC (and CFD) primarily the integrated effect of surface pressures, suffer at this Kn and is also the result of differences free-molecular-flow aerodynamics contain a significant in computational approaches and grids. contribution from shear stress. Free-molecular-flow aerodynamics for the Stardust Predictions from the three DSXiIC solutions at zero geometry are computed using a collisionless DSMC ap- degrees angle-of-attack for axial coefficient are shown proach discussed in Ref. 2. The results are presented in Fig. 3. The plot also contains the free-molecular in Fig. 2. Since the geometry is axisymmetric, static value, and three hypersonic-continuum predictions aerodynamics can be described by the variation of ax- (from CFD calculations discussed subsequently), ial force coefficient (CA), a normal-force coefficient A bridging function selected as appropriate to recre- (CN),and a moment coefficient (Cm)with respect to ate the data within the Kn range 10.0 to 0.001 is angle-of-attack (a).The reference area is the frontal included in Fig. 3. The bridging function formula area of the vehicle (0.51887 m’),and the reference for the axial coefficient is; length is the diameter (0.8128 m). Unless otherwise specified, moments are taken about the nose of the vehicle. half-angle) as shown in Fig. 8. Table 3 3-D Results from DSMC (Ref. 5 method). The question arises as to whether t,he gyroscopic stability of the spinning capsule (originally at five rotations-per-minute) will be sufficient to retard the destabilizing aerodynamic forces until the capsule has passed through the altitudes at which the capsule is unstable. The aerodynamic forces are proportional to the dynamic pressure. In the free-molecular-flow regime, dynamic pressures are usually small because of low atmospheric densities. Stardust SRC, however, is smaller than past entry vehicles. Free-molecular and transitional flow conditions, therefore, persist to lower altitudes than previous vehicles experienced. Lower altitudes correspond to higher densities. In addition, the where entry velocity at 12.6 km/s is higher than any other Earth entry. These two factors combine to result in non-negligible dynamic pressures (and thus aerody- CA,~,,,and CA,~are the values of the axial coeffi- namic forces) in the rarefied flow regimes. Further- cient at the free molecular and continuum limits. This more, the interior of the capsule is somewhat empty equation approximates the monotonic decrease in CA so its rotational inertia (and thus gyroscopic stability across the transitional regime. Ideally, bridging func- even at five rotations-per-minute) is small. Prelimi- tions could be used to describe the variation of CA, nary six-degree-of-freedom (6-DOF) calculations indi- CN,and C,,, across a large angle-of-attack range in cate that the gyroscopic stability is not sufficient to this regime. This would eliminate the need to com- retard the destabilizing aerodynamic forces. As a re- pute a large matrix of DSMC solutions. Figures 4- sult, the capsule's angle-of-attack will increase from its 5 present the normal-force and moment coefficients desired zero degree orientation towards the 60-degree at 10 degree angle-of-attack compared with bridging trim point early in the trajectory. Large angles of in- functions analogous to Eqs. 1-2. Note, the bridging cidence are worrisome since the capsule is stable flying functions yield good agreement with the CA (CY= 0') backwards. Off-nominal attitudes or pitch rates at at- and CN (a = loo) results, but are ill-suited for the mospheric interface could result in a backwards entry. non-monotonicity of the moment coefficient. (If the In addition, large incidence angles early in the flight moment coefficient were taken about the center-of- can result in incidence angles above 10 degrees at peak gravity location rather than the nose, the variation heating. Large angles-of-attack dramatically increase of C, with Kn is monotonic.) the afterbody heating near the shoulder regions and Figure 6 shows the shift in the center-of-pressure may damage the afterbody thermal protection system. (c.P.) location across the transitional regime. The Further discussion of the low-density aerodynamics of c.p. is at 0.26 body diameters (0.26D) back from the the SRC are included in Wilmoth et. a1.2. nose in the free-molecular limit. This location is well forward of the continuum value which is 0.72D. For Hypersonic Aerodynamics the vehicle to be statically stable, the center-of-gravity As the capsule continues its descent below 66 km at- (c.g.) must be located ahead of the c.p. Stardust titude, Kn drops below 0.001 and continuum methods (with its c.g. currently specified at 0.35D) is unstable can be used to describe the flow about (and the forces in the free-molecular-flow region. Figure 7 confirms on) the capsule. In this hypersonic portion of the en- this fact by presenting the expected moment coefficient try, the flowfield is dominated by a strong bow shock. about that c.g. location at different Knudsen numbers. Forebody pressures are two orders of magnitude larger The figure reveals that at the highest altitudes (free- than afterbody pressures. The afterbody can, there- molecular limit), the capsule will seek to trim at 60- fore, be neglected when computing the aerodynamic degrees incidence. It becomes stable about CY = Oo characteristics at small angles-of-attack in this regime. when Kn drops below 0.09. The Langley Aerothermodynamics Upwind Relaxation The decrease in stability with increasing rarefac- Algorithm (LAURA) CFD code7 is used to compute tion (i.e., increasing Kn) is a result of the increased solutions at nine points in the trajectory's hypersonic shear stress contribution to the aerodynamic forces. regime. LAURA is an upwind-biased, point-implicit This trend has been observed in shuttle flights and relaxation algorithm for obtaining the numerical solu- documented €or the blunt Soyuz capsule by Ivanov6. tion to the Navier-Stokes equations for three dimen- The divergence between continuum stability and free- sional, viscous, hypersonic flows in thermochemical molecular stability increases with bluntness (i.e., cone nonequilibrium'. It has been used to describe the cluded as the dashed line. (Newtonian flow assumes Table 4 Axisymnietric Results from LAURA. that the free-stream flow is turned parallel t,o the surface. Local pressure is then a function only of the local surface's inclination angle to the free stream.) Figure 1.5636 10 presents the variation of the axial coefficient with 1.4959 angle-of-attack for CFD predictions above Mach 12. 1.4828 Increased angle-of-attack results in a small decrease in axial force across the Mach range. 46.54 5496 1.4939 Figures 11 and 12 display predicted normal-force 45.75 and moment coefficients as a function of Mach num- 44.44 ber from 35 to 7 at 5 and 10 degrees angle-of-attack. 43.24 2724.5 1.510 The marked decrease in normal-force and increase in 41.60 1.506 moment coefficients below Mach 12 is a result of the sonic line shifting from the sphere-cone tangency point to a location on the shoulder of the 60-degree forebody cone. This shift occurs as the flowfields exhibit less real-gas effects and begin to resemble ideal-gas flows.

t(S) M Cy CA CN Crn Pressure distributions (and thus aerodynamic forces) 32. 42.7 10. 1.4807 0.10903 -0.05483 are affected by the sonic character of the shock layer. 44. 40.5 10. 1.4455 0.08874 -0.06308 When supersonic, the pressure distributions on the conical flank are flat, which is characteristic of conical flow, When the entire forebody shock layer is subsonic, the elliptic nature of that flow results in higher, more rounded distributions. Figures 10-12 show that the Newtonian flow approximation is accurate only when the sonic line resides on the spherical nose. The net ef- I 78 11 12.2 (1 5. 11 1.4889 11 0.04452 (1 -0.03220 I fect of the sonic line shift below Mach 12 is a decrease 78 11 12.2 11 10. 11 1.4242 1) 0.07508 11 -0.05172 in the static stability margin (the c.p. moves forward 82 11 10.5 11 5. 11 1.498 11 0.04074 11 -0.02822 to 0.58D back from the nose). 86 I( 8.5 I 5. 1.496 0.03036 I -0.01895 The hypersonic regime aerodynamics are compli- 92 11 7.15 I 5. 1.477 0.02270 I -0.01309 cated by forebody shape change due to ablation. Thus far, the discussion of hypersonic aerodynamics has ex- cluded this shape change. As the vehicle encounters aerodynamics of several blunt bodies including Mars heating as high as 1200 W/cm2, the PICA forebody Pathfinderg. Table 4 presents the zero-degree angle- heatshield ablates and begins to recede. Figure 13 of-attack CA results. Three-dimensional solutions at presents the predicted recession at the nose and the 5 and 10 degrees angle-of-attack are computed for the shoulder for the Stardust overshoot trajectory. Reces- forebody at the nine trajectory points (Table 5). sion begins in the transitional-flow regime and con- For continuum conditions with Mach numbers above tinues down to Mach 7.6. Surface recession decreases 12, 11 species thermochemical nonequilibrium effects the frontal area (Le., diameter) and increases the nose are included. At and below Mach 12, the flow is radius. Figure 13 supplied the information used to assumed to be in chemical equilibrium. The axisym- describe the ablated shape discussed in the Sample metric solutions are computed on shock-aligned grids Return Capsule Geometry section. A LAURA solu- with 30 points along the forebody and 64 points nor- tion is generated on the ablated shape (Mach 35.4). A mal to the surface. The cell Reynolds number for the comparison of forebody pressures and axial coefficients first cell off the wall is unity. Three-dimensional solu- for the original and ablated geometry as predicted by tions utilize an axis-singularity-free grid with a 58 by LAURA is presented in Fig. 14. The shape change 26 cell surface definition. Confidence in these compu- results in a decrease in axial coefficient of 0.8 percent. tational grids for accurately resolving surface pressures This change is primarily a result of the ablated shape's stems from previous experiences'0,'' on similar geome- rounder shoulder. A Newtonian flow approximation of tries. the ablated shape predicts a 0.6 percent decrease in the Figure 9 presents the LAURA calculations for zero axial coefficient. angle-of-attack axial coefficient. Little variation in the A comparison of the normal-force and moment co- predicted values occurs across the entire hypersonic- efficients between the nonablated and ablated shape continuum regime (above Mach 38 is the transitional shows little change. These aerodynamic coefficients regime where CA increases as was shown in Fig 3). are, however, referenced to their respective areas, di- A Newtonian flow prediction for the capsule is in- ameters, and nose locations. The total drag on the voliiclt: will tlccrease with ablation shapc change more iii Figs. 15- 17. Mnrko did not, include the tnoment, than the 0.8 percent indicated as a result of the de- coefficient measurements in his report. Ile in(-lrided crease in reference area. In creating an aerodynamic c.p. locations at a subset of his test conditions which, data base, these reference shifts must be tracked accu- combined with the normal coefficient data, were used rately. to compute the mornent coefficients shown in Fig. 17. Wind tunnel testing around Mach 1.0 is difficult due Supersonic Aerodynamics to reflected shock interference. Though Marko does Below Mach 7, forebody-only CFD will not accu- not suggest this as a potential source of errors in his rately predict the aerodynamics. The calculations measurements, the data contain oscillations in CN and must include the afterbody and wake. Such calcu- C, at Mach 1.0. lations are computationally expensive. Fortunately, In an attempt to augment the definition of the tran- wind tunnel data for configurations similar to the SRC sonic region aerodynamics, the CFD code TLNS3D exist. In the low hypersonic and supersonic region, (Thin Layer Navier Stokes 3-Dimensional)14 was used WalkerI2 measured the static aerodynamics on blunted to examine the flight conditions between Mach 0.6 and 60-degree cones in the JPL 20-in. supersonic wind tun- 2.0. The results are included in Figs 15-17. Some nel. The Reynolds number for these tests, based on questions exist as to the accuracy of these CFD solu- diameter, is 4.0 million. (The expected flight Reynolds tions. The concerns center around computation of the numbers in this speed regime are around 0.2 million.) wake flow. The TLNS3D solver requires a turbulence The 60-degree sphere-cone models Walker tested pos- model to be used in order to avoid numerical instabil- sessed a range of shoulder radii which envelopes the ities in the massive recirculation wake zone. However, expected Stardust value. He performed measurements none of the available turbulence models are accurate on a sharp-shouldered model and one with a shoulder in such a separated flow region. Extensive grid res- radius equal to 5 percent of the base radius. The Star- olution studies were performed, but questions remain dust ablated geometry has a shoulder radius at 3.25 as to the solution’s accuracy. The largest question in percent of its base radius. Unfortunately, the nose the CFD predictions occurs in CN though not shown, bluntness of his models (30 percent of the base radius) the predicted value at M = 0.6, and CY = 5 degrees is is not as large as the Stardust ablated geometry’s (59 negative. percent of the base radius) and the wind tunnel models had no afterbody. Subsonic Aerodynamics Figures 15-17 present CA,CN, and C, as a func- The Stardust SRC entry scenario planned to de- tion of Mach number for cy = 5’. (The transonic and ploy a parachute at 3 km altitude corresponding to subsonic data in the plots are discussed later.) In a Mach number of 0.16. The deployment occurs 400 the supersonic regime, the figures indicate that little seconds after atmospheric interface. Of these 400 sec- change in the aerodynamic coefficients occurs between onds of entry, 200 are spent at Mach numbers less Mach 7.15, where the last LAURA solution is gen- than 0.6. The authors were not aware of any exist- erated, and Mach 4 where the Walker data begins. ing subsonic wind tunnel data on the SRC shape. A While Mach 3.98 is the highest value Walker tests for wind tunnel investigation of the Stardust SRC (0.30 the models closest to Stardust, he did examine similar scale ablated shape geometry) was conducted at Mach 60-degree cones up to Mach 9.5 in the JPL 21-in hyper- 0.16. The force-and-moment model of the SRC was sonic wind tunnel. His results show no change in the constructed from high density foam and covered with a aerodynamics between Mach 9.5 and Mach 4. He also fiberglass skin. Hard points within the structure were compared his Mach 9.5 results to modified Newtonian reinforced with aluminum and wood. The model was predictions and saw poor agreement. This observa- sting mounted to a six component balance through tion agrees with earlier results displayed in Figs. 9-12 the base. The after-body conical portion was fitted which revealed the Newtonian approximation to be with 6 flush mounted pressure orifices in a longitu- accurate only down to Mach 12 where the sonic-line dinal ray. (These pressure taps were incorporated to shift occurs. Note, the solid line in Figs 15-17 labeled supply information necessary to calibrate the baromet- “database” is included to indicate trends. ric parachute-deploy switch.) The model was tested in the ViGYAN Low Speed Transonic Aerodynamics Wind Tunnel in Hampton, Virginia. This tunnel is a Wind tunnel measurements examining the same 60- conventional, straight-through, open-return type lay- degree wind tunnel models Walker examined at super- out with a 3’ by 4’ open-jet test section. The model sonic speeds were performed at transonic conditions was attached to an angle-of-attack mechanism which by Marko in the NASA Ames 2 by 2 Transonic wind was swept from 0 to 28 degrees inclination. Bal- tunnel13. The data were measured at a Reynolds num- ance data were reduced to coefficient form accounting ber based on diameter of 1.0 million; the flight value for balance interactions, sting deflections, and model is near 0.2 million. These measurements are included cavity pressures. The tunnel was run at a dynamic Oscillations grew rapidly and diverged until the cap- Table G Vigyan Subsonic Data ( M = 0.16 ), sule began tumbling. If the c.g. was moved forward to 0.29D, the divergent behavior was eliminated and CA CN the capsule established itself in a limit cycle oscillation 0.8739 0.0000 with amplitude near 10 degrees. 0.8759 0.0053 -0.0058 The addition of different sized drogue parachutes 0.8779 0.0119 -0.0115 was examined as a means of stabilizing the original c.g. 0.8794 0.0177 -0.0 171 location configuration. A parachute with drag area of 0.8809 0.0242 -0.0227 at least 0.208 m2 was required to damp large pertur- 12.02 0.8838 0.0357 -0.0332 bations. Details of these tests are discussed in Ref. 16.01 0.8822 0.0485 -0.0446 17. 20.00 0.8774 0.0613 -0.0573 At hypersonic speeds, ballistic range testsI8 do not 24.01 0.8607 0.0723 -0.0676 discern significant changes in the values of the dynamic 28.01 0.8212 0.0855 -0.0757 derivatives with Mach number. In addition, past ex- perience with 6-DOF simulations have also indicated pressure of 0.018 atm. (The expected flight dynamic that large variations in the dynamic derivatives at pressure is 0.012 atm.) Reynolds numbers based on the higher Mach numbers have little effect on the diameter for the tests were 0.9 million. The resulting hypersonic-flight dynamics of the vehicle. aerodynamic coefficients are listed in Table 6 and plot- ted in figures 18-20 as a function of angle-of-attack. Conclusions Note, the normal-force and moment coefficients may Successful return of interstellar dust and cometary be considered linear over the angle-of-attack range ex- material by the Stardust Sample Return Capsule re- amined. The data from these tests are also included quires an accurate description of the Earth entry at the far left hand side of Figs. 15-17. The laminar or vehicle's aerodynamics. This description must span turbulent nature of the boundary layer for the flight the hypersonic-rarefied, hypersonic-continuum, super- case is not known, nor is it known if the wind tunnel sonic, transonic, and subsonic flow regimes. Data from test case was turbulent. numerous sources are compiled. These include Di- rect Simulation Monte Carlo analyses, thermochemical Dynamic Derivatives nonequilibrium CFD, transonic CFD, existing wind Accurate six degree-of-freedom trajectory simula- tunnel data, and new wind tunnel data. tions of the SRC entry require knowledge of the dy- A static instability is revealed in the free-molecular namic stability of the capsule. This requirement is and early transitional-flow regime. The high entry especially true in the transonic and subsonic speed velocity, small size, and low rotational inertia of the regimes. capsule combine to allow this instability to introduce Uselton et al.15 examined the dynamic stability of large angles-of-attack during the high-altitude portion blunted 60-degree and 70-degree cones at Mach num- of the entry. In the extreme, this instability could re- bers between 3.0 and 0.6. He demonstrated that sult in a rear-facing entry of the capsule. Alleviation such shapes can suffer a dynamic instability at small of the instability requires either 1) an alteration to the angles-of-attack in the transonic flight regime. That is, capsule's geometry, 2) a substantial increase in the spin though they remain statically stable, when Mach num- rate from its original five rotations-per-minute speci- ber decreases below 2.0 an increase in incidence angles fication, or 3) a repositioning of the center-of-gravity (a wobbling motion) may occur. Bendura" examined from its current location at 0.35 diameters(D) back the dynamic stability of blunted 60-degree cones in from the nose to a position closer to 0.26D. the low subsonic regime and revealed a sensitive de- In the transitional-flow regime, a simple monotonic pendence on c.g. location. The desire for Stardust is bridging function (spanning the K'n range from 0.001 that the capsule remain in a controlled flight through to 10.0) can be used to describe the variation of the these speed regimes and that large oscillations do not axial and normal-force coefficients from their free- exist at the Mach 0.16 parachute deployment. molecular value to their continuum value. This same Since the capsule spends the last 200 seconds of its approach does not appear accurate for the moment entry at subsonic conditions, its attitude at parachute coefficient's non-monotonic variation (when moments deploy is influenced most by its subsonic dynamic sta- are taken about the nose). bility. To establish this property of the capsule, low In the hypersonic-continuum regime, CFD solutions subsonic dynamic stability tests were conducted in reveal that the Newtonian flow assumption is reason- the 20 Foot Spin Tunnel at Langley Research Center. ably accurate as long as the sonic line remains on the The tests revealed that the configuration was dynam- vehicle's spherical nose. This is true for angles-of- ically unstable at the conditions o€ the test due to the attack of 5 degrees or less down to a Mach number aft-location of the c.g. (0.35D back from the nose). of 12. r>C he sonic linc shift. from the spherical nose to the Altitude Aerodynamics of Reentry capsule,” 20th In- shoulder region below Mach 12 is accompanied by a ternational Symposium on Rarefied Gas Dyiianiics, forward movement of the center-of-pressure (0.72D to Beijing, China, Aug, 1996. 0.58D) which decreases the static stability of the ve- 7Cheatwood, F. M., Gnoffo, P. A.,“User’s Manual hicle. This decrease in static stability is smaller than for the Langley Aerothermodynamic Upwind Relax- the one associated with the transition from continuum ation Algorithm (LAURA),” NASA TM 4674, Apr., to free-molecular flow (0.72D to 0.26D). 1996. The primary effect of ablation shape change on the ‘Gnoffo, P. A., Gupta, R. N., and Shinn, J. L., vehicle’s aerodynamics is a decrease in the drag coefi- ‘“Conservation Equations and Physical Models for Hy- cient resulting from the rounding of the shoulders and personic Air Flows in Thermal and Chemical Nonequi- decreased frontal area. Uncertainties in the degree of librium,” NASA TP-2867, Feb. 1989. shape change will translate directly into uncertainties ’Braun, R. D., Powell, R. W., Engelund, W, C., in the landing foot print. Gnoffo, P. A., Weilmuenster, IC. J., and Mitcheltree, Finally, a dynamic instability in the subsonic regime R. A., “Mars Pathfinder Six-Degree-of-Freedom Entry will result in a tumbling motion in the terminal portion Analysis,” J. of Spacecraft and Rockets, Vol 32, No, of the trajectory. To facilitate a successful parachute 6, Nov.-Dec., 1995, pp. 993-1000. deployment at M = 0.16 and 3 km altitude, the center- ‘“Gnoffo, P. A., ”Computation of Near-Wake, Aer- of-gravity should be moved forward to 0.29 body diam- obrake Flowfields,” J. of Spacecraft and Rockets, Vol. eters back from the nose or a stabilizing drogue chute, 29, No. 2, Mar-Apr, 1992. pp. 182-189. with drag area at least 0.208 m2,should be deployed “Nettelhorst, H. L., Mitcheltree, R. A., “Grid Res- prior to onset of subsonic speeds. olution and Solution Convergence for Mars Pathfinder Forebody,” NASA TM 1.09173, Dec., 1994. Acknowledgments 12Walker, B. and Weaver, R. W., “Static Aerody- Dr. Y. K. Chen of NASA Ames Research Center namic Characteristics of Blunted Cones in the Mach- supplied the surface recession estimate. Mr. William Number Range from 2.2 to 9.5”, JPL TR-32-1213, Willcockson of Lockheed-Martin Astronautics sup- Dec. 1967. plied the 3-DOF estimated trajectory. Prasun Desai of 13Marko, W. J., “Static Aerodynamic Characteris- NASA LARC was helpful in many discussions and per- tics of Three Blunted Sixty Degree Half-Angle Cones formed 6-DOF simulations which revealed the static at Mach Numbers from 0.6 to 1.3,” TR 32-1298, JPL, instability in the transitional-flow regime. Thanks are July, 1968 also extended to Drs. J. N. Moss and D. F. Rault I4Vatsa, V. N., Turkel, E., and Abolhassani, J. (LARC) for supplying additional DSMC solutions and S., “Extension of Multigrid Methodology to Super- W. A. Wood (LARC) for several LAURA CFD solu- sonic/Hypersonic 3-D Viscous Flows,” NASA Con- tions. tractor Report 187612, Aug., 1991. 15Uselton B., L., Shadow, T. O., Mansfield, A. C., References “Damping in Pitch Derivatives of 120 and 140 Deg ‘Atkins, K. L., Brownlee, D. E., Duxbury, T., Yen, Blunted Cones at Mach Numbers 0.6 through 3.0,” C., and Tsou, P. , “STARDUST: Discovery’s Interstel- AEDC TR-70-49. 1970. lar Dust and Cometary Sample Return Mission,” Pro- I6Bendura, R. J.,“Low Subsonic Static and Dy- ceedings from the 1997 IEEE Aerospace Conference, namic Stability Characteristics of Two Blunt 120° Feb., 1997. Cone Configurations,” NASA TN D-3853, Feb., 1967. 2Wilmoth, R. G., Mitcheltree, R. A., “Low-Density I7Mitcheltree, R. A., Fremaux, C. M., “Subsonic Aerodynamics of the Stardust Sample Return Cap- Dynamics of Stardust Sample Return Capsule,” NASA sule,” AIAA Paper 97-2510, June, 1997. TM 110329, March 1997. 3Bird, G. A.,“The G2/A3 Program Users Manual,” “Krumins, Maigonis V., “A Ballistic Range G.A.B. Consulting Pty Ltd., Killara, N.S.W., Aus- Study of the Aerodynamic Characteristics of Mars tralia, March,1992. Probe/Lander Shapes,” AIAA Paper 67-167, Jan ‘Rault, D.F., Cestero, F.J, Shane, R.W., “Space- 1967. craft Aerodynamic Characteristics During Aerobrak- ing Maneuver in Planetary Atmospheres,” AIAA Pa- per 96-1890. ’Wilmoth, R.G., LeBeau, G. J., and Carlson, A. B., “DSMC Grid Methodologies for Computing Low- Density, Hypersonic Flows About Reusable Launch Vehicles,” AIAA Paper 96-1812, June 1996. ‘Ivanov, M. S., Markelov, G.N., Gimelshein, S. F., and Antonov, S. G., “DSMC Studies of High- Maximum Radius = 0.4064 rn L, A 0.3 - R,,, = 0.21 16 ctl V Free Molecular 0.2 - 0 DSMC:Ref.4 30-deg. cone - A DSMC: Ref. 5 0 CFD: LAURA 0.1 - -u - Bridging Function

R,,,,,., = 0.01905 m O.?L ' ' "'104 ' ' "'10~~' '"'10.1 ' ' "'10~' ' "'lo? ' '"'li2 Knudsen Number

~i~.1 Stardust sampleReturn capsulegeometry. Fig. 4 Variation of the normal-force coefficient in the transitional-flow regime.

cr=loo

V Free Molecular 0 DSMC:Ref.4 A DSMC: Ref. 5 0 0 CFD:LAURA - Bridging Function I5

-O.O6I--L-0.08

Fig. 2 Free-molecular-flow aerodynamics. Fig. 5 Variation of the moment coefficient in the transitional-flow regime.

a=O0 0.8 2.22.1 1 p Free Molecular 0 DSMC: Ref. 4 2.01.9 i A DSMC: Ref. 5 c, 1.8 0.5 17 CFD: LAURA Free Molecular -Bridging Function 1.7 D 0.4 DSMC: Ref. 1.6 v 3 0 DSMC: Ref. 4

1.5 ~ A DSMC: Ref. 5 1.4 0 CFD: LAURA 1.3 -Bridging Function 0.1 1

0.9;. ' ' "'10-3 ' '"'10-2 ' '"'10-1' ' "'100 ' '"'101 ' ' "'% Knudsen Number

Fig. 3 Variation of the axial-force coefficient in Fig. 6 Variation of the center-of-pressure location the transitional-flow regime. in the transitional-flow regime. qc,!D = 0.36 2.0 Hypersonic ree Molecular (Kn = IO) 1.9 __ Newtonian 0 DSMC: Ref. 4 .8 1 0 CFD: LAURA M = 35 A DSMC: Ref. 5 1.7 h CFD: LAURA M = 25 0 CFD: LAURA M = 17 c, 1.6 VCFD: LAURA M = 12 1.5 CA 1.4 v 1.3 1.2 1 .I

-o.1o""""'""''"""''""~"''"''""''' 1.0 " " """' """ "1 0 10 20 30 40 50 60 70 80 90 a, deg

Fig. 7 Moment coefficient variation with angle-of- Fig. 10 Variation of axial-force coefficient with attack at different Knudsen numbers. angle-of-attack in the hypersonic-flow regime.

1.o 0.10 Hypersonic 0.9 1 a=loo 0.8 0.08

0.06 U CN - 0.04 d 0.02 d .- - - Newtonian -C- CFD: LAURA 0.1

, , , , , , ;;;;r, , %li0.0 0.00 301, 40 50 60 70 80 90 10 20 30 Cone Half-Angle Mach Number

Fig. 8 Comparison of center-of-pressure location Fig. 11 Variation of normal-force coefficients in for various cone half-angles. the hypersonic-flow regime.

2.0 Hypersunic 0.00 Hypersonic a.0. .- - - Newtonian 0 CFD: LAURA -0.02

Crn(no8e.) -0.04

-----Newtonian -0.06 1.2 t +CFD: LAURA I 1.o -0.08 10 20 30 40 0 10 20 30 Mach Number Mach Number

Fig. 9 Variation of axial-force coefficients in the Fig. 12 Variation of the moment coefficient in the hypersonic-flow regime. hypersonic-flow regime. 0.060 - Transonic - Supersonic a=5O o.60 F Database 0.50 - 0.050 - - Nose 0 CFD:LAURA V CFD:TLNS3D f 0.40 - 0.040 - A Windtunnet Walker P ; wnthuum CN ; 0 Windtunnel: Marko a -0- 0.30 bsnlnbnal Shoulder 0.030 - 9 Windtunnel: Vigyan

0.20 -

0.10 - V

I 0.00 ' ' ' ' 0.000 " " I " " I " " I " " I " " ' 0 20 40 60 80 100 0 2 4 6 8 10 Mach Number

Fig. 13 Predicted surface recession during the en- Fig. 16 Comparison of normal-force coefficient try trajectory. predictions in the transonic and subsonic regimes.

0.000 Transonic - Supersonic a=5O

-0.01 0

20000 - P, N/m2 Cm(nose) -0.020 15000 - - Nonablated, C, = 1.483 - - -- Ablated, C, = 1.468 10000 - -0.030

5000 -

-0.040 1 0 2 4 6 8 10 Mach Number

1.6 Transonic - Supersonic Subsonic '.OF

c, 0.81 Database 0.7 1.2 0 CFD:LAURA V CFD:TLNSBD A Windtunnet Walker 0.6 Run2 0 Windtunnet Marko 1 0 Run6 9 Windtunnel: Vigyan 0.9

4 6 8 10 Mach Number

Fig. 15 Comparison of axial-force coefficient pre- Fig. 18 Axial-force coefficient measurements at dictions in the transonic and subsonic regimes. subsonic conditions (M=0.16). Subsonic

0.20

Run2 0 Run6

...... 0 5 10 15 20 25 a,deg

Fig. 19 Normal-force coefficient measurements at subsonic conditions (M=0.16).

Subsonic O.O2 F

-0.10t. ' ' ' ' ' ' ' ' 1' ' ' ' 1' ' ' ' ' ' ' ' " ' ' 1 0 5 10 15 20 25 a,deg

Fig. 20 Moment coefficient measurements at subsonic conditions (M=0.16).