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Research Papers: Flows in Complex Systems

# Hydraulic Loss of Finite Length Dividing Junctions

[+] Author and Article Information
András Tomor

Department of Fluid Mechanics,
Faculty of Mechanical Engineering,
Budapest University of
Technology and Economics,
Bertalan Lajos Street 4-6,
Budapest H-1111, Hungary
e-mail: tomor@ara.bme.hu

Gergely Kristóf

Department of Fluid Mechanics,
Faculty of Mechanical Engineering,
Budapest University of
Technology and Economics,
Bertalan Lajos Street 4-6,
Budapest H-1111, Hungary
e-mail: kristof@ara.bme.hu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 12, 2016; final manuscript received October 2, 2016; published online January 19, 2017. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 139(3), 031104 (Jan 19, 2017) (11 pages) Paper No: FE-16-1303; doi: 10.1115/1.4034876 History: Received May 12, 2016; Revised October 02, 2016

## Abstract

A general hydraulic loss coefficient correlation for perpendicular, cylindrical, finite length dividing pipe junctions is developed and implemented in a discrete dividing-flow manifold model. Dividing-flow manifolds are used in several technical appliances, e.g., in water and wastewater treatment, swimming pool technology, air engineering, and polymer processing. Ensuring uniform flow distribution is a major goal of a flow manifold system design, whose accuracy is usually determined by the accuracies of applied flow coefficients. Coefficient of turning losses is calculated by a computational fluid dynamics (CFD)-based approach applying a nonlinear fit. In the case of a single-phase flow, the loss coefficient depends on four dimensionless parameters: the Reynolds number, the ratio of port and header flow velocities, the diameter ratio, and the ratio of the port length and the diameter of the pipe. Instead of experimentally covering this four-dimensional parameter space, more than 1000 judiciously chosen three-dimensional simulations were run to determine the loss coefficient for the parameter range most used in engineering practice. Validated results of our novel resistance formula show that the velocity and port length to header diameter ratios have a significant effect on the turning loss coefficient, while the diameter ratio and Reynolds number dependency are weaker in the investigated parameter ranges.

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## Figures

Fig. 1

Types of flow manifolds

Fig. 2

Geometrical model of the junction

Fig. 3

A typical mesh for the investigated flow manifold segment. Presented geometry: D2/D1 = L2/D1 = 0.625 (D1 = 0.02 m). Cell number: 240,000 (a) numerical mesh with boundary conditions and (b) mesh zone details.

Fig. 4

Major geometrical and flow properties of a dividing junction

Fig. 5

Representative results of the fitting procedure: total pressure loss as a function of the velocity ratio for fitting both loss coefficients. Re1 = 80,000… 200,000.

Fig. 6

Representative results—loss coefficients as a function of Re1; D2/D1 = L2/D1 = 0.625 (a) fitting two loss coefficients and (b) fitting only one loss coefficient (assuming ζ1 = 1)

Fig. 7

Turning loss coefficients as a function of the velocity ratio for the two different approaches

Fig. 8

Structure of a dividing-flow manifold

Fig. 9

Locations of demonstrated velocity profiles

Fig. 10

Comparison of simulated (present) and measured [36] inlet velocity profiles; vb = 1.07 m/s

Fig. 11

Comparison of simulated (present) velocity profiles with experimental data [36] around the bifurcation region; vb = 1.07 m/s, (a) profile P2, (b) profile P3, and (c) profile P4

Fig. 12

Turning loss coefficients as a function of the velocity ratio—comparison of calculated values with literature data (a) D2/D1 = 0.625, Re1 = 10,000 and (b) D2/D1 = 0.75, Re1 = 300,000

Fig. 13

Turning loss coefficients as a function of the velocity ratio—comparison of calculated values with literature data: the small vicinity of the critical velocity ratio

Fig. 14

Turning loss coefficient as a function of the ratio of the port length and the inner diameter of the header pipe for fitting both loss coefficients—validation of the asymptotic values for large L2/D1. Re1 = 300,000.

Fig. 15

Turning loss coefficient as a function of the diameter ratio for three different port lengths to header diameter ratios

Fig. 16

Effect of Reynolds number on the turning loss coefficient

Fig. 17

Comparison of calculated dimensionless volume flow rate distributions to experimental data (a) comparison with data of Acrivos et al. [30] and (b) comparison with data of Bajura [37]

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