Thermodynamic Analysis of Molecular Dynamics Simulations of Evaporation and Condensation
E.A.T. van den Akker, A.J.H. Frijns, A.A. van Steenhoven Introduction
When a gas or vapour is flowing through a microchannel, the Knudsen number can become too large for the Navier-Stokes approach to be valid; molecular quantities become important. Modelling techniques that include the particle nature of the fluids should be used, for example Molecular Dynamics (MD).
Comparison with Experimental Results
The results from Molecular Dynamics simulations are compared to experimental results for Argon, found in literature. The MD results depend on the cutoff radius rc : the normal value of rc = 2.5rvdw gives bad results, the larger value rc = 4.5rvdw gives results close to experimental values. ρl (kg m−3 ) 987 1172 1162
Temperature profile 140 120 100 80 60 40 20 Temperature 1600 1400 1200 Density n (kg/m3) 1000 800 600 400 200 0
MD(2.5rvdw ) MD(4.5rvdw ) exp.
ρg (kg m−3 ) 89.3 53.9 60.1
P (kPa) 1823 1106 1213
Hl (kJ/kg) -62.4 -80.0 -78.6
Density profile
Hg (kJ/kg) 42.3 50.0 48.0
Density
−10
−5
0 position (a)
5
10
15
MD-simulations have been shown to give accurate results both in the gas phase and in the liquid phase. In a two-phase flow, important for effective micro channel cooling, the phase transition between liquid and gas is important. This phase transition can be modelled in MD, and it should be thermodynamically correct. Here, the MD-model of evaporation and condensation is validated thermodynamically by comparing simulation results to experimental results for Argon.
Temperature T (K)
0
0
5
10 15 Location z (nm) Pressure profile
20
0
5
10 15 Location z (nm) Enthalpy profile
20
8000
Pressure 80 60 Enthalpy h (kJ/kg) 40 20 0 −20 −40 −60 −80
Enthalpy
6000
Pressure p (kPa)
4000
2000
0
−2000
−4000 0 5 10 15 Location z (nm) 20 0 5 10 15 Location z (nm) 20
Simulation Parameters
Using Molecular Dynamics, a micro-canonical (NVE -constant) ensemble is generated with truncated shifted Lennard-Jones particles. The cut-off radius was varied between 2.5rvdw and 4.5rvdw . A small attractive force is used to keep the liquid in the left side; this small force only affects the two most left nanometers of Argon. On the right side, the simulation box is closed with a reflecting wall. In the other directions, periodic boundary conditions are used. The size of the simulation box is 6.1nm × 6.1nm × 25.8nm. The temperature (determined by the total energy in the system) is almost 120 K here; this is between the triple point and critical point, so indeed the phases gas and liquid are both possible. Within a relatively short simulation time, the simulation has reached equilibrium, as can be seen in the temperature plot and pressure plot; the temperatures in the liquid part and gas part are the same, and the same holds for the pressure.
All quantities are predicted reasonably well with the larger cutoff radius, only the vapor density and vapor pressure is underestimated. The reason for this is the finite cut-off radius used in the simulations; although the influence of particles far away is small, and the net force due to these distant interactions will be zero, the pressure due to these long-range interactions is not zero and plays a role. The pressure can be corrected (by a pressure-tail-correction), but the density not. The results from the MD-simulation with cutoff radius rc = 4.5rvdw are good enough to continue simulations of phase transition with this larger cutoff radius.
Future Research
6 .0 n m (liq u id p a rt)
1 7 .8 n m (g a s p a rt)
L iq u id
E v a p o ra tio n
G a s
H e a t
Now that the phase transition in MD simulations has been validated to experimental results, the simulation will be enlarged. On the gas side, the simulation will be coupled to Direct Monte Carlo Simulations. Furthermore, walls will be added to the model, to simulate a microchannel. When heat is transferred through these walls to the liquid, and the liquid is flowing, evaporation in a real microchannel can be simulated. This can be used to design better micro-channels.
6 .1 n m
n m 6 .1
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