Discrete Vortex Method for Simulating Unsteady Flow Around Pitching Aerofoils
Amodi® ed discretevortex method to simulatetheseparatedowaround an aerofoil undergoing pitching motion is described. The vorticity generated in the thin layer around the body is discretized into vortices in accordance withthemultipanel surfacerepresentation. Byconvectionand diffusionthevorticesarereleased fromthebody and advanced in the wake as determined by the Biot± Savart law and random-walk model, respectively. Both unsteady static and pitching casesare presented, and comparison with the test data illustratesthat, without priorknowledge of the developing separation and reattachment points for the model, good agreement has been achieved. Nomenclature A = area of body (section) B = volume within the body c = aerofoil chord Fb = volume within the control zone Fw = volume outside the control zone K = number of subpanels for each panel k = unit vector k = reduced pitch rate k = X c/2V l = panel length m = index number of subpanel within the panel N = number of panels for the body P = static pressure Re = Reynolds number r, r = position vector and its magnitude S = surface of the body s, n = unit vector along and normal to the surface t = time U = ¯ ow velocity V = velocity Z = position in the form of complex number z = vortex position in the form of complex number a = angle of attack C = circulation c = circulation density 4 t = time step d = distance of nascent vortex off the body m = kinematic viscosity q = ¯ uid density r = vortex core radius W ,W = vector potential and stream function X = rotational velocity x = vorticity Subscripts