Feasibility Study of Constant Eddy-Viscosity Assumption in Gradient-Based Design Optimization

Abstract

A feasibility study is carried out by investigating the effects of a usual assumption of constant turbulent eddy viscosity on the aerodynamic design using an adjoint variable method, one of the most efficient gradient-based optimization techniques. Accurate unsteady and steady flow analyses are followed by the aerodynamic sensitivity analysis for the Navier–Stokes equations coupled with two-equation turbulence models. A challengeable approach for high-lift design optimization at higher angles of attack is also proposed, which is based on unsteady sensitivity analysis using a dual time-stepping method and the chimera overset grid scheme. Through the comparison of the sensitivity gradients with respect to all of the design variables including angle of attack, it is observed that the constant turbulent eddy-viscosity assumption might provide inaccurate gradients in sensitivity analyses such as transonic airfoil with a strong shock and high-lift airfoil at a high angle of attack close to stall angle. Simultaneously, however, the final design results indicate that both approaches are acceptable in engineering applications. Both the single- and multi-element airfoil design optimizations using the constant eddy-viscosity assumption are carefully assessed in terms of design accuracy, computer memory overheads, and total design time in various design examples.