Improved Wave Diagram Procedure for Shock Reflection from an Open End of a Duct

Recently derived improved boundary conditions for the reflection of weak shock waves from an open end of a duct can be well approximated by a centered expansion wave if the center of the later is located on the leading characteristic of the reflected wave and some distance e outside the duct. A relation is derived between e/D (D is the duct diameter), the shock pressure ratio p1/p0, and γ (the ratio of specific heats). This relationship is represented with sufficient accuracy by the empirical formula eD=(0.90+0.677(p1/p0)−1)(γ+1.08)−3.8. This result makes it possible to apply the improved boundary conditions without losing the convenience of of the customarily used wave diagram procedure.