Title:
The Extension of Analytic Hypersonic Force Coefficients for Conceptual Design Using the Divergence Theorem

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Grant, Michael J.
Braun, Robert D.
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Abstract
This study investigates the type and performance of analytic Newtonian aerodynamic solutions made possible using the Divergence Theorem. A reformulation of the Newtonian surface pressure calculation enables a mathematically equivalent divergence calculation to be performed as a substitute. This manipulation enables analytic force coefficients to be derived for shapes of increasing complexity while also reducing computational cost when compared to existing analytic solutions. The divergence solutions are obtained by converting the physical flow field into a mathematical flow field that is constant in direction but with magnitude that is equivalent to the Newtonian pressure coefficient. This unique property allows various mathematical techniques that are not available with the traditional Newtonian calculation to be performed that further reduce computational cost. The results of this investigation enable the construction of analytic relations for new hypersonic configurations of interest, and this approach serves as the foundation to construct efficient hybrid exact-approximate solutions for more complex configurations. Comparisons of the current analytic database to a state-of-the-art hypersonic design tool illustrate the computational advantages of the analytic relations to support hypersonic conceptual design.
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2012-08
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