Direct numerical simulation of supersonic nanoparticles flow in free-molecule regime using the angular coefficient method

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We employ molecular flow methods to numerically simulate the supersonic nanoparticles flow in free-molecule regime. To streamline the computational complexity, interaction forces between the gas and solid particles are disregarded. We first develop a discrete phase model (DPM) method that integrates the non-rigid body collision model, enabling an accurate simulation of nanoparticle diffusion under the influence of the drag force and Brownian motion force. The nanoparticles considered in this study have sizes below 10 nm, and the accuracy of the DPM method is verified by comparing its results with experimental data. Subsequently, we theoretically and numerically investigate the transmission probability and number density of N2 molecules flowing through two-dimensional (2D) channels and three-dimensional (3D) tubes by using the angular coefficient (AC) method and the direct simulation Monte Carlo (DSMC) method. The findings indicate that as the diameter of the nanoparticle (dp) decreases to 1 nm, the diffusion coefficient (D) and the root mean square displacement (x) of nanoparticles approach the N2 molecules. The microscopic velocity of most N2 molecules falls within the range of 62–1400 m/s, and the macroscopic velocity of N2 flow falls within the range of Ma = 1.28–1.35. In contrast to the DSMC method, the AC method exhibits enhanced accuracy even with a reduced number of grids and obviates the process for large-scale sampling. Additionally, the solution time required by the AC method is approximately 1/10 and 1/13–1/32 of the DSMC method in 3D cylindrical tubes and 2D channels, respectively. Moreover, the AC method demonstrates superior adaptability when dealing with complex geometries.