## Calculation of minimum critical Reynolds number for laminar-turbulent transition in pipe flows

### Abstract

This article describes the calculation of the minimum critical Reynolds number for laminar-turbulent transition in pipe flows. From the conclusions of our previous experimental study, it is clear that a transition occurs near the pipe inlet and the critical Reynolds number $R_{c}$ takes the minimum value of about 2000 in the case of a straight pipe. Moreover, in our previous calculations of laminar entrance pipe flow, it was found that near the pipe inlet a large pressure gradient in the radial direction exists, which decreases as the Reynolds number Re increases. Thus, we have built a new transition macromodel to determine $R_{c}$ using the effect of the radial pressure gradient. The calculated results were $R_{c}(min)$ = 3750 when the number of radial grid points $J0$ = 51 and 2200 when \linebreak $J0$ = 101.

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### Key words

hydrodynamic stability, grid refinement, thermodynamics

### AMS subject classifications

76E05, 65M50, 80A05

### Links to the cited ETNA articles

 [18] Vol. 23 (2006), pp. 202-218 Kenshu Shimomukai and Hidesada Kanda: Numerical study of normal pressure distribution in entrance flow between parallel plates, I. Finite difference calculations [19] Vol. 30 (2008), pp. 10-25 K. Shimomukai and H. Kanda: Numerical study of normal pressure distribution in entrance pipe flow

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