Modified lattice Boltzmann solution for non-isothermal rarefied gas flow through microchannel utilizing BSR and second-o
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Modified lattice Boltzmann solution for non‑isothermal rarefied gas flow through microchannel utilizing BSR and second‑order implicit schemes Ehsan Kamali Ahangar1 · Morteza Izanlu2 · Shabnam Dolati Khakhian3 · Abdulmajeed A. Mohamad4 · Quang‑Vu Bach5 Received: 21 May 2020 / Accepted: 25 July 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract Thermal microscale gas flow was simulated into a coplanar microchannel was simulated at a broad range of Knudsen numbers. Attempts were made to improve the accuracy of slip velocity on walls using a modified model with two relaxation times based upon the mesoscopic method. The temperature jump of fluid flow at the wall was captured by a model with a single relaxation time using a second-order implicit method. The Zou–He boundary conditions were employed at both inlet and outlet boundaries, and bounce-back/specular reflection distribution functions were applied to the impermeable walls. The non-equilibrium distribution functions were also used as the inlet temperature boundary condition. A fully developed temperature profile was considered at the microchannel outlet. A pressure ratio of 2 was considered in the simulations, and various parameters such as dimensionless pressure, pressure deviation from the linear pressure, dimensionless velocity at various Knudsen numbers, centerline velocity and slip velocity of the fluid, centerline temperature and fluid temperature on the wall, Nusselt number with changing Knudsen and Prandtl numbers, parameter k along the microchannel length and Cf·Re values were evaluated in the slip and transition flow regimes. The results of the direct simulation Monte Carlo were used to evaluate the correctness of the numerical model. The consistency of the two methods indicated the accuracy of the proposed method. Keywords Microscale gas flow · Mesoscopic method · Second-order implicit method · Bounce-back/specular reflection · Thermodynamics List of symbols B Molecular slip coefficient BBC Bounce-back BSR Bounce-back/specular reflection c Lattice speed (m s−1) * Quang‑Vu Bach [email protected] 1
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 91775‑1111, Iran
2
Faculty of Mechanical Engineering, Semnan University, Semnan 35131‑19111, Iran
3
Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 15916‑34311, Iran
4
Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada
5
Institute of Research and Development, Duy Tan University, Danang 550000, Vietnam
C∗ Temperature jump coefficient Cf Skin friction coefficient ci Discrete velocity vectors (m s−1) cs Sound speed (m s−1) c̄ Mean molecular velocity (m s−1) d Molecular diameter (m) DSMC Direct simulation Monte Carlo Ec Eckert number f Local distribution function (for fluid flow) g Local distribution function (for thermal fluid flow) H Height of the microchannel (m) Kn Knudsen number, Kn = λ/H lu Length unit L Length
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