Theoretical and numerical predictions of shock wave attenuation with frictional drag and heat transfer effects

Shock tubes are shock-forming devices used in a wide range of research fields. In ideal shock tube theory, the shock wave strength can be calculated from the initial states and thermodynamic properties of the driver and driven gases. However, as the shock wave propagates further, wall interactions affect the shock strength. Previous theoretical studies have mainly focused on predicting shock attenuation and pressure variations behind the shock wave as functions of the shock propagation distance. In this study, additional quantitative predictions are provided, including the deceleration of the contact surface and the amounts of wall shear stress and wall heat flux, providing detailed quantitative insights into the physics of wall interactions. The correlation between the relative contributions of shock attenuation factors in the region between the shock wave and the contact surface and the Reynolds number is analyzed. By varying the diaphragm pressure ratio and the initial test gas density, it is shown that as the Reynolds number behind the shock wave increases, the rate of increase in the state of total momentum exceeds that of total energy, which leads to a larger relative contribution of wall shear stress to shock attenuation. However, because heat transfer due to forced convection increases, this trend is less pronounced than the variation in the Reynolds number. The accuracy of our theoretical model is validated by comparing its predictions with experimental data over diaphragm pressure ratios from 3:1 to 200:1 and with numerical simulations over diaphragm pressure ratios from 7:1 to 30:1.