| The perturbation theory is used to develop sensitivity equations for the Euler equations. Expansions of the governing equations are used to form continuous sensitivity equations that are then discretized and solved in the framework of an unstructured Cartesian-grid computational simulation code. Several expansions of boundary conditions are developed for the computational method, to allow the prediction of variation of the flow near the surface of the body of interest and at the farfield. The sensitivity equation solver is used to predict the sensitivity of the surface and off-body flow to variations of boundary shape and flight condition. The method produces estimated sensitivities with fewer iterations than a complete new solution. Several test problems are evaluated, including a three-dimensional rectangular wing, a near-axi-symmetric body, and supersonic deflection of control surfaces. The effects of grid resolution and compressibility in the generating flowfield are evaluated for the method. New approaches are developed for the prediction of surface pressure sensitivity to Mach number variation. Comparison is made of these predictions to test-derived pressure and force trends. The capability is demonstrated to independently evaluate the effects of changes in camber, twist, angle of attack, and thickness and to assemble an estimate for the forces and moments on a wing having a combination of these geometric changes. A new approach to solve for angle of attack variations at the body surface is developed for axi-symmetric and planar-type geometries. This method is used to predict lift and pitching moment increments for an axi-symmetric body and is shown to produce good predictions of the effects of angle of attack variation on a three-dimensional wing and control-surface deflection for vehicle trim. Results indicate that the sensitivity methodology is sufficiently accurate to produce approximate solutions suitable for design optimization trade studies. |
