Numerical and experimental investigation of oblique shock wave reflection off a water wedge

Abstract

Shock wave interaction with solid wedges has been an area of much research in past decades, but so far, very few results have been obtained for shock wave reflection off liquid wedges. In this study, numerical simulations are performed using the inviscid Euler equations and the stiffened gas equation of state to study the transition angles, reflection patterns, and triple point trajectory angles of shock reflection off solid and water wedges. Experiments using an inclined shock tube are also performed and schlieren photography results are compared to simulations. Results show that the transition angles for the water wedge cases are within 5.3% and 9.2%, for simulations and experiments respectively, compared to results obtained with the theoretical detachment criterion for solid surfaces. Triple point trajectory angles are measured and compared with analytic solutions, agreement within 1.3• is shown for the water wedge cases. The transmitted wave in the water observed in the simulation is quantitatively studied, and two different scenarios are found. For low incident shock Mach numbers, M s = 1.2 and 2, no shock wave is formed in the water but a precursor wave is induced ahead of the incident shock wave and passes the information from the water back into the air. For high incident shock Mach numbers, M s = 3 and 4, precursor waves no longer appear but instead a shock wave is formed in the water and attached to the Mach stem at every instant. The temperature field in the water is measured in the simulation. For strong incident shock waves, e.g., M s = 4, the temperature increment in the water is up to 7.3K.

Evolution of a shock generated by an impulsively accelerated, sinusoidal piston

“…Later, the shock-tube experiment of Denet et al (2015) and the direct numerical simulations of Lodato, Vervisch & Clavin (2016 confirmed the triple-point formation of a shock reflected off a wavy wall, but did not relate the formation time to the initial perturbation size of the wall. Wan et al (2017) investigated numerically and experimentally the triple-point trajectory due to shock interaction with a water wedge. Mostert et al (2018a,b) hypothesized a sinusoidal perturbation in the Mach-number distribution for both initially flat and cylindrical shock geometry, finding that a shock curvature singularity, as a prelude to the formation of a triple point, occurs at a critical time τ c that is inversely proportional to the initial perturbation amplitude, .…”

“…Wan et al. (2017) investigated numerically and experimentally the triple-point trajectory due to shock interaction with a water wedge. Mostert et al.…”

Numerical investigation of shock wave attenuation in channels using water obstacles

“…Further verification and validation simulations for water-hammer and underwater explosion driven plastic deformation and rupture of metallic plates with twophase flow and empirical cavitation modeling are given by Cirak et al (2007) and Deiterding et al (2009). Lastly, for further validation and verification, a combined numerical and experimental study on different shock wave reflection patterns, transition angles and triple point trajectory angles for oblique shock wave reflection off a water wedge at different inclination angles and for a range of shock Mach numbers is provided by Wan et al (2017).…”

Shock wave interaction with a transcritical fuel droplet

“…There are many reports on simulation of droplet/shock interactions using sharp-interface and diffuse-interface approaches at subcritical conditions [39][40][41][42][43][44]. However, there are only two reports that simulate the fuel droplet-shock interaction at transcritical conditions [45,46].…”