Numerical solution of the downwash associated with a blown-flap system

Abstract

For blown-flap aircraft, large downwashes typically occur downstream of the wing due to the high downward momentum of the lifting jet. To determine the velocities induced by the wing- and jet-flap circulation, a threedimensional, nonlinear, finite-element model that can predict downwash angles at any desired location has been developed. Vortex lattices positioned on the wing, flap, and thin jet sheet provide vortex filaments and control points to satisfy kinematic and dynamic boundary conditions. To simplify the mixed-boundary value problem and to reduce computer run time, the rollup of the wake in the spanwise direction has been neglected. In addition, the spanwise distribution of circulation in the wake is assumed to be elliptic in form. A reasonably fast and stable iterative method that allowed a self-consistent wake path to be found was used. Predicted downwash and lift coefficients generally agree with experimental values for various test conditions; but further improvements, such as fuselage modeling, might enhance the accuracy of the model. Nomenclature AH = wing aspect ratio C = airfoil chord length Cy/C=flap chord ratio Cj = blowing coefficient Cr = root chord length CX = velocity induced in the x direction due to a unit vorticity Ff = turning force of jet in radial direction nij =jet mass flow rate over blown flap M = number of chord wise wing lattice divisions S = total wing area S' = equivalent blown wing area V = freestream velocity Vj - velocity of blown jet Vt = average tangential velocity surrounding the blown jet Vx = velocity in the x direction due to the wing lattice Vxw = velocity in the x direction due to the wake lattice Vz = velocity in the z direction due to the wing lattice Vzw = velocity in the z direction due to the wake lattice x = distance in the downstream direction parallel with the freestream