**6. Flowfield characteristics**

*Hypersonic Vehicles - Past, Present and Future Developments*

**5.3 Initial and boundary conditions**

the whole flowfield.

**5.4 Computational grid**

*Trajectory points and initial conditions.*

The scheme is stable for a Courant number ≤2. Local time steps are used to accelerate to a steady-state solution by setting the time step at each point to the maximum

The freestream conditions for each trajectory point are tabulated in **Table 5**, which are used as initial conditions. The freestream flow values are used to initialize

The boundary conditions are as follows: a no-slip condition and isothermal wall is considered as a solid wall boundary condition. At the inflow, all the flow variables are taken at the freestream values as tabulated in **Table 5**. A symmetry condition is imposed on the centre line upstream and downstream of the reentry vehicle. All

The body oriented grids are generated using a homotopy scheme. The stretched grids are generated in an orderly manner. The grid-stretching factor is selected as 5,

*M<sup>∞</sup> p∞***, Pa** *T∞,* **K** 1.2 4519 210 1.4 3952 213 2.0 2891 219 3.0 2073 224 5.0 1238 232 6.0 1064 234

value allowed by the local Courant-Friedrichs-Lewy (CFL) condition.

variables are extrapolated at the outer computational boundary.

*Enlarged view of computational grid; (a) Soyuz; (b) MUSES-C; and (c) OREX.*

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**Figure 6.**

**Table 5.**

**Figure 7** depicts the velocity vector plots over the Apollo, the Apollo-II, the OREX and the MUSES-C space vehicles. It can be visualized from the vector plots that all the significant flowfield features such as a bow shock wave, rapid expansion fans at the shoulder, recirculation region with a converging free-shear layer and formation of the vortex flow in the base-shell region are well captured for *M∞* = 5.0. The wake flowfield immediately behind the space vehicle base exhibits complex flow characteristics. The formation of the bow shock wave on the fore-body

**Figure 7.** *Close-up views of velocity vector plots (a) Apollo; (b) ARD; (c) OREX and (d) MUSES-C at M∞ = 5.0.*

depends on *RN* and *αN* and *M∞*. The bow shock wave moves close to the fore-body with the increasing *M∞* and the stand-off distance between the bow shock wave and the fore body decreases with the increasing *M∞*. The Mach contour plots over the OREX and the MUSES-C are depicted in **Figure 8** for *M∞* = 1.2. The wake flowfield, immediately behind the capsule base, exhibits complex flow characteristics as observed in the vector plots.

Mach contours over the CARINA and Beagle-2 modules are exhibited in **Figure 9** for *M∞* = 1.2. The Mach contours over the SRE capsule for *θ* = 25° at *M∞* = 2.0 and 3.0 are shown in **Figure 10**. The bow shock wave does not follow the fore-body contour, which is due to small value of *RN* and presence of semi-cone angle *θ* as compared to the OREX, the MUSES-C and the Apollo.

**Figure 11(a)** and **(b)** depicts velocity vector and Mach contour plots, respectively, over the double-cone (25/55°) configuration at *M∞* = 3. Despite its geometric simplicity, the double-cone shows the complex flowfield characteristics. A separation bubble can be observed on the vector plots. The separation and reattachment points are marked with the symbols "*S*" and"*R*"in the vector plots. It can also be seen from the vector plots that all the significant flowfield features are well captured such as the formation of conical shock wave on the tip, rapid expansion fan on the corner, recirculation region with converging free-shear layer and formation of the vortex flow in the aft region of the sharp-tipped double cone configuration.

The above numerical simulations over various reentry space capsules show that the separated flow can be found in the base region of the reentry capsules. The flow around the capsule is divided into two regions; inside and outside of the

**Figure 8.** *Mach contours over capsules at M∞ = 1.2 (a) OREX and (b) MUSES-C.*

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expansion fan.

**Figure 10.**

**Figure 11.**

freestream Mach number.

behavior results the base drag.

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

recirculation zone, and the shear layer separating the regions. The flowfield is very complex because of the back-shell. The wake flowfield, immediately behind the capsule base, exhibits vortex flow behavior. The formation of the bow shock wave on the fore body of the capsule depends on geometrical parameters such as spherical cap radius and the apex cone angle, and the value of the freestream Mach number. A low pressure is observed immediately downstream of the base which is characterized by a low-speed recirculating flow region, which can be attributed to filling-of the growing space between the shock wave and the reentry module. This flowfield

**Figure 12(a)** and **(b)** depicts the variation of surface pressure coefficient *Cp* over the surface and the base plane, respectively, of the SRE capsule at *M∞* = 6.0, where *s* is measured along the surface of the fore-body. The *s* = 0 is the location of the stagnation point. The *Cp* variations is gradually decreasing over the spherical cap and remain nearly constant in the conical section of the SRE as depicted in **Figure 12(a)**. A sudden fall in *Cp* is seen on the sharp shoulder of the SRE. In the base region of the SRE, the *CpB* remains nearly linear variation on the base plane as seen in **Figure 12(b)**. The *CpB* is high on the corner due to presence of the

**Figure 13(a)** shows variation of *Cp* over the MUSES-C capsule at *M∞* = 3.0. A sudden drop in *Cp* is observed on the shoulder of the MUSES-C accompanied by a negative pressure coefficient *Cp*. The *CpB* is shown in **Figure 13(b)** for the MUSES-C space vehicle. The *CpB* remains near to a constant value on the base plane. It is important to mention here that the *CpB* variation is gradual attributed to beveled shape shoulder of the MUSES-C. Thus, the *Cp* and *CpB* variations over the SRE and the MUSES-C exhibit the influence of the geometrical parameters and

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

*Mach contour over SRE module at (a) M∞ = 2.0 and (b) M∞ = 3.0 at θ = 25°.*

*(a) velocity vector and (b) Mach contours over double-cone module.*

**Figure 9.** *Mach contours over (a) CARINA; and (b) Beagle-2 module at M∞ = 1.2.*

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

**Figure 10.**

*Hypersonic Vehicles - Past, Present and Future Developments*

observed in the vector plots.

configuration.

the OREX, the MUSES-C and the Apollo.

*Mach contours over capsules at M∞ = 1.2 (a) OREX and (b) MUSES-C.*

*Mach contours over (a) CARINA; and (b) Beagle-2 module at M∞ = 1.2.*

depends on *RN* and *αN* and *M∞*. The bow shock wave moves close to the fore-body with the increasing *M∞* and the stand-off distance between the bow shock wave and the fore body decreases with the increasing *M∞*. The Mach contour plots over the OREX and the MUSES-C are depicted in **Figure 8** for *M∞* = 1.2. The wake flowfield, immediately behind the capsule base, exhibits complex flow characteristics as

Mach contours over the CARINA and Beagle-2 modules are exhibited in **Figure 9** for *M∞* = 1.2. The Mach contours over the SRE capsule for *θ* = 25° at *M∞* = 2.0 and 3.0 are shown in **Figure 10**. The bow shock wave does not follow the fore-body contour, which is due to small value of *RN* and presence of semi-cone angle *θ* as compared to

**Figure 11(a)** and **(b)** depicts velocity vector and Mach contour plots, respectively, over the double-cone (25/55°) configuration at *M∞* = 3. Despite its geometric simplicity, the double-cone shows the complex flowfield characteristics. A separation bubble can be observed on the vector plots. The separation and reattachment points are marked with the symbols "*S*" and"*R*"in the vector plots. It can also be seen from the vector plots that all the significant flowfield features are well captured such as the formation of conical shock wave on the tip, rapid expansion fan on the corner, recirculation region with converging free-shear layer and formation of the vortex flow in the aft region of the sharp-tipped double cone

The above numerical simulations over various reentry space capsules show that the separated flow can be found in the base region of the reentry capsules. The flow around the capsule is divided into two regions; inside and outside of the

**126**

**Figure 9.**

**Figure 8.**

*Mach contour over SRE module at (a) M∞ = 2.0 and (b) M∞ = 3.0 at θ = 25°.*

**Figure 11.** *(a) velocity vector and (b) Mach contours over double-cone module.*

recirculation zone, and the shear layer separating the regions. The flowfield is very complex because of the back-shell. The wake flowfield, immediately behind the capsule base, exhibits vortex flow behavior. The formation of the bow shock wave on the fore body of the capsule depends on geometrical parameters such as spherical cap radius and the apex cone angle, and the value of the freestream Mach number. A low pressure is observed immediately downstream of the base which is characterized by a low-speed recirculating flow region, which can be attributed to filling-of the growing space between the shock wave and the reentry module. This flowfield behavior results the base drag.

**Figure 12(a)** and **(b)** depicts the variation of surface pressure coefficient *Cp* over the surface and the base plane, respectively, of the SRE capsule at *M∞* = 6.0, where *s* is measured along the surface of the fore-body. The *s* = 0 is the location of the stagnation point. The *Cp* variations is gradually decreasing over the spherical cap and remain nearly constant in the conical section of the SRE as depicted in **Figure 12(a)**. A sudden fall in *Cp* is seen on the sharp shoulder of the SRE. In the base region of the SRE, the *CpB* remains nearly linear variation on the base plane as seen in **Figure 12(b)**. The *CpB* is high on the corner due to presence of the expansion fan.

**Figure 13(a)** shows variation of *Cp* over the MUSES-C capsule at *M∞* = 3.0. A sudden drop in *Cp* is observed on the shoulder of the MUSES-C accompanied by a negative pressure coefficient *Cp*. The *CpB* is shown in **Figure 13(b)** for the MUSES-C space vehicle. The *CpB* remains near to a constant value on the base plane. It is important to mention here that the *CpB* variation is gradual attributed to beveled shape shoulder of the MUSES-C. Thus, the *Cp* and *CpB* variations over the SRE and the MUSES-C exhibit the influence of the geometrical parameters and freestream Mach number.

**Figure 12.** *Variation of pressure coefficient (a) over SRE module (b) on base region.*

**Figure 13.** *Variation of pressure coefficient (a) over MUSES-C (b) on base region.*
