Remarks on Unsteady Newtonian Flow Theory

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Abstract
Summary: Unsteady high Mach number flows past oscillating cones and oscillating wedges are studied according to Newtonian impact theory, with and without centrifugal force corrections. It is found that, contrary to existing theories, the centrifugal force contribution in unsteady flow is significant and not negligible; for example, it contributes one-half to the dynamic stability derivatives of an oscillating wedge and one-third to that of an oscillating cone. It is also shown that in both cases the dynamic stability derivatives calculated by Newtonian impact theory with centrifugal force correction agree exactly with those obtained by gas-dynamic theory in the double limit γ → 1 and M∞ → ∞, independently. These conclusions are expected to hold for more general three-dimensional unsteady Newtonian flow when the Newtonian shock layer is attached.

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