Minimization of body of revolution aerodynamic drag at supersonic speeds

Abstract

Purpose This study aims to decrease the aerodynamic drag of the body of revolution at supersonic speeds. Supersonic area rule is widely used in modern supersonic aircraft design. Further reduction of the aerodynamic drag is possible in the framework of Euler and Reynolds averaged Navier–Stokes (RANS) equations. Sears–Haack body of revolution shape variation, which decreased its aerodynamic drag in compressible inviscid and viscous gas flow at Mach number of 1.8 under constraint of the volume with lower bound equal to volume of initial body, was numerically investigated. Design/methodology/approach Calculations were carried out in two-dimensional axisymmetric mode in the framework of Euler and RANS with SST model with compressibility correction equations at structured multiblock meshes. Variation of the radius as function of the longitudinal coordinate was given as a polynomial third-order spline through five uniformly distributed points. Varied parameters were increments of the radius of the body at points that defined spline. Drag coefficient was selected as an objective function. Parameter combinations corresponding to the objective function minimum under volume constraint were obtained by mixed-integer sequential quadratic programming at second-order polynomial response surface and IOSO algorithm. Findings Improving variations make front part of the body become slightly blunted, transfer part of volume from front part of the body to back part and generate significant back face. In the framework of RANS, the best variation decreases aerodynamic drag by approximately 20 per cent in comparison with Sears–Haack body. Practical implications The results can be applied for the aerodynamic design of the bullets and projectiles. The second important application is knowledge of the significance of the difference between linearized slender body theory optimization results and optimization results obtained by modern computational fluid dynamics (CFD) optimization techniques. Social implications Knowledge about the magnitude of the difference between linearized slender body theory optimization results and optimization results obtained by modern CFD optimization techniques can stimulate further research in related areas. Originality/value The optimization procedure and optimal shapes obtained in the present work are directly applicable to the design of small aerodynamic drag bodies.