On the Stability of Gradient Based Turbulent Flow Control without Regularization

TL;DR

This paper examines the challenges of using adjoint-based gradient methods for turbulent flow control, highlighting issues with sensitivity growth and computational overflow in long control horizons.

Contribution

It demonstrates the instability of gradient-based turbulence control methods without regularization, especially over extended control periods, using adjoint solvers and sensitivity analysis.

Findings

Large control horizons cause sensitivity values to grow excessively.

Sensitivity growth leads to computational overflow issues.

Adjoint methods face stability challenges in turbulent flow control.

Abstract

In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and direct numerical simulations. Optimization results obtained with round and plane jet configurations are presented. The results indicate that using large control horizons poses a serious problem for the control of turbulent flows due to existence of very large sensitivity values with respect to control parameters. Typically these sensitivities grow in time and lead to arithmetic overflow in the computations. This phenomena is illustrated by a sensitivity study performed with an exact tangent-linear solver obtained by algorithmic differentiation techniques.