Lattice Boltzmann Simulation of the Hydrodynamic Entrance Region of Rectangular Microchannels in the Slip Regime

Niya Ma; Zhipeng Duan; Hao Ma; Liangbin Su; Peng Liang; Xiaoru Ning; Boshu He; Xin Zhang

doi:10.3390/mi9020087

Lattice Boltzmann Simulation of the Hydrodynamic Entrance Region of Rectangular Microchannels in the Slip Regime

Micromachines (Basel). 2018 Feb 16;9(2):87. doi: 10.3390/mi9020087.

Authors

Niya Ma¹, Zhipeng Duan², Hao Ma³, Liangbin Su⁴, Peng Liang⁵, Xiaoru Ning⁶, Boshu He⁷, Xin Zhang^{8

9}

Affiliations

¹ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. 15121339@bjtu.edu.cn.
² School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. zpduan@bjtu.edu.cn.
³ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. 16121364@bjtu.edu.cn.
⁴ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. 16116368@bjtu.edu.cn.
⁵ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. 14121328@bjtu.edu.cn.
⁶ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. 17121369@bjtu.edu.cn.
⁷ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. hebs@bjtu.edu.cn.
⁸ School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China. zhangxin@bjtu.edu.cn.
⁹ Beijing Key Laboratory of Powertrain for New Energy Vehicle, Beijing Jiaotong University, Beijing 100044, China. zhangxin@bjtu.edu.cn.

Abstract

Developing a three-dimensional laminar flow in the entrance region of rectangular microchannels has been investigated in this paper. When the hydrodynamic development length is the same magnitude as the microchannel length, entrance effects have to be taken into account, especially in relatively short ducts. Simultaneously, there are a variety of non-continuum or rarefaction effects, such as velocity slip and temperature jump. The available data in the literature appearing on this issue is quite limited, the available study is the semi-theoretical approximate model to predict pressure drop of developing slip flow in rectangular microchannels with different aspect ratios. In this paper, we apply the lattice Boltzmann equation method (LBE) to investigate the developing slip flow through a rectangular microchannel. The effects of the Reynolds number (1 < Re < 1000), channel aspect ratio (0 < ε < 1), and Knudsen number (0.001 < Kn < 0.1) on the dimensionless hydrodynamic entrance length, and the apparent friction factor, and Reynolds number product, are examined in detail. The numerical solution of LBM can recover excellent agreement with the available data in the literature, which proves its accuracy in capturing fundamental fluid characteristics in the slip-flow regime.

Keywords: apparent friction factor and Reynolds number product; entrance region; hydrodynamic development length; lattice Boltzmann equation method (LBE); rectangular microchannels; slip flow.