Session: 12-06-03: Modeling of Nano- and Micro-Scale Phase Change Processes

Paper Number: 173272

Validity of the Schrage Equation in the Prediction of Evaporation and Condensation Rate of Dodecane in a High-Pressure Nitrogen Gas 

Phase change of liquid fuel in a high-pressure air is a process that affects fuel-air mixing in a variety type of engines. Accurate prediction of fuel evaporation rate in air is imperative to develop advanced propulsion systems with high performance. Although numerous studies have shown that the Schrage equation can accurately predict the evaporation and condensation rate of monatomic fluids, diatomic fluids, polar fluids, and alkane fluids, the validity of the Schrage equation in predicting the evaporation and condensation rate of alkane in the presence of air has never been verified. The main objective of this work to use molecular dynamics (MD) simulations to test the validity of accuracy of Schrage equation in predicting evaporation and condensation rate of dodecane (a diesel surrogate) in air (approximated as a N₂ gas) at various N₂ gas pressures.

In the MD model, the intra- and intermolecular interactions of dodecane molecules are modeled by the united-atom (UA) potential model. The intermolecular interactions between dodecane and N₂ molecules are modeled by Lennard-Jones potential with the parameters tuned to fit the experimental data of the solubility of N₂ gas in liquid dodecane at various temperatures. The validity of the Schrage equation is tested in the dodecane-N₂ model system at a temperature ranging from 400 K to 500 K and N₂ gas pressure ranging from 0 to 30 atm (i.e., from below the critical pressure 18 atm to above the critical pressure of dodecane).

The mass accommodation coefficient (MAC), which is defined as the fraction of vapor molecules that strike the interface and are accommodated to the liquid phase, is an important parameter that determines the evaporation and condensation rate at a liquid-gas interface. Our MD simulation results show that the MAC of dodecane decreases as N₂ gas pressure increases. Hence, a high-pressure N₂ gas results in a higher resistance to the liquid-vapor phase change at the fuel-air interface and reduces the evaporation and condensation rate for the given vapor density difference across the interface.

In the Schrage equation, it is usually assumed that condensation MAC is the same as the evaporation MAC. However, we find the evaporation MAC is higher than the condensation MAC at the evaporating dodecane surface and is lower than the condensation MAC at the condensation dodecane surface. The difference between the evaporation MAC and the condensation MAC increases as the evaporation and condensation rate increases. The evaporation MAC equals to the condensation MAC only when the liquid dodecane is in equilibrium with the vapor dodecane, i.e. when no evaporation or condensation occurs. If the difference between the evaporation MAC and the condensation MAC are not taken into account in the Schrage equation, it could overpredict the evaporation and condensation rate of dodecane by over 30%.

We also find from our MD simulations that a high N₂ gas pressure increases the saturated dodecane vapor pressure at the given temperature by more than 10%. The higher saturated vapor density is mainly because the mixing of dodecane vapor with N₂ gas reduces the Gibbs free energy of dodecane vapor. Neglecting the saturated density increase in the presence of the high N₂ gas could significantly underpredict the evaporation rate and overpredict the condensation rate of dodecane.

Presenting Author: Jordan Hartfield Missouri University of Science and Technology

Presenting Author Biography: Jordan Hartfield is a Ph.D. student from Department of Mechanical and Aerospace Engineering at Missouri University of Science and Technology.

Authors:

Jordan Hartfield Missouri University of Science and Technology
Wazih Tausif Missouri University of Science and Technology
Zhi Liang Missori University of Science and Technology