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

A. L. Gaitonde*, D. P. Jones

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)

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 accuracy of the original system. Preliminary work carried out in this area is presented. Results of calculations for heave, pitch and ramp test cases are presented.

Translated title of the contributionThe use of pulse responses and system reduction for 2D unsteady flows using the Euler equations
Original languageEnglish
Pages (from-to)483-492
Number of pages10
JournalThe Aeronautical Journal
Volume106
Issue number1063
Publication statusPublished - Sep 2002

Bibliographical note

Publisher: The Royal Aeronautical Society

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