Discrete Adjoint-based Optimization Methodology And Applied Research For Laminar Flow Wing

Nowadays,laminar flow technique is one of the most promising drag reduction approaches,so it is urgent to develop an efficient and reliable design approach to promote the development of laminar flow technique.The gradient-based optimization algorithm using discrete adjoint approach is one of the most efficient ways to handle the industrial design problem,which involves thousands of design variables.For the fully turbulent flow,the gradient-based optimization algorithm using discrete adjoint approach has been developed maturely and widely used.However,the gradient-based optimization algorithm incorporating laminar-to-turbulent transition is subject to the complexity of the transition phenomenon,the numerical noise effect introduced by the transition prediction method in the design space,and the low accuracy,low efficiency,huge memory usage and etc.when solving the coupled-adjoint equations.The relevant theoretical system needs to study more.In this paper,the RANS solver and several transition prediction approaches are coupled,and the reliable transition prediction approaches based on the wind tunnel test calibration is developed.Then,the Jacobian-free fashion,hybrid automatic differentiation algorithm,and LBGS(Linear Block Gauss-Seidel)/CK(Coupled Krylov)algorithms are used to solve the coupled adjoint equations incorporating laminar-to-turbulent transition accurately and efficiently.Finally,the gradient-based optimization framework for laminar flow wing is constructed based on the coupled adjoint equations,and it is successfully applied in the drag reduction for the two-dimensional airfoils,quasi three-dimensional,and three-dimensional laminar flow wings.The main contributions and conclusions are summarized as follows:1)Reliable and robust transition prediction approaches,which can be used for industrial applications,are developed by coupling RANS solver and transition prediction module.The transition prediction module involves linear stability theory and the transition criterion based on boundary layer characters.A transonic wind tunnel test for a large swept-wing configuration is carried out,and it is used to calibrate the limiting N factors.The results have supplemented the international limiting N factors diagram for similar cases.The RANS-BLCode-LST and RANS-BLCode-AFT/Cl transition prediction methods have been verified by the transonic wind tunnel test,the NLF(2)-0416 airfoil and NLF(2)-0415 wing.Both the TS wave and the CF vortices-induced transition phenomenon can be accurately captured,and the prediction error of the transition position is not more than 5%chord length.Related research has laid a theoretical foundation for the development of the gradient-based optimization method for laminar flow wing.2)A reliable,accurate and efficient discrete adjoint-based laminar flow wing optimization framework is developed,which considers both TS waves and CF vortices instabilities.The smoothed intermittency function and transition locations convergence criterion(O(10-6))are proposed to remove the numerical noise,ensuring the smoothness of the design space.The smooth design space improves the performance of gradient-based algorithm.Then,the Jacobian-free fashion and hybrid reverse automatic differentiation appreared to construct the fully analytic-style coupled-adjoint equations.The whole procedure avoids using finite difference and complex differentiation,which exist in the current coupled-adjoint equations.These techniques ensure the gradient information solved efficiently and accurately.The storage requirement is lowered obviously.The study on the laminar flow wing shows that CK algorithm can save 84.4%time compared with the LBGS method.With the other optimization-related technologies,an efficient and robust gradient-based optimization system for laminar flow wing is established and can handle the problem involving both TS waves and CF vortices instabilities.3)The design conditions of Cessna 172 Skyhawk and Honda Jet are selected to study laminar flow airfoils optimization.The TS waves dominate transition for airfoils.The single-point optimization for Cessna 172 Skyhawk design condition gains 75.7%and 73.4%chord laminar region on the upper and lower surface,respectively.The total drag is reduced by 52.27%compared with the initial airfoil.The multi-point optimization for Honda Jet design condition improves the comprehensive performance significantly compared with the initial airfoil,and the total drag at different conditions are reduced by 28.64%,47.0%,9.5%,and 33.85%,respectively.The optimization results conclude that an effective trade-off between viscous drag,pressure drag,and shock wave drag is the key to exploit the potential of the laminar flow drag reduction fully.With the boundary layer information,including momentum thickness,displacement thickness,etc.,the drag reduction mechanism of viscous and pressure drag is revealed.The study verifies the applicability of the laminar flow wing gradient-based optimization system.4)The laminar wing optimizations are carried out based on an infinite span-wise swept wing with 25° swept angle,and a typical regional aircraft—a wing-body configuration with 20° swept angle at the leading edge.Both TS waves and CF vortices instabilities are considered by the reliable and accurate optimization design system.The optimized infinite span-wise wing gains 59.4%and 46.6%laminar region on the upper and lower surface,respectively,and total drag is reduced by 43.34%compared with the initial configuration.For the wing-body configuration,the inner upper wing surface maintains a 20%laminar region approximately,and the outer wing surface gains a maximum of 61.4%laminar region.The total drag is reduced by 10.48%.The Reynolds number based on the local chord is decreasing from the wing root to the wing tip gradually,which mainly causes the transition locations variation along the span-wise direction.The design results show that the established laminar flow wing optimization system can handle the optimization problem for the complex three-dimensional configuration,considering both TS waves and CF vortices.