Computational Study of Shock Mitigation and Drag Reduction by Pulsed Energy Lines

A series of numerical experiments were performed in which energy was deposited ahead of a cone traveling at supersonic/hypersonic speeds. The angle of attack was zero, and the cone half-angles ranged from 15 to 45 deg. The Mach numbers simulated were 2, 4, 6, and 8. The energy was deposited instantaneously along a finite length of the cone axis, ahead of the cone’s bow shock, causing a cylindrical shock wave to push air outward from the line of deposition. The shock wave would sweep the air out from in front of the cone, leaving behind a low-density column/tube of air, through which the cone (vehicle) propagated with significantly reduced drag. The greatest drag reduction observed was 96%. (One-hundred percent drag reduction would result in the complete elimination of drag forces on the cone.) The propulsive gain was consistently positive, meaning that the energy saved as a result of drag reduction was consistently greater than the amount of energy “invested ” (i.e., deposited ahead of the vehicle). The highest ratio of energy saved/energy invested was approximately 6500 % (a 65-fold “return ” on the invested energy). We explored this phenomenon with a high-order-accurate multidomain weighted essentially nonoscillatory finite difference algorithm, using interpolation at subdomain boundaries. This drag-reduction/shock-mitigation technique can be applied locally or globally to reduce the overall drag on a vehicle. Nomenclature a0 = speed of sound b = 3.94 (constant within Plooster characteristic radius) Dcb = drag-along cone base Dcs = drag-along cone sides Dtot = total drag-along cone E0 = Plooster study energy deposited per unit length M = Mach number p = pressure R0 = Plooster study characteristic radius r = Plooster study dimensional radius ur = radial-velocity component ux = axial-velocity component uθ = azimuthal-velocity component γ = 1.4 (ratio of specific heats for air) λ = Plooster study dimensionless radius ρ = density I