Sensitivity Analysis for Forced Response in Turbomachinery Using an Adjoint Harmonic Balance Method

Journal of Turbomachinery

2019

This paper describes the development and initial application of an adjoint harmonic balance (HB) solver. The HB 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 simulation-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 computational fluid dynamics (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 HB 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.

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

Engels-Putzka¹,

Backhaus

Journal of Turbomachinery

2019

Forced Response Sensitivity Analysis Using an Adjoint Harmonic Balance Solver

Engels-Putzka

Backhaus

Volume 2C: Turbomachinery

2018

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 implemen-tational 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.

Adjoint Process Chain for Forced Response Analysis Using a Harmonic Balance Method

Engels-Putzka

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

2017

Self Cite

This paper describes the setup and validation of a process chain for aeroelastic sensitivity analysis using adjoint methods. In particular, the adjoint of an harmonic balance solver is applied to capture unsteady effects. The interaction between different blade rows is simulated by an "external" coupling of the adjoint harmonic balance solver with a steady adjoint solver. The adjoint process is applied to a turbine stage and the results are compared to finite differences of forward computations. KEYWORDS AEROELASTICITY, FORCED RESPONSE, HARMONIC BALANCE, ADJOINT METHODS NOMENCLATURE Symbols i complex unit F mod modal force F Fourier transform k harmonic index K number of higher harmonics m circumferential mode order N number of sampling points q vector of conservative flow variables x vector of grid coordinates ω angular frequency Abbreviations HB harmonic balance CEV constant eddy viscosity VEV variable eddy viscosity