Unsteady adjoint of pressure loss for a fundamental transonic turbine vane

TL;DR

This paper investigates the use of unsteady adjoint methods with large eddy simulations to optimize pressure loss predictions in transonic turbine vanes, highlighting challenges with turbulence and potential solutions like artificial viscosity.

Contribution

It demonstrates the effectiveness and limitations of unsteady adjoint methods in high-fidelity turbomachinery simulations, and proposes energy-based metrics to identify divergence regions.

Findings

Unsteady adjoint captures gradients for short time intervals effectively.

Long-term averaged objectives cause adjoint divergence due to turbulence.

Artificial viscosity can help stabilize adjoint solutions.

Abstract

High fidelity simulations, e.g., large eddy simulation are often needed for accurately predicting pressure losses due to wake mixing in turbomachinery applications. An unsteady adjoint of such high fidelity simulations is useful for design optimization in these aerodynamic applications. In this paper we present unsteady adjoint solutions using a large eddy simulation model for a vane from VKI using aerothermal objectives. The unsteady adjoint method is effective in capturing the gradient for a short time interval aerothermal objective, whereas the method provides diverging gradients for long time-averaged thermal objectives. As the boundary layer on the suction side near the trailing edge of the vane is turbulent, it poses a challenge for the adjoint solver. The chaotic dynamics cause the adjoint solution to diverge exponentially from the trailing edge region when solved backwards in time. This results in the corruption of the sensitivities obtained from the adjoint solutions. An energy analysis of the unsteady compressible Navier-Stokes adjoint equations indicates that adding artificial viscosity to the adjoint equations can potentially dissipate the adjoint energy while potentially maintain the accuracy of the adjoint sensitivities. Analyzing the growth term of the adjoint energy provides a metric for identifying the regions in the flow where the adjoint term is diverging. Results for the vane from simulations performed on the Titan supercomputer are demonstrated.