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Calculation of compressible indicial response

Published online by Cambridge University Press:  04 July 2016

S. T. Shaw  and
N. Qin
S. T. Shaw
Affiliation:
Centre for Computational Aerodynamics, Cranfield College of Aeronautics, UK
N. Qin
Affiliation:
Centre for Computational Aerodynamics, Cranfield College of Aeronautics, UK
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Abstract

The present paper addresses the problem of extracting indicial response functions from solutions of the Navier-Stokes equations. Two approaches are considered.

In the first, the indicial response is computed directly by modifying the local grid velocity to reflect the step change in plunge velocity. The computed data are then fitted using an assumed form for the response function and numerical optimisation techniques.

In the second (indirect) approach, the general form of the lift transfer operator is determined analytically from the functional form of the assumed response. Using the lift transfer operator explicit solutions of the in-phase and quadrature components of the normal force time history can be obtained. The unknown coefficients in the response function are then extracted from computed data for harmonic motion by fitting the time history using the explicit solution.

Computed response functions are presented for a range of Mach numbers and are compared with analytical results and indicial models currently used within the rotorcraft community. For the cases considered there is no significant difference between the response functions determined using the direct or indirect approach. Comparison of the computed results with existing models suggests that generalisation of the response to step changes in incidence using a two-pole approximation of the circulatory response together with the Prandtl-Glauert factor is not possible. However, comparison with higher order semi-empirical models is much improved, providing some justification for the use of such models. In addition to these observations, the extracted response functions suggest improvements to piston theory to account for thickness effects. The proposed modification of piston theory is based upon properties of the static pressure distribution and so can be used in conjunction with both CFD and experimental data.

Type
Research Article
Information
The Aeronautical Journal , Volume 104 , Issue 1042 , December 2000 , pp. 665 - 673
Copyright
Copyright © Royal Aeronautical Society 2000 

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