3 Integrated Design on Aerodynamic and Stealth of Airfoil. Fig.7 K and characteristics distribution of NACA series airfoils at four receiving azimuthal angles. In order to validate the developed optimization algorithm, results are presented for both incompressible and compressible inverse problem in steady and unsteady flow and accurate results are obtained. So choosing theoptimal airfoil with high aerodynamic performance and low scattering characteristics is a compromised process. Also, a novel solution is presented to remove singularity problem of the adjoint boundary condition. The steepest decent technique is utilized as gradient optimizer. So, the adjoint equation is also expanded based on CF idea for calculation of objective function gradient vector. This airfoil shape is advantageous for certain applications, as a wider range of. The adjoint lattice Boltzmann method is extended for both the incompressible and compressible flows by selecting the circular function idea for calculating the equilibrium distribution functions. For symmetrical wings or wing tips, lift is created due to the angle of attack. New mathematical derivation based on compressible lattice Boltzmann equations (LBE) is developed which can find target shape of an airfoil with available desired pressure distribution. In this study, the developed adjoint lattice Boltzmann scheme based on the circular function (CF) is extended for airfoil inverse design problems in laminar incompressible and compressible flows. A new optimization techniques based on the adjoint lattice Boltzmann method is derived for airfoil inverse design in laminar compressible flows.
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