Electronic Transactions on Numerical Analysis (ETNA)

Volume 30, pp. 168-186, 2008.

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

Hidesada Kanda

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 $R_{c} (m i n)$ = 3750 when the number of radial grid points $J 0$ = 51 and 2200 when \linebreak $J 0$ = 101.

Full Text (PDF) [489 KB], BibTeX

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

< Vol. 30 (2008)