Airfoil inverse design based on laminar compressible adjoint lattice Boltzmann method

Abstract

A new optimization techniques based on the adjoint lattice Boltzmann method is derived for airfoil inverse design in laminar compressible flows. 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. 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. 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. So, the adjoint equation is also expanded based on CF idea for calculation of objective function gradient vector. The steepest decent technique is utilized as gradient optimizer. Also, a novel solution is presented to remove singularity problem of the adjoint boundary condition. 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.

Adjoint-based shape optimization for compressible flow based on volume penalization method

“…In comparison, the present scheme allows to embed an arbitrary complex geometry in a Cartesian grid system by employing the level-set function. In addition, existing shape/topology optimization schemes [51]- [53] combining LBM and the density-based method are typically limited to a subsonic regime. This is because, LBM has inherent problems in solving compressible flows at high Mach numbers, and the density-based method cannot clearly define the fluid-solid interface.…”

“…However, since the previous studies still rely on body-fitted meshes, they need to regenerate computational meshes after the shape is updated in each forward-adjoint iteration. To avoid the bottlenecks of mesh generation, the continuous adjoint methods combined with lattice Boltzmann method (LBM) have also been developed [51]- [53]. However, since LBM is originally established based on the low Mach number assumption [54], their applications are limited to subsonic regimes (Ma < 0.8).…”