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The use of pulse responses and system reduction for 2D unsteady flows using the Euler equations

Published online by Cambridge University Press:  04 July 2016

A. L. Gaitonde  and
D. P. Jones
A. L. Gaitonde
Affiliation:
Department of Aerospace Engineering, University of Bristol, UK
D. P. Jones
Affiliation:
Department of Aerospace Engineering, University of Bristol, UK
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Abstract

This paper describes the application of the theory of pulse responses to a linearised Euler scheme on a moving grid. The impulse responses of such a linear system are memory functions or temporal representations of the manner in which, and the time over which a perturbation remains active in the response of the system. The exact response of the linear system to an arbitrary input can then be predicted via convolution. The linearised Euler scheme is derived from a full nonlinear Euler method based on Jameson’s cell-centred scheme which has been modified to make it time-accurate and has the necessary terms to account for grid motion. The discrete form of the full Euler equations are linearised about the corresponding nonlinear steady mean flow assuming the unsteadiness in the flow and grid are small. The resulting set of differential equations for the flow perturbations are solved at each time step using a dual-time scheme. These equations can be easily solved to obtain pulse responses, which capture the entire frequency content of the linear system. These pulse responses then provide a simple and efficient method for calculating the system response to many different inputs via convolution. A further use of the pulse responses is their potential to allow a reduced-order linear model to be constructed, which preserves some of the accuracyof the original system. Preliminary work carried out in this area is presented. Results of calculations for heave, pitch and ramp test cases are presented.

Type
Research Article
Information
The Aeronautical Journal , Volume 106 , Issue 1063 , September 2002 , pp. 483 - 492
Copyright
Copyright © Royal Aeronautical Society 2002 

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