An Experimental Investigation on Focussing of Weak Shock Waves in Air

Citation

Kulkarny, Vijay Anand (1975) An Experimental Investigation on Focussing of Weak Shock Waves in Air. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KK7V-6827. https://resolver.caltech.edu/CaltechETD:etd-09042007-082903

Abstract

The behavior of focussing weak shock waves is experimentally investigated with a view to observe and understand the processes occurring near the focus, especially the processes that control the maximum amplitude. Concave reflectors are used against the endwall of a large 17" diameter shock tube, to focus the plane incident shock. Reflectors producing line and point foci, and cusped and smooth caustics are examined for incident shock Mach numbers ranging between 1.005 to 1.5. The flowfield is observed with spark shadowgraphs to visualize the motion of various wavefronts. Pressure histories measured at various points in the flow with miniature piezoelectric gauges provide additional information about the various processes occurring near the focus. Shadowgraphs show that for weak shocks, the observed foci are predominantly nonlinear, even though away from the focus, the shockfronts appear to be almost acoustic. Thus a weak shockfront, after the focus, crosses itself and forms a loop, which is an essential feature of acoustic wavefronts. Nonetheless, at the focus, distortion in the geometry of the fronts due to nonlinear effects is very prominent. Inherently nonlinear phenomena, such as formation of three-shock intersections, lead to foci of finite size, in which, as the pressure measurements show, the amplitudes are finite. The amplitude dependence of these phenomena confirms that they are basically nonlinear. The geometrical distortion and the focus are larger for stronger shock waves, and the maximum amplification is smaller. Further, when the distortion becomes significant compared to the size of the initial shockfront, a transition occurs in the geometry of the focussed shockfront. In this case, the focussed front does not cross and remains "unlooped", which is consistent with the nonlinear behavior predicted by shock dynamics. The transition in the geometry of the wavefronts is related to the behavior of the three-shock intersections formed near the focus. In fact, it is shown that the occurrence of crossed or uncrossed shockfronts is very parallel to the occurrence of regular or Mach reflection, respectively, in the case of a shock diffracted by a wedge. (The reflecting wedge surface corresponds to the axis of symmetry in a focussing process.) The dependence on the steepness of the approaching waves is also similar in the two cases; rapid convergence of waves suppresses nonlinear effects, whereas in a slow convergence, nonlinear effects gain prominence. The pressure histories at various locations, when correlated with the waves occurring there, show that nonlinear diffraction processes are very important. In fact, it is shown that the formation of the three-shock intersection occurs due to nonlinear distortion and breaking of a compressive diffraction, and that, in the focus, the limiting and reduction of the peak amplitude occurs by a diffracted expansion overtaking the shock due to nonlinear effects.

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