Shock Wave Reflections in Pseudosteady Flows

A shock wave that is propagating with a constant velocity with respect to the laboratory frame of reference could be investigated using steady flow concepts and theories by attaching a frame of reference to it. In such a frame of reference, the shock wave is stationary, and the entire flow field is known as either pseudostationary or pseudosteady. The just-mentioned transformation, known as the Galilean transformation, is shown schematically in Fig. 3.1. In Fig. 3.1a a constant velocity shock wave having a velocity of VS is seen to propagate from left to right, towards a flow having a velocity Vi and to induce behind it a flow velocity Vj. The velocities with respect to a frame of reference attached to the shock wave are shown in Fig. 3.1b. In this frame of reference the flow in state (i) propagates towards the stationary shock wave with the velocity ui = VS − Vi. Upon passing through the shock wave its velocity is reduced to uj = VS − Vj. The velocity field shown in Fig. 3.1b is obtained actually by superimposing a velocity equal to the shock-wave velocity but opposite in its direction on the velocity field shown in Fig. 3.1a. The flow field of Fig. 3.1b is pseudosteady, and hence can be treated using the steady flow theories.