Calculation of steady and unsteady pressures on wings at supersonic speeds with a transonic small-disturbance code

Abstract

A transonic unsteady aerodynamic and aeroelasticity code has been developed for application to realistic aircraft configurations. The code is called CAP-TSD (computational aeroelasticity program-transonic smalldisturbance) and uses a time-accurate approximate factorization algorithm for solution of the unsteady transonic small-disturbance equation that is efficient for solution of steady and unsteady transonic flow problems including supersonic freestream flows. This code can treat complete aircraft geometries with multiple lifting surfaces and bodies. Applications to wings in supersonic freestream flow are presented. Comparisons with selected exact solutions from linear theory are presented, showing generally favorable results. Calculations for both steady and oscillatory cases for the F-5 wing and the Royal Aerospace Establishment tailplane models are compared with experimental data and also show good overall agreement. Selected steady calculations are also compared with the results from a steady flow Euler code. Nomenclature c = airfoil chord c/ a = section lift-curve slope c r = wing reference chord Cjj = pressure coefficient C p = unsteady pressure coefficient normalized by oscillation amplitude / = function defining position of lifting surface k = reduced frequency, = coc r /2£7 M = freestream Mach number t = time, nondimensionalized by U/c r U = freestream velocity a = angle of attack 7 = ratio of specific heats A? = nondimensional time step i? = fractional semispan coordinate 6 = phase angle between unsteady lift and pitch angle 0 = disturbance velocity potential o> = angular frequency Subscripts 0 = mean value 1 = dynamic value