Quantitative measure and visualization for local shock strength in two-dimensional flow

Abstract

The concept of local shock strength and a quantitative measure index str of local shock strength are proposed, derived from the oblique shock relation and the monotonic relationship between total pressure loss ratio and normal Mach number. Utilizing the high density gradient characteristic of shock waves and the oblique shock relation, a post-processing algorithm for two-dimensional flow field data is developed. The objective of the post-processing algorithm is to obtain specific shock wave location coordinates and calculate the corresponding str from flow filed data under the calibration of the oblique shock relation. Validation of this post-processing algorithm is conducted using a standard model example that can be solved analytically. Combining the concept of local shock strength with the post-processing algorithm, a local shock strength quantitative mapping approach is established for the first time. This approach enables a quantitative measure and visualization of local shock strength at distinct locations, represented by color mapping on the shock structures. The approach can be applied to post-processing numerical simulation data of two-dimensional flows. Applications to the intersection of two left-running oblique shock waves (straight shock waves), the bow shock in front of a cylinder (curved shock wave), and Mach reflection (mixed straight and curved shock waves) demonstrate the accuracy, and effectiveness of the mapping approach in investigating diverse shock wave phenomena. The quantitative mapping approach of str may be a valuable tool in the design of supersonic/hypersonic vehicles and the exploration of shock wave evolution.