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Research Papers: Flows in Complex Systems

# Experimental Investigation of Microscale Effects in Perforated Plate Aerodynamics

[+] Author and Article Information
Ryszard Szwaba

Tomasz Ochrymiuk

e-mail: tomasz.ochrymiuk@imp.gda.pl

Tomasz Lewandowski

e-mail: tomasz.lewandowski@imp.gda.pl
Institute of Fluid Flow Machinery,
Fiszera 14,
Gdansk PL80-952, Poland

Justyna Czerwinska

Artorg Center,
University of Bern,
Murtenstrasse 50,
Bern CH 3010, Switzerland
e-mail: justyna.czerwinska@artorg.unibe.ch

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 28, 2013; final manuscript received June 27, 2013; published online September 23, 2013. Assoc. Editor: Prof. Ali Beskok.

J. Fluids Eng 135(12), 121104 (Sep 23, 2013) (10 pages) Paper No: FE-13-1056; doi: 10.1115/1.4024962 History: Received January 28, 2013; Revised June 27, 2013

## Abstract

This paper contains an extensive analysis of the flow in microholes based on an experimental investigation. Experiments of the gas flow past a perforated plate with microholes ($110μm$) were carried out. A wide range of pressure differences between the inlet and the outlet were investigated for that purpose. Two distinguishable flow regimes were obtained: the laminar flow with the slip effects and the turbulence transition regime for a very low Reynolds number. The results are in good agreement with the theory, simulations, experiments for large scale perforated plates, and compressible flows in microtubes. The relation between the mass flow rate and the Knudsen, Reynolds, and Mach numbers for the laminar and transitional regime was obtained. It is a quadratic function of the Reynolds and Knudsen numbers ($ReKn$) based on the hole's diameter. The value of the first order tangential momentum accommodation coefficient was estimated. It shows a strong relation to the inlet Knudsen number.

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## Figures

Fig. 1

Top: view of the test section: (1) flow meter, (2) control valve, (3) compensatory chamber, (4) membrane location, (5) second chamber, (6) second valve, and (7) cut-off valve to the vacuum tanks. Bottom: schematic representation of the experiment.

Fig. 2

Schematic representation of the perforated plate (D = 110 μm, L = 500 μm) and the microscopic picture

Fig. 3

Nondimensional number dependencies: (a) the Mach number as a function of the Reynolds number, and (b) the Knudsen number as a function of the Reynolds number

Fig. 4

Mass flow rate as a function of the outlet: (a) Reynolds number, and (b) Knudsen number

Fig. 5

Pressure drop distribution as a function of: (a) the Reynolds and Knudsen numbers at the outlet, and (b) the mass flow rate

Fig. 6

Transition to turbulence in plots of the velocity as a function of the pressure drop: (a) the laminar and turbulence transition regime and (b) only the laminar regime

Fig. 7

Transition to turbulence and compressibility effects shown as changes of the mass flow rate

Fig. 8

Normalized mass flow rate to the critical mass flow rate as a function of the Knudsen and Reynolds numbers

Fig. 9

Comparison with the other experiments for the perforated plates: (a) perforated plates in parallel flow [27] and (b) perforated plates with various microholes [5]

Fig. 10

Comparison with the experimental data in Ref. [50]: (a) the pressure drop as a function of the Reynolds and Knudsen numbers and (b) the mass flow rate as a function of the Knudsen number

Fig. 11

Normalized mass flow rate as a function of the Reynolds and Knudsen numbers at the outlet. The plot contains our experimental data, experiments [50], (a) 3-D compressible Navier–Stokes simulations with 1st-order slip boundary conditions [51] and (b) the theoretical prediction for isothermal gas flow in the channel without slip, with 1st- and 2nd-order slip boundary conditions (see Eq. (18)).

Fig. 12

Normalized mass flow rate between the slip and no-slip value as a function of the outlet Reynolds and Knudsen numbers for laminar flow. The plot shows our experiments and 3-D compressible Navier–Stokes simulations with 1st-order slip boundary conditions [51].

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