Vortex-stretched flow around a cranked delta wing

Abstract

A numerical method that solves the Euler equations for compressible flow is used to study vortex stretching. The particular case simulated is subsonic flow M& -0.3, a. = 10 deg around a twisted and cambered cranked-and-cropped delta wing. This geometry induces multiple leading-edge vortices in a straining velocity field that brings about flow instabilities, but the result is a state of statistical equilibrium. The discretization contains over 600,000 cells and offers sufficient degrees of freedom in the solution to exhibit the onset of chaotic vortex flow that could well lead to turbulence. The simulated results are compared with windtunnel measurements. The agreement at inboard sections is reasonable for the position and strength of the leading-edge vortex; but outboard, it is poor because of the complex transition to disordered vortex flow at the tip. Overall, lift and drag coefficients agree well, however. Nomenclaturee y ,e z -Cartesian unit vectors FD = total flux differences H(q) = qV+p[Q,e x ,e y ,e z ] flux M w = freestream Mach number n =unit normal vector p = static pressure p t = total pressure q = [p,pu,pv,pw] variables u,v,w = Cartesian components of V V = velocity vector x,y,z = Cartesian coordinates a. = angle of attack p = density F = artificial viscosity model a? = vorticity curl V