AN INTEGRAL SOLUTION TO THE FLAT-PLATE LAMINAR BOUNDARY-LAYER FLOW EXISTING INSIDE AND AFTER EXPANSION WAVES AND AFTER SHOCK WAVES MOVING INTO QUIESCENT FLUID WITH PARTICULAR APPLICATION TO THE COMPLETE SHOCK-TUBE FLOW

摘要

A solution to the unsteady two-dimensional laminar boundary-layer flow inside centered expansion waves and behind both centered expansion waves and shock waves is obtained by utilizing an extension of the Karman-Poblbausen method. The Prandtl unsteady-boundary-layer equations are integrated normal to the surface bounding the flow and are transformed into a conical coordinate system. The resulting hyperbolic differential equations are integrated in closed form for flow- behind shock waves and by numerical methods for the flow inside or following expansion waves. An integral technique is applied at the discontinuities existing at the trailing edge of the expansion fan and at contact discontinuities (entropy discontinuities) so that the characteristic solutirn may proceed across these discontinuities.