Numerical analysis of homogeneous condensation in rarefaction wave in a shock tube by the space-time CESE method

A detailed numerical investigation has been carried out for the homogeneous condensation of water vapor in a non-stationary rarefaction wave generated in a shock tube. The space-time CESE method has been adopted to simulate the mutual interaction of condensation with the rarefaction wave for an extremely long time. It is found that the homogeneous condensation in the rarefaction wave has a significant influence on the flow due to the latent heat release and the continuous change of cooling rate. Three stages can be defined in this process: the initial stage which contains the onset of the condensation and the formation of the condensation shock waves in both downstream and upstream directions, the oscillating stage which is characterized as the repeat of quench and onset of condensation in the expansion fan approximately in a logarithm time manner, and the asymptotic stage which the oscillating waves are damping out with time and no apparent condensation shock wave is formed.