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Research Papers: Materials and Fabrication

Estimation of Leak Flow Rates Through Narrow Cracks

[+] Author and Article Information
Chungpyo Hong1

Department of Mechanical Engineering, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japanhong@rs.noda.tus.ac.jp

Yutaka Asako

Department of Mechanical Engineering, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan

Jae-Heon Lee

Department of Mechanical Engineering, Hanyang University, Heangdang-dong, Sungdong-ku, Seoul, 133-791, Korea

1

Corresponding author.

J. Pressure Vessel Technol 131(5), 051405 (Sep 02, 2009) (8 pages) doi:10.1115/1.3147984 History: Received July 11, 2008; Revised November 25, 2008; Published September 02, 2009

Abstract

The estimation of the gaseous leak flow rates through a narrow crack is important for a leak-before-break analysis as a method of nondestructive testing. Therefore, the methodology to estimate the gaseous leak flow rates in a narrow crack for a wide range of flow conditions, from no-slip to slip flow and from unchoked to choked flow, by using $f⋅Re$ (the product of friction factor and Reynolds number) correlations obtained for a microchannel, was developed and presented. The correlations applied here were proposed by the previous study (Hong, , 2007, “Friction Factor Correlations for Gas Flow in Slip Flow Regime  ,” ASME J. Fluids Eng., 129, pp. 1268–1276). The detail of the calculation procedure was appropriately documented. The fourth-order Runge–Kutta method was employed to integrate the nonlinear ordinary differential equation for the pressure, and the regular-Falsi method was employed to find the inlet Mach number. An idealized crack, whose opening displacement ranges from $2 μm$ to $50 μm$, with the crack aspect ratio of 200, 1000, and 2000, was chosen for sample estimation. The present results were compared with both numerical simulations and available experimental measurements. The results were in excellent agreement. Therefore, the gaseous leak flow rates can be correctly predicted by using the proposed methodology.

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Figures

Figure 1

Flow model in a narrow crack

Figure 2

Pressure distributions as a function of x

Figure 4

Pressure distributions and Mach numbers

Figure 6

Mach numbers as a function of x

Figure 9

Leak flow rate as a function of pstg

Figure 10

Leak flow rate per unit depth as a function of pout/pstg

Figure 8

Leak flow rate per unit depth as a function of pstg: (a) h=50 μm and (b) h=2 μm

Figure 7

Pressure distributions and Mach numbers

Figure 5

Pressure distributions as a function of x

Figure 3

Flow chart of Runge–Kutta and regular-Falsi method

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