Theoretical and Numerical Analysis of Shock Wave Propagation Through Different Dusty-Gas Mixture Layers.

Two-Phase dusty-gas shock wave propagation through regions of non-uniform particle loading is studied theoretically and numerically. Two problems were investigated: the first is that of a dusty-gas stock reflected from a rigid wall and the second is that of a dusty-gas shock passing through regions of non-uniform dust loading. In the numerical approach, a method based on the Roe and backward difference schemes was developed to solve the one dimensional unsteady dusty-gas flow equations providing smoother solutions than previous numerical studies of these problems. A novel feature of the present study is that using an analytical approach, based on equilibrium flow theory, the study state flow structure was found and compared to the numerically computed structure to provide partial validation for the numerical calculations. For fully dispersed dusty-gas shock waves, a new artificial weak compression method which does not require preliminary ad hoc guesses was developed to create the deviations between the gas and the particle flow properties behind the shock needed to initiate the numerical integration. To find the transmitted shock strength for a dusty-gas shock propagating through a region of non-uniform dust loading, a linearized method and an iterative (exact) method, which has been used in the pure gaseous case, were extended and applied to the dusty-gas mixture flows. Also, based on the iterative method, it was possible to prove that when the dust loading ahead of the dusty-gas shock becomes infinite the problem of shock propagation becomes identical to the shock reflection problem, thus providing a new connection between the interface and reflection problems.PhDAerospace engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161521/1/8720252.pd