The transient flow field near the surface of a substrate impacted by a pulsating supersonic jet emerging from a long tube is investigated using a simplified axially symmetric numerical approach. In the system being modeled, the pulses are created using a rotary valve located at the tube entrance. This flow situation approximates the conditions existing in the Shock-Induced Cold Spray process for coating surfaces with metallic particles. Previous numerical studies of transient supersonic jets either focused on jets emerging from orifices or did not give details of the complex supersonic flow field in the jet impact region. The current approximate numerical method considers the flow within the long tube and in the jet impact region. The procedure involves two stages. The upstream pressure variation with time is first determined using a one-dimensional compressible flow approximation of the entire tube and rotary valve arrangement. The resulting pressure versus time curve serves as the transient inlet boundary condition for an axially symmetric computational fluid dynamic solution of the flow through the tube and region of jet impact on the substrate. The numerical solutions of substrate pressure on the jet centerline versus time are compared with available experimental results and predict certain general features of the substrate pressure traces. Although the simplified model is only in fair agreement with some aspects of the experimental curves, it is shown to be useful in explaining certain peculiar flow features. With the aid of the numerical solution, an explanation for the movement and instability of the bow shock wave which forms ahead of the substrate is described.

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