Shock-Wave Compression and Joule-Thomson Expansion

Structurally stable atomistic one-dimensional shock waves have long been simulated by injecting fresh cool particles and extracting old hot particles at opposite ends of a simulation box. The resulting shock profiles demonstrate tensor temperature, $T_{xx}\ne T_{yy}$ and Maxwell’s delayed response, with stress lagging strain rate and heat flux lagging temperature gradient. Here this same geometry, supplemented by a short-ranged external “plug” field, is used to simulate steady Joule-Kelvin throttling flow of hot dense fluid through a porous plug, producing a dilute and cooler product fluid.

Figure 1

Density profile and snapshot from a typical 1D shock wave simulation with a steeply repulsive pair potential in two space dimensions. Simulation cell dimensions $10\sqrt{3}\times 250$. The spatially averaged density profile was obtained using Lucy’s weight function. The snapshot shows a small section of length 20 near the shock front.

Figure 2

A Joule-Thomson snapshot. The motion is left-to-right with cooled fluid exiting at the right boundary. The density snapshot uses Lucy’s weight function, $(5/12)(1+|x|)[1-(|x|/3){]}^3$.

Figure 3

Time-averaged pressure tensor and velocity (left); time-averaged mass, momentum, and energy fluxes (centre); tensor temperature (right). The system dimensions are $200\times 40$. The mass flux of unity is imposed by the rate at which fresh particles are inserted at the left boundary.