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Analytical studies and computational fluid dynamics simulations are presented to study the formation and stability of stationary symmetric and asymmetric vortex pairs over slender conical bodies in an inviscid incompressible flow at high angles of attack. The analytical method is based on an eigenvalue analysis on the motion of the vortices under small perturbations. A three-dimensional time-accurate Euler code is used to compute five typical flows studied by the analytical method on extraordinarily fine grids with strict convergence criteria. Both the theory and the computation show that the vortices over a delta wing are stable and those over a wing-body configuration at the low angle of attack are symmetric and stable, but become asymmetric and bistable at higher angles of attack; that is, the vortices shift to one of two stable mirror-imaged asymmetric configurations. The computational results agree well with the analytical predictions, demonstrating the existence of a global inviscid hydrodynamic instability mechanism responsible for the asymmetry of separation vortices over slender conical bodies.

Theoretical analyses of the stability of symmetric and asymmetric vortex pairs over slender conical wing-body combinations consisting of a slender circular or elliptic cone and a flat-plate delta wing under small perturbations in an inviscid incompressible steady flow at high angles of attack with or without sideslip are presented. The three-dimensional flow problem is reduced to a problem in two dimensions, for which a general stability condition for vortex pairs can be applied. The stationary positions of symmetric and asymmetric vortex pairs and their stabilities are examined for various geometric configurations, angles of attack, and sideslip. Results of the analyses are compared with available experimental data and used to help gain insight into the flow behavior.

A numerical method is demonstrated for solving the steady and unsteady Euler equations on stationary Cartersian grids for the purpose of time-domain simulation of aeroelastic problems. Wall boundary conditions are implemented on nonmoving mean chord positions by assuming the airfoil being thin and undergoing small deformation, whereas the full nonlinear Euler equations are used in the flowfield for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body-fitted grids and thus can be easily deployed in any fluid-structure interaction problem involving relatively small deformation of a thin body. The first-order wall boundary conditions are used in solving the full Euler equations, and the results are compared with the Euler solutions using the exact boundary conditions and known experimental data. It is shown that the first-order boundary conditions are adequate to represent airfoils of typical thicknesses with small deformation for both steady and unsteady calculations. Flutter boundaries are accurately predicted by this method for the Isogai wing model test case.

A multi-grid version of the full potential code called Flo-27 is used to mathematically investigate the transonic equivalence rule with lift. The theoretical results of the transonic equivalence rule with lift are outlined and designs for two pairs of equivalent wing models are presented that will specifically satisfy the assumptions made in the theoretical rule at freestream Mach number = 0.94. The computational results are evaluated.

The inner and outer solutions of the transonic equivalence rule, for aerodynamic configurations with sufficiently high lift, are re-examined for matching. The equivalence rule clarifies the accuracy levels of the theory, with considerations of higher order corrections and shock discontinuities in the outer flow. The equivalence rule can be useful in transonic wind-tunnel wall corrections, as well as for studying the impact of sonic-boom at low-supersonic flight speed.