Influence of Viscosity Coefficient Variation in Discrete Adjoint Method

The economy of aircraft has received more and more attention, and the influence of the constant viscosity assumption in discrete adjoint system on the optimization would no longer be ignored. In this paper, we studied the influence of constant viscosity assumption on the stability of the adjoint equation and gradient accuracy. In the viscosity coefficient variation, the laminar viscosity was treated by the Sutherland criterion and the turbulence viscosity was studied by the SA and SST turbulence model, respectively. The ONERA M6 case was adopted to make comparisons of the convergence history of the adjoint equation and the gradient accuracy. The convergence history showed that the viscosity coefficient variation did not significantly affect the stability of the adjoint equation. The gradient variation due to the viscosity coefficient variation at the shock wave separation region was very distinct from the shock-free region, indicating that the viscosity variation could not be ignored in the design problems with large viscous effects, such as shock wave boundary layer interference separation. To furtherly research the influence of the constant viscosity assumption on the aerodynamic optimization design, the optimization benchmark CRM was carried out firstly with the constant viscosity assumption, then restarted with the viscosity variation in second stage. It was presented that the optimization results in second stage could furtherly improve the aerodynamic performance of the aircraft, demonstrating that the variation of the viscosity coefficient also had a significant effect on the shock-free region. From the assessment above, the viscosity variation could significantly improve the accuracy in gradient computation, maintaining the computational stability and convergence. Therefore, the assumption of constant viscosity was not suitable for the high-fidelity aircraft design.