On a Class of Multi-Shock Interactions in a Perfect Gas

Abstract

SummaryThe paper deals with a class of shock-wave systems that are of importance in the design and operation of supersonic intakes. It is shown that, when n− 1 wedge shocks, all of the same family, meet at a point, together with a tail shock and a bow shock, then the equations of motion which describe the flow near the shock confluence or junction are reducible to a polynomial equation of degree 10. Numerical results are obtained for the special case of the four-shock confluence and it is shown that, the number of solutions of physical interest, m4, may be 0, 2 or 4. It is found that the m4=0 solution can be interpreted physically in three different ways. These are a Guderley type flow, a confluence of three shocks with a Prandtl-Meyer expansion fan or the appearance of a shock system containing more than one confluence point. The methods developed also permit the discussion of multi-confluence wave systems and a number of examples are given. Finally, the Prandtl-Meyer compression fan is brought within the scope of the method by approximating it with a system of shock waves of weak intensity and minimum entropy.