Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow

Abstract

Analytical indicial aerodynamic functions are calculated for a number of trapezoidal wings in subsonic flow, with Mach number 0.3 ≤ Ma ≤ 0.7. The formulation herein proposed extends well-known aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. First, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state of the art computational fluid dynamics solvers as cross validated benchmark. Indicial functions are calculated for a step change in angle of attack and for a sharp edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following the encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories.

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ORCID for Andrea Da Ronch: orcid.org/0000-0001-7428-6935

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