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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Vetrovec, J. , 2008, “Engine Cooling System with a Heat Load Averaging Capability,” SAE Paper No. 2008-01-1168. http://papers.sae.org/2008-01-1168/
Park, K. S. , Won, J. P. , and Heo, H. S. , 2002, “ Thermal Flow Analysis of Vehicle Engine Cooling System,” KSME, Int. J., 16(7), pp. 975–985. [CrossRef]
Pigford, R. L. , Ashraf, M. , and Miron, Y. D. , 1983, “ Flow Distribution in Piping Manifolds,” Ind. Eng. Chem. Fundam., 22(4), pp. 463–471. [CrossRef]
Hamm, V. , Collon-Drouaillet, P. , and Fabriol, R. , 2008, “ Two Modelling Approaches to Water-Quality Simulation in a Flooded Iron-Ore Mine (Saizerais, Lorraine, France): A Semi-Distributed Chemical Reactor Model and a Physically Based Distributed Reactive Transport Pipe Network Model,” J. Contam. Hydrol., 96(1–4), pp. 97–112. [CrossRef] [PubMed]
Liseth, P. , 1976, “ Wastewater Disposal by Submerged Manifolds,” J. Hydr. Div. ASCE, 102(1), pp. 1–14. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0006426
Antisari, L. V. , Trivisano, C. , Gessa, C. , Gherardi, M. , Simoni, A. , Vianello, G. , and Zamboni, N. , 2010, “ Quality of Municipal Wastewater Compared to Surface Waters of the River and Artificial Canal Network in Different Areas of the Eastern Po Valley (Italy),” Water Qual., Exposure Health, 2(1), pp. 1–13. [CrossRef]
Wang, J. , 2008, “ Pressure Drop and Flow Distribution in Parallel-Channel Configurations of Fuel Cells: U-Type Arrangement,” Int. J. Hydrogen Energy, 33(21), pp. 6339–6350. [CrossRef]
Wang, J. , 2010, “ Pressure Drop and Flow Distribution in Parallel-Channel Configurations of Fuel Cells: Z-Type Arrangement,” Int. J. Hydrogen Energy, 35(11), pp. 5498–5509. [CrossRef]
Bassiouny, M. K. , and Martin, H. , 1984, “ Flow Distribution and Pressure Drop in Plate Heat Exchangers–I U-Type Arrangement,” Chem. Eng. Sci., 39(4), pp. 693–700. [CrossRef]
Wang, J. , Gao, Z. , Gan, G. , and Wu, D. , 2001, “ Analytical Solution of Flow Coefficients for a Uniformly Distributed Porous Channel,” Chem. Eng. J., 84(1), pp. 1–6. [CrossRef]
Sarbu, I. , and Ostafe, G. , 2016, “ Optimal Design of Urban Water Supply Pipe Networks,” Urban Water J., 13(5), pp. 521–535. [CrossRef]
Czetany, L. , and Lang, P. , 2016, “ Impact of Inlet Boundary Conditions on the Fluid Distribution of Supply Duct,” Appl. Mech. Mater., 861, pp. 384–391. [CrossRef]
Czetany, L. , Szantho, Z. , and Lang, P. , 2017, “ Rectangular Supply Ducts With Varying Cross Section Providing Uniform Air Distribution,” Appl. Therm. Eng., 115, pp. 141–151. [CrossRef]
Wang, J. , 2011, “ Theory of Flow Distribution in Manifolds,” Chem. Eng. J., 168(3), pp. 1331–1345. [CrossRef]
Wang, J. , 2013, “ Design Method of Flow Distribution in Nuclear Reactor Systems,” Chem. Eng. Res. Des., 91(4), pp. 595–602. [CrossRef]
Wang, J. , and Wang, H. , 2015, “ Discrete Method for Design of Flow Distribution in Manifolds,” Appl. Therm. Eng., 89(1), pp. 927–945. [CrossRef]
Sarbu, I. , 2014, “ Nodal Analysis of Urban Water Distribution Networks,” Water Resour. Manage., 28(10), pp. 3143–3159. [CrossRef]
Kulkarni, A. V. , Roy, S. S. , and Joshi, J. B. , 2007, “ Pressure and Flow Distribution in Pipe and Ring Spargers: Experimental Measurements and CFD Simulation,” Chem. Eng. J., 133(1–3), pp. 173–186. [CrossRef]
Gandhi, M. S. , Ganguli, A. A. , Joshi, J. B. , and Vijayan, P. K. , 2012, “ CFD Simulation for Steam Distribution in Header and Tube Assemblies,” Chem. Eng. Res. Des., 90(4), pp. 487–506. [CrossRef]
Idelchik, I. E. , 2008, Handbook of Hydraulic Resistance, 3rd ed., Jaico Publishing House, Mumbai, India, pp. 413–451.
Miller, D. S. , 1990, Internal Flow Systems, 2nd ed., BHRA (Information Services), Cranfield, UK, pp. 303–361.
Rennels, D. C. , and Hudson, H. M. , 2012, Pipe Flow, Wiley, Hoboken, NJ, pp. 177–200. [CrossRef]
Liu, W. , Long, Z. , and Chen, Q. , 2012, “ A Procedure for Predicting Pressure Loss Coefficients of Duct Fittings Using Computational Fluid Dynamics (RP-1493),” HVACR Res., 18(6), pp. 1168–1181. http://www.tandfonline.com/doi/abs/10.1080/10789669.2012.713833
Badar, A. W. , Buchholz, R. , Lou, Y. , and Ziegler, F. , 2012, “ CFD Based Analysis of Flow Distribution in a Coaxial Vacuum Tube Solar Collector With Laminar Flow Conditions,” Int. J. Energy Environ. Eng., 3(1), p. 24. [CrossRef]
Ramamurthy, A. S. , Qu, J. , Vo, D. , and Zhai, C. , 2006, “ 3-D Simulation of Dividing Flows in 90 Deg Rectangular Closed Conduits,” ASME J. Fluids Eng., 128(5), pp. 1126–1129. [CrossRef]
Štigler, J. , Klas, R. , Kotek, M. , and Kopecký, V. , 2012, “ The Fluid Flow in the T-Junction. The Comparison of the Numerical Modeling and PIV Measurement,” Procedia Eng., 39(1), pp. 19–27. [CrossRef]
Ito, H. , and Imai, K. , 1973, “ Energy Losses at 90° Pipe Junctions,” J. Hydraul. Div. ASCE, 99(9), pp. 1353–1368. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0020090
Tomor, A. , and Kristóf, G. , 2017, “ Hydraulic Loss of Finite Length Dividing Junctions,” ASME J. Fluids Eng., 139(3), p. 031104. [CrossRef]
Menter, F. R. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Costa, N. P. , Maia, R. , Proença, M. F. , and Pinho, F. T. , 2006, “ Edge Effects on the Flow Characteristics in a 90 Deg Tee Junction,” ASME J. Fluids Eng., 128(6), pp. 1204–1217. [CrossRef]
Celik, I. B. , Ghia, U. , Roache, P. J. , and Freitas, C. J. , 2008, “ Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” ASME J. Fluids Eng., 130(7), p. 078001. [CrossRef]
Mikhailovsky, E. M. , and Novitsky, N. N. , 2015, “ A Modified Nodal Pressure Method for Calculating Flow Distribution in Hydraulic Circuits for the Case of Unconventional Closing Relations,” St. Petersburg Polytech. Univ. J.: Phys. Math., 1(2), pp. 120–128.
Rockmore, D. N. , 2000, “ The FFT: An Algorithm the Whole Family Can Use,” Comput. Sci. Eng., 2(1), pp. 60–64. [CrossRef]


Grahic Jump Location
Fig. 1

Different types of hydraulic junctions

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 13

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In