An analytical and numerical study of the interaction of rarefaction waves with area changes in ducts. Part 2: Area enlargements

A quasi-steady flow analysis that is analytical for an inviscid flow of a perfect gas is presented to obtain asymptotic solutions for the flow at late times, after all transient disturbances from the interaction process have subsided. Analytical results are given and discussed for the boundary between the two possible asymptotic wave patterns that are predicted and the corresponding asymptotic strengths of the transmitted, reflected and other waves, all as a function of both the incident rarefaction-wave strength and area-enlargement ratio. This was done for both perfect diatomic gases and air with gamma = 7/5 and perfect monatomic gases with gamma = 5/3. Numerical results obtained by employing the random-choice method to solve the nonstationary equations of motion are presented and discussed for the complete unsteady rarefaction-wave interaction with the area enlargement, for numerous different combinations of rarefaction-wave strengths and area-enlargement ratios.