Computation of wind tunnel wall effects in ducted rotor experiments

Abstract

Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed. A multiple image method is used to account for tunnel wall interference effects and a detailed method of singularities model is used for the ducted rotor. The size of the rotor wake is computed, taking into account the tunnel walls. Several ducted rotor model/wind tunnel dimension ratios are examined, ranging between 0.02 and 0.50. In addition, ducted rotor disk loading coefficients, CT , between - 30 and 0.89 are considered (the negative values correspond to the rotor acting as a propeller; the positive values indicate that the rotor is a turbine). Values of ideal propeller thrust are reduced by over 30% at the highest value of propeller disk loading (CT = — 30). The tunnel wall effect for a ducted turbine is less than for a ducted propeller and is opposite in direction. For the nearoptimum condition CT. =0.89, the ideal turbine power is increased by about 8% for the largest model/tunnel ratio considered. Nomenclature CP. = ideal thrust power coefficient for DAP (diffuseraugmented propeller) or ideal power coefficient for DAWT (diffuser-augmented wind turbine) CT() = disk loading coefficient based on freestream dynamic head D = dimension of wind tunnel test section E = complete elliptic integral, Eq. (5) K = complete elliptic integral, Eq. (4) kn = function of ring vortex coordinates and field point coordinates, Eq. (3) TV = the number of images along the side of a square image array q = velocity in r direction r = radial coordinate rp = ideal power augmentation ratio R = diffuser radius at a particular value of z S = the number of vortex rings used to represent the diffuser surface T = total number of vortices used to represent both the diffuser and the wake u = velocity in x direction U0 = freestream velocity, dimensional v = velocity in y direction w = velocity in z direction (axial direction) x = lateral coordinate in plane perpendicular to mean flow y = vertical coordinate in plane perpendicular to mean