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Research Papers: Flows in Complex Systems

# Experimental Study on Aerodynamics of Microelectromechanical Systems Based Single-Crystal-Silicon Microscale Supersonic Nozzle

[+] Author and Article Information
Toshiyuki Toriyama

e-mail: toriyama@se.ritsumei.ac.jp
Department of Micro System Technology,
Ritsumeikan University,
1-1-1 Nojihigashi, Kusatsu,
Shiga 525-8577, Japan

To support the above-mentioned experimental evidence, CFD analysis (CFX ver. 6.1) was carried out for the flow field around the pressure tap. If a secondary flow, which disturbs the main core flow field parallel to the channel wall, is induced at vicinity of the pressure tap, the pressure gradient normal to the wall $∇p$ is generated. The nozzle has favorable density (pressure) gradient $∇ρ$ along the divergent channel section. Therefore, span-wise vortex ω is generated at the inlet region of the pressure tap due to the vorticity equation, i.e., $Dω/Dt∝∇ρ×∇p$ [16]. Indeed, the span-wise vortex was generated at 10 μm, 20 μm, and 30 μm diameters but disappeared at a 5 μm diameter.

Indeed, $(h/ρuCp)Pr2/3F(β)=Cf/2$ holds for Falkner–Skan-type flow [23,24]. The factor F(β) is a measure of the pressure gradient. If β > 0, the pressure gradient is negative or favorable. Naturally, β = 0 and F(0) = 1 denote a flat plate. $0<β≪1$ and $F(β)≅1$ hold for our nozzle flow. This corresponds to the modest pressure gradient. Thus, the Reynolds analogy is reliable.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 26, 2012; final manuscript received March 18, 2013; published online May 23, 2013. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng. 135(8), 081101 (May 23, 2013) (11 pages) Paper No: FE-12-1475; doi: 10.1115/1.4024080 History: Received September 26, 2012; Revised March 18, 2013

## Abstract

In this paper, the design, microfabrication, and direct measurement of the static pressure distribution for the aerodynamics of a single-crystal-silicon microscale supersonic nozzle are described. The microscale supersonic nozzle has a convergent–divergent section and a throat area of 100μm × 300μm. The microscale supersonic nozzle was fabricated by silicon bulk micromachining technology. The degree of the rarefaction of nozzle flow was determined by the Knudsen number (Kn). The operation envelope that determines whether the continuum or rarefied flow assumption is appropriate can be expressed as a function of Kn and related parameters. The effect of nonadiabatic operation on microscale nozzle flow was investigated on the basis of wall heat transfer. These physical correlations were taken into account for the classical Shapiro's equations to analyze the microscale nozzle flow aerodynamics (Shapiro, 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, Ronald, New York, Chap. 7,8; Greitzer et al., 2006, Internal Flow, Cambridge University, Cambridge, UK, Chap. 2,10). Furthermore, the solutions of Shapiro's equations were compared with the experimental results by the authors and other research institutions in order to demonstrate the validity of the proposed aerodynamics design concept for microscale continuum flow.

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## Figures

Fig. 1

Calculation of Kn for each device reported by other research institutions (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 2

Comparison of calculated operation envelope of the governing equation of motion and experimental data (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 3

Relationship between Nu and (2x/dH)/RePr (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 4

Relationship between Nu and Kn (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 5

Divergent section of microscale nozzle contour on the basis of method of the characteristics

Fig. 6

Exposed schematic views of device structures observed from front (a) and back (b) sides

Fig. 7

Scanning electron microscope images of exposed view of nozzle and wall static pressure taps. (a) Convergent-divergent nozzle section and (b) Exposed view of throat from downstream to upstream.

Fig. 8

Photomicrographs of fabricated device. (a) Layer #2 (front side), (b) layer #2 (back side), (c) layer #3, and (d) assembled multilayer structure.

Fig. 9

Schematic views of device fixture for pressure measurement. (a) Device fixed to interface and (b) configuration of mechanical seals.

Fig. 10

Schematic view of experimental setup for pressure measurement

Fig. 11

Result of direct measurement of static pressure distribution along divergent section of nozzle wall

Fig. 12

Comparison of solution for one-dimensional isentropic nozzle flow and experimental data obtained by the authors and other research institutions (MIT [5,9], UTRC [10], Tohoku [12], and Pennsylvania [13,14])

Fig. 13

Definition of elementary control volume

Fig. 14

Basic concept of recovery factor

Fig. 15

Comparison of experimental results and calculations on the basis of on Eqs. (23) and (25)

Fig. 16

Comparison of calculations and experimental results (MIT [5,9], UTRC [10], Tohoku [12], and Pennsylvania [13,14])

Fig. 17

Variations in FA, FT0, and Fcf as a function of flow Mach number

Fig. 18

Comparison of calculated operation envelope of the governing equation of motion and present experimental data (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 19

Comparison of experimental relationship between Nu and (2x/dH)/RePr (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

Fig. 20

Comparison of experimental relationship between Nu and Kn (MIT [5,9], UTRC [10], MIT (silp) [11], Tohoku [12], and Pennsylvania [13,14])

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