Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2025-01-01T10:01:53.629Z Has data issue: false hasContentIssue false
  • English
  • Français

Rarefied flow separation in microchannel with bends

Published online by Cambridge University Press:  28 August 2020

Minh Tuan Ho Open the ORCID record for Minh Tuan Ho [Opens in a new window] ,
Jun Li Open the ORCID record for Jun Li [Opens in a new window] ,
Wei Su ,
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window] ,
Matthew K. Borg ,
Zhihui Li  and
Yonghao Zhang Open the ORCID record for Yonghao Zhang [Opens in a new window]
Minh Tuan Ho
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, GlasgowG1 1XJ, UK
Jun Li*
Affiliation:
Center for Integrative Petroleum Research, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
Wei Su
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, GlasgowG1 1XJ, UK
Lei Wu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Matthew K. Borg
Affiliation:
School of Engineering, University of Edinburgh, EdinburghEH9 3FB, UK
Zhihui Li
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang621000, PR China
Yonghao Zhang*
Affiliation:
James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, GlasgowG1 1XJ, UK
*
†Email addresses for correspondence: junli@kfupm.edu.sa, yonghao.zhang@strath.ac.uk
†Email addresses for correspondence: junli@kfupm.edu.sa, yonghao.zhang@strath.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

Based on an accurate numerical solution of the kinetic equation using well-resolved spatial and velocity grids, the separation of rarefied gas flow in a microchannel with double rectangular bends is investigated over a wide range of Knudsen and Reynolds numbers. Rarefaction effects are found to play different roles in flow separation (vortex formation) at the concave and convex corners. Flow separations near the concave and convex corners are only observed for a Knudsen number up to $0.04$ and $0.01$, respectively. With further increase of the Knudsen number, flow separation disappears. Due to the velocity slip at the solid walls, the concave (convex) vortex is suppressed (enhanced), which leads to the late (early) onset of separation of rarefied gas flows with respect to the Reynolds number. The critical Reynolds numbers for the emergence of concave and convex vortices are found to be as low as $0.32\times 10^{-3}$ and $30.8$, respectively. The slip velocity near the concave (convex) corner is found to increase (decrease) when the Knudsen number increases. An adverse pressure gradient appears near the concave corner for all the examined Knudsen numbers, while for the convex corner it only occurs when the Knudsen number is less than $0.1$. Due to the secondary flow and adverse pressure gradient near the rectangular bends, the mass flow rate ratio between the bent and straight channels of the same length is a non-monotonic function of the Knudsen number. Our results clarify the diversified and often contradictory observations reported in the literature about flow rate enhancement and vortex formation in bent microchannels.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A26
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Agrawal, A., Djenidi, L. & Agrawal, A. 2009 Simulation of gas flow in microchannels with a single 90$^{\circ }$ bend. Comput. Fluids 38 (8), 1629–1637.CrossRefGoogle Scholar
Berman, A. S. 1966 Erratum: free molecule transmission probabilities. J. Appl. Phys. 37 (12), 4598.CrossRefGoogle Scholar
Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press.Google Scholar
Biswas, G., Breuer, M. & Durst, F. 2004 Backward-facing step flows for various expansion ratios at low and moderate Reynolds numbers. Trans. ASME: J. Fluids Engng 126 (3), 362–374.Google Scholar
Bradshaw, P. & Wong, F. Y. F. 1972 The reattachment and relaxation of a turbulent shear layer. J. Fluid Mech. 52 (1), 113–135.CrossRefGoogle Scholar
Broadwell, J. E. 1964 Study of rarefied shear flow by the discrete velocity method. J. Fluid Mech. 19 (3), 401–414.CrossRefGoogle Scholar
Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24 (1), 113–151.CrossRefGoogle Scholar
Gu, X. J. & Emerson, D. R. 2009 A high-order moment approach for capturing non-equilibrium phenomena in the transition regime. J. Fluid Mech. 636, 177–216.CrossRefGoogle Scholar
Ho, M. T. & Graur, I. 2014 Numerical study of unsteady rarefied gas flow through an orifice. Vacuum 109, 253–265.CrossRefGoogle Scholar
Ho, M. T., Li, J., Wu, L., Reese, J. M. & Zhang, Y. 2019 A comparative study of the DSBGK and DVM methods for low-speed rarefied gas flows. Comput. Fluids 181, 143–159.CrossRefGoogle Scholar
Kulakarni, N. K., Shterev, K. & Stefanov, S. K. 2015 Effects of finite distance between a pair of opposite transversal dimensions in microchannel configurations: DSMC analysis in transitional regime. Intl J. Heat Mass Transfer 85, 568–576.CrossRefGoogle Scholar
Lee, S. Y. K., Wong, M. & Zohar, Y. 2001 Gas flow in microchannels with bends. J. Micromech. Microengng 11 (6), 635–644.CrossRefGoogle Scholar
Li, J. 2011 Direct simulation method based on BGK equation. In Proceedings of the 27th International Symposium on Rarefied Gas Dynamics (ed. Levin, D. A., Wysong, I. J. & Garcia, A. L.), vol. 1333, pp. 283–288. AIP.Google Scholar
Li, J. 2020 Multiscale and Multiphysics Flow Simulations of Using the Boltzmann Equation. Springer.CrossRefGoogle Scholar
Liu, W., Tang, G., Su, W., Wu, L. & Zhang, Y. 2018 Rarefaction throttling effect: influence of the bend in micro-channel gaseous flow. Phys. Fluids 30 (8), 082002.CrossRefGoogle Scholar
Loyalka, S. K. 1968 Momentum and temperature-slip coefficients with arbitrary accommodation at the surface. J. Chem. Phys. 48 (12), 5432–5436.CrossRefGoogle Scholar
Maharudrayya, S., Jayanti, S. & Deshpande, A. P. 2004 Pressure losses in laminar flow through serpentine channels in fuel cell stacks. J. Power Sources 138 (1–2), 1–13.CrossRefGoogle Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1), 1–18.CrossRefGoogle Scholar
Raju, R. & Roy, S. 2004 Hydrodynamic model for microscale flows in a channel with two 90 deg bends. J. Fluids Engng 126 (3), 489–492.CrossRefGoogle Scholar
Rovenskaya, O. I. 2016 Computational study of 3D rarefied gas flow in microchannel with 90 bend. Eur. J. Mech. B/Fluids 59, 7–17.CrossRefGoogle Scholar
Sazhin, O. 2009 Rarefied gas flow through a channel of finite length into a vacuum. J. Expl Theor. Phys. 109 (4), 700–706.CrossRefGoogle Scholar
Shakhov, E. M. 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 95–96.CrossRefGoogle Scholar
Sharipov, F. 2004 Numerical simulation of rarefied gas flow through a thin orifice. J. Fluid Mech. 518, 35–60.CrossRefGoogle Scholar
Sharipov, F. & Graur, I. A. 2012 Rarefied gas flow through a zigzag channel. Vacuum 86 (11), 1778–1782.CrossRefGoogle Scholar
Sharipov, F. & Seleznev, V. 1998 Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 (3), 657–706.CrossRefGoogle Scholar
Su, W., Ho, M. T., Zhang, Y. & Wu, L. 2020 a GSIS: an efficient and accurate numerical method to obtain the apparent gas permeability of porous media. Comput. Fluids 206, 104576.CrossRefGoogle Scholar
Su, W., Wang, P., Liu, H. & Wu, L. 2019 a Accurate and efficient computation of the Boltzmann equation for Couette flow: influence of intermolecular potentials on Knudsen layer function and viscous slip coefficient. J. Comput. Phys. 378, 573–590.CrossRefGoogle Scholar
Su, W., Wang, P., Zhang, Y. & Wu, L. 2019 b A high-order hybridizable discontinuous Galerkin method with fast convergence to steady-state solutions of the gas kinetic equation. J. Comput. Phys. 376, 973–991.CrossRefGoogle Scholar
Su, W., Zhu, L., Wang, P., Zhang, Y. & Wu, L. 2020 b Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations? J. Comput. Phys. 407, 109245.CrossRefGoogle Scholar
Titarev, V. A. 2007 Conservative numerical methods for model kinetic equations. Comput. Fluids 36 (9), 1446–1459.CrossRefGoogle Scholar
Titarev, V. A. 2012 a Implicit high-order method for calculating rarefied gas flow in a planar microchannel. J. Comput. Phys. 231 (1), 109–134.CrossRefGoogle Scholar
Titarev, V. A. 2012 b Rarefied gas flow in a planar channel caused by arbitrary pressure and temperature drops. Intl J. Heat Mass Transfer 55 (21-22), 5916–5930.CrossRefGoogle Scholar
Titarev, V. A. 2013 Rarefied gas flow in a circular pipe of finite length. Vacuum 94, 92–103.CrossRefGoogle Scholar
Valougeorgis, D. & Naris, S. 2003 Acceleration schemes of the discrete velocity method: gaseous flows in rectangular microchannels. SIAM J. Sci. Comput. 25 (2), 534–552.CrossRefGoogle Scholar
Varade, V., Agrawal, A., Prabhu, S. V. & Pradeep, A. M. 2015 Early onset of flow separation with rarefied gas flowing in a 90$^{\circ }$ bend tube. Exp. Therm. Fluid Sci. 66, 221–234.CrossRefGoogle Scholar
Varoutis, S., Day, C. & Sharipov, F. 2012 Rarefied gas flow through channels of finite length at various pressure ratios. Vacuum 86 (12), 1952–1959.CrossRefGoogle Scholar
Wang, M. & Li, Z. 2004 Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method. Intl J. Heat Fluid Flow 25 (6), 975–985.CrossRefGoogle Scholar
Wang, P., Ho, M. T., Wu, L., Guo, Z. & Zhang, Y. 2018 A comparative study of discrete velocity methods for low-speed rarefied gas flows. Comput. Fluids 161, 33–46.CrossRefGoogle Scholar
White, C., Borg, M. K., Scanlon, T. J. & Reese, J. M. 2013 A DSMC investigation of gas flows in micro-channels with bends. Comput. Fluids 71, 261–271.CrossRefGoogle Scholar
Xiong, R. & Chung, J. N. 2008 Effects of miter bend on pressure drop and flow structure in micro-fluidic channels. Intl J. Heat Mass Transfer 51 (11-12), 2914–2924.CrossRefGoogle Scholar
Yang, J. Y. & Huang, J. C. 1995 Rarefied flow computations using nonlinear model Boltzmann equations. J. Comput. Phys. 120 (2), 323–339.CrossRefGoogle Scholar