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research-article

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

[+] Author and Article Information
Anna Engels-Putzka

Institute of Propulsion Technology, German Aerospace Center (DLR), Linder Höhe, 51147 Cologne, Germany
anna.engels-putzka@dlr.de

Jan Backhaus

Institute of Propulsion Technology, German Aerospace Center (DLR), Linder Höhe, 51147 Cologne, Germany
jan.backhaus@dlr.de

Christian Frey

Institute of Propulsion Technology, German Aerospace Center (DLR), Linder Höhe, 51147 Cologne, Germany
christian.frey@dlr.de

1Corresponding author.

ASME doi:10.1115/1.4041700 History: Received September 20, 2018; Revised October 04, 2018

Abstract

This paper describes the development and initial application of an adjoint harmonic balance solver. The harmonic balance method is a numerical method formulated in the frequency domain which is particularly suitable for the simulation of periodic unsteady flow phenomena in turbomachinery. Successful applications of this method include unsteady aerodynamics as well as aeroacoustics and aeroelasticity. Here we focus on forced response due to the interaction of neighboring blade rows. In the CFD-based design and optimization of turbomachinery components it is often helpful to be able to compute not only the objective values -- e.g. performance data of a component -- themselves, but also their sensitivities with respect to variations of the geometry. An efficient way to compute such sensitivities for a large number of geometric changes is the application of the adjoint method. While this is frequently used in the context of steady CFD, it becomes prohibitively expensive for unsteady simulations in the time domain. For unsteady methods in the frequency domain, the use of adjoint solvers is feasible, but still challenging. The present approach employs the reverse mode of algorithmic differentiation (AD) to construct a discrete adjoint of an existing harmonic balance solver in the framework of an industrially applied CFD code. The paper discusses implementational issues as well as the performance of the adjoint solver, in particular regarding memory requirements. The presented method is applied to compute the sensitivities of aeroelastic objectives with respect to geometric changes in a turbine stage.

Copyright (c) 2018 by ASME
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