Date of Award
Doctor of Philosophy
Ahmad D. Vakili
Roger Crawford, Jimmy Wu, John Caruthers, Ralph Kimberlin, Frank Collins
An investigation of the vortex breakdown phenomenon using flow visualization qualitatively and quantitatively was conducted with a 70° delta wind under conditions of steady and unsteady pitch, roll and combinations of pitch and roll. Testing was carried out in the water tunnel located in the Mechanical Engineering Department of the Royal Military College of Canada, Kingston, Ontario.
Steady state roll experiments with the delta wing pitched at 30° showed that the behavior of vortex breakdown as a function of roll angle could be considered linear over the front half of the delta wing; however, the behavior beyond a certain critical roll angle was nonlinear. The steady state coupling effect for simultaneous variations in pitch and roll appeared to be a superposition of the individual effects of pure pitch and pure roll.
For the unsteady analysis, the 70° delta wing was oscillated in pitch about the center chord at a mean angle of attack of 30° with an amplitude of oscillation of ±5°. The study was conducted at four values of reduced frequencies ranging Kpitch + 0.12 and Kpitch= 0.52. The observations showed that the unsteady behaviour of the vortex core angle as a function of angle attack was independent of reduced pitch frequency. Unsteady roll experiments were carried out with the 70° delta wing fixed at a pitch angle of 30° with roll oscillations of ±18° about the wing's level position. Tests were conducted at the same pitch frequencies as for the unsteady pitch analysis which corresponded to reduced frequencies that varied from kroll =0.05 to kroll=0.19. Unsteady maneuvering experiments were carried out with the 70° delta wing oscillating in pitch about a mean angle of attack of 30° with an amplitude of ±5° while undergoing a corresponding roll oscillation about the centerline with an amplitude of ±18°. The unsteady maneuvering experiments were conducted at the same pitch frequencies as for pure pitch and pure roll and the reduced frequencies were also kept consistent. The results showed that, for all unsteady motions, a hysteresis effect existed that increased with reduced frequency. The results showed that the coupling effect existed that increased with reduced frequency. The results showed that the coupling effect of pitch and roll for the right wing was a reduction in hysteresis; however, the coupling effect for the left win was an increase in hysteresis.
For all motions investigated, the results of this study showed that an increase in reduced frequency also resulted in an increase in the amount of phase lag. For pure pitching and rolling motion, there was a notable increase in phase lag when the delta wing transitioned from the downstroke to the upstroke as compared to the transition from the upstroke to the downstroke. The coupling effects of unsteady pitch and roll was an apparent superposition of the phase lag.
Empirical prediction equations for steady state conditions were examined under modification for leading edge geometry. Limited success was obtained in predicting the location of the vortex breakdown for conditions of pure pitch and pure roll; however, neither equation accurately predicted the effects of the coupled variations of pitch and roll.
Kowal, Harry James, "An Investigation of Unsteady Vortex Flow Over A Maneuvering Delta Wing. " PhD diss., University of Tennessee, 1997.