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Research Papers: Technical Forum

Time Domain Simulation of the Vibration of a Steam Generator Tube Subjected to Fluidelastic Forces Induced by Two-Phase Cross-Flow

[+] Author and Article Information
Téguewindé Sawadogo

e-mail: teguewinde-pierre.sawadogo@polymtl.ca

Njuki Mureithi

e-mail: njuki.mureithi@polymtl.ca
BWC/AECL/NSERC Chair of Fluid-Structure Interaction,
Department of Mechanical Engineering,
École Polytechnique de Montréal,
C.P. 6079 Succursale Centre-ville,
Montréal, QC, H3C 3A7, Canada

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Mechanical Design. Manuscript received May 4, 2012; final manuscript received December 4, 2012; published online May 21, 2013. Assoc. Editor: Jong Chull Jo.

J. Pressure Vessel Technol 135(3), 030905 (May 21, 2013) (12 pages) Paper No: PVT-12-1053; doi: 10.1115/1.4023426 History: Received May 04, 2012; Revised December 04, 2012

Having previously verified the quasi-steady model under two-phase flow laboratory conditions, the present work investigates the feasibility of practical application of the model to a prototypical steam generator (SG) tube subjected to a nonuniform two-phase flow. The SG tube vibration response and normal work-rate induced by tube-support interaction are computed for a range of flow conditions. Similar computations are performed using the Connors model as a reference case. In the quasi-steady model, the fluid forces are expressed in terms of the quasi-static drag and lift force coefficients and their derivatives. These forces have been measured in two-phase flow over a wide range of void fractions making it possible to model the effect of void fraction variation along the tube span. A full steam generator tube subjected to a nonuniform two-phase flow was considered in the simulations. The nonuniform flow distribution corresponds to that along a prototypical steam-generator tube based on thermal-hydraulic computations. Computation results show significant and important differences between the Connors model and the two-phase flow based quasi-steady model. While both models predict the occurrence of fluidelastic instability, the predicted pre-instability and post instability behavior is very different in the two models. The Connors model underestimates the flow-induced negative damping in the pre-instability regime and vastly overestimates it in the post instability velocity range. As a result the Connors model is found to underestimate the work-rate used in the fretting wear assessment at normal operating velocities, rendering the model potentially nonconservative under these practically important conditions. Above the critical velocity, this model largely overestimates the work-rate. The quasi-steady model on the other hand predicts a more moderately increasing work-rate with the flow velocity. The work-rates predicted by the model are found to be within the range of experimental results, giving further confidence to the predictive ability of the model. Finally, the two-phase flow based quasi-steady model shows that fluidelastic forces may reduce the effective tube damping in the pre-instability regime, leading to higher than expected work-rates at prototypical operating velocities.

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References

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Figures

Grahic Jump Location
Fig. 2

Fluid forces on a typical tube

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Fig. 3

Variation of the drag coefficient of a single cylindrical body with the Reynolds number. Sources Refs. [32,33].

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Fig. 1

Single flexible tube in a rotated triangular array

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Fig. 5

Variation of the steady drag coefficient of a tube in a rotated triangular array (P/D = 1.5) with the Reynolds number for 60% void fraction. The upstream velocity, the diameter and the length of the tube are used as nondimensionalization parameters.

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Fig. 6

Comparison of theoretical and experimental critical velocities for a cluster of seven flexible tubes in a rotated triangular tube array (P/D = 1.5): ○ quasi-steady theory, □ experiments. Source Ref. [17].

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Fig. 7

Comparison of theoretical and experimental critical velocities for 1 single flexible tube in a rotated triangular tube array (P/D = 1.5): ○ quasi-steady theory, □ experiments, ♦ Connors. Source Ref. [17].

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Fig. 4

Variation of the lift coefficient of a tube in a rotated triangular array (P/D = 1.5) with the quasi-static displacement in the lift direction at 60% void fraction for various Reynolds numbers: ○ ReG=9.2×104, □ ReG=1.4×105,× ReG=1.6×105,Δ ReG=1.9×105.

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Fig. 9

Displacement and fluidelastic force in the lift direction at node 90 at the velocity V(s): (a) displacement (Connors model), (b) force per unit length (Connors model), (c) force per unit length (quasi-steady model), and (d) displacement (quasi-steady model)

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Fig. 10

Tube response to turbulence and fluidelastic forces at the velocity V(s): (a) Node 98 (Connors model); (b) Node 98 (quasi-steady model); (c) Node 78 (Connors model); and (d) Node 78 (quasi-steady model).

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Fig. 11

Tube response at the velocity 2.5 × V(s): (a) Node 98 (Connors model); (b) Node 98 (quasi-steady model); (c) Node 78 (Connors model); and (d) Node 78 (quasi-steady model). Both turbulence and fluidelastic forces are applied from 0 s–1.5 s while after 1.5 s, only fluidelastic forces (FE) are applied.

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Fig. 12

Vibration spectra given by the quasi-steady model at mid-span node 98 at the velocity 1.5 × V(s): (a) 1.0 s–1.5 s; (b) 1.5 s–2.0 s; (c) 2.0 s–2.5 s; (d) 2.5 s–3.0 s; (e) 3.0 s–3.5 s; and (f) 3.5 s–4.0 s. Both turbulence and fluidelastic forces are applied from 0 s to 2 s while after 2 s, only fluidelastic forces are applied.

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Fig. 8

Tube vibration response in the lift direction at a mid-span node given by the Connors model (K = 5.5) and the quasi-steady model (μ = 1): (a) stable response using the Connors model; (b) stable response using the quasi-steady model; (c) onset of instability using the Connors model; (d) onset of instability using the quasi-steady model; (e) unstable response using the Connors model; (f) unstable response using the quasi-steady model. The critical velocities obtained using the eigenvalue analysis are Uc-CN = 3.7 m/s and Uc-QS = 4.1 m/s, respectively, for the Connors model and the quasi-steady model.

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Fig. 13

Normal impact forces at node 78 in the lift direction at the velocity V(s): (a) Connors model and (b) quasi-steady model

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Fig. 14

Normal impact forces at node 94 in the lift direction at the velocity 2.5 × V(s): (a) Connors model; (b) quasi-steady model. Both turbulence and fluidelastic forces are applied from 0 s to 1.5 s while after 2 s, only fluidelastic forces are applied.

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Fig. 15

Flow velocity distribution and the location of the nodes on the U-tube. The void fraction distribution is shown in Fig. 16.

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Fig. 16

Void fraction distribution along the U-tube

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