**1. Introduction**

A space vehicle may be designed with several trajectory options such as nonlifting (steep or shallow), lifting (skipping or diving), terminal (gravity assist), thrusting (jet-on) reentry. The base pressure and heat flux are of paramount importance for smooth deployment of parachute and successful landing of a spacecraft. Cassanto [1] has carried out a number of wind tunnel and free-flight experiments to obtain the base pressure. Lamb et al. [2] have reviewed the base pressure on the reentry vehicle at high speed, which depends on wake flow characteristic, freestream conditions and edge properties of boundary layer at the shoulder of the module. The base pressure correlation for supersonic flows are compared by Kawecki [3] using the ground test data and with different vehicles such as ABC, MK-3, 4, 12, MTV, reentry F, REX, RVTO, SAMAST, TVX and WAC. A supersonic analysis of the SPR INT blunted cone-flare is carried out by Terry and Barber [4] employing computational fluid dynamics (CFD) method as well as wind-tunnel

testing at Mach 3. Experimental and numerical computations by Togiti et al. [5] of the flow behind a truncated cylinder in a supersonic flow reveals almost constant base pressure coefficient. Base flow investigation of the Apollo AS-202 is presented in detail by Walpot et al. [6].

The bow shock wave is formed ahead the blunt body which is enclosed by a subsonic-supersonic region between the blunt body and the bow shock wave. The wall pressure distribution, the location of the sonic line and shock stand-off distance on the spherical cap region have been analytically analyzed by Chester [7] and Freeman [8] at very high speeds with an adiabatic index near to unity which predicts a singular point at 60° from the stagnation point. However, the analytical approach [9] for the high-speed flow over the blunt-body is found to be the most difficult and complex. The flowfield over the reentry capsule becomes further complicated due to the presence of bevel at the shoulder and shape of the base shell of the reentry module.

Aerodynamic analyses of the COMmercial Experiment Transport (COMET) reentry capsule have been carried out by Wood et al. [10] solving the thin layer laminar Navier-Stokes at high speeds. Yamamoto and Yoshioka [11] have performed flowfield computation over the Orbital Reentry EXperiments (OREX) using CFD method in conjunction with flight aerodynamic data. Ivanov [12] cataloged different shapes for non-winged reentry vehicles. The aerodynamic characterization of the CARINA reentry module in the low supersonic Mach regimes has been performed employing numerical and experimental methods [13]. The flowfield simulations over the Beagle-2 spacecraft have been obtained by Liever et al. [14] using CFD code for low supersonic to hypersonic speeds. Mehta [15] has numerically simulated flowfield over atmospheric reentry demonstrator (ARD) and space recovery experiment (SRE).

Wind tunnel testing of the orion crew module (OCM) has been carried out by Ross et al. [16] to obtain the aerodynamic forces. Murphy et al. [17] have presented experimental static aerodynamic data for the OCM reentry capsule and analyzed with the help of surface flow visualization and computational results. Shape optimization design method has been presented by Zhenmiz et al. [18] for the conceptual design of reentry capsules. Ali et al. [19] have studied effects of nose-bluntness ratio on the aerodynamic performance of reentry capsules. CFD analyses of space vehicle are performed employing H3NS and FLUENT code by Viviani et al. [20] to analyze the flowfield over various capsules. Chen et al. [21] have carried out numerical simulations of flowfield for aerodynamic design of reentry capsules. Weiland [22] has presented aerodynamic characteristics of several non-winged capsules. Effects of geometrical parameters over fore-body of various reentry vehicles have been numerically investigated at high speeds [23, 24].

The flowfield feature of shock wave interaction over a double-cone module includes a local flow separation attributed to the semi-cone angle of the doublecone configuration. It has been also observed that these flowfields are controlled by the vorticity in the incoming boundary layer and the strength and the orientation of the shock wave. Numerical and experimental studies have been performed by many researchers [25–27].

It is worth to mention here that considerable difficulties encountered for obtaining aerodynamic data from wind-tunnel testing are attributed to model-sting interference effects. The shock tunnel is having short duration of testing time. In free flight experiments, a scaled model is launched inside a range and orthogonal shadowgraphs are taken as the capsule flies by each shadow graph station. The CFD approach provides flowfield behaviour and aerodynamic coefficients without the sting interference effect. In the present Chapter, numerical studies were undertaken for a freestream Mach number range of 1.2–6.0. The numerical simulation is to solve

**117**

*Numerical Simulation of Base Pressure and Drag of Space Reentry Capsules at High Speed*

the axisymmetric laminar compressible Navier-Stokes equations on a single-block structured grid, i.e., the number of grid points in the radial direction in each zone of the computational region is same. Surface pressure variations over the vehicles are computed which reveal a systematic understanding of the flow features over the capsule at high speeds. It also reveals the effect of geometrical parameters on aerodynamic base drag coefficient. The unsteady flow characteristics of the OREX

A base pressure experiment for determining the atmospheric pressure profile of planets applicable for Mars, Venus and Jupiter entry probe is presented by Cassanto [29]. The results of a reentry vehicle flight test have demonstrated by Nieden et al. [30] for feasibility of the experiment to obtain the atmospheric pressure profile. The fore-body shape of the reentry vehicle affects the base pressure [31]. Cassanto [32] wind-tunnel data with a sting attached to a model at Mach 4 predict 25–50% higher than the flight data. The Euler code (SAN DIAC) has been employed to compute flowfield over a large number of space vehicles by Noack et al. [33]. Comparisons were made between numerical and experimental results by McWherter et al. [34]

Theoretical studies of the fluid dynamics in the base flow region of the vehicle were presented by Baum [35]. They found in the analysis that the outside flow M > 1 is distinguished from relative low velocity core M < 1 of the base flow regimes by a

The base pressure for sphere-cone configuration [36] at zero angle of attack was found to be a strong function of cone-angle and bluntness ratio. Analysis of flight-test base pressure data [37] for 10° sharp-cone has shown radial base pressure gradient in laminar flow. It is experimentally found that the base pressure is function of Reynolds number under laminar flow condition. Cassanto et al. [38] have investigated local flow effects on base pressure for the 10° sharp-cone configurations. Free-flight base pressure obtained using telemetry technique was compared with the sting-supported wind-tunnel data at Mach 4. Effects of Mach number on ratio of the base to freestream pressure (*pB*/*p∞*) in laminar and turbulent case are carried out in wind-tunnel and free-flight testing [38]. Correlation of free-flight base pressure data for Mach 4–19 has been obtained by Cassanto et al. [39]. Afterbody configuration [40] affects the base pressure ratio levels by about 25% compared to experimental studies. Base pressure measurements on slender cones at zero angle of attack with laminar flow condition on after-body were presented for Mach 11.9. Full-scale flight test base pressure results for a blunt planetary entry probe configuration having a blunt body 52° sphere-cone are analyzed by Cassanto [29]. The base pressure experiment is applicable for Mars, Venus, Jupiter reentry probe missions. The base pressure measurements on a 9° semi-cone angle at Mach range of 3.50–9.20 have been carried out by Zarin [41]. Flight-test base pressure measurements were conducted by Bulmer [42] for Mach number range of 0.5–15. The shapes of the Viking, Mars Path Finder (MPF), Mars Exploration Rovers (MER), Phoenix, Mars Science Laboratory (MSL), Mu-Science Engineering Satellite (MUSES-C) are similar to the Apollo capsule [43]. Aeroassist Flight Experiment (AFE) configurations have been analyzed numerically using two different Navier-Stokes flow solvers by Venkatapathy et al. [44]. The effect of base flow at low supersonic speeds on the sonic line location at hypersonic speed on aerodynamic coefficients has been analyzed by Gnoffo et al. [45]. Tam [46] and Menne [47] have computed flowfield over Viking, Bioconic and AFE vehicles employing Euler flow solver. A spherical

*DOI: http://dx.doi.org/10.5772/intechopen.83651*

and the Beagle-2 are analyzed in Ref. [28].

**2. Review of the base pressure data**

using parabolized Navier-Stokes code SPRINT.

separated flow.

*Numerical Simulation of Base Pressure and Drag of Space Reentry Capsules at High Speed DOI: http://dx.doi.org/10.5772/intechopen.83651*

the axisymmetric laminar compressible Navier-Stokes equations on a single-block structured grid, i.e., the number of grid points in the radial direction in each zone of the computational region is same. Surface pressure variations over the vehicles are computed which reveal a systematic understanding of the flow features over the capsule at high speeds. It also reveals the effect of geometrical parameters on aerodynamic base drag coefficient. The unsteady flow characteristics of the OREX and the Beagle-2 are analyzed in Ref. [28].
