Energy Deposition/Absorption Effects on a Planar Shock Wave

Abstract

E NERGY deposition for modification of the external flowfield around a vehicle is a well-known technique and has been studied and used to reduce the drag on the objectsflying at supersonic speeds. Since the 1950s, energy deposition in the supersonic flow was proposed as an alternative technique to reduce drag on flying objects [1,2]. Many papers discuss the significant drag decrease by energy deposition in front of an object. Analytical, numerical, and experimental studies were reported [3–11]. Many energy deposition applications share the same flowfield structure: in front of a shock wave, energy is deposited and results in large pressure changes behind the shock wave. This note aims to analytically study a simplified, yet related, one-dimensional problem, which is shown in Fig. 1. In front of a stationary planar normal shock wave, there is a region (with lengthL) in which energy is deposited or absorbed. There are three regions in the flowfield: the predeposition region 1, the preshock and postdeposition region 2, and the postshock region 3. Between regions 1 and 2, energy is deposited/absorbed with a strength of _ Q. The properties in each region can be considered constant. This note aims to obtain the preshock energy deposition/absorption effects on the postshock properties. This problem has applications in external flows, such as the drag reduction for flying objects, and in internal flows, such as supersonic, heated/cooled gas into a combustor.