Scaling Of Hugoniot Curves For Shock-Compressed Liquids

In previous studies of shock compression, pressure P, specific volume v, specific internal energy e, shock velocity Us, and particle velocity up have typically been presented in a dimensional form. For different materials, the plots of P - v, P - u(p), or Us - u(p), often called Hugoniot curves, are different. Here, we predict the behavior of shock-compressed liquids through proper scaling of the Rankine-Hugoniot (RH) equations and dimensionless Hugoniot curves. The characteristic density and velocity scales are the density rho(0) and bulk speed of sound c(b0) of the undisturbed liquid, respectively. Two dimensionless numbers arise from the scaled RH equations, one for the initial condition of pressure and the other for the initial condition of internal energy. Under normal conditions, these two numbers do not affect the solutions of the dimensionless RH equations. The dimensionless Hugoniot curves P/(rho(0)c(b0)(2)) vs v rho(0), U-s/c(b0) vs u(p)/cb(0), and P/(rho(0)c(b0)(2)) vs u(p)/c(b0) of different liquids merge reasonably well onto a single curve. The dimensionless Hugoniot curve v rho(0) vs U-s/c(b0) or v rho(0) vs u(p)/c(b0), often omitted in the previous work, is thus found to be useful in the understanding of shock compression. The v rho(0) vs U-s/c(b0) curve clearly shows that the dependence of the specific volume ratio v rho(0) on U-s/c(b0) is different for moderate and strong shocks. For a moderate strength shock (U-s/c(b0) <= 10), a new approximation relation is proposed for shock velocity Us and particle velocity u(p) as (U-s - u(p))/c(b0) approximate to (U-s/c(b0))(n), where the exponent is determined empirically as n = 0.55 - 0.6. This new approximation relation is different from the commonly used linear relation between Us and up and better predicts the behavior of shock-compressed liquids. Using the new approximation relation, the ratio v rho(0) under moderate strength shocks can be approximated by a power law v rho(0) approximate to (U*(s))(n-1). For stronger shocks, the decrease in the specific volume ratio is slower and is bounded.