**7. Base pressure and drag coefficients**

Characteristics of flow features around the blunt body at supersonic speeds are described in the above section. The high surface pressure on the fore-body results in the high aerodynamic drag which is required for the aero-braking application. The base pressure coefficient can be calculated using following expression

$$\mathbf{C}\_{\rm PBS} = \frac{(\mathbf{p}\_{\rm BS} - \mathbf{p}\_{\rm m})}{\frac{1}{2}\rho\_{\rm m}\mathbf{V}\_{\rm m}^{2}}\tag{5}$$

**129**

reentry vehicle and can be expressed as

*Base drag coefficient on various reentry capsules.*

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

ARD −0.5 −0.25 −0.15 −0.05 — Soyuz — −0.50 −0.40 −0.20 — Apollo −0.30 −0.30 −0.20 −0.05 — Apollo-II −0.25 −0.30 −0.20 −0.08 — OREX −0.75 −0.30 −0.20 −0.10 — OREX (S) −0.90 −0.40 −0.25 −0.18 — CARINA −0.50 −0.30 −0.20 −0.05 — MUSSES-C −0.70 −0.30 −0.20 −0.10 — Beagle-2 −0.8 −0.28 −0.15 −0.10 — Double-cone, 25/55° — −0.25 −0.20 — −0.05 SRE, *θ* = 25° −0.82 −0.30 −0.20 — −0.01 SRE, *θ* = 30° −0.80 −0.32 −0.20 — −0.01 SRE, *θ* = 35° −0.70 −0.30 −0.20 — −0.01

*M***∞ = 1.2** *M***∞ = 2.0** *M***∞ = 3.0** *M***∞ = 5.0** *M***∞ = 6.0**

) −0.9920 −0.7288 −0.3571 −0.1387 −0.0396

*M***∞ = 1.2** *M***∞ = 2.0** *M***∞ = 3.0** *M***∞ = 5.0** *M***∞ = 6.0**

−0.261 × 10<sup>−</sup><sup>4</sup> −0.331 × 10<sup>−</sup><sup>4</sup> −0.146 × 10<sup>−</sup><sup>4</sup> −0.467 × 10<sup>−</sup><sup>5</sup>

−0.517 × 10<sup>−</sup><sup>5</sup> −0.159 × 10<sup>−</sup><sup>4</sup> −0.360 × 10<sup>−</sup><sup>4</sup> −0.851 × 10<sup>−</sup><sup>4</sup>

−0.622 × 10<sup>−</sup><sup>5</sup> −0.254 × 10<sup>−</sup><sup>4</sup> −0.111 × 10<sup>−</sup><sup>4</sup> −0.355 × 10<sup>−</sup><sup>4</sup>

−0.383 × 10<sup>−</sup><sup>6</sup> −0.138 × 10<sup>−</sup><sup>4</sup> −0.318 × 10<sup>−</sup><sup>4</sup> −0.177 × 10<sup>−</sup><sup>4</sup>

The aerodynamic drag is influenced by the fore-body shape. The fore-body aerodynamic drag coefficient for various reentry configurations at high speeds is earlier computed and tabulated in Ref. [56]. After body drag *CDB* is calculated by integrating the surface pressure coefficient variation excluding the fore-body of the

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

*CpBS* = −2/(*γM∞*

**Table 6.**

Double cone

SRE *θ* = 20°

SRE *θ* = 25°

SRE *θ* = 30°

SRE *θ* = 35°

**Table 7.**

2

**Capsules** *CpBS*

*Pressure coefficient at base stagnation point of various reentry modules.*

**Capsule** *CDB*

OREX −0.117 × 10<sup>−</sup><sup>5</sup> −0.555 × 10<sup>−</sup><sup>6</sup> −0.244 × 10<sup>−</sup><sup>7</sup> −0.723 × 10<sup>−</sup><sup>9</sup> OREX (S) −0.228 × 10<sup>−</sup><sup>5</sup> −0.124 × 10<sup>−</sup><sup>5</sup> −0.539 × 10<sup>−</sup><sup>6</sup> −0.170 × 10<sup>−</sup><sup>6</sup> Carina −0.389 × 10<sup>−</sup><sup>4</sup> −0.649 × 10<sup>−</sup><sup>5</sup> −0.978 × 10<sup>−</sup><sup>5</sup> −0.162 × 10<sup>−</sup><sup>5</sup>

MUSES-C −0.261 × 10<sup>−</sup><sup>4</sup> −0.512 × 10<sup>−</sup><sup>5</sup> −0.245 × 10<sup>−</sup><sup>5</sup> −0.196 × 10<sup>−</sup><sup>5</sup> Beagle-2 −0.790 × 10<sup>−</sup><sup>5</sup> −0.430 × 10<sup>−</sup><sup>5</sup> −0.210 × 10<sup>−</sup><sup>5</sup> −0.710 × 10<sup>−</sup><sup>6</sup>

−0.268 × 10<sup>−</sup><sup>3</sup> −0.606 × 10<sup>−</sup><sup>4</sup> −0.337 × 10<sup>−</sup><sup>4</sup> −0.200 × 10<sup>−</sup><sup>3</sup>

where subscript *BS* represents the base-stagnation point as depicted in **Figure 1(b)**. **Table 6** shows the computed base pressure coefficient *CPBS* of the various capsules configurations at different freestream Mach numbers *M∞*. **Table 6** shows OREX with smooth shoulder (beveled) and with a sharp corner. The *CPBS* is high in the case of the OREX (S) as compared to the OREX with smooth shoulder. It again exhibits the effects of the shoulder shape geometry on the *CPBS*.


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

#### **Table 6.**

*Hypersonic Vehicles - Past, Present and Future Developments*

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

**7. Base pressure and drag coefficients**

of the shoulder shape geometry on the *CPBS*.

*CPBS* = \_\_\_\_\_\_\_\_

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

Characteristics of flow features around the blunt body at supersonic speeds are described in the above section. The high surface pressure on the fore-body results in the high aerodynamic drag which is required for the aero-braking application. The

> (*pBS* − *p*∞) \_1 <sup>2</sup> <sup>ρ</sup>∞V∞

where subscript *BS* represents the base-stagnation point as depicted in **Figure 1(b)**.

**Table 6** shows the computed base pressure coefficient *CPBS* of the various capsules configurations at different freestream Mach numbers *M∞*. **Table 6** shows OREX with smooth shoulder (beveled) and with a sharp corner. The *CPBS* is high in the case of the OREX (S) as compared to the OREX with smooth shoulder. It again exhibits the effects

<sup>2</sup> (5)

base pressure coefficient can be calculated using following expression

**128**

**Figure 12.**

**Figure 13.**

*Pressure coefficient at base stagnation point of various reentry modules.*


#### **Table 7.** *Base drag coefficient on various reentry capsules.*

The aerodynamic drag is influenced by the fore-body shape. The fore-body aerodynamic drag coefficient for various reentry configurations at high speeds is earlier computed and tabulated in Ref. [56]. After body drag *CDB* is calculated by integrating the surface pressure coefficient variation excluding the fore-body of the reentry vehicle and can be expressed as

$$\mathbf{C}\_{DB} = \frac{2\pi f\_l (C\_{Pb}) \, r\_l \sin \varphi d\mathbf{x}}{A\_{\text{max}}} \tag{6}$$

**131**

**Author details**

Education, India

University, Singapore

Rakhab C. Mehta1,2

provided the original work is properly cited.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

1 Department of Aeronautical Engineering, Noorul Islam Center for Higher

2 School of Mechanical and Aerospace Engineering, Nanyang Technological

\*Address all correspondence to: drrakhab.mehta@gmail.com

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

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

where *r* and *ψ* are local radius and local inclination angle in the *x*-direction station *i* respectively. *Amax* is the maximum cross-sectional area of the reentry module. **Table 7** shows the base body aerodynamic drag *CDB* for various reentry modules. The present numerical simulation will be validated in future with experimentally measured data in order to assess the error bands between them. The influence of geometrical parameters of the space reentry capsules and freetream Mach number on the base pressure coefficient and the base drag coefficient can be seen in **Tables 6** and **7**.
