Host: The Japan Society of Vacuum and Surface Science
Name : Annual Meeting of the Japan Society of Vacuum and Surface Science 2023
Location : [in Japanese]
Date : October 31, 2023 - November 02, 2023
1. Introduction
In the Direct Simulation Monte Carlo (DSMC) method[1] which is generally used to analyze rarefied gas flows in, e.g., vaccum chambers and space, porous media have been modeled by randomly arranged solid cells as obstacles[2], packed cylinders or spheres[3], or using geometries imaged by computed tomography[4]. Unlike these conventional ways, a novel porous media model called virtual solid cell (VSC)[5] will be demonstrated in this abstract and at the meeting.
2. VSC model
In the VSC model, porous media is treated as a fluid domain, and the same effects as the conventional models are achieved by setting a stochastic limit corresponding to the porosity on the inter-cell transfer of gas molecules. The advantage of the VSC model as a stochastic approach enables one-dimensional (1D) simulation of a rarefied gas flow passing through porous media, contributing to a significant reduction in computation time[5]. In addition, it can be applied to complex porous media with various porosities and to rough surfaces as a new surface boundary model. These two application examples of the VSC model are described below.
Figure 1(a) shows the number density distribution of N2 gas flow passing through a porous wall formed with multiple cross-shaped obstacles. The geometrical porosity of the porous wall is 0.445, and the cross-shaped obstacles are modeled using VSCs with a porosity of 0.1. The gas pressures Pin at the upstream boundary and Pout at the downstream boundary are 1 Pa and 0 Pa, respectively. The top and bottom boundary conditions are specified as symmetry. The N2 gas mainly flows through the gap between the cross-shaped obstacles. In contrast, some obstacles with a higher N2 number density than the main flow indicate that N2 molecules are trapped inside the obstacles. As shown in this example, the VSC model can represent porous media with various porosities.
Figure 1(b) illustrates the temperature distribution of He gas enclosed between parallel plates. The Knudsen number Kn with reference to the distance between the plates is 4.59. The conditions of the wall temperatures and thermal accommodation coefficients are given in Fig. 1(b). In this example, two VSC layers are adopted to model surface roughness at the right side of the top wall. Thus, the simulated gas temperature is higher on the right side, especially in the vicinity of the VSC layers, than on the left side between the parallel plates. The gas temperature approaches the top wall temperature inside the VSC layers due to repeated molecular reflections as on a rough surface. This example depicts that the VSC model can also mimic surface roughness.
3. Summary
The VSC model to treat porous media in the DSMC method has been briefly demonstrated in this abstract. The conventional porous media models with complex geometry can be simplified by a stochastic procedure in the VSC model. Consequently, the VSC model enables 1D simulation of a rarefied gas flow passing through porous media, contributing to a significant reduction in computation time. It also facilitates the treatment of complex porous media with various porosities. Furthermore, the VSC model shows its potential as a new boundary model to describe surface roughness. Further details will be presented at the meeting.
References
[1] G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford Univ. Press, 1994).
[2] A. Saito et al., Trans. Jpn. Soc. Mech. Eng. B. 61, 248 (1995).
[3] Y. Kawagoe et al., Microfluid Nanofluid 20, 162 (2016).
[4] C. Christou and K. Dadzie, Society of Petroleum Engineers, Heriot-Watt Univ., SPE-173314-MS (2015).
[5] K. Denpoh, Vac. Surf. Sci. 66, 490 (2023).
