Unsteady compressible lifting surface analysis for rotary wings using velocity potential modes

The compressible, unsteady lifting surface problem of a helicopter blade in hover using the velocity potential formulation is solved using a modal expansion technique. The mathematical formulation of the problem is presented and a panel method which has previously been applied to its solution is described. The modal approach is offered as an alternate solution method.;The choice of functions to be used as modes in the velocity potential formulation is explained. The choice is made based on previous studies using acceleration potential or pressure modes. Special attention is paid to account for the features of the flow about a rotor blade. The modal approach is used in conjunction with both a collocation technique and a Galerkin type of solution. The modal coefficients so obtained are used to evaluate aerodynamic loads and inflow velocities.;The present results are shown to correlate well with available experimental and previous theoretical results. The differences with two-dimensional and lifting line theory results are brought out. The modal and panel methods of solution are compared and it is shown that the modal approach provides savings in computational effort. It is also shown that the modal approach is superior to the panel method in the computation of inflow velocities in the neighborhood of the blade.;Parametric studies on the modal technique are carried out and it is shown that a small number of modes are sufficient to adequately represent the velocity potential distribution on the surface. The collocation technique is seen to be not very sensitive to the location of control points. The Galerkin approach to satisfying the normal velocity boundary condition is also seen to not provide significant improvement in the predicted results when compared to the collocation technique using the optimum control point locations.