Determination of dynamic velocity in the Prandtl equations

The purpose of this paper is to describe the developed method for determining the dynamic velocity (friction velocity) in the equations of L. Prandtl for the entire range of adequacy of the semi-empirical theory of turbulent flow. A widely used classical approach to determining the dynamic speed of air flow in a closed loop, based on the coefficient of hydraulic resistance and tangent stress, is considered. This article describes a precise method of determining dynamic velocity equation of Prandtl, based on the average air flow speed in the pipe, and taking into account the characteristics of laminar, transitional and turbulent layers of the vent stream. A graphical comparison of the calculation of the dynamic air flow velocity in a smooth pipe is made without taking into account and taking into account the influence of the near-wall laminar layer and the transition sub layer. The presented graphs clearly demonstrate that for a purely turbulent flow, as the Reynolds number increases, the calculated data of the classical method approaches the calculated parameters of the proposed method, which is explained by a decrease in the influence of the laminar layer and the transition sublayer on the resulting air flow velocity. The proposed method for calculating the dynamic air flow velocity is accurate, since it takes into account the influence of wall sub layers, so it can be used to solve problems where it is necessary to understand and account for the physical properties and influence of the laminar and transition layers of the General flow of both gas and liquid flows. For example, this method is applicable when considering the countercurrent interaction of the liquid flowing down the inner wall of the pipe and the upward air flow.

Keywords: аir flow, dynamic air flow velocity, average air flow velocity, L. Prandtl’s system of equations, laminar sub layer, transition sub layer, turbulent core.
For citation:

Fomin A.N., Kuznetsov S.N. Determination of dynamic velocity in the Prandtl equations. MIAB. Mining Inf. Anal. Bull. 2020;(11-1):213-220. [In Russ]. DOI: 10.25018/0236-14932020-111-0-213-220.

Acknowledgements:
Issue number: 11
Year: 2020
Page number: 213-220
ISBN: 0236-1493
UDK: 622.4
DOI: 10.25018/0236-1493-2020-111-0-213-220
Article receipt date: 26.05.2020
Date of review receipt: 02.08.2020
Date of the editorial board′s decision on the article′s publishing: 10.10.2020
About authors:

Fomin A.N., research associate, senior lecturer of the Department «Technological machines and equipment», e-mail: an_fomin@mail.ru, Federal state budgetary educational institution of higher education «North Caucasus mining and metallurgical Institute (state technological University)», 362021, Vladikavkaz, Russia;
Kuznetsov S.N., Cand. Sci. (Eng.), Administration of the Head of the Republic of North Ossetia-Alania and the Government of the Republic of North Ossetia-Alania, 362000, Vladikavkaz, Russia.

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