High-speed flying vehicle with hypergeometrically shaped windward aerodynamic surface

Abstract

This work discusses the problem of reducing the drag due to lift at high-speed flight conditions. To accelerate the optimization algorithm convergence and to study characteristic features of the optimal delta wing the procedure of the geometry parameters system selection is developed within the framework of the linear theory. It is established that the hypergeometrical directrix of the wing describes near to optimum aerodynamic shape and corresponds to a superelliptical distribution of the local angle of attack over the wing span. Differences between the results of the theoretical studying and the direct numerical optimization based on the Euler's equations are analyzed. Configuration of the high-speed flying vehicle, designed under HEXAFLY-INT project, with hypergeometrically profiled windward surface is proposed to enhance aerodynamic performance. Flow fields and aerodynamic loads numerical studying is carried out in a wide range of the Mach number. Nomenclature X = axis directed along the free stream R  = aerodynamic force velocity 2 n  = nozzle exit normal Y = axis of lift force I = flow momentum Z = lateral axis y = normalized normal coordinate M = Mach number z = normalized lateral coordinate V = free stream velocity Re = Reynolds number α = angle of attack C P = pressure coefficient N = number of elements q = pressure velocity F = objective function G = constraint function Subscripts C D = aerodynamic drag coefficient fl = flat wing C L = lift coefficient EXT = external C m = pitching moment coefficient f = mass flow rate ν = eigenvalue u = eigenvector H = Hessian matrix n = relative sweepback μ = Mach angle χ = sweep angle at the leading edge φ = perturbation velocity potential λ = Lagrange multiplier E = form parameter 2 F 1 = Gauss hypergeometric function ψ = twist angle L = fuselage length S = reference area 1 Head of Research Group, Aerodynamics Department, TsAGI, c.a.t@tsagi.ru, not a member of the AIAA Downloaded by UNIVERSITY OF ILLINOIS on October 1, 2015 | http://arc.aiaa.org |