The study of the effects of triangular roughness on the thermal creep flow in Knudsen pumps with DSMC method

Authors

1 Department of Mechanical Engineering, Engineering Faculty. Razi University, Iran

2 Department of Mechanical Engineering, Engineering Faculty. Razi University, Iran.

Abstract

In this study, the effects of wall roughness on the flow parameters in Knudsen pumps are investigated using the particle-based direct simulation Monte Carlo method. For this purpose, the thermal creep flow in a microchannel with a linear temperature gradient on the walls is solved in a wide range of Knudsen numbers (0.1 ≤ Kn ≤ 10). The roughness is modeled as triangular elements on the walls. A comprehensive study is done on the geometrical parameters of the roughness, including height (0 ≤ε≤10), aspect ratio (1 ≤ξ≤3), and the distance of the elements (1 ≤χ≤5). Evaluation of the results indicates that the mass flow rate of the thermal creep flow in rough channels, no matter how small the roughness, has a significant reduction compared to the smooth channel. For example, a reduction of 26% is observed for a tinny roughness of ε=1.25%. It is also observed that the aspect ratio and the distance of the rough elements do not have a significant effect on the flow parameters in the studied range.

Keywords


[1] An S, Qin Y, Gianchandani YB (2015) A monolithic high-flow Knudsen pump using vertical Al2O3 channels in SOI. J Microelectromech Syst 24(5): 1606-1615.
[2] Gupta NK, Gianchandani YB (2011) Porous ceramics for multistage Knudsen micropumps modeling approach and experimental evaluation. J Micromech Microeng 21(9): 095029.
[3] Takata S, Sugimoto H, Kosuge S (2007) Gas separation by means of the Knudsen compressor. Eur. J Mech B Fluids 26(2): 155-181.
[4] Bell AD (2013) Human powered Knudsen pump for pneumatic pharmaceutical delivery. University of Louisville, Electronic Theses and Dissertations. Paper 97.
[5] McNamara S, Gianchandani YB (2005) On-chip vacuum generated by a micromachined Knudsen pump. J Microelectromech Syst 14(4): 741-746.
[6] Kugimoto K, Hirota Y, Yamauchi T, Yamaguchi H, Niimi T (2018) A novel heat pump system using a multi-stage Knudsen compressor. Int J Heat Mass Transfer 127(A): 84-91.
[7] Vargo SE, Muntz EP (2001) Initial results from the first MEMS fabricated thermal transpiration-driven vacuum pump. Proc AIP Conference 585(1).
[8] Gupta NK, Gianchandani YB (2008) Thermal transpiration in zeolites: A mechanism for motionless gas pumps. Appl Phys Lett 93(19): 193511.
[9] Gupta NK, Gianchandani YB (2009) A planar cascading architecture for a ceramic Knudsen micropump. Proc 15th Int Conf on Solid-State Sensors, Actuators and Microsystems.
[10] Pharas K, McNamara S (2010) Knudsen pump driven by a thermoelectric material. J Micromech Microeng 20(12): 125032.
[11] Aoki K, Degond P, Mieussens L, Nishioka M,  Takata S (2007) Numerical simulation of a Knudsen pump using the effect of curvature of the channel. Proc Rarefied Gas Dynamics. MS Ivanov and AK Rebrov, Eds. Novosibirsk: 1079-1084.
[12] Hu Y, Werner C, Li D (2003) Influence of three-dimensional roughness on pressure-driven flow through microchannels. J Fluids Eng 125(5): 871-879.
[13] Kleinstreuer C, Koo J (2004) Computational analysis of wall roughness effects for liquid flow in micro-conduits. J Fluids Eng 126(1): 1-9.
[14] Cao BY, Chen M, Guo ZY (2006) Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation. Int J Eng Sci 44(13-14): 927-937.
[15] رجبی رمضان، ثقفیان محسن (1395) بررسی عددی اثر تلفات اصطکاکی و زبری سطح بر جریان سیال و انتقال حرارت در میکروکانالها با استفاده از بسط اختلالات. روش­های عددی در مهندسی 156-143 :(1)35.
[16] Zhang C, Chen Y, Deng Z, Shi M (2012) Role of rough surface topography on gas slip flow in microchannels. Phys Rev E 86(1): 016319.
[17] Noorian H, Toghraie D, Azimian AR (2014) The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation. Heat Mass Transfer 50(1): 95-104.
[18] Rovenskaya OI, Croce G (2016) Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes. Microfluid Nanofluid 20(5): 81.
[19] Jia J, Song Q, Liu Z, Wang B (2018) Effect of wall roughness on performance of microchannel applied in microfluidic device. Microsyst Technol 25: 2385-2397.
[20] Yamamoto K, Takeuchi H, Hyakutake T (2005) Effect of surface grooves on the rarefied gas flow between two parallel walls. Proc AIP Conference 762(1): 156-161.
[21] Baier T, Hardt S, Shahabi V, Roohi E (2017) Knudsen pump inspired by Crooks radiometer with a specular wall. Phys Rev Fluids 2: 033401.
[22] Shahabi V, Baier T, Roohi E, Hardt S (2017) Thermally induced gas flows in ratchet channels with diffuse and specular boundaries. Sci Rep 7: 41412.
[23] Lotfian A, Roohi E (2019) Radiometric flow in periodically patterned channels: Fluid physics and improved configurations. J Fluid Mech 860: 544-576.
[24] Amiri-Jaghargh A, Roohi E, Niazmand H (2013) DSMC simulation of low knudsen micro/nano flows using small number of particles per cells. J Heat Transfer 135(10): 101008-101008.
[25] Amiri-Jaghargh A, Roohi E, Stefanov S, Nami H, Niazmand H (2014) DSMC simulation of micro/nano flows using SBT-TAS technique. Comput Fluids 102: 266-276.
[26] Liou WW, Fang YC (2000) Implicit boundary conditions for direct simulation Monte Carlo method in MEMS flow predictions. CMES-Computer Modeling in Engineering & Sciences 1(4): 119-128.
[27] Akhlaghi H, Roohi H (2014) Mass flow rate prediction of pressure–temperature-driven gas flows through micro/nanoscale channels. Continuum Mech Thermodyn 26(1): 67-78.
[28] Alexander FJ, Garcia AL, Alder BJ (1998) Cell size dependence of transport coefficients in stochastic particle algorithms. Phys Fluids 10(6): 1540-1542.
[29] Hadjiconstantinou NG (2000) Analysis of k Phys. Fluids 12(10): 2634-2638.
[30] Takata S, Funagane H (2013) Singular behaviour of a rarefied gas on a planar boundary. J Fluid Mech 717: 30-47.
[31] Mozafari MS, Roohi E (2017) On the       thermally-driven gas flow through divergent micro/nanochannels. Int J Mod Phys C 28(12): 1750143.