Unsteady Trailing Vortex Evolution Behind a Wing In Ground Effect

The unsteady evolution of trailing vortex sheets in ground effect is simulated by the use of a discrete vortex method. The ground effect is included by image method. Two cases of unsteady vortex evolution behind lifting lines (an elliptic loading and a fuselage/flap-wing configuration) are simulated for several ground heights. The present method is validated by comparison of the simulated wake roll-up shapes to published numerical results. For a lifting line with an elliptic loading, the ground has the effect of moving the wingtip vortices laterally outward and suppressing the development of the vortex. An increase in the wing loading has the effect of moving the wingtip vortex more laterally outward. The rotation of the wake vortices behind a fuselage/part-span flap configuration in ground effect is less than the case of flight out of the ground effect. Nomenclature b = span C(, t) = point on a lifting line in the complex plane C ′(o, t) = point on an image lifting line in the complex plane h = ground height; distance from a lifting line to the ground N = number of point vortices Re = vortex Reynolds number rc = vortex core radius rcj0 = initial vortex core radius r ji = distance from the i th point to the j th point T = total time, s t = time, s u = induced velocity in downstream direction v = induced velocity in spanwise direction x = distance in downstream direction y = distance in spanwise direction z = distance in vertical direction z ̄ = complex conjugate of z in the complex plane = circulation of a lifting line j = circulation of a vortex at the j th point o = circulation of an image lifting line 0 = maximum circulation γ = vortex sheet strength; distance between the origin of a vortex core to a point in space t j = growth age δ = smoothing factor δt = time step τ = pseudotime