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Fluid-Structure Interaction

Simplified Fluid-Structure Model for Duckbill Valve Flow

[+] Author and Article Information
J. Wang1

Department of Mechanical Engineering,  McMaster University, Hamilton, Ontario, L8S4L8, Canada

D. S. Weaver, S. Tullis

Department of Mechanical Engineering,  McMaster University, Hamilton, Ontario, L8S4L8, Canada

1

Corresponding author.

J. Pressure Vessel Technol 134(4), 041301 (Jul 31, 2012) (8 pages) doi:10.1115/1.4005941 History: Received June 26, 2011; Revised December 14, 2011; Published July 31, 2012; Online July 31, 2012

Duckbill valves (DBVs), made of a fabric reinforced layered rubber composite, are extensively used for nonreturn axial water flows with low back pressures. Fluid–structure interaction (FSI) is directly involved in the opening process of the DBV, with the opening depending on the pressure differential across the valve. In this paper, a simplified FSI model of the DBV is presented using a finite element method (FEM). The valve is modeled as a laminated thick shell structure with some simplifications to the boundary conditions. The pressure load acting on the shell surface of the DBV is a function of the variable valve cross-sectional area and determined, for preliminary analysis purposes, by using a simple potential flow model for the fluid mechanics. The hyperelasticity of the rubber and orthotropy of the fiber reinforcement, as well as large deflections of the DBV, are considered in the simulation. The valve is modeled as being closed when the upstream pressure is applied, and the transient opening process is tracked until a steady state opening is achieved. Several static cases of viscous flow passing through the deformed valve structure have also been carried out to compare the pressure and velocity fields of fluid flow with the corresponding pressure and velocity distribution predicted by the simplified model and to compare the hydraulic performance of the DBV predicted by both models.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry model of duckbill valve

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Figure 2

Laminate structure of a valve material sample

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Figure 3

Stress-strain relations of rubber predicted by the first order Mooney–Rivlin model

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Figure 4

Schematic diagram of DBV shell model showing original and deformed shapes of the duckbill valve

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Figure 5

Finite element mesh and boundary conditions of DBV shell model

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Figure 6

Transient response of calculation

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Figure 7

(a) Pressure drop-discharge relationship; (b) area-discharge relationship; (c) velocity-discharge relationship

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Figure 8

Exit velocity-pressure drop relationship

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Figure 9

Jet flow of DBV CFD model. The streamlines are colored by velocity magnitude, also shown is the valve surface and on the pipe upstream of the valve inlet and downstream of the valve exit

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Figure 10

Comparisons of 1D potential flow versus 3D viscous flow. The positions of 1D pressure and velocity magnitude notations are identical to the ones of the above contour lines intersecting with the center lines

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Figure 11

Dimensionless comparisons of 1D potential flow versus 3D viscous flow. The cross-section area averaged pressure and velocity fields of the viscous flow are used for comparison with the 1D Bernoulli results (lines represent 1D simulations, and points are 3D simulations).

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Figure 12

Error analysis of dimensionless pressure and velocity fields in the DBV. The pressure drops predicted by both methods are matched very well within 5%, while the velocities are very sensitive near the inlet. The velocity errors at the duckbill part for the 5 kPa driven pressure case are >5%, indicating that the viscous flow may affect the velocity evaluation.

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Figure 13

Displacement of DBV in y direction under the driving pressure of 10 kPa

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Figure 14

Effective stress distributions on each layer of laminate shell structure of DBV: (a) external rubber layer; (b) middle fiber layer; (c) internal rubber layer

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Figure 15

Deformation shapes of exit area under various driving pressures of 5 kPa, 10 kPa, and 20 kPa

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