Numerical Investigation of the Drag of Rockets at Subsonic, Transonic and Supersonic Speeds

Abstract

To compute the trajectory of a rocket the knowledge of the external aerodynamics and the resulting forces is essential. The drag coefficient is an important parameter in the computation of rocket trajectory in case of vertical ascent. For compressible flows, at subsonic and supersonic velocities, the drag coefficient is a function of the Reynolds number and of the Mach number. Both dimensionless numbers depend on the temperature, however, not in the same way. For that reason, the Mach number dependency and the Reynolds number dependency are different. Since in the atmosphere pressure and temperature are functions of the height, the drag of rockets is also dependent on the height of the rocket in the atmosphere. In this work, the dependence of the drag on the shape of the rocket is investigated at different heights and velocities, i.e. Reynolds and Mach numbers. For this purpose, the historical rocket from Johannes Winkler, the first liquid propulsion rocket in Europe, and a modern rocket geometry were chosen and compared. These rockets were investigated numerically with the commercial Navier–Stokes solver STAR-CCM+. A detailed analysis of the drag coefficient, split into friction, pressure and wave drag was performed at these heights, Mach numbers and Reynolds numbers for the different aerodynamic shapes and rockets. In particular on the transonic and supersonic range the shock wave system leading to the wave drag was analysed in detail. Graphs of the corresponding friction, pressure, wave and total drag coefficients as a function of the Reynolds and as a function of the Mach numbers at different heights and a detailed analysis of these results are shown for the two rockets, the historical and a modern one.