Hafskjold Bjørn, Bedeaux Dick, Kjelstrup Signe, Wilhelmsen Øivind
PoreLab, Department of Chemistry, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.
PoreLab, SINTEF Energy Research, Trondheim, Norway.
Phys Rev E. 2021 Jul;104(1-1):014131. doi: 10.1103/PhysRevE.104.014131.
We have considered a shock wave as a surface of discontinuity and computed the entropy production using nonequilibrium thermodynamics for surfaces. The results from this method, which we call the "Gibbs excess method" (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock-front region, but with different assumptions about local equilibrium. Nonequilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number M≈2 and a strong shock with M≈6 and with a Prandtl number of the gas Pr≈1.4 in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed, and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.
我们将冲击波视为不连续面，并使用表面非平衡热力学计算了熵产生。我们将这种方法的结果称为“吉布斯过剩方法”（GEM），并与另外三种替代方法的结果进行了比较，这三种方法均基于激波前沿区域的熵平衡，但对局部平衡有不同假设。非平衡分子动力学（NEMD）模拟用于模拟由与 Lennard-Jones/样条势相互作用的粒子组成的单组分气体中的热爆炸。这为理论分析提供了数据。研究了两种情况，一种是马赫数 M≈2 的弱激波，另一种是马赫数 M≈6 且气体普朗特数 Pr≈1.4 的强激波。对于这两种马赫数，四种理论方法在随时间变化的表面过剩熵产生方面给出了一致的结果。发现内能在激波前沿仅略微偏离平衡值。压力分布与纳维-斯托克斯方程一致。弱激波和强激波中的熵产生大致与马赫数的平方成正比，并以大致相同的相对速率随时间衰减。在这两种情况下，气体中约 97%的总熵产生发生在冲击波中。GEM 表明，激波的大部分动能可逆地转化为焓和熵，少量以产生的熵的形式耗散。冲击波以几乎恒定的速度传播，我们发现由 NEMD 模拟确定的超压与稳态激波的兰金-于戈尼奥条件吻合得很好。
