Non-Symmetry in the Shock Refraction at a Closed Interface as a Recovery Mechanism

Abstract

The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges.

Shock–Discharge Interaction Model Extended into the Third Dimension

“…As the plots in Figure 3 demonstrate, the distributions for δ r and δ x in the radial and longitudinal directions are fully symmetrical, as well as those in Figure 4, exhibiting the same tendency and maximum locations. With projecting the profiles into the two planes of symmetry in Figures 3 and 4, it can be seen that they are similar to those obtained with the 2D model in [27] (Figure 5). In the plot of Figure 5, the curve used for comparison at the moment of time n t = 1.0 is the one crossing the sphere pole.…”

“…In the slow-fast scenario present at the entrance of the heated spot, the ratio of normal components of the Mach number in (7) was obtained using the refraction equation that assumes that the reflected wave is a rarefaction wave. For the shock and gas conditions considered here, the function M 2n = f (M 1n ) was determined in [27] and the factors ζ and η in (17) can also be borrowed from there. With those parameters in place, the radial component of the front distortion δ r and its projections into the Cartesian basis δ x , δ y , δ x were calculated using Equations ( 20) and (21).…”

“…the function M2n = f (M1n) was determined in [27] and the factors ζ and η in (17) can also be borrowed from there. With those parameters in place, the radial component of the front distortion δr and its projections into the Cartesian basis δx, δy, δx were calculated using Equations ( 20) and (21).…”