Adaptive Mesh Euler Equation Computations of Vortex Breakdown in Delta Wing Flow

Abstract

A solution method for the three-dimensional Euler equations is formulated and implemented. The solver uses an unstructured mesh of tetrahedral cells and performs adaptive refinement by mesh-point embedding to increase mesh resolution in regions of interesting flow features. The fourth-difference artificial dissipation is increased to a higher order of accuracy using the method of Holmes and Connell. A new method of temporal integration is developed to accelerate the explicit computation of unsteady flows. The solver is applied to the solution of the flow around a sharp edged delta wing, with emphasis on the behavior of the leading edge vortex above the leeside of the wing at high angle of attack, under which conditions the vortex suffers from vortex breakdown. Large deviations in entropy, which indicate vortical regions of the flow, specify the region in which adaptation is performed. Adaptive flow calculations are performed at ten different angles of attack, at seven of which vortex breakdown occurs. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, which demonstrates the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, with which fairly good agreement is seen in cases in which the location of breakdown is over the wing. A series of unsteady calculations involving a pitching delta wing were performed. The use of the acceleration technique is validated. A hysteresis in the normal force is observed, as in experiments, and a lag in the breakdown position is demonstrated.