Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> B. Computational Fluid Dynamics (CFD) <s> A novel method of calculating dynamic stability derivatives using Computational Fluid Dynamics is presented. This method uses a non-linear, reduced-frequency approach to simulate the response to a forced oscillation using a single frequency component at the forcing frequency. This provides an order of magnitude improvement in computational e ciency over similar time-dependent schemes without loss of generality. The reduced-frequency approach is implemented with an automated Cartesian mesh scheme. This combination of Cartesian meshing and reduced-frequency solver enables damping derivatives for arbitrary flight condition and geometric complexity to be e ciently and accurately calculated. The method is validated for 3-D reference missile and aircraft dynamic test configurations through the transonic and high-alpha flight regimes. Comparisons with the results of time-dependent simulations are also included. <s> BIB001 </s> Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> B. Computational Fluid Dynamics (CFD) <s> A Computational Fluid Dynamics analysis of the dynamics of probe and capsule shapes at supersonic flight conditions is performed using an automated, inviscid Cartesian-mesh scheme. This analysis uses static and dynamic free-oscillation simulations to develop static and dynamic aerodynamic coecients for three configurations: the Viking, Genesis, and Mars Exploration Rover capsules. These computed coecients are compared against data reduced from ballistic-range free-flight testing. A comparison of data reduction methods for capsule shapes from computational simulations and range data is included. Free-flight simulations agree well with available flight data for both fully-coupled simulations and aerodynamic database fly-throughs based on the developed aerodynamic coecients. A sensitivity analysis of the aerodynamic coecients for trajectory simulations at constant altitude is included. <s> BIB002 </s> Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> B. Computational Fluid Dynamics (CFD) <s> Viscous, free-oscillation simulations with the OverĔow solver are used to predict the aerodynamic behavior of non-liĕing capsule shapes in the supersonic speed regime. Computations using hybrid Reynolds-averaged Navier-Stokes turbulence models are examined for two novel atmospheric-entry capsule conđgurations: an idealized inĔatable decelerator concept, and the Orion Crew Module. ăe simulation results are validated against nonlinear aerodynamic models determined from free-Ĕight ballistic-range data analysis. For the Orion Crew Module, two separate methods of reducing identical range data, along with common models tested in separate range facilities, are included. ăe computations demonstrate the efficiency and accuracy of dynamic simulations for developing a nonlinear aerodynamic performance database. Analysis indicates that the typical nonlinear, bluff-body behavior is characterized by a rate-dependent dynamic response, which is not currently accounted for in common aerodynamic models. <s> BIB003 </s> Survey of Blunt Body Dynamic Stability in Supersonic Flow <s> B. Computational Fluid Dynamics (CFD) <s> A method for performing dynamic simulations of entry vehicles is developed. This capability uses existing infrastructure within the US3D flow solver, developed for doing fluid structure interaction (FSI) simulations, to allow for up to six degree of freedom (6DoF) simulations. Inviscid, free-to-oscillate simulations of the Mars Science Laboratory (MSL) capsule at Mach2.5and3.5are used to evaluate di↵erent data reduction methods. It is found that many simulations may be required to get reliable data. The computed pitch damping coecients show comparable trends to ballistic range data, though they di↵er in magnitude, particularly at high angles of attack. Preliminary viscous simulation results are presented, and show improved agreement with experimental data compared to the inviscid analysis. <s> BIB004
Employing state-of-the-art CFD tools to predict dynamic stability has been attempted in recent years in an effort to build on the semi-empirical methods. Murman BIB001 , BIB002 in 2007 used inviscid Cartesianmesh methods to simulate free and forced oscillation tests of bodies in order to extract the damping characteristics. This was first applied to slender bodies BIB001 and then extended to the blunt body shapes of Viking, Genesis, and MER BIB002 . In BIB001 , both a time dependent and a more computationally efficient reduced frequency approach were examined for missile and fighter aircraft shapes. Moderate agreement with experimental data and between methodologies was found, demonstrating the potential for use of computational methods as well as the possibility of using a more cost efficient approach than a purely time dependent scheme. In BIB002 , the BIB002 time dependent approach was extended to blunt bodies, and results were in moderate qualitative agreement with experimental data (Fig. 13) . Additional fidelity was incorporated into the method by Murman in BIB003 with viscous, Reynolds-averaged-Navier-Stokes (RANS) free oscillation simulations (using the Overflow solver) of the Orion crew module and an inflatable aerodynamic decelerator (IAD) shape. Again, moderate agreement with the available ballistic range data was found (Fig. 14) . A key observation of this work, however, was the dependence of the CFD results on the initial release angle of attack for the free oscillation simulation. This can be seen in Fig. 14 . As the initial angle is increased, the pitch rate at which the body passes through any particular angle of attack also increases. During the dynamic pitching motion, the pressure field on the aftbody lags the motion of the oscillating forebody (this process and its importance to the dynamic stability phenomenon will be elaborated on in later sections)  , BIB003 . The magnitude of the time delay is dependent on the pitch rate of the body, and thus it is suggested that the assumption within the post processing techniques of ballistic range data that the dynamic coefficients are independent of pitch rate should be reconsidered BIB003 . The most recent CFD work in this area was conducted by Stern et al BIB004 using dynamic simulation with the flow solver FUN3D which allow for active grid deformation as the body rotates with up to six degrees of freedom. Their results were for a single degree of freedom, free oscillation simulation of the MSL entry vehicle using both inviscid and viscous simulations. The inviscid results were able to predict static aerodynamic coefficients which agreed well with experiment. Moderate agreement between the simulation and experiment was found for the value of the pitch damping coefficient for a Mach number of 2.5 and the small angles of attack at Mach 3.5. Error was attributed to the inviscid modeling and the assumptions within the modeling of the aerodynamics and the damping, in particular their lack of dependence on the angular rate. Preliminary results for the viscous simulations showed significant promise, with much better agreement for the Mach 3.5 case. Although these improvements come at an increased computational cost, continued work with this particular methodology could yield significant contributions to the modeling community and the fundamental understanding of blunt body dynamic stability.