**1. Introduction**

The characteristics of the unsteady flowfield over a hemisphere-cylinder model and a bulbous heat shield of a satellite launch vehicle at turbulent flow and at transonic speeds and a laminar flow over a conical spike attached to a forward facing blunt body at supersonic speed are numerically simulated by solving time-dependent compressible axisymmetric Navier-Stokes equations.

Hsieh [1] has conducted wind-tunnel tests of a hemisphere-cylinder model at zero angle of attack and freestream Mach number M∞ = 0.7 − 1.3 to investigate viscous-inviscid interaction. Hsieh [2] has solved full potential equation to analyze wind-tunnel results and found that the inviscid analysis is unable to predict the external flowfield satisfactory. This is due to the fact that the shock wave-turbulent boundary layer interaction causes a separated flow between M∞ = 0.80 − 0.90 on the hemisphere-cylinder model in a high speed wind-tunnel testing. The numerical simulations analyze the unsteady flow caused by shock wave-turbulent boundary layer at transonic Mach numbers.

A bulbous payload shroud is generally selected to accommodate an increased payload volume of the satellite in a launch vehicle. All launch vehicles require a heat shield to protect the satellite from aerodynamic loading, heating, aero-acoustic vibration, and other environmental conditions during the ascent phase of the flight and to provide aerodynamic forward surface. The wind-tunnel tests for Titan I − IV were conducted during 1955 to 1996 and summarized by Brower [3]. The estimation of flowfield characteristics around such a heat shield configu‐ ration is of great aerodynamic importance, as well as research interest. For the ascent flight, during the transonic speed range, their study is particular important because of such resulting phenomena as terminal shock wave movements, frequently coupled with substantial free‐ stream dynamic pressure. Flow induced vibrations are important design requirement of

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aerospace launch vehicles. Awrejcewicz, and Krysko [4] have developed numerical simulation of a cylindrical panel within transonic ideal-gas flow stream and solved dynamics for all intervals of the frequency. These parameters directly depend on the intensity of the vorticity components of the turbulence, the strength of the shock wave, and the mechanism of their interaction, all of which are implicitly linked to the specific configuration of a bulbous heat shield of a satellite launch vehicle. The numerical flow simulation over a bulbous payload shroud at transonic Mach number range is very useful to decide the geometrical configuration for minimum buffeting load and minimum aerodynamic drag requirement. The terminal shock wave of sufficient strength to interact with the boundary layer can cause flow separation and flowfield may become unstable as observed in the high speed cinematography [5]. Therefore, it is desirable to determine the location of the terminal shock wave on the heat shield and the strength of the terminal shock wave as a function of transonic Mach numbers range. The strength of the terminal shock wave and the mechanism of their interaction are related to the specific configuration of the heat shield satellite launch vehicle. Fluctuations of pressure level in shock waves and in separated flow regions can cause flow instabilities and then leads to buffeting phenomenon [6] – [7]. The features of the transonic flowfield can be delineated through the wind-tunnel data such as schlieren photographs and oil flow patterns. It is characterized by a normal or a terminal shock wave, supersonic pocket on the cylindrical region of the heat shield, shock wave/turbulent boundary layer interaction, and a separation bubble may be caused by the shock wave/turbulent boundary layer interaction on the cylindrical section of the heat shield. The main features of transonic flowfield around a bulbous heat shield are illustrated in Fig. 1. The terminal shock waves are an essential feature of transonic flow [8]. As the freestream Mach number increases from subsonic values a shock wave system appears near the shoulder. The flow is called transonic if both subsonic (M < 1) and supersonic (M > 1) regions are present in the field.

The transonic range begins when the highest Mach number reaches unity (M = 1) on the heat shield. The general features of the flow are as present once the sonic velocity occurs at the shoulder and remains throughout the whole transonic range. There is a local supersonic region ahead of the main shoulder shock. The near normal shock wave grows and moves downstream as the freestream Mach number increases. The difficulties to analyze the flowfield are associ‐ ated with the detail design and a quantitative theoretical prediction. For the former, a sufficient wind-tunnel test data is required; the latter is due to nonlinearity of the equation governing transonic flow requires Computational Fluid Dynamics approach. In the boat-tail region, a local separation results, due to sharp discontinuity in the longitudinal of the payload shroud. The regions of flow separation impose additional complexity to aerodynamic and structural design aspects [9] – [13]. The complex flowfield at the transonic speeds is also observed during the experimental investigation of the bulbous heat shield. Experimental studies [14] – [15] have been made to understand flow behavior at transonic Mach numbers. These experimental investigations were limited to the measurement of surface pressure distribution, oil flow patterns, shadowgraphs and schlieren pictures for various heat shield models at transonic Mach number range. Recently analyses of Ares launch vehicle are carried out in the transonic speed and reported in a series of papers by Pinier [16], Piatak et al. [17] and Sekula et al. [18]. The current work reveals the paramount importance of aerodynamics at transonic Mach range.

**Figure 1.** Schematic flowfield on bulbous heat shield at transonic Mach number.

oscillation regimes.

A high-speed flow over a blunt body generates a bow shock wave in front of it, which causes a rather high surface pressure, and as a result, high aerodynamic drag. The surface pressure on the blunt body can be reduced if a conical shock wave is generated by mounting a forward facing spike. The aerospike produces a region of re-circulating separated flow that shields the blunt-nosed body from the incoming flow as shown in Fig. 2. The literature review reveals that addresses the mechanism how the unstable flow is initiated and how it persists [19] – [20]. The combination of the numerical simulations with experimental investigations has found to be a powerful tool to analyze unsteady flow and first results of a renewed investigation of the aerospike problem. The aerospike has been known since the 1950's to cause an unstable flow [21]. Wood [22] has distinguished five different types of flow regimes over spiked cones based on the semi-cone angle and flow characteristics which may correspond to the fluctuation and

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85

Bogdonoff and Vas [23] were the first to identify the two modes of unstable axisymmetric separation, the fluctuation mode and the oscillation mode by varying flat faced and hemi‐ spherical blunt bodies. The flowfield problem associated with the blunt-nosed spike bodies

**Figure 1.** Schematic flowfield on bulbous heat shield at transonic Mach number.

aerospace launch vehicles. Awrejcewicz, and Krysko [4] have developed numerical simulation of a cylindrical panel within transonic ideal-gas flow stream and solved dynamics for all intervals of the frequency. These parameters directly depend on the intensity of the vorticity components of the turbulence, the strength of the shock wave, and the mechanism of their interaction, all of which are implicitly linked to the specific configuration of a bulbous heat shield of a satellite launch vehicle. The numerical flow simulation over a bulbous payload shroud at transonic Mach number range is very useful to decide the geometrical configuration for minimum buffeting load and minimum aerodynamic drag requirement. The terminal shock wave of sufficient strength to interact with the boundary layer can cause flow separation and flowfield may become unstable as observed in the high speed cinematography [5]. Therefore, it is desirable to determine the location of the terminal shock wave on the heat shield and the strength of the terminal shock wave as a function of transonic Mach numbers range. The strength of the terminal shock wave and the mechanism of their interaction are related to the specific configuration of the heat shield satellite launch vehicle. Fluctuations of pressure level in shock waves and in separated flow regions can cause flow instabilities and then leads to buffeting phenomenon [6] – [7]. The features of the transonic flowfield can be delineated through the wind-tunnel data such as schlieren photographs and oil flow patterns. It is characterized by a normal or a terminal shock wave, supersonic pocket on the cylindrical region of the heat shield, shock wave/turbulent boundary layer interaction, and a separation bubble may be caused by the shock wave/turbulent boundary layer interaction on the cylindrical section of the heat shield. The main features of transonic flowfield around a bulbous heat shield are illustrated in Fig. 1. The terminal shock waves are an essential feature of transonic flow [8]. As the freestream Mach number increases from subsonic values a shock wave system appears near the shoulder. The flow is called transonic if both subsonic (M < 1)

The transonic range begins when the highest Mach number reaches unity (M = 1) on the heat shield. The general features of the flow are as present once the sonic velocity occurs at the shoulder and remains throughout the whole transonic range. There is a local supersonic region ahead of the main shoulder shock. The near normal shock wave grows and moves downstream as the freestream Mach number increases. The difficulties to analyze the flowfield are associ‐ ated with the detail design and a quantitative theoretical prediction. For the former, a sufficient wind-tunnel test data is required; the latter is due to nonlinearity of the equation governing transonic flow requires Computational Fluid Dynamics approach. In the boat-tail region, a local separation results, due to sharp discontinuity in the longitudinal of the payload shroud. The regions of flow separation impose additional complexity to aerodynamic and structural design aspects [9] – [13]. The complex flowfield at the transonic speeds is also observed during the experimental investigation of the bulbous heat shield. Experimental studies [14] – [15] have been made to understand flow behavior at transonic Mach numbers. These experimental investigations were limited to the measurement of surface pressure distribution, oil flow patterns, shadowgraphs and schlieren pictures for various heat shield models at transonic Mach number range. Recently analyses of Ares launch vehicle are carried out in the transonic speed and reported in a series of papers by Pinier [16], Piatak et al. [17] and Sekula et al. [18]. The current work reveals the paramount importance of aerodynamics at transonic Mach range.

and supersonic (M > 1) regions are present in the field.

84 Computational and Numerical Simulations

A high-speed flow over a blunt body generates a bow shock wave in front of it, which causes a rather high surface pressure, and as a result, high aerodynamic drag. The surface pressure on the blunt body can be reduced if a conical shock wave is generated by mounting a forward facing spike. The aerospike produces a region of re-circulating separated flow that shields the blunt-nosed body from the incoming flow as shown in Fig. 2. The literature review reveals that addresses the mechanism how the unstable flow is initiated and how it persists [19] – [20]. The combination of the numerical simulations with experimental investigations has found to be a powerful tool to analyze unsteady flow and first results of a renewed investigation of the aerospike problem. The aerospike has been known since the 1950's to cause an unstable flow [21]. Wood [22] has distinguished five different types of flow regimes over spiked cones based on the semi-cone angle and flow characteristics which may correspond to the fluctuation and oscillation regimes.

Bogdonoff and Vas [23] were the first to identify the two modes of unstable axisymmetric separation, the fluctuation mode and the oscillation mode by varying flat faced and hemi‐ spherical blunt bodies. The flowfield problem associated with the blunt-nosed spike bodies can be distinguished by a conical blunt body with a total angles of the conical faces varied from 300 to 1800 [22] or a hemisphere-cylinder body [24]. Kabelitz [25] has observed two distinct unsteady flow modes, namely, oscillation and pulsation [26] in the spike attached to the bluntnosed (flat-faced) cylindrical body. Experimental studies have been focused on identifying the boundaries of the unsteady region. The flow just outside the separated shear layer approaching the body's shoulder can be turned by an attached conical shock, and then the shock structure is stable because an equilibrium condition is reached between escaping and recirculating flows in the separated region. Kistler [27] was the first to make detailed fluctuating wall pressure measurements under the separated supersonic turbulent boundary layer upstream of a forward step.

plished by an attached conical shock wave, a detached strong shock is generated, which pushes high-pressure flow from the reattachment zone at the body's face into the recirculating region of the separated shear layer. This high-pressure flow that gets into the separated flow region inflates the separation bubble, and the shock structure is pumped upstream. This gives rise to self-excited shock oscillations during which the conical fore-shock wave and the accompany‐ ing shear layer oscillate laterally and their shape changes periodically from concave to convex. This type of flowfield is unsteady in nature. The separated shear layer with an inflection point in the velocity profile is inherently unstable [21], and when this hits the body at the reattach‐ ment point selective amplification of the disturbances takes place, and this would cause the surface pressure to fluctuate in the flow separation region. The point of reattachment could be shifting to and fro along the body surface because of these shock oscillations. Because of this unsteady oscillation of the separation bubble, pronounced variations in the locations of separation shock, conical shock wave ahead of the blunt cone, and the reattachment point on the blunt cone surface are observed in different models with identical freestream conditions. Panaras et al. [30] have numerically simulated unsteady flows at high speeds around spikedblunt bodies. The experimental studies are also carried out to know the effect of variations to

The main aim of the present Chapter to analyze the unsteady flow characteristics and wall pressure fluctuations and oscillations over the hemisphere-cylinder, the bulbous payload shroud of a typical satellite launch vehicle and the conical spike attached to the forward facing blunt body. The numerical simulations present glimpse of the instantaneous flowfield features

The Navier-Stokes equations describe the motion of a viscous, heat conducting compressible

density, temperature, and total energy, and *u*, the velocity components. The governing fluid

( ) 0 *<sup>j</sup>*

 dt

> t

+ + -=

r

( ) ( ) 0 *<sup>i</sup> i j ij ij*

( ) ( ) 0 *j i ij j*

+ =

*j u*

*t x* r

*j u uu p t x*

*j*

rr

 r

*E E pu u q t x*

¶ ¶

r

¶ ¶

¶ ¶

, be the coordinates, *p*, *ρ*, *T* and *E* the pressure,

Unsteady Flowfield Characteristics Over Blunt Bodies at High Speed

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87

¶ ¶ (1)

¶ ¶ (2)

+ + - += é ù ë û ¶ ¶ (3)

the spike diameter to blunt body diameter ratio.

**2. Governing fluid dynamics equations**

fluid. In the Cartesian tensor notation, let *x*<sup>j</sup>

dynamics equations can be written as

over various models at high speeds.

**Figure 2.** Schematic flowfield over spiked-blunt body.

For a range of spike lengths the flow can became unsteady with two modes of instability observed. The oscillation mode involves the motion of the fore-shock due to the spike tip. The pulsation mode features a large-scale motion of the bow shock associates with blunt body. Spike length to diameter (*L/D*) ratio of 0.9, half-cone angle of blunt body *70*<sup>0</sup> *, M*<sup>∞</sup> *= 2.21, Re*<sup>D</sup> *= 0.12 × 10*<sup>6</sup> for oscillation modes and *L/D* ratio of *1.0*, half-cone angle of blunt body *90*<sup>0</sup> *, M*<sup>∞</sup> *= 6, Re*<sup>D</sup> *= 0.13 × 10*<sup>6</sup> for the pulsation modes are numerically investigated by Badcock et al. [28]. Feszty et al. [29] have conducted a computational analysis of the pulsation mode using computational fluid dynamics.

Flowfield over a conical spike attached to a blunt body is analyzed to understand the periodic oscillations of flowfield. The laminar Navier-Stokes equations are solved using multi-stage Runge-Kutta time stepping method. If the turning angle of the flow is too large to be accom‐ plished by an attached conical shock wave, a detached strong shock is generated, which pushes high-pressure flow from the reattachment zone at the body's face into the recirculating region of the separated shear layer. This high-pressure flow that gets into the separated flow region inflates the separation bubble, and the shock structure is pumped upstream. This gives rise to self-excited shock oscillations during which the conical fore-shock wave and the accompany‐ ing shear layer oscillate laterally and their shape changes periodically from concave to convex. This type of flowfield is unsteady in nature. The separated shear layer with an inflection point in the velocity profile is inherently unstable [21], and when this hits the body at the reattach‐ ment point selective amplification of the disturbances takes place, and this would cause the surface pressure to fluctuate in the flow separation region. The point of reattachment could be shifting to and fro along the body surface because of these shock oscillations. Because of this unsteady oscillation of the separation bubble, pronounced variations in the locations of separation shock, conical shock wave ahead of the blunt cone, and the reattachment point on the blunt cone surface are observed in different models with identical freestream conditions. Panaras et al. [30] have numerically simulated unsteady flows at high speeds around spikedblunt bodies. The experimental studies are also carried out to know the effect of variations to the spike diameter to blunt body diameter ratio.

The main aim of the present Chapter to analyze the unsteady flow characteristics and wall pressure fluctuations and oscillations over the hemisphere-cylinder, the bulbous payload shroud of a typical satellite launch vehicle and the conical spike attached to the forward facing blunt body. The numerical simulations present glimpse of the instantaneous flowfield features over various models at high speeds.
