Research Papers: Fundamental Issues and Canonical Flows

Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows

[+] Author and Article Information
Leila Issa

Department of Mathematics,
Lebanese American University,
Beirut 1102 2801, Lebanon
e-mail: leila.issa@lau.edu.lb

Issam Lakkis

Department of Mechanical Engineering,
American University of Beirut,
Beirut 1107 2020, Lebanon
e-mail: issam.lakkis@aub.edu.lb

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 5, 2013; final manuscript received November 27, 2013; published online March 10, 2014. Assoc. Editor: Daniel Attinger.

J. Fluids Eng 136(5), 051201 (Mar 10, 2014) (9 pages) Paper No: FE-13-1535; doi: 10.1115/1.4026199 History: Received September 05, 2013; Revised November 27, 2013

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

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Shan, X., Wang, Z., Jin, Y., Wu, M., Hua, J., Wong, C., and Maeda, R., 2005, “Studies on a Micro Combustor for Gas Turbine Engines,” J. Micromech. Microeng., 15(9), p. S215–S221. [CrossRef]
Isomura, K., Murayama, M., Teramoto, S., Hikichi, K., Endo, Y., Togo, S., and Tanaka, S., 2006, “Experimental Verification of the Feasibility of a 100 W Class Micro-scale Gas Turbine at an Impeller Diameter of 10 mm,” J. Micromech. Microeng., 16(9), p. S254–S261. [CrossRef]
Diab, N., and Lakkis, I., 2012, “DSMC Simulations of Squeeze Film Between a Micro Beam Undergoing Large Amplitude Oscillations and a Substrate,” Proceedings of the ASME 2012 10th International Conference on Nanochannels, Microchannels, and Minichannels, ICNMM2012.
Senturia, S. D., 2001, Microsystem Design, Springer, New York.
Epstein, A., 2004, “Millimeter-Scale, Micro-electro-mechanical Systems Gas Turbine Engines,” ASME J. Eng. Gas Turbines Power, 126, p. 205–226. [CrossRef]
Maxwell, J., 1879, “On Stresses in Rarified Gases Arising From Inequalities of Temperature,” Philos. Trans. R. Soc. London, 170, pp. 231–256. [CrossRef]
Karniadakis, G., Beskok, A., and Aluru, N., 2005, Microflows and Nanoflows: Fundamentals and Simulation, Vol. 29, Springer, New York.
Al-Bender, F., Lampaert, V., and Swevers, J., 2005, “The Generalized Maxwell-Slip Model: A Novel Model for Friction Simulation and Compensation,” IEEE Trans. Autom. Control, 50(11), pp. 1883–1887. [CrossRef]
Cao, B., Chen, G., Li, Y., and Yuan, Q., 2006, “Numerical Analysis of Isothermal Gaseous Flows in Microchannel,” Chem. Eng. Technol., 29(1), pp. 66–71. [CrossRef]
Arkilic, E., Schmidt, M., and Breuer, K., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178. [CrossRef]
Jang, J., and Wereley, S., 2004, “Pressure Distributions of Gaseous Slip Flow in Straight and Uniform Rectangular Microchannels,” Microfluid. Nanofluid., 1(1), pp. 41–51. [CrossRef]
Graur, I., Meolans, J., and Zeitoun, D., 2006, “Analytical and Numerical Description for Isothermal Gas Flows in Microchannels,” Microfluid. Nanofluid., 2(1), pp. 64–77. [CrossRef]
Venerus, D., and Bugajsky, D., 2010, “Compressible Laminar Flow in a Channel,” Phys. Fluids, 22, p. 046101. [CrossRef]
Stevanovic, N., 2007, “A New Analytical Solution of Microchannel Gas Flow,” J. Micromech. Microeng., 17(8), p. 1695–1702. [CrossRef]
Qin, F., Sun, D., and Yin, X., 2007, “Perturbation Analysis on Gas Flow in a Straight Microchannel,” Phys. Fluids, 19, p. 027103. [CrossRef]
Zohar, Y., Lee, S., Lee, W., Jiang, L., and Tong, P., 2002, “Subsonic Gas Flow in a Straight and Uniform Microchannel,” J. Fluid Mech., 472(1), pp. 125–151. [CrossRef]
Cai, C., Sun, Q., and Boyd, I., 2007, “Gas Flows in Microchannels and Microtubes,” J. Fluid Mech., 589(589), pp. 305–314. [CrossRef]
Lakkis, I., 2008, “System-Level Modeling of Microflows in Circular and Rectangular Channels,” ICNMM2008, ASME.
Issa, L., and Lakkis, I., 2013, “Reduced Order Models of Low Mach Number Isothermal Flows in Microchannels,” Proceedings of ICNMM2013 the ASME 2013 11th International Conference on Nanochannels, Microchannels, and Minichannels.
Batchelor, G. K., 2000, An Introduction to Fluid Dynamics, Cambridge University, Cambridge, UK.
Majda, A., and Lamb, K. G., 1991, Simplified Equations for Low Mach Number Combustion With Strong Heat Release, Springer, New York.


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Fig. 1

Inertia-free isothermal model

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Fig. 3

Schematic for first set of simulations

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Fig. 4

Pressure at inlet to main section for set 1

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Fig. 5

Average volume flow rate predicted by the model (- - - -) compared with fluent (—–)

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Fig. 6

Schematic for second set of simulations

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Fig. 7

Pressure at inlet (—–) and outlet (- - -) of main section versus time (CFD)

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Fig. 8

Volume flow rate at inlet (—–) and outlet (- - -) of main section versus time (CFD)

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Fig. 9

Comparison of time evolution of mean volume-flow rate between model (- -o- -) and CFD (—–) for different values of Mach number

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Fig. 10

Comparison of time evolution of inlet and outlet volume-flow rates between model (- -o- -) and CFD (—–) for case (i)

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Fig. 11

Comparison of time evolution of inlet and outlet volume-flow rates between model (- -o- -) and CFD (—–) for case (ii)

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Fig. 12

Comparison of time evolution of inlet and outlet volume-flow rates between model (- -o- -) and CFD (—–) for case (iii)

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Fig. 13

Time evolution of inlet (—–) and outlet (- - -) volume-flow rates. Kn=0.00216.

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Fig. 14

Time evolution of inlet (—–) and outlet (- - -) volume flow rates. Kn=0.013.



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