**1. Introduction**

346 Computational Simulations and Applications

Santiago, J.L.; Coceal, O., Martilli, A. & Belcher, S, E. (2008). Variation of the Sectioanl Drag

Sato, A. & Sada, K. (2002). A wind tunnel experiment on tracer gas concentration fluctuation near a cubical model building, *J. Soc. Civil Engi.*, 706, 41-49, [in Japanese] Shirasawa, T.; Endo, Y., Yoshie, R., Mochida, A. & Tanaka, H. (2008). Comparison of LES

Smagorinsky, J. (1963). General circulation experiments with the primitive equations,

Takewaki, H.; Nishiguchi, A. & Yabe, T. (1985). Cubic Interpolated Pseudo-particle method (CIP) for solving hyperbolic-type equations, *J. Comput. Phys.*, 61, 261-268 Yabe, T. & Takei, E. (1988). A new higher-order Godunov method for general hyperbolic

Xie, Z.T.; Coceal, O. & Castro, I.P. (2008). Large-eddy simulation of flows over random

Van Driest, E.R. (1956). On turbulent flow near a wall, *J. Aerospace Sci.*, 23, 1007-1011

building, *J. Environ. Eng.*, AIJ, 73 [627], 615-622[in Japanese].

*Monthly Weather Review*, 91[3], 99-164

equations, *J. Phys. Soc. Jpn.*, 57[8], 2598-2601

urban-like obstacles, *Bound.-Layer Meteor.*, 129, 1-23

445-457.

Coefficient of a Group of Buildings with Packing Density, *Bound.-Layer Meteor*, 128,

and Durbin type k-ε model for gas diffusion in weak wind region behind a

A high-speed flow-past a reentry capsule generates a bow shock wave which causes a rather high surface pressure and as a result the development of high aerodynamic drag which is require for aero-braking purposes. Highly blunt configurations are generally preferred to decelerate space-capsule for safe returning on the Earth after performing the experiments. The bow shock wave is detached from the blunt fore-body and is having a mixed subsonicsupersonic region between them. The wall pressure distribution, the location of the sonic line and shock stand-off distance on the spherical cap region have been analytically calculated at very high speeds with an adiabatic index near to unity which gives a singular point at 60 deg from the stagnation point (Chester, 1956; Freeman 1956). The analytical approach for the high-speed flow over the blunt-body is considerably difficult and complex (Lighthill 1957). The flow-field over the reentry capsule becomes further complicated due to the presence of corner at the shoulder and the base shell of the reentry module.

Reentry capsule configurations significantly differ from each other due to entry conditions, trajectory, and a number of aerodynamic factors such as aerodynamic axial force, normal force, static moment, damping coefficients. This leads to the necessity to investigate the influence of the shape of blunted bodied on the flow field and aerodynamic characteristics. (Bedin et al., 1992) have presented aerodynamic characteristics and geometrical parameters for the sixteen different reentry modules using experimental data of ballistic test facility. Aero-assist flight experiment (AFE) configurations have been analyzed using two different Navier-Stokes flow solvers by (Venkatapathy et al., 1991). Aerodynamic heating and pressure along with the fore-body and wake-flow structure during atmospheric entry of the Mars Pathfinder spacecraft have been computed by (Hass & Venkatapathy, 1995) using the commercially available general atmospheric simulation program (GASP 2.2). An aerodynamic analysis of the commercial experiment transport (COMET) reentry capsule has been carried out by (Wood et al., 1996) solving the laminar thin layer Navier-Stokes LAURA code for low supersonic to hypersonic speeds. The LAURA code is an upwind, point implicit, second-order accurate fluid dynamics solver based on an extension of the Roe fluxdifference splitting scheme. (Yamomoto & Yoshioka, 1995) carried out flow field computation over the OREX (orbital reentry experiments) using computational fluid dynamics approach coupled with the thermal response of the heat shield material using

Computations of Flowfield over Reentry Modules at High Speed 349

Aerodynamic performance of Commercial Experiment Transport (COMET) reentry capsule (Allen & Cheng, 1970) is carried out using both the Euler and the laminar thin-layer Navier-Stokes solver LAURA code based on upwind point implicit, and Roe flux difference splitting scheme for supersonic speed range. The small shoulder radius causes a strong compression and acceleration of the flow around the edge of the heat shield, thinning the boundary layer producing locally high heating on the shoulder. (Weinbaum, 1966, & Wood

The conservatism of the after body thermal protection system (TPS) heat shield design of the reentry module will shift the centre of gravity, which reduces the static stability. Wind tunnel test data are usually having the sting interference effects; however shock tunnel having short duration of testing time and free flight (ballistic range) data exist. In the free flight experiments, a scaled model is shot inside a range and orthogonal shadowgraphs are taken as the capsule flies by each shadow graph station. There is no sting in the free flight test. The base flow features observed from the shadow graphs show several known wake features such as shear layers, neck region and recompression shocks. The reentry capsule is usually having a high drag shape with good static stability margin, a simple generic shape to take maximum advantage of available aerodynamic data, nose radius selection for minimum structural mass with maximum drag, leading to a maximum radius limited by the range of bluntness ratios, corner radii minimized for maximum drag, but constrained by structural/ thermal requirements. Figure 2 shows the geometrical details of the various reentry capsules (Mehta, 2006). The large nose radius produces large drag, and the short body length reduces the total weight, resulting in a small ballistic coefficient. To ensure the deployment of the parachute in the transonic region, the attitude of the capsule must be maintained within the limit in the whole speed range. Most of the basic configuration parameters such as nose radii or body lengths are decided mainly from the thermal protection requirement. The centre of gravity of the capsule is located in-forward of the centre of pressure, to get statically stable. (Hiraki et al., 1998) measured the unsteady surface pressure of the oscillating MUSES-C reentry capsule and found that the base pressure is responsible for the dynamic instability. One oscillation cycle corresponds to approximately 150 in non-dimensional time. The dynamic instability occurs at very low reduced frequencies by numerical simulation (Teramoto et al. 2001, & Toramoto & Fujii, 2000) of thin layer RANS using lower-upper alternating direction implicit factorization implicit algorithm in conjunction with higher order by the MUSCL interpolation of primitive variables. Unsteady flow is carried out employing multistage time stepping method (Mehta, 2006). Table 1(a) shows the dimensional detail of the reentry capsule. The sonic line is located on the OREX-type configuration on the shoulder whereas in the case of the DART's reentry capsule as descried in the schematic sketch in Figure 1. The location of the sonic line is at the junction of the spherical blunt cone. Thus, it is noticed from the figure that the flow field over the reentry capsule needs a high aerodynamic drag with good static stability margin which leads to the selection of an axisymmetric shape of large angle sphere-cone combination. The fore-body geometry of the ARD module is having a spherical cap; the OREX capsule is having combination of the spherical cap with cone. The outer capsule consists of spherically blunted cone/fare. These capsules cover most of the existing reentry modules. Geometrical details of the ARD, Apollo, Apollo-II, MUSES-C, OREX and spherically blunted cone are displayed in Fig. 2. Table 1(b) summarized the geometrical parameters used in various spherically blunted-cone/flare reentry vehicles. (Fujimoto & Fujii, 2006) have numerically found that the shoulder radius has a great influence on the pressure

et al. 1996) have analyzed the wake flow field of the capsules.

finite element method in conjunction with the aerodynamic flight data. (Tam, 1992) has computed flow field at hypersonic Mach numbers over Viking, Biconic and AFE reentry capsules employing IEC3D (Inviscid Equilibrium Computation in 3-Dimension). (Menne, 1994) has computed flow field over Viking similar to the Apollo type module and Biconic configurations for freestream Mach numbers 2.0 and 3.0 by solving compressible Euler equations. The inviscid analysis is unable to show the flow separation in the back shell region of the reentry capsule. The aerodynamic characterization of the CARINA reentry module in the low supersonic Mach regimes has been performed employing numerical and experimental methods (Solazzo et al., 1994). The flow field simulation over the ARD (ESA's atmospheric reentry demonstrator) module has been computed numerically by (Walpot, 2001) at hypersonic speeds. Developments relating to the base pressure and the base heating prediction for wide range of cone and wedge have been reviewed for supersonic and hypersonic Mach numbers by (Lamb & Oberkampf, 1995). The flow field simulations over the Beagle-2 spacecraft have been carried out by (Liever et al., 2003) using CFD-FASTRAN code for low supersonic to hypersonic speeds. A numerical simulation code has been applied for super orbital reentry flow and has been used to the flow field prediction around the MUSES-C reentry module (Osu et al., 2002). Supersonic and hypersonic flow past a slender cone (Tai & Kao, 1994) has been numerically simulated by solving Navier-Strokes using an explicit multi-stage Roe's method. The flow fields around blunt reentry modules (Teramoto et al., 2001) were numerically analyzed in order to investigate the mechanism of dynamic instability of the capsule at freestream Mach number of 1.3. The blunt and short reentry capsule tends to be dynamically unstable at low supersonic Mach number attributed primarily to the delay in base pressure (Teramoto & Fujii, 2001). Numerical studies have been done by (Ottens, 2001) employing a laminar Navier-stokes flow solver for two different types of Delft aerospace reentry test (DART) demonstrators reentry capsules.

The frontal shape of the reentry body can be classified either employing as a spherical cap as in the case of the Apollo and the ARD, or combination of the spherical nose or blunted-body with cone as in the case of the OREX and the Beagle-2, or a spherical blunt-cone/flare configuration as proposed by DART. The flow field features over the reentry capsule can be delineated through the experimental and numerical flow simulations (Mehta, 2006) at high speeds. Figure 1 shows schematic flow field features over the OREX and the DART capsules. The significant flow features are described by the following. In the fore-body region, the fluid decelerates through the bow shock wave depending on the cruise speed and altitude. As the shoulder of the capsule, the flow turns and expands rapidly and boundary layer detached, forming a free shear layer that separates the inner re-circulating flow region behind the base from the outer flow field. The latter is recompressed and turned back to the freestream direction, first by the so-called lip shock, and further downstream by recompression shock. At the end of the re-circulating flow past the neck, the shear layer develops in the wake trail. A complex inviscid wave structure often includes a lip shock wave (associates with the corner expansion) and wake trail (adjacent to the shear layer confluence). The corner expansion process is a modified Prandtl-Meyer patter distorted by the presence of the approaching boundary layer. An excellent review of the thermodynamic and chemical-kinetic models used for computational fluid dynamics simulations of a nonequilibrium flow field is reported by (Gnoffo & Pettnelli, 1995). Another review of the after body aero-thermal flight data and thermal protection system design for Mercury, Gemini, Project Fire, Apollo, Reentry F, Mars Viking, Galileo, Mars Pathfinder, MIRKA, Atmospheric Reentry Demonstrator (ARD) is given by (Wright et al., 2006). The flight data analysis of the various reentry capsules will be very useful for the numerical simulation purposes.

finite element method in conjunction with the aerodynamic flight data. (Tam, 1992) has computed flow field at hypersonic Mach numbers over Viking, Biconic and AFE reentry capsules employing IEC3D (Inviscid Equilibrium Computation in 3-Dimension). (Menne, 1994) has computed flow field over Viking similar to the Apollo type module and Biconic configurations for freestream Mach numbers 2.0 and 3.0 by solving compressible Euler equations. The inviscid analysis is unable to show the flow separation in the back shell region of the reentry capsule. The aerodynamic characterization of the CARINA reentry module in the low supersonic Mach regimes has been performed employing numerical and experimental methods (Solazzo et al., 1994). The flow field simulation over the ARD (ESA's atmospheric reentry demonstrator) module has been computed numerically by (Walpot, 2001) at hypersonic speeds. Developments relating to the base pressure and the base heating prediction for wide range of cone and wedge have been reviewed for supersonic and hypersonic Mach numbers by (Lamb & Oberkampf, 1995). The flow field simulations over the Beagle-2 spacecraft have been carried out by (Liever et al., 2003) using CFD-FASTRAN code for low supersonic to hypersonic speeds. A numerical simulation code has been applied for super orbital reentry flow and has been used to the flow field prediction around the MUSES-C reentry module (Osu et al., 2002). Supersonic and hypersonic flow past a slender cone (Tai & Kao, 1994) has been numerically simulated by solving Navier-Strokes using an explicit multi-stage Roe's method. The flow fields around blunt reentry modules (Teramoto et al., 2001) were numerically analyzed in order to investigate the mechanism of dynamic instability of the capsule at freestream Mach number of 1.3. The blunt and short reentry capsule tends to be dynamically unstable at low supersonic Mach number attributed primarily to the delay in base pressure (Teramoto & Fujii, 2001). Numerical studies have been done by (Ottens, 2001) employing a laminar Navier-stokes flow solver for two different

types of Delft aerospace reentry test (DART) demonstrators reentry capsules.

The frontal shape of the reentry body can be classified either employing as a spherical cap as in the case of the Apollo and the ARD, or combination of the spherical nose or blunted-body with cone as in the case of the OREX and the Beagle-2, or a spherical blunt-cone/flare configuration as proposed by DART. The flow field features over the reentry capsule can be delineated through the experimental and numerical flow simulations (Mehta, 2006) at high speeds. Figure 1 shows schematic flow field features over the OREX and the DART capsules. The significant flow features are described by the following. In the fore-body region, the fluid decelerates through the bow shock wave depending on the cruise speed and altitude. As the shoulder of the capsule, the flow turns and expands rapidly and boundary layer detached, forming a free shear layer that separates the inner re-circulating flow region behind the base from the outer flow field. The latter is recompressed and turned back to the freestream direction, first by the so-called lip shock, and further downstream by recompression shock. At the end of the re-circulating flow past the neck, the shear layer develops in the wake trail. A complex inviscid wave structure often includes a lip shock wave (associates with the corner expansion) and wake trail (adjacent to the shear layer confluence). The corner expansion process is a modified Prandtl-Meyer patter distorted by the presence of the approaching boundary layer. An excellent review of the thermodynamic and chemical-kinetic models used for computational fluid dynamics simulations of a nonequilibrium flow field is reported by (Gnoffo & Pettnelli, 1995). Another review of the after body aero-thermal flight data and thermal protection system design for Mercury, Gemini, Project Fire, Apollo, Reentry F, Mars Viking, Galileo, Mars Pathfinder, MIRKA, Atmospheric Reentry Demonstrator (ARD) is given by (Wright et al., 2006). The flight data analysis of the various reentry capsules will be very useful for the numerical simulation purposes. Aerodynamic performance of Commercial Experiment Transport (COMET) reentry capsule (Allen & Cheng, 1970) is carried out using both the Euler and the laminar thin-layer Navier-Stokes solver LAURA code based on upwind point implicit, and Roe flux difference splitting scheme for supersonic speed range. The small shoulder radius causes a strong compression and acceleration of the flow around the edge of the heat shield, thinning the boundary layer producing locally high heating on the shoulder. (Weinbaum, 1966, & Wood et al. 1996) have analyzed the wake flow field of the capsules.

The conservatism of the after body thermal protection system (TPS) heat shield design of the reentry module will shift the centre of gravity, which reduces the static stability. Wind tunnel test data are usually having the sting interference effects; however shock tunnel having short duration of testing time and free flight (ballistic range) data exist. In the free flight experiments, a scaled model is shot inside a range and orthogonal shadowgraphs are taken as the capsule flies by each shadow graph station. There is no sting in the free flight test. The base flow features observed from the shadow graphs show several known wake features such as shear layers, neck region and recompression shocks. The reentry capsule is usually having a high drag shape with good static stability margin, a simple generic shape to take maximum advantage of available aerodynamic data, nose radius selection for minimum structural mass with maximum drag, leading to a maximum radius limited by the range of bluntness ratios, corner radii minimized for maximum drag, but constrained by structural/ thermal requirements. Figure 2 shows the geometrical details of the various reentry capsules (Mehta, 2006). The large nose radius produces large drag, and the short body length reduces the total weight, resulting in a small ballistic coefficient. To ensure the deployment of the parachute in the transonic region, the attitude of the capsule must be maintained within the limit in the whole speed range. Most of the basic configuration parameters such as nose radii or body lengths are decided mainly from the thermal protection requirement. The centre of gravity of the capsule is located in-forward of the centre of pressure, to get statically stable. (Hiraki et al., 1998) measured the unsteady surface pressure of the oscillating MUSES-C reentry capsule and found that the base pressure is responsible for the dynamic instability. One oscillation cycle corresponds to approximately 150 in non-dimensional time. The dynamic instability occurs at very low reduced frequencies by numerical simulation (Teramoto et al. 2001, & Toramoto & Fujii, 2000) of thin layer RANS using lower-upper alternating direction implicit factorization implicit algorithm in conjunction with higher order by the MUSCL interpolation of primitive variables. Unsteady flow is carried out employing multistage time stepping method (Mehta, 2006).

Table 1(a) shows the dimensional detail of the reentry capsule. The sonic line is located on the OREX-type configuration on the shoulder whereas in the case of the DART's reentry capsule as descried in the schematic sketch in Figure 1. The location of the sonic line is at the junction of the spherical blunt cone. Thus, it is noticed from the figure that the flow field over the reentry capsule needs a high aerodynamic drag with good static stability margin which leads to the selection of an axisymmetric shape of large angle sphere-cone combination. The fore-body geometry of the ARD module is having a spherical cap; the OREX capsule is having combination of the spherical cap with cone. The outer capsule consists of spherically blunted cone/fare. These capsules cover most of the existing reentry modules. Geometrical details of the ARD, Apollo, Apollo-II, MUSES-C, OREX and spherically blunted cone are displayed in Fig. 2. Table 1(b) summarized the geometrical parameters used in various spherically blunted-cone/flare reentry vehicles. (Fujimoto & Fujii, 2006) have numerically found that the shoulder radius has a great influence on the pressure

Computations of Flowfield over Reentry Modules at High Speed 351

ARD 3.36 2.80 0.014 2.04 – 33.0 Apollo 4.595 3.95 0.186 3.522 – 32.5 Beagle - 2 2.8 3.0 0.21 3.5 30 43 COMET 1.22 1.32 - 1.22 - 5 Apollo-II 4.74 3.95 0.1975 2.686 – 33.0

shoulder 1.35 3.40 0.001 1.508 50.0 15.0

shoulder 1.35 3.457 – 1.508 50.0 15.0 CARINA 1.97 1.0 0.25 1.172 – 13.0 Gemini - 90.0 - 70.2 - 20 Project fire 70.2 58.79 - 38.86 33 Mars path finder 0.6638 2.6492 0.0662 70.19 46.63 Mercury 30 74.50 - 58.38 - 20 Viking 0.912 1.875 0.0914 2.0964 20 33.6 MUSES-C 2.0 4.0 – 2.0 45.0 45.0

> Base diameter, D Semi-cone angle, 73.91 25 77.89 30 82.29 35

level behind the body and separation position. Gnoffo et al. have found that laminar, wind-side heating levels may decrease with increasing angle of attack resulting from an increase in the effective radius of curvature with sonic line movement from the hemispherical nose to the aft shoulder of the blunt cone. Numerical simulation of the flow field is required over various geometrical parameters of the capsules in order to meet the aerodynamic and mission requirements. The numerical simulation of axisymmetric laminar compressible time dependent Navier-Stokes is carried out using a multi-stage Runge-Kutta time stepping scheme. A local time-step is used to simulate the flow over

Hypersonic calculations about complex geometries require large amounts of computer sources, but solution adaptive grids, convergence, acceleration, parallel processing may make run time manageable. The thin-layer approximation (Edwards 1992) is invoked, because viscous effects are generally present boundary layer near the wall. This

Table 1. (b) Geometrical parameters of spherically blunted cone reentry bodies.

Corner radius, RC

Overall length, L

Semicone angle, <sup>N</sup> deg

Backshell angle, <sup>B</sup> deg

Frontal diameter, D

Capsule

OREX smooth

OREX sharp

Spherical radius, RN

Table 1. (a) Geometrical parameters of reentry capsules.

various reentry configurations.

**2. Numerical schemes** 

Fig. 2. Geometrical details of various reentry capsules.

(a) flowfield over OREX capsule (b) flowfield over spherical blunt cone

Apollo-II

Spherically blunted-

cone OREX

Fig. 1. Representation of flow features on blunted body at supersonic speeds.

Fig. 2. Geometrical details of various reentry capsules.

Apollo ARD

MUSE-C


Table 1. (a) Geometrical parameters of reentry capsules.


Table 1. (b) Geometrical parameters of spherically blunted cone reentry bodies.

level behind the body and separation position. Gnoffo et al. have found that laminar, wind-side heating levels may decrease with increasing angle of attack resulting from an increase in the effective radius of curvature with sonic line movement from the hemispherical nose to the aft shoulder of the blunt cone. Numerical simulation of the flow field is required over various geometrical parameters of the capsules in order to meet the aerodynamic and mission requirements. The numerical simulation of axisymmetric laminar compressible time dependent Navier-Stokes is carried out using a multi-stage Runge-Kutta time stepping scheme. A local time-step is used to simulate the flow over various reentry configurations.
