Research Papers: Technical Forum

On the Damping in Tube Arrays Subjected to Two-Phase Cross-Flow

[+] Author and Article Information
J. E. Moran

Hatch Ltd.
Niagara Falls, ON, L2E 7J7
e-mail: jmoran@hatch.ca

D. S. Weaver

Department of Mechanical Engineering,
McMaster University,
Hamilton, ON, L8S 4L7, Canada
e-mail: weaverds@mcmaster.ca

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Pressure Vessel Technology. Manuscript received February 21, 2012; final manuscript received November 30, 2012; published online May 21, 2013. Assoc. Editor: Njuki W. Mureithi.

J. Pressure Vessel Technol 135(3), 030906 (May 21, 2013) (13 pages) Paper No: PVT-12-1021; doi: 10.1115/1.4023421 History: Received February 21, 2012; Revised November 30, 2012

An experimental study was conducted to investigate the mechanism of damping in tube arrays subjected to two-phase cross-flow, mainly focusing on the influence of void fraction and flow regime. The model tube bundle had a parallel-triangular configuration, with a pitch ratio of 1.49. The two-phase flow loop used in this research utilized Refrigerant 11 as the working fluid, which better models steam-water than air-water mixtures in terms of vapour-liquid mass ratio as well as permitting phase changes due to pressure fluctuations. The void fraction was measured using a gamma densitometer, introducing an improvement over the homogeneous equilibrium model (HEM). Three different damping measurement methodologies were implemented and compared in order to obtain a more reliable damping estimate: the traditionally used half-power bandwidth, the logarithmic decrement and an exponential fitting to the tube decay response. The experiments showed that the half-power bandwidth produces higher damping values than the other two methods, due to the tube frequency shifting triggered by fluctuations in the added mass and coupling between the tubes, which depend on void fraction and flow regime. The exponential fitting proved to be the more consistent and reliable approach to estimating damping. A dimensional analysis was carried out to investigate the relationship between damping and two-phase flow related parameters. As a result, the inclusion of surface tension in the form of the capillary number appears to be useful when combined with the two-phase component of the damping ratio (interfacial damping). A strong dependence of damping on flow regime was observed when plotting the interfacial damping versus the void fraction, introducing an improvement over the previous results obtained by normalizing the two-phase damping, which does not exhibit this behavior.

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Fig. 1

Aerodynamic component of damping as a function of pitch velocity. Adapted from Weaver and El-Kashlan [6].

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Fig. 2

Variation of the components of the total fluid damping with void fraction [9]

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Fig. 3

Comparison between design guideline and available damping data, Pettigrew and Taylor [19]

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Fig. 4

Diagram of the two-phase flow loop and tube array geometry: (1) main pump, (2) orifice plates for mass flux measurement, (3) flow control valves, (4) heaters, (5) test section, (6) shell-and-tube condenser, and (7) gamma densitometer

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Fig. 5

Side-view of the test section, showing a schematic diagram of the model tube bundle, the location of the strain gauges and the electromagnets

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Fig. 6

Half-power bandwidth method for calculating the damping ratio. The plot shows the fitting performed on actual data recorded during this research.

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Fig. 7

Exponential fitting to the decay trace. At point (a), the electromagnets are shut-off. The interval between (b) and (c) is used for the fitting, avoiding the turbulent excitation seen at point (d).

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Fig. 8

Flow regime data for the test series A based on the map by Ulbrich and Mewes [29]

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Fig. 9

Total damping ratio, ζT, versus RAD void fraction. The mass fluxes and flow regimes observed are indicated in each plot.

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Fig. 10

Normalized two-phase damping ratio versus HEM void fraction. The continuous line shows the design guideline suggested by Pettigrew and Taylor [19] (see Fig. 3)

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Fig. 11

Comparison between the void fractions predicted by the HEM and the gamma densitometer measurements, as a function of HEM pitch velocity

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Fig. 12

Comparison between the exponential fitting and the logarithmic decrement methods for a mass flux of 250 kg/m2s. The bubbly, intermittent, and dispersed flow regions are indicated.

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Fig. 13

Damping based on the half-power bandwidth and exponential fitting methods versus the HEM void fraction for a pitch mass flux of 250 kg/m2s. The areas labeled I, II, and III represent the bubbly, intermittent, and dispersed flow regimes, respectively.

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Fig. 14

Damping based on the half-power bandwidth and exponential fitting methods versus the RAD void fraction. The pitch mass flux was 250 kg/m2s.

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Fig. 15

Hydrodynamic mass ratio versus void fraction for a mass flux of 250 kg/m2s. The continuous line represents the theoretical hydrodynamic mass ratio.

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Fig. 16

Histogram of frequency (100 samples) showing the magnitude of the shifting phenomenon for different void fractions. The mass flux was 200 kg/m2s. The dashed lines representing a Gaussian approximation to the data are shown only as a reference.

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Fig. 17

Interfacial damping as a function of void fraction for all mass fluxes studied. Solid line is based on the LOESS methodology. The shaded bands indicate the change of flow regime zones for the different mass fluxes.

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Fig. 18

Approximation of the interfacial damping behavior based on the LOESS. The shaded bands indicate the change of flow regime zones for the different mass fluxes.




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