Flow Topology Optimization at High Reynolds Numbers Based on Modified Turbulence Models

TL;DR

This paper advances flow topology optimization for high-Reynolds-number turbulent flows by developing modified turbulence models and strategies for modeling solids, enabling effective aerodynamic design at Reynolds numbers up to one million.

Contribution

It introduces a new approach to apply flow topology optimization to turbulent flows at high Reynolds numbers, including a modified turbulence model and a solid recognition method.

Findings

Validated the modified turbulence model at Re up to one million.

Proved the effectiveness of the ToOpt method on a rotor-like geometry.

Developed a strategy for setting Darcy's source term based on flow variables.

Abstract

Flow topology optimization (ToOpt) based on Darcy's source term is widely used in the field of ToOpt. It has a high degree of freedom and requires no initial configuration, making it suitable for conceptual aerodynamic design. Two problems of ToOpt are addressed in this paper to apply the ToOpt method to high-Reynolds-number turbulent flow. First, the relationship between the minimum magnitude of Darcy's source term needed to model the solid and the characteristic variables of the flow (freestream velocity, length scale and fluid viscosity) at high Reynolds numbers is quantitively studied. A strategy for setting Darcy's source term is then proposed. Second, the modified Launder - Sharma k-e (LSKE) model with modification terms related to Darcy's source is developed. The ToOpt of a low-drag profile in turbulent flow is studied using the new model. The model is validated to reflect the influence of solids on turbulence even at Reynolds numbers as high as one million. Finally, a wall-distance computation method that can recognize the solid modeled by Darcy's source term is developed and integrated into the modified shear stress transport (SST) turbulence model. The ToOpt of a rotor-like geometry, which is of great importance in aerodynamic design, is conducted using the modified SST model, proving the model's ability to handle the ToOpt of turbomachinery.