AAS 07-307 TRAJECTORY AND AEROTHERMODYNAMIC ANALYSIS OF TOWED-BALLUTE AEROCAPTURE USING DIRECT SIMULATION MONTE CARLO Kristin L. Gates Medlock,* Alina A. Alexeenko,† and James M. Longuski ‡ We investigate trajectories and aerothermodynamics of ballute-assisted, low- to high-mass, Mars-entry systems. Ballutes permit aerocapture at higher altitudes and allow for lower thermal protection system (TPS) mass, due to lower heat fluxes, than traditional aeroshells. Because the velocity change is achieved at high altitudes, rarefaction can be considerable. To account for rarefaction we employ the Direct Simulation Monte Carlo (DSMC) method, which is based on kinetic flow modeling. Trajectory calculations are presented for Mars entry with varying vehicle masses (0.1– 100 tons). In addition, detailed aerothermodynamic analysis is conducted for the maximum heat flux conditions, for the 0.1 ton case. The DSMC results indicate that the CD for Mars is higher than the CD calculated for air at the same Knudsen number. Also, the DSMC analysis predicts a lower heat flux than analytic approximations suggest. Heat flux on the ballute, according to the DSMC analysis, is low enough that a smaller ballute may be used. INTRODUCTION ALLUTE aerocapture combines the benefit of capture in a single pass with the advantages of high B altitude capture, such as lower heating rates and lower deceleration forces, than achieved with traditional aeroshells. As its name suggests, a ballute is a cross between a balloon and a parachute. The ballute’s large area-to-mass ratio facilitates capture at high altitudes. During ballute aerocapture, the orbiter approaches the planetary body on a hyperbolic trajectory, deploying the ballute before entering the atmosphere, as shown in Figure 1. Inside the atmosphere, the vehicle begins to decelerate at a rapidly increasing rate. Once the desired velocity change is achieved, the ballute is released allowing the orbiter to exit the atmosphere, where it can propulsively raise periapsis and achieve the desired orbit. Research has been conducted to investigate the benefits and feasibility of ballute aerocapture at multiple destinations. 1–14 For this paper, we use the Hypersonic Planetary Aero-assist Simulation System (HyperPASS) 15 to obtain ballute entry trajectories. Aerothermodynamic analysis is performed for specific * Doctoral Candidate, Purdue University, School of Aeronautics & Astronautics, West Lafayette, Indiana, 701 West Stadium Ave., 47907-2045, Student Member AIAA. † Assistant Professor, Purdue University, School of Aeronautics & Astronautics, West Lafayette, Indiana, 701 West Stadium Ave., 47907-2045, Member AIAA. ‡ Professor, Purdue University, School of Aeronautics & Astronautics, West Lafayette, Indiana, 701 West Stadium Ave., 47907-2045, Member AAS, Associate Fellow AIAA. 1 points (e.g. at maximum heat flux) along the trajectories using the DSMC 16 solver SMILE (Statistical Modeling In Low-density Environment).17 ballute orbiter trajectory release Figure 1 Ballute Aerocapture BALLUTE VEHICLE SPECIFICATIONS Previous studies of ballute aerothermodynamics using the DSMC method were conducted for Earth returns and Titan missions by Moss et al. 18 and Gnoffo et al. 19 Moss finds that a 4:1 configuration (ring radius : cross-sectional tube radius, depicted in Figure 2) allows the spacecraft’s wake to pass through the torus’ ring without disturbing the flow around the ballute. Because of this favorable result, we use the 4:1 ratio for the ballute configurations. § Rt rt Figure 2 Cross-Sectional View of Tube of Toroidal Ballute rt= R t 4 (1) § See the notation section, located after the conclusion and acknowledgements, for mathematical nomenclature. 2 Following this assumption, the ballute cross-sectional area, A, and the ballute surface area, S, are 2 2 2 A=π Rt , S = π R t (2) We determine the size of the toroidal ballute by substituting Eq. (2) into the expression for ballistic coefficient: mms c+ ball m s c + σ S CB = = (3) CAD CA D We assume an initial ballistic coefficient of 0.5 and an initial C D of 2 for each case, allowing us to solve Eq. (3) for the large ballute radius, Rt. Figure 3 and Table 1 display the resulting ballute and spacecraft configurations for each case. s ballute Table 1 A BALLUTE CONFIGURATIONS 0.1 ton 1 ton 10 ton 100 ton orbiter Parameter D B case case case case axis of symmetry A 2.866 m 9.063 m 28.66 m 90.63 m B 11.46 m 36.25 m 114.6 m 262.5 m C C 6.614 m 20.92 m 66.14 m 209.2 m D 1.600 m 3.438 m 7.406 m 15.96 m Figure 3 Configuration of the Ballute and Orbiter BALLUTE AEROCAPTURE TRAJECTORIES We perform ballute-aerocapture trajectory simulations using the HyperPASS program, which assumes point-mass vehicle representation, inverse-square gravity field, spherical planetary bodies, rotating atmosphere (with planet), and exponentially interpolated atmosphere. Table 2 gives the vehicle parameters used for the simulations. Table 2 VEHICLE PARAMETERS FOR BALLUTE SIMULATIONS AT MARS 0.1 ton case 1 ton case 10 ton case 100 ton case Parameter Orbiter Ballute Orbiter Ballute Orbiter Ballute Orbiter Ballute m, [kg] 100 3.223 1000 32.23 10,000 322.3 100,000 3223 A, [m 2] 2.00 1.032x10 2 9.28 1.032x10 3 43.1 1.032x10 4 200 1.032x10 5 Rn, [m] 0.798 1.433 1.719 4.532 3.703 14.33 7.979 45.32 3 The trajectories are propagated using a CD that varies with Knudsen number. Previous studies of ballute- 4,13 assisted aerocapture were based on a constant CD = 1.37. Knudsen number is defined as the molecular mean-free path divided by the characteristic length: λ Kn = (4) L The mean-free path is inversely proportional to the number density of gas molecules and, therefore, decreases with increasing altitude. The characteristic length of the flow around the towed toroidal ballute is the diameter of the torus tube ( L = 2r t). The CD vs. Kn model that we use is based on Moss’ Direct Simulation Monte Carlo (DSMC) results for air 18 , depicted in Figure 4. The simulations are initiated at an altitude of 350 km, instead of the typical 150 km Mars entry altitude, so that an initial CD of 2 can be assumed for all four ballute sizes. 2.5 2 Air (Moss) 1.5 Cd 1 0.5 0 0.001 0.01 0.1 1 10 100 Knudsun Number = λ/L Figure 4 Drag Coefficient as a Function of Knudsen Number for Air 18 The simulation parameters at Mars are shown in Table 2, with the target apoapsis chosen to achieve a 4-day parking orbit. For all cases presented here, we assume that the ballute is not released. Table 2 ENTRY AND TARGET CONDITIONS FOR BALLUTE SIMULATION AT MARS Condition Mars Entry/Exit Altitude, km 350 Inertial Entry Speed, km/s 5.877 Inertial Entry FPA, deg -17.56 to -17.59 Target Apoapsis Altitude, km 97508.2 4 For the 0.1 ton case, we compare the trajectory calculation with the variable CD model to the trajectory calculation for a constant CD model with the same initial conditions. Figure 5 shows the altitude vs. time for 0.1 ton Mars aerocapture with constant and variable CD. The influence of variable CD is negligible for the initial part of the trajectory down to an altitude of about 150 km, where the atmosphere is still free molecular. The effects of variable CD is pronounced at lower altitudes and result in a longer time to exit. 400 350 constant C =1.37 300 D 250 variable C D 200 150 altitude (km) 100 50 0 0 200 400 600 800 time (s) Figure 5 Altitude vs. Time Comparison of Constant CD and Variable CD models for 0.1 ton Case 400 EXIT ENTRY 350 300 250 constant variable C D C =1.37 200 D 150 altitude(km) 100 50 0 4.0 4.5 5.0 5.5 6.0 velocity (km/s) Figure 6 Altitude vs. Velocity Comparison of Constant CD and Variable CD models for 0.1 ton Case 5 The velocity-altitude map for the constant (1.37) and variable CD models of 0.1 ton Mars ballute aerocapture is shown in Figure 6. There is a significant difference in exit velocity, 4.43 km/s vs. 4.53 km/s, for a constant CD and a variable CD, respectively. Thus, the effects of variable CD are significant for targeted ballute aerocapture. Note that this comparison is based on the same entry conditions for each model, whereas if the same exit conditions were targeted, then the constant CD model would predict a trajectory that penetrates deeper into the atmosphere where heating rates are higher. The stagnation-point heating rates and free-molecular heating rates are calculated by HyperPASS using 3 ρ Qstag = Cv (5) Rn and 1 Q = ρν 3 (6) fm 2 Equation (5) is similar to the Sutton-Graves stagnation-point heating approximation 20 . The predicted stagnation point heating rates for the constant and variable CD models are shown in Figure 7. The constant CD model with the same entry conditions predicts a trajectory with a maximum heating rate 2% higher than the more accurate variable CD model. If the trajectories were calculated for the same target orbit and different entry-flight-path angle, the heating rate for constant CD would be even higher. 3.0 constant 2.5 CD=1.37 2.0 ) 2 1.5 (W/cm 1.0 variable C D 0.5 Stagnation-PointHeating Rate 0.0 0 200 400 600 800 time (s) Figure7 Heating Rate vs. Time Comparison of Constant CD and Variable CD models for 0.1 ton Case 6 Now, we present results comparing four different sized ballute systems using the variable CD model.