Numerical analysis on shock-cylinder interaction using immersed boundary method

Abstract

The problem of shock interaction with a rigid circular cylinder has been investigated using a compressible immersed boundary method coupled with high-order weighted-essentially non-oscillatory (WENO) scheme. First, the accuracy of the developed code is validated. Then, influences of the incident shock Mach number on the flow-field structure and dynamic drag coefficient, as well as time evolution of the flow field are studied. For different shock Mach number, the flow structure shows very different features. At a given dimensionless time, both the normalized shock detachment distance and the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder decreases with increasing shock Mach number. However, location of the upper triple point varies non-monotonically with shock Mach number. For a case with given shock Mach number, the trajectory of the upper triple point and the time evolution of the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder can both be predicted by linear correlation. Nevertheless, the time evolution of the normalized shock detachment distance is biased to be non-linear. Meanwhile, time evolution of force exerted on the cylinder is quite unsteady for a case with given shock Mach number and given cylinder diameter. For small shock Mach number, there exists a negative valley, and it disappears when the incident shock Mach number increases to a large value, e.g., 1.7. Furthermore, correlations to predict the occurrence of the peak drag and its value under different shock Mach numbers have been proposed.