Fluid-Structure Interaction

Drag Coefficient and Two-Phase Friction Multiplier on Tube Bundles Subjected to Two-Phase Cross-Flow

[+] Author and Article Information
W. G. Sim

Department of Mechanical Engineering
Hannam University
Taejeon 306-791, Korea

Njuki W. Mureithi

Department of Mechanical Engineering
Ecole Polytechnique
Montreal, QC H3C 3A7, Canada

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 22, 2011; final manuscript received April 19, 2012; published online November 28, 2012. Assoc. Editor: Samir Ziada.

J. Pressure Vessel Technol 135(1), 011302 (Nov 28, 2012) (10 pages) Paper No: PVT-11-1054; doi: 10.1115/1.4007285 History: Received February 22, 2011; Revised April 19, 2012

An approximate analytical model, to predict the drag coefficient on a cylinder and the two-phase Euler number for upward two-phase cross-flow through horizontal bundles, has been developed. To verify the model, two sets of experiments were performed with an air–water mixture for a range of pitch mass fluxes and void fractions. The experiments were undertaken using a rotated triangular (RT) array of cylinders having a pitch-to-diameter ratio of 1.5 and cylinder diameter 38 mm. The void fraction model proposed by Feenstra et al. was used to estimate the void fraction of the flow within the tube bundle. An important variable for drag coefficient estimation is the two-phase friction multiplier. A new drag coefficient model has been developed, based on the single-phase flow Euler number formulation proposed by Zukauskas et al. and the two-phase friction multiplier in duct flow formulated by various researchers. The present model is developed considering the Euler number formulation by Zukauskas et al. as well as existing two-phase friction multiplier models. It is found that Marchaterre's model for two-phase friction multiplier is applicable to air–water mixtures. The analytical results agree reasonably well with experimental drag coefficients and Euler numbers in air–water mixtures for a sufficiently wide range of pitch mass fluxes and qualities. This model will allow researchers to provide analytical estimates of the drag coefficient, which is related to two-phase damping.

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Fig. 1

Test loop 1 and test section

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Fig. 2

Test loop 2 and test section

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Fig. 3

Pressure measurement

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Fig. 4

Void fraction versus mass quality given by the homogeneous model (—) and nonhomogeneous model (Gp = 800 (kg/(m2 s)) (---) and Gp = 200 (kg/(m2 s)) (……)

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Fig. 5

Two-phase friction multiplier versus mass quality given by homogeneous model (—) and nonhomogeneous model (Gp = 800 (kg/(m2 s)) (---) and Gp = 200 (kg/(m2 s)) (……)

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Fig. 6

Grant flow regime map for two-phase flow and present test regime for test loop 1 (Gp (kg/(m2 s)) = 800 (●)) and test loop 2 (Gp (kg/(m2 s)) = 100 (♦), 200 (▴), and 400 (▪))

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Fig. 7

Momentum flux for homogeneous flow (open symbols) and nonhomogeneous flow (filled symbols): Gp (kg/(m2 s)) = 100 (♦,⋄), 400 (●,○), and 800 (▴,▵)

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Fig. 8

Drag coefficients measured on each tube of test loop 1 and comparison with analytical results

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Fig. 9

(a) Two-phase friction multiplier and (b) two-phase Euler number for Gp = 800 (kg/(m2 s)), KTP = 3. (○), test result; (---), Marchaterre; and (—), homogeneous

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Fig. 10

Drag coefficients for (a) Gp = 200 (kg/(m2 s)) and (b) Gp = 800 (kg/(m2 s)). (*) (tube 1) and (○) (tube 4), test result; (---), Marchaterre; (—), homogeneous; and (…), Levy

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Fig. 11

(a) Frictional pressure drop, (b) two-phase friction multiplier, and (c) two-phase Euler number, obtained by present model (lines) and experiments (symbols) for Gp (kg/(m2 s)) = 100 (♦,—), 200 (▪, – · –), 400 (●, – –), 800 (▴,---), and homogeneous (— · — ·)

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Fig. 12

Two-phase drag coefficients obtained by present model (line) and experiments (♦ from drag force measurement and ▴ from pressure drop measurement) for (a) Gp = 200 (kg/(m2 s)) and (b) Gp = 800 (kg/(m2 s))




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