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Research Papers: Flows in Complex Systems

Junction Losses for Arbitrary Flow Directions

[+] 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 April 26, 2017; final manuscript received October 16, 2017; published online December 4, 2017. Assoc. Editor: Kwang-Yong Kim.

J. Fluids Eng 140(4), 041104 (Dec 04, 2017) (13 pages) Paper No: FE-17-1251; doi: 10.1115/1.4038395 History: Received April 26, 2017; Revised October 16, 2017

Two hydraulic losses take effect at the junction point of three cylindrical conduits. These two quantities are considered to be functions of the three signed flow rates and two geometrical parameters: the cross-sectional area ratio and the angle between the main conduit and branch tube. A new design of experiment is developed for exploring the parameter space with continuous response surfaces, which cover both dividing and combining flow regimes with a general trigonometric formula. The loss coefficients are determined by using a steady-state, single-phase, three-dimensional (3D) computational fluid dynamics (CFD) model. To help the analytical treatment, a new reference velocity formulation is introduced. The new loss coefficient formula is validated against known empirical correlations for different junction types and flow directions. The obtained continuous solution promotes the applicability of the resistance model in hydraulic network models.

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Figures

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Fig. 3

A typical numerical mesh for the junction. Geometry: D2/D1 = 1, α = 90 deg. The number of cells is 1 million: (a) Numerical resolution of the whole computational domain and boundary conditions and (b) details of mesh zones.

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Fig. 1

Different types of hydraulic junctions

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Fig. 4

Validation of velocity profiles against experimental data [30]; origin of the coordinate system (x = 0) is located on the centerline of the main conduit. Re1 = 32,000: (a) inlet velocity profile, (b) velocity profile in the main conduit collinear with the centerline of the branch for different mesh resolutions, and (c) velocity profile in the main conduit collinear with the centerline of the branch—basic-mesh solution with discretization error bars.

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Fig. 5

Schematic of a junction: (a) flow and geometrical properties and (b) implementation in network models

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Fig. 6

Illustration of a representative system of equations; the solution is the intersection curve of the plane and the sphere. C = 0.1.

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Fig. 7

All physically possible cases and the investigated parameter range. Extreme geometric cases of the present study: C = 0.1 and 1.

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Fig. 8

Loss coefficients of a combining junction as a function of Reynolds number Rej for different geometries and γ polar angles: (a) Ct1 and (b) Ct2

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Fig. 12

Loss coefficients as a function of the angle between the main conduit and branch tube; A2/A1 = 0.8: (a) Ct1 and (b)Ct2

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Fig. 9

Loss coefficients as a function of the γ polar angle; geometry: α = 90 deg and C = 1. γ = 0 corresponds to the position where X = 3/2, Y = 0 and Z = −3/2: (a) Ct1 and (b) Ct2.

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Fig. 10

Loss coefficients as a function of the γ polar angle—validation of simulation results against correlations of previous studies [2022, 27]; geometry: α = 90 deg and A2/A1 = 1 (a) Ct1; normalized root-mean-square error (NRMSE) = 0.073 and (b) Ct2; NRMSE = 0.059

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Fig. 11

Loss coefficients as a function of the γ polar angle—validation of simulation results against correlations and data of previous studies [20,21]; geometry: α = 60 deg and A2/A1 = 0.2: (a) Ct1; NRMSE = 0.061 and (b) Ct2; NRMSE = 0.043

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Fig. 13

Loss coefficients as a function of the cross-sectional area ratio; α = 90 deg: (a) Ct1 and (b) Ct2

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