Numerical Simulation and Density Measurement of a Shock Wave Discharged from the Open End of a Shock Tube

In observing axisymmetric shock wave phenomena by optical flow visualization refractive index changes along the light ray path through the phenomena, we have to determine the density distribution of the axisymmetric phenomena by solving the integral equation which relates the change of the refractive index with the fringe distribution. The present paper reports on the result of flow visualization and numerical simulation of spherical shock waves discharged into free space from the open end of a circular cross-sectional shock tube for shock Mach number 1.5 in air. The axisymmetric shock wave flow is visualized by pulsed laser double-exposure holographic interferometry. Its density distribution was quantitatively evaluated from the three-dimensional holographic interferometric fringe distribution. To compare experimental isopycnics with numerical simulation, we used the total variation diminishing (TVD) finite-difference scheme. The computational results agreed very well with the experimental results. The complicated flow field behind an expanding spherical shock wave can be quantitatively observed. A point explosion test was conducted to examine the process of the present data evaluation method to see how much the collimated light deviated across the spherical shock front.