Stability-analysis-based optimization to control flow separation over a diffusing passage

Abstract

We present a stability-analysis-based optimization approach that minimizes the growth rate of the least stable mode associated with the flow structure governing flow separation. We compare this approach with a classic optimization approach that minimizes an integral function related to pressure loss. We analyze both approaches on a two-dimensional model that mimics the diffusing passage present in the aft portion of the suction side of a low-pressure turbine. This zone is prone to boundary layer detachment at low Reynolds numbers, while fully attached flow is present at higher Reynolds numbers. The goal of the optimization is to design a local blowing technique to prevent boundary layer detachment at low Reynolds numbers and thereby reducing the dynamic head pressure loss with a minimum energy input. We simulate the problem using the compressible Reynolds-averaged Navier–Stokes equations (with the k–ω turbulence model) and perform a stability analysis on the mean flow. We then use the stability information and associated sensitivity (through adjoints) to provide insights into local blowing and thereby guide the optimization. The two optimization strategies use the blowing location, blowing rate, and blowing angle as the optimization variables. The first strategy minimizes a classic global integral function, including input and output pressure losses. The second approach minimizes the amplification rate of the least stable eigenvalue resulting from a stability analysis. The targeted mode governs the detached recirculation, and stabilizing its amplification rate leads to attached flow and minimum losses. Indeed, both strategies lead to attached flows and similar optimal values for the blowing location and to enhanced performance. It is concluded that the stability-analysis-based optimization provides results comparable to those from a classic optimization approach and can be useful for cases where there is no clear integral functional to guide the optimization procedure (e.g., pressure loss).