Abstract
Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.
Highlights
For modelling ideal gas flow, there are in general two approaches, the microscopic and the macroscopic approach
It shall be shown that the applicability of R13 with PBC (Phenomenological Boundary Conditions) is not limited to one-dimensional systems
Based on the Onsager theory, which utilizes the second law of thermodynamics, evaporation boundary conditions (PBC) for the R13 equations are derived
Summary
For modelling ideal gas flow, there are in general two approaches, the microscopic and the macroscopic approach. Entropy 2018, 20, 680 the transition regime, i.e., 4 × 10−2 < Kn < 2.5 [4], may be those with large mean free paths, e.g., in vacuum or aerospace applications, or those with small characteristic lengths, which can be found in microflows In this regime, rarefaction effects are observed, such as temperature jump and velocity slip at interfaces, Knudsen layers in front of interfaces, transpiration flow, thermal stresses or heat transfer without temperature gradients [4,5,6,7,8]. The Onsager theory assumes linear relations between fluxes and forces and allows one to break the entropy balance into sets of equations, which we utilize as evaporation/condensation boundary conditions [13,14].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
