Shape Optimization of Busemann-Type Biplane Airfoil for Drag Reduction Under Non-Lifting and Lifting Conditions Using Genetic Algorithms

The focus of this chapter is on the shape optimization of the Busemann-type biplane airfoil for drag reduction under both non-lifting and lifting conditions using genetic algorithms. The concept of biplane airfoil was first introduced by Adolf Busemann in 1935. Under design conditions at a specific supersonic flow speed, the Busemann biplane airfoil eliminates all wave drag due to its symmetrical biplane configuration; however, it produces zero lift. Previous research has shown that the original Buse‐ mann biplane airfoil shows a poor performance under off-design conditions. In order to address this problem of zero lift and to improve the off-design-condition perform‐ ance, shape optimization of an asymmetric biplane airfoil is performed. The commer‐ cially available computational fluid dynamics (CFD) solver ANSYS FLUENT is employed for computing the inviscid supersonic flow past the biplane airfoil. A single-objective genetic algorithm (SOGA) is employed for shape optimization under the nonlifting condition to minimize the drag, and a multi-objective genetic algorithm (MOGA) is used for shape optimization under the lifting condition to maximize both the lift and the lift-to-drag ratio. The results obtained from both SOGA and MOGA show a significant improvement in the design and off-design-condition performance of the optimized Busemann biplane airfoil compared to the original airfoil. the baseline Busemann biplane off-design the flow-hysteresis They also problem of its drag by shape optimization. This addresses the aerodynamic shape optimization of two-dimensional symmetric Busemann biplane airfoil under both design and off-design conditions for reducing its wave drag, and the alleviation of the flow-hysteresis and choked-flow effects using a single-objective genetic algorithm. The symmetric Busemann biplane airfoil generates zero lift; this problem is addressed by introducing asymmetry in the shape of two profiles of the biplane. The asymmetric configuration is shape optimized for maximum lift and minimum drag by employing a multi-objective genetic algorithm. The flow field is computed using the commercial CFD software ANSYS FLUENT. Body-fitted H-grids around the airfoils are generated using the ICEM software. Random airfoil shapes with constraints in a given generation of the genetic algorithm are obtained using the Bezier curves (third-order polynomials). objective genetic algorithm (MOGA) are employed to optimize the shape of the Busemann-type biplane airfoil under non-lifting and lifting conditions, respectively, to improve its performance under off-design conditions. The commercially available CFD solver FLUENT is employed to calculate the flow field on an unstructured mesh generated using the ICEM grid generation software. A second-order accurate steady-density-based solver in FLUENT is employed to compute the supersonic flow field. The optimization results for the non-lifting case show a significant improvement in reducing the drag coefficient under off-design conditions for the optimized Busemann-type biplane airfoil shape compared to the original shape. The flow-hysteresis phenomenon during acceleration and the choked-flow phenom‐ enon during deceleration are both alleviated significantly for the optimized shape. For the lifting case, the optimized Busemann biplane airfoil is able to significantly reduce the drag coefficient under off-design conditions while generating lift at the same time.