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Research Papers: Multiphase Flows

Mathematical Model for Viscoplastic Fluid Hammer

[+] Author and Article Information
Gabriel M. Oliveira, Admilson T. Franco

Research Center for Rheology
and Non-Newtonian Fluids (CERNN),
Post-Graduate Program in Mechanical
and Materials Engineering (PPGEM),
Federal University of
Technology - Paraná (UTFPR),
Av. Sete de Setembro,
Curitiba, PR 3165, Brazil

Cezar O. R. Negrão

Research Center for Rheology
and Non-Newtonian Fluids (CERNN),
Post-Graduate Program in Mechanical
and Materials Engineering (PPGEM),
Federal University of
Technology - Paraná (UTFPR),
Av. Sete de Setembro,
Curitiba, PR 3165, Brazil
e-mail: negrao@utfpr.edu.br

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 22, 2015; final manuscript received June 29, 2015; published online August 10, 2015. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 138(1), 011301 (Aug 10, 2015) (8 pages) Paper No: FE-15-1054; doi: 10.1115/1.4031001 History: Received January 22, 2015

The current work presents a mathematical model to simulate “viscoplastic fluid hammer”-overpressure caused by sudden viscoplastic fluid deceleration in pipelines. The flow is considered one-dimensional, isothermal, laminar, and weakly compressible and the fluid is assumed to behave as a Bingham plastic. The model is based on the mass and momentum balance equations and solved by the method of characteristics (MOC). The results show that the overpressures taking place in viscoplastic fluids are smaller than those occurring in Newtonian fluids and also that two pressure gradients-one negative and one positive-are possibly noted after pressure stabilization. The pressure stabilizes nonuniformly on the pipeline because viscoplastic fluids present yield stresses. Overpressure magnitudes depend not only on the ratio of pressure wave inertia to viscous effect but also on the Bingham number. The pipeline designer should take into account the viscoplastic fluid behavior reported in this paper when engineering a new pipeline system.

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References

Figures

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Fig. 1

Illustration of the physical problem

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Fig. 2

Spatial and temporal grid

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Fig. 3

Effect of mesh size for λ = 1.0 and BR = 0.5: (a) time evolution of pressure at Z = 0.6 and (b) axial pressure distribution at T = 0.4

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Fig. 4

Comparisons of the numerical results with experimental data [25] and with an analytical solution. Time evolution of pressure: (a) at the valve position and (b) at pipe midpoint position.

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Fig. 5

Time evolution of the axial pressure distribution for λ = 1.0: (a) and (b) BR = 0 and (c) and (d) BR = 0.5

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Fig. 11

Final pressure distribution as a function of the Bingham number for λ = 1.0

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Fig. 10

Effect of λ on the final pressure distribution for (a) BR = 0.25 and (b) BR = 0.75

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Fig. 9

Effect of the Bingham number on the time evolution of pressure at the valve position for (a) λ = 0.1, (b) λ = 1.0, (c) λ = 5.0, and (d) λ = 10.0

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Fig. 8

Time evolution of the axial pressure distribution for λ = 0.1: (a) BR = 0 and (b) BR = 0.5

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Fig. 7

Effect of the Bingham number on the time evolution of (a) pressure and (b) velocity at pipe midpoint position for λ = 1.0

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Fig. 6

Time evolution of the axial velocity distribution for λ = 1.0: (a) BR = 0 and (b) BR = 0.5

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