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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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References

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Figures

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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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