Employing the Time Domain Unsteady Discrete Adjoint Method for Shape Optimization of 3D Multi-row Turbomachinery Configurations

[+] Author and Article Information
Georgios Ntanakas

Rolls-Royce Deutschland, Blankefelde-Mahlow, Germany; National Technical University of Athens, School of Mechanical Engineering, Lab of Thermal Turbomachines, Athens, Greece

Marcus Meyer

Rolls-Royce Deutschland, Blankefelde-Mahlow, Germany

Kyriakos Giannakoglou

National Technical University of Athens, School of Mechanical Engineering, Lab of Thermal Turbomachines, Athens, Greece

1Corresponding author.

ASME doi:10.1115/1.4040564 History: Received December 03, 2017; Revised June 12, 2018


In turbomachinery, the steady adjoint method has been successfully used for the computation of derivatives of various objective functions with respect to design variables in gradient-based optimization. However, the continuous advances in computing power and the accuracy limitations of the steady state assumption lead towards the transition to unsteady CFD computations in the industrial design process. Previous work on unsteady adjoint for turbomachinery applications almost exclusively rely upon frequency-domain methods, for both the flow and adjoint equations. In contrast, in this paper, the development the discrete adjoint to the URANS solver for 3D multi-row applications, in the time-domain, is presented. The adjoint equations are derived along with the adjoint to the 5-stage Runge-Kutta scheme. Communication between adjacent rows is achieved by the adjoint sliding interface method. An optimization workflow that uses unsteady flow and adjoint solvers is presented and tested in two cases, with objective functions accounting for the transient flow in a turbine vane and the periodic flow in a compressor three-row setup.

Rolls-Royce plc
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