**7. Conclusions**

The numerical simulations are carried out over the hemisphere-cylinder model and the bulbous heat shield of a satellite launch vehicle at transonic Mach number. The time-dependent compressible axisymmetric Navier-Stokes equations are solved employing multi-stage Runge-Kutta time-stepping scheme with Baldwin-Lomax turbulence model. The pressure fluctua‐ tions are computed at different location on the model. The unsteady flowfield characteristics are analyzed using fast Fourier transform. The numerical analysis also includes the numerical flow visualization and comparison with the available experimental data.

The key concern of research into the area of protruding spikes ahead of blunt bodies is the unstable flow that has been observed to exist for particular families of blunt bodies in super‐ sonic and hypersonic flow. The length of the spike had an impact on the frequency and mode of oscillations. In this study the spike length was the principle parameter of variation on both flat faced and hemispherical blunt bodies. To this point, the focus of numerical simulations had remained on the effects that variation to the spike length and blunt body profile had on the resulting flow. Research into spike tipped blunt bodies has typically focused on variations to two main design variables; the length of the spike relative to the diameter of the blunt body, and the geometric shape of the blunt body itself. This research has drawn conclusions about the different flow regimes and the relative spike lengths that this is observed to occur for specific flow conditions. It is the objective of this project to contribute to this understanding by analyzing the effect that variations to the spike diameter relative to the blunt body diameter have on the characteristics of the flow. The numerical analysis is extended to simulate the flow over spiked-blunt body under laminar condition. The numerical simulations captured pressure oscillations in the separation region. A limit cycle is obtained that describes the selfsustained oscillation of Van der Pol equation.

### **Nomenclature**

d(Cp)/dt

**Figure 25.** Phase trajectory, *M*∞ *= 6.8* and *L/D = 0.5*.

112 Computational and Numerical Simulations

sustained oscillation of Van der Pol equation.

**7. Conclusions**

Cp Cp Cp

The numerical simulations are carried out over the hemisphere-cylinder model and the bulbous heat shield of a satellite launch vehicle at transonic Mach number. The time-dependent compressible axisymmetric Navier-Stokes equations are solved employing multi-stage Runge-Kutta time-stepping scheme with Baldwin-Lomax turbulence model. The pressure fluctua‐ tions are computed at different location on the model. The unsteady flowfield characteristics are analyzed using fast Fourier transform. The numerical analysis also includes the numerical

The key concern of research into the area of protruding spikes ahead of blunt bodies is the unstable flow that has been observed to exist for particular families of blunt bodies in super‐ sonic and hypersonic flow. The length of the spike had an impact on the frequency and mode of oscillations. In this study the spike length was the principle parameter of variation on both flat faced and hemispherical blunt bodies. To this point, the focus of numerical simulations had remained on the effects that variation to the spike length and blunt body profile had on the resulting flow. Research into spike tipped blunt bodies has typically focused on variations to two main design variables; the length of the spike relative to the diameter of the blunt body, and the geometric shape of the blunt body itself. This research has drawn conclusions about the different flow regimes and the relative spike lengths that this is observed to occur for specific flow conditions. It is the objective of this project to contribute to this understanding by analyzing the effect that variations to the spike diameter relative to the blunt body diameter have on the characteristics of the flow. The numerical analysis is extended to simulate the flow over spiked-blunt body under laminar condition. The numerical simulations captured pressure oscillations in the separation region. A limit cycle is obtained that describes the self-

flow visualization and comparison with the available experimental data.


#### **Subscripts**

*D* = diameter *rms* = root-mean-square *t* = turbulent ∞ = freestream **Superscripts** − = time mean ' = turbulent fluctuation
