A gas flow field behind a normal shock wave inflicts a step function in velocity, temperature, and pressure upon a polydisperse spray suspended in the flow. As a result, there are large differences in velocity and temperature between the carrying gas and the droplets of the spray immediately after the shock. These differences gradually decrease in a relaxation zone which ends at a distance, where the so-called far-field begins, at which the droplets eventually travel at a velocity which is close to the host fluid velocity. Thus, the investigation of the relaxation zone may be regarded as the analysis of a near-field problem in contradistinction to far-field problems that have been analyzed by Greenberg, Tambour and their coworkers employing a sectional approach. Treatment of a near-field problem via a sectional approach requires derivation of new generalized sectional-equations that extend the previous sectional-equations that were derived by Tambour for far-field problems. Such new generalized sectional-equations are derived in the present paper. They rigorously account for the heritage of momentum and enthalpy that droplets carry with them as they “move” from one size section to another due to evaporation and coalescence processes, for example, a large droplet formed by coalescence (of two small droplets) will differ from the originally large droplets since the properties of the newly formed droplet depend on the properties of the small droplets which participate in the coalescence process, and generally in the near-field, small droplets differ in velocity and enthalpy from large ones. These effects, as well as the influence of the velocity lag between droplets and the most fluid, between droplets of various sizes, and between droplets of the same size on the evolution in pointwise droplet size distributions along the axial direction are presented here. The computed results also include changes of velocities and temperatures of each droplet size-section in the relaxation zone.
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