Trajectories of Shock-Wave and Contact Surface in Real Shock-Tube Flow

摘要

The deviation of shock velocity and contact surface velocity from the ideal velocities in low pressure shock tubes has been investigated analytically. Viscous effects and heat conduction to the shock tube walls have been taken into account. Momentum and continuity equations have been applied to a control volume fixed with respect to the contact surface. By using Mirels' solutions for the boundary layer thickness, the algebraic system can be solved for the unknown shock velocity and contact surface velocity by interation. In this interative process the gas properties and boundary layer properties in the n-th iteration are assumed to depend on the shock velocity and contact surfaces velocity of the (n-1)-th iteration. Flow nonuniformities and real gas effects have been taken into account in the form of a correction factor derived from Connor and Anderson. The change of shock velocity as well as the change of contact surface velocity have been considered, thus giving the trajectories of shock wave and contact surface as functions of initial conditions, shock tube geometry and gas properties. It has been found that both the shock wave and the contact surface decelerate. This result agrees with previous experimental investigations by Anderson and Kelly. (Author)