Repetition Frequency Dependence of Wave Drag Reduction Induced by Laser-Pulse-Energy Depositions

Abstract

The mechanisms of drag reduction in a Mach 2 supersonic flow induced by repetitively deposited laser pulse energy are investigated through computational fluid dynamics based on Navier-Stokes equations for an axis-symmetric flow. The effectively deposited energy into the flow is determined by fitting a measured stagnation pressure history. With the repetition frequency lower than 20 kHz, the experimental flow-field, the residence time of baroclinically-generated vortex rings in the shock layer and drag reduction characteristics are well simulated by the axis-symmetric computation. At the lower frequency below 5 kHz, the low-density bubbles successively generated by energy depositions behave in an almost independent manner, so the drag reduction can be estimated by superimposing single pulses. At a middle frequency from 5 to 14 kHz, there is weak interaction among the successive vortex rings, but the behavior can be assumed to be almost independent. At even higher frequency, a quasi-stationary vortex ring is observed in the shock layer and grows according to frequency increases and the shape of the shock transit from the bow shock to the oblique one. The drag reduction is related to the number and the residence time of the vortex rings. Nomenclature d model : diameter of the model D w/o ED : baseline drag ΔD : drag reduction E : deposited energy per pulse f : laser pulse repetition frequency N vortex : number of vortex rings in Eq. (5) P s : pressure at stagnation point P s,w/o ED : pressure at stagnation point without energy deposition q 0 : total input power per unit mass Q : spatial distribution of deposited energy source r 0 : radius of deposited energy source s : distance of energy deposition area from model head s model : depth of the model head of calculation t : elapsed time v 0 : volume of deposited energy source x 0 : center position of deposited energy source η : efficiency of energy deposition η a : effectively deposited energy ratio  : step function in Eq. (1) defined in Eq. (2) τ : deposited energy pulse duration τ vortex : residence time of vortex ring in shock layer