New acceleration potential method for supersonic unsteady aerodynamics of lifting surfaces, further extension of the nonplanar supersonic doublet point method, and nonlinear, nongradient optimized rational function approximations for supersonic, transient

A new method is devised for the calculation of pressure and aerodynamic influence coefficients on lifting-surface configurations oscillating in supersonic flow. The scheme is based upon the concept of the acceleration potential doublet and provides a simpler alternative to the Doublet Point method. The kernel function is expressed in a form analytic on the Mach boundary, and the nonplanar interference is treated by a finite-difference approximation. The normalwash is averaged over a trapezoidal averaging region instead of the rectangular region of the Doublet Point method. The concept of kernel separation into steady and unsteady parts is reserved for averaging regions lying directly downstream of the sending point. Good comparisons are observed with other methods. The nonplanar, supersonic Doublet-Point method is further extended to the treatment of surfaces with non-zero dihedral angle.;Rational-function approximation in the Laplace domain with consistently optimized lag-states is presented for supersonic unsteady aerodynamics. The new approximation provides the capability to predict the transient response of lifting-surfaces in supersonic flow by using an analytic continuation from pure oscillatory motion to a general motion. The lag-states in the resulting unsteady aerodynamic state-space form are determined through a nonlinear, nongradient optimization procedure. Repeated optimized lag-state values are replaced by a higher order pole in the rational unsteady aerodynamic transfer-function. Although the multiple-pole arises out of a repeated lag-state, its use in a non-repeated case drastically reduces the cost of optimization while retaining the fit accuracy as well as the total number of augmented-states in the formulation. The rational function approximations are inadequate for transonic regime.