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Research Papers: Fluid-Structure Interaction

# Prediction of Streamwise Fluidelastic Instability of a Tube Array in Two-Phase Flow and Effect of Frequency Detuning

[+] Author and Article Information
Stephen Olala

BWC/AECL/NSERC Chair of Fluid-Structure
Interaction
Department of Mechanical Engineering,
École Polytechnique de Montréal,
C.P. 6079, Succursale Centre-ville,
e-mail: stephen.olala@polymtl.ca

Njuki W. Mureithi

BWC/AECL/NSERC Chair of Fluid-Structure
Interaction
Department of Mechanical Engineering,
École Polytechnique de Montréal,
C.P. 6079, Succursale Centre-ville,
e-mail: njuki.mureithi@polymtl.ca

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received September 25, 2015; final manuscript received August 4, 2016; published online October 11, 2016. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 139(3), 031301 (Oct 11, 2016) (15 pages) Paper No: PVT-15-1220; doi: 10.1115/1.4034467 History: Received September 25, 2015; Revised August 04, 2016

## Abstract

Experimental measurements of the steady forces on a central cluster of tubes in a rotated triangular array $(P/D=1.5)$ subjected to two-phase air–water cross-flow have been conducted. The tests were done for a series of void fractions and a Reynolds number (based on the pitch velocity), $Re=7.2×104.$ The forces obtained and their derivatives with respect to the static streamwise displacement of the central tube in the cluster were then used to perform a quasi-steady fluidelastic instability analysis. The predicted instability velocities were found to be in good agreement with the dynamic stability tests. Since the effect of the time delay was ignored, the analysis confirmed the predominance of the stiffness-controlled mechanism in causing streamwise fluidelastic instability. The effect of frequency detuning on the streamwise fluidelastic instability threshold was also explored. It was found that frequency detuning has, in general, a stabilizing effect. However, for a large initial variance in a population of frequencies (e.g., $σ2=7.84$), a smaller sample drawn from the larger population may have lower or higher variance resulting in a large scatter in possible values of the stability constant, $K,$ some even lower than the average (tuned) case. Frequency detuning clearly has important implications for streamwise fluidelastic instability in the steam generator U-bend region where in-plane boundary conditions, due to preload and contact friction variance, are poorly defined. The present analysis has, in particular, demonstrated the potential of the quasi-steady model in predicting streamwise fluidelastic instability threshold in tube arrays subjected to two-phase cross-flows.

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## Figures

Fig. 1

Two-phase test loop and array configuration

Fig. 2

Test section

Fig. 3

Instrumented tubes: (a) central tube mounted on linear motor and (b) instrumented neighboring tube

Fig. 4

Variation of the drag and lift coefficients with tube C dimensionless displacement for tube C

Fig. 5

Variation of the drag and lift coefficients with tube C dimensionless displacement for tube 1

Fig. 6

Variation of the drag and lift coefficients with tube C dimensionless displacement for tube 4

Fig. 7

Variation of the drag and lift coefficients with tube C dimensionless displacement for tube 2

Fig. 8

Variation of the drag and lift coefficients with tube C dimensionless displacement for tube 3

Fig. 9

Variation of the derivative of the drag coefficient with void fraction for (a) tubes C, 2, and 4, and (b) tubes 1 and 3

Fig. 10

Flexible tubes configuration for stability analysis—single column

Fig. 11

Flexible tubes configuration for stability analysis—multiple columns

Fig. 12

Effect of the number of flexible tubes on the critical velocity for a column of tubes (refer to Fig. 10)

Fig. 13

Effect of the number of flexible tubes on the critical velocity for multiple columns of tubes (refer to Fig. 11)

Fig. 14

Comparison between present analysis and dynamic stability test: (a) flexible central cluster (Fig. 11(f)) and (b) two partially flexible columns (Fig. 11(d))

Fig. 15

Instability map: comparison of present analysis with published data, ▲ two flexible columns in air–water two-phase flow with tubes flexible in flow (present analysis),◆ two partially flexible columns in air–water two-phase flow (present analysis), ▶ central flexible cluster in air–water two-phase flow (present analysis), ★ a fully flexible array in air–water two-phase flow (present analysis), ● axisymmetrically flexible tube bundles in air–water two-phase flow [34], ▽ a single flexible column in air flow with tubes flexible in flow [17], ◁ a central flexible cluster in air flow with tubes flexible in flow [17], ◻ a central flexible cluster in air–water two-phase flow with tubes flexible in flow, fn = 28 Hz [18], ◇ a central flexible cluster in air–water two-phase flow with tubes flexible in flow, fn = 14 Hz [18], and ☆ two partially flexible columns in air–water two-phase flow with tubes flexible in flow [18]

Fig. 16

Evolution of eigenvalue with flow velocity for 90% void fraction, σ2 = 0 (0% detuning): (a) real part and (b) imaginary part

Fig. 17

Modes of vibration for 90% void fraction, σ2 = 0 (0% detuning): (a) unstable mode (mode 1) and (b) mode 2

Fig. 18

Evolution of eigenvalue for seven arrays, original population σ2 = 0.49 (5% detuning): (a) real part and (b) imaginary part

Fig. 19

Evolution of eigenvalue for seven arrays, original population σ2 = 1.96 (10% detuning): (a) real part and (b) imaginary part

Fig. 20

Evolution of eigenvalue for seven arrays, original population σ2 = 7.84 (20% detuning): (a) real part and (b) imaginary part

Fig. 21

Effect of frequency detuning on streamwise stability constant: (a) σ2 = 0.49 (5% detuning) and (b) σ2 = 7.84 (20% detuning)

Fig. 22

Effect of random frequency detuning on streamwise stability constant, 2 Hz ≤ f ≥ 14 Hz

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