Research Papers: Fluid-Structure Interaction

Two-Phase Flow-Induced Forces on Piping in Vertical Upward Flow: Excitation Mechanisms and Correlation Models

[+] Author and Article Information
M. J. Pettigrew

Fellow ASME
BWC/AECL/NSERC Chair of Fluid–Structure
Department of Mechanical Engineering,
École Polytechnique de Montréal,
C.P. 6079, Succursale Centre-Ville,
Montréal, PQ, H3C 3A7, Canada

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 4, 2011; final manuscript received March 29, 2013; published online May 21, 2013. Assoc. Editor: Jong Chull Jo.

J. Pressure Vessel Technol 135(3), 030907 (May 21, 2013) (16 pages) Paper No: PVT-11-1198; doi: 10.1115/1.4024210 History: Received November 04, 2011; Revised March 29, 2013

Momentum variation in two-phase flow generates significant low frequency forces, capable of producing unwanted and destructive vibrations in nuclear or petroleum industries. Two-phase flow-induced forces in piping were previously studied over a range of diameters from 6 mm to 70 mm in different piping element geometries, such as elbows, U-bends, and tees. Dimensionless models were then developed to estimate the rms forces and generate vibration excitation force spectra. It was found that slug flow generates the largest forces due to the large momentum variation between Taylor bubbles and slugs. The present study was conducted with a 52 mm diameter U-bend tube carrying a vertical upward flow. Two-phase flow-induced forces were measured. In addition, two-phase flow parameters, such as the local void fraction, bubble size and velocity, and slug frequency were studied to understand the relationship between the force spectra and the two-phase flow patterns. A new two-phase flow pattern map, based on existing transition models and validated using our own local void fraction measurements and force spectra, is proposed. This paper also presents a comparison of the present dimensionless forces with those of previous studies, thus covers a wide range of geometries and Weber numbers. Finally, a dimensionless spectrum is proposed to correlate forces with large momentum variations observed for certain flow patterns.

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Fig. 1

(a) Test loop and (b) test section for the 52 mm diameter U-bend tube

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Fig. 2

Vertical flow regime map from Taitel et al. [7] and conditions studied for the 52 mm diameter U-bend test section. Transition boundaries are A from bubbly to slug flow, B from bubbly to finely dispersed bubbly flow, C from finely dispersed bubbly to churn flow, D to annular flow, and E from slug to churn flow. Flow patterns are identified as (I) bubbly flow, (II) finely dispersed bubbly flow, (III) slug flow, (IV) churn flow, and (V) annular flow.

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Fig. 3

Calibration procedure: (a) Set-up and (b) force signals

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Fig. 4

Optical fibers tips

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Fig. 5

Observed flow for conditions (a) 2, (b) 3, (c) 5, (d) 6, (e) 8, (f) 10, (g) 13, (h) 18, and (i) 20; (see Fig. 2 for identification of the flow conditions). Bubbly flow and slugs, which consist of water and bubbles, appear in white and Taylor bubbles in black, surrounded by the falling liquid film where some bubbles are observable.

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Fig. 6

Void signal for β = 25%: (a) Condition 1, (b) Condition 2, (c) Condition 4, (d) Condition 5; (flow conditions are identified in Fig. 2)

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Fig. 7

Void signal for β = 50%: (a) Condition 6, (b) condition 7, (c) condition 9, and (d) condition 10

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Fig. 8

Void signal for β = 75%: (a) Condition 11, (b) Condition 12, (c) Condition 14, (d) Condition 15

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Fig. 9

Void signal for β = 95%: (a) Condition 18 and (b) Condition 20

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Fig. 10

Bubble size histograms for some of the conditions 2–16 (Fig. 2)

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Fig. 11

Bubble velocity histograms for some of the conditions 2–16 (Fig. 2)

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Fig. 12

Proposed vertical flow pattern map and conditions studied for the 52 mm diameter U-bend test section. Transition boundaries are: A from bubbly to slug flow, B from bubbly to unstable slug flow, C from bubbly to unstable slug or churn flow, D to annular flow, E from slug to unstable slug flow, and F from unstable slug flow to churn flow. Flow patterns are identified as (I) bubbly flow, (II) slug flow, (III) unstable slug flow, (IV) churn flow, and (V) annular flow. The dotted lines represent the model from Taitel et al. [7] (Fig. 2) and the dashed line — delimits the spherical cap bubble flow regime, based only on our visual observations.

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Fig. 13

Bubble velocity in * spherical cap bubble flow, + bubbly flow, ○ stable slug flow, and × unstable slug flow

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Fig. 14

Variation of the rms value of forces versus superficial mixture velocity: ▪ present study and ▴ previous results from Giraudeau et al. [6] for (a) β = 25%, (b) β = 50%, (c) β = 75%, and (d) β = 95%

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Fig. 15

Main peak frequency versus velocity for (a) β = 25%, (b) β = 50%, (c) β = 75%, and (d) β = 95%

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Fig. 16

(a) Force spectra and (b) the superficial mixture velocity versus frequency peaks

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Fig. 17

Spectra of the averaged void signals for (a) bubbly flow from Park et al. [31] and for (b) slug flow from Matuszkiewicz et al. [34]

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Fig. 18

Dimensionless forces for various diameters and geometries

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Fig. 19

Force spectra with 52 mm and for β = 75%

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Fig. 20

Dimensionless spectra with 20 mm [6] and 52 mm diameter tube with their approximations

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Fig. 21

Dimensionless spectra model with 20 mm and 52 mm diameter tube

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Fig. 22

(a) Dimensional spectra and (b) dimensionless spectra with model (solid line) in terms of void fraction for slug, unstable slug, churn, and churn/annular flow conditions in 20 and 52 mm diameter U-tube

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Fig. 23

Comparison between experiments (dotted line) and models (solid line) for slug flow in 52 mm diameter U-tube: (a) Condition 7, (b) condition 10, (c) condition 12, and (d) condition 16



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