arXiv subjects

Bjørn Hafskjold

Publications and source records attributed to Bjørn Hafskjold.

5 recordsLinked to original sources

arXiv2021

Theory and simulation of shock waves: Entropyproduction and energy conversion

We have considered a shock wave as a surface of discontinuity and computed the entropy production using non-equilibrium 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. Non-equilibrium 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 $M \approx 2$ and a strong shock with $M \approx 6$ and with a Prandtl number of the gas $Pr \approx 1.4$ 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.

physics.flu-dyn↗

arXiv2020

Nonequilibrium thermodynamics of surfaces captures the energy conversions in a shockwave

The local entropy production in a shock wave was analysed in the framework of non-equilibrium thermodynamics (NET) of surfaces. We show that the thermodynamic state variables in the shock front are equal to their equilibrium values, despite lack of global equilibrium in the dense gas. This observation was used to develop a theory for the entropy production in a shock wave using Gibbs' surface excess properties. The theoretical results were compared with a numerical evaluation of the entropy balance for the shock front and confirmed by non-equilibrium molecular dynamics (NEMD) simulations. The NET analysis shows that the dominant contribution to the entropy production is the dissipation of kinetic and compression energy. This opens the door to accurate representations of energy conversions in shock waves.

physics.flu-dyn↗

arXiv2019

Thermodynamic properties of the 3D Lennard-Jones/spline model

The Lennard-Jones (LJ) spline potential is a truncated LJ potential such that both the pair potential and the force continuously approach zero at $r_c \approx 1.74σ$. We present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. The critical point for the model is estimated to be $T_c^*=0.885 \pm 0.002$ and $P_c^*=0.075 \pm 0.001$, respectively. The triple point is estimated to be $T_{tp}^*=0.547 \pm 0.005$ and $P_{tp}^*=0.0016 \pm 0.0002$. The coexistence densities, saturation pressure, and supercritical isotherms of the LJ/s model were fairly well represented by the Peng-Robison equation of state. We find that Barker-Henderson perturbation theory works less good for the LJ spline than for the LJ model. The first-order perturbation theory overestimates the critical temperature and pressure by about 10% and 90%, respectively. A second-order perturbation theory is not much better. Our assessment is that mean compressibility approximation gives a poor representation of the second-order perturbation term. Our main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system.

physics.chem-ph↗

arXiv2018

Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations

We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.

physics.flu-dyn↗

arXiv2018

Non-isothermal transport of multi-phase fluids in porous media. The entropy production

We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.

physics.flu-dyn↗