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A supercritical airfoil is geometrically optimized using the new developed adjoint compressible lattice Boltzmann method. Minimizing the drag coefficient and eliminating the shock wave on the supercritical airfoil surface are considered as the cost function with constraint of fixed lift coefficient. The continuous adjoint method is applied to able designers to implement large number of design variables in actual optimization problems. The adjoint equation based on the specified cost function and constrains is successfully derived. Discretization of the governing equations is carried out using the finite volume approach and 3 order of the MUSCL scheme. The supercritical SC(2)0410 airfoil, which has a strong shock on the top surface at transonic cruise conditions, is numerically optimized using the inviscid developed algorithm to eliminate the shock and reduce the wave drag. To validate the obtained results and show viscosity effect on the results, the base airfoil and optimized one are experimentally tested in a transonic wind tunnel at the same conditions. Pressure distribution on the surface of both the base and optimal airfoil are extracted from the experimental tests and compared with those of numerical simulations. The results indicate that the developed approach can be properly used for supercritical airfoil shape optimization for elimination the shock and reduction the wave drag.

Wave Drag Reduction of SC(2)0410 Airfoil using New Developed Inviscid Compressible Adjoint Method