Direct Simulation Monte Carlo Analysis of Flow in Knudsen Pumps with Square-Shaped Wall Roughness

Document Type : Research Article

Authors

Department of Mechanical Engineering, Razi University, Kermanshah, Iran

Abstract

Thermal creep Knudsen pumps are made up of micro/nanochannels subjected to a temperature gradient. In such a combination, the fluid flows from the cold side to the hot side based on the thermal creep phenomenon. Due to the widespread use of Knudsen pumps in various applications, much research has been done to improve their technology. In this work, the effects of wall surface roughness on the flow field characteristics are investigated using the molecular-based direct simulation Monte Carlo method. The surface roughness is modeled by square bumps on the wall. The roughness parameters, including relative roughness, roughness aspect ratio, and roughness distance, are studied in a wide range, that is, 0 ≤ ε ≤ 10, 0.5 ≤ ξ ≤ 2, and 3 ≤ χ ≤ 10, respectively. It is concluded that the existence of roughness, no matter how small, has a significant effect on the flow conditions; so that the subminiature roughness of ε = 0.5% results in a 24% decrease in the mass flow rate. This emphasizes the importance of considering the role of surface roughness in the calculation of the performance of Knudsen pumps. Furthermore, the results indicate that the mass flow rate is independent of the relative roughness and the roughness distance for ε ≤ 1.25% and χ ≤ 5, respectively.

Keywords

Main Subjects


[1] H. Yamaguchi, G. Kikugawa, Molecular dynamics study on flow structure inside a thermal transpiration flow field, Physics of Fluids, 33(1) (2021) 012005.
[2] S.E. Vargo, E.P. Muntz, Initial results from the first MEMS fabricated thermal transpiration-driven vacuum pump, AIP Conference Proceedings, 585(1) (2001) 502-509.
[3] N.K. Gupta, Y.B. Gianchandani, A planar cascading architecture for a ceramic Knudsen micropump, in:  TRANSDUCERS 2009 - 2009 International Solid-State Sensors, Actuators and Microsystems Conference, Denver, CO, 2009, pp. 2298-2301.
[4] N.V. Toan, N. Inomata, N.H. Trung, T. Ono, Knudsen pump produced via silicon deep RIE, thermal oxidation, and anodic bonding processes for on-chip vacuum pumping, Journal of Micromechanics and Microengineering, 28(5) (2018) 055001.
[5] K. Kugimoto, Y. Hirota, Y. Kizaki, H. Yamaguchi, T. Niimi, Performance prediction method for a multi-stage Knudsen pump, Physics of Fluids, 29(12) (2017) 122002.
[6] J. Ye, J. Shao, J. Xie, Z. Zhao, J. Yu, Y. Zhang, S. Salem, The hydrogen flow characteristics of the multistage hydrogen Knudsen compressor based on the thermal transpiration effect, International Journal of Hydrogen Energy, 44(40) (2019) 22632-22642.
[7] K. Aoki, P. Degond, L. Mieussens, M. Nishioka, S. Takata, Numerical Simulation of a Knudsen Pump Using the Effect of Curvature of the Channel, in:  Rarefied Gas Dynamics, Novosibirsk, 2007, pp. 1079-1084.
[8] D.M. Bond, V. Wheatley, M. Goldsworthy, Numerical investigation of curved channel Knudsen pump performance, International Journal of Heat and Mass Transfer, 76 (2014) 1-15.
[9] D.M. Bond, V. Wheatley, M. Goldsworthy, Numerical investigation into the performance of alternative Knudsen pump designs, International Journal of Heat and Mass Transfer, 93 (2016) 1038-1058.
[10] M.S. Mozaffari, E. Roohi, On the thermally-driven gas flow through divergent micro/nanochannels, International Journal of Modern Physics C, 28(12) (2017) 1750143.
[11] G. Tatsios, G. Lopez Quesada, M. Rojas-Cardenas, L. Baldas, S. Colin, D. Valougeorgis, Computational investigation and parametrization of the pumping effect in temperature-driven flows through long tapered channels, Microfluidics and Nanofluidics, 21(5) (2017) 99.
[12] B.-Y. Cao, M. Chen, Z.-Y. Guo, Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation, International Journal of Engineering Science, 44(13) (2006) 927-937.
[13] C. Zhang, Y. Chen, Z. Deng, M. Shi, Role of rough surface topography on gas slip flow in microchannels, Physical Review E, 86(1) (2012) 016319.
[14] O.I. Rovenskaya, G. Croce, Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes, Microfluidics and Nanofluidics, 20(5) (2016) 81.
[15] J. Jia, Q. Song, Z. Liu, B. Wang, Effect of wall roughness on performance of microchannel applied in microfluidic device, Microsystem Technologies, 25(6) (2019) 2385-2397.
[16] X. Wang, T. Su, W. Zhang, Z. Zhang, S. Zhang, Knudsen pumps: a review, Microsystems & Nanoengineering, 6(1) (2020) 26.
[17] K. Yamamoto, H. Takeuchi, T. Hyakutake, Effect of Surface Grooves on the Rarefied Gas Flow Between Two Parallel Walls, AIP Conference Proceedings, 762(1) (2005) 156-161.
[18] J. Shao, J. Ye, Y. Zhang, S. Salem, Z. Zhao, J. Yu, Effect of the microchannel obstacles on the pressure performance and flow behaviors of the hydrogen Knudsen compressor, International Journal of Hydrogen Energy, 44(40) (2019) 22691-22703.
[19] J. Ye, J. Shao, Z. Hao, S. Salem, Y. Zhang, Y. Wang, Z. Li, Characteristics of thermal transpiration effect and the hydrogen flow behaviors in the microchannel with semicircular obstacle, International Journal of Hydrogen Energy, 44(56) (2019) 29724-29732.
[20] N. Mirnezhad, A. Amiri-Jaghargh, The study of the effects of triangular roughness on the thermal creep flow in Knudsen pumps with DSMC method, Journal of Solid and Fluid Mechanics, 10(4) (2020) 97-109.
[21] G.E. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer-Verlag New York, 2005.
[22] W. Wagner, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, Journal of Statistical Physics, 66(3) (1992) 1011-1044.
[23] G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, 1994.
[24] A. Amiri-Jaghargh, E. Roohi, H. Niazmand, S. Stefanov, DSMC Simulation of Low Knudsen Micro/Nanoflows Using Small Number of Particles per Cells, Journal of Heat Transfer, 135(10) (2013).
[25] A. Amiri-Jaghargh, E. Roohi, S. Stefanov, H. Nami, H. Niazmand, DSMC simulation of micro/nano flows using SBT–TAS technique, Computers & Fluids, 102 (2014) 266-276.
[26] W.W. Liou, Y.C. Fang, Implicit Boundary Conditions for Direct Simulation Monte Carlo Method in MEMS Flow Predictions, Computer Modeling in Engineering & Sciences, 1(4) (2000) 119--128.
[27] T. Ohwada, Y. Sone, K. Aoki, Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard‐sphere molecules, Physics of Fluids A: Fluid Dynamics, 1(9) (1989) 1588-1599.
[28] H. Akhlaghi, E. Roohi, Mass flow rate prediction of pressure–temperature-driven gas flows through micro/nanoscale channels, Continuum Mechanics and Thermodynamics, 26(1) (2014) 67-78.
[29] F.J. Alexander, A.L. Garcia, B.J. Alder, Cell size dependence of transport coefficients in stochastic particle algorithms, Physics of Fluids, 10(6) (1998) 1540-1542.
[30] N.G. Hadjiconstantinou, Analysis of discretization in the direct simulation Monte Carlo, Physics of Fluids, 12(10) (2000) 2634-2638.