Interaction of rarefaction waves with area reductions in ducts

An analytical and numerical study is conducted on the interaction of a rarefaction wave with a gradual, monotonic area reduction of finite length in a duct producing transmitted and reflected rarefaction waves. After determining domains and boundaries between four different wave patterns that occur at late times (after all local transient disturbances from the interaction process have subsided) by means of a quasi-steady flow analysis which is analytical for an inviscid perfect gas flow, the final constant strengths of the transmitted, reflected, etc. waves are shown as a function of both the incident rarefaction wave strength and area reduction ratio for diatomic gases (and air) having a specific heat ratio of 7/5. The random choice method was then used to numerically solve the conservation equations governing the one-dimensional, nonstationary gas flow for many different combinations of rarefaction wave strength and area reduction ratio.