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Void fraction predictive method based on the minimum kinetic energy

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Abstract

This paper presents a new void fraction predictive method for two-phase gas–liquid flows inside tubes for horizontal and vertical upward flows based on the principle of minimum kinetic energy. Non-uniformities of the velocity profiles are taken into account in the development of the method through empirical factors defined by the momentum coefficients ratio. A regression analysis to correlate the momentum coefficients ratio based on a broad databank gathered from the literature covering horizontal and vertical upward flows is performed. The proposed method has proven more accurate than the current methods available in the literature, as it predicts 92 and 85 % of the experimental data for horizontal and vertical saturated flows, respectively, within a ±10 % error band. The experimental database includes results for saturated flow and covers mass velocities ranging from 70 to 800 kg/m2 s and from 37 to 4500 kg/m2 s and tube internal diameters from 0.5 to 13.8 mm and 6 to 89 mm for horizontal and vertical upward flows, respectively.

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Abbreviations

A :

Area, m2

c i :

Constant and exponent, non-dimensional

C 0 :

Distribution parameter, non-dimensional

d :

Diameter, m

dA :

Cross-sectional area element, m2

g :

Gravitational acceleration, m/s2

G :

Mass velocity, kg/m2 s

j :

Superficial velocity, m/s

K :

Momentum coefficient, non-dimensional

T :

Temperature, °C

u :

In situ velocity, m/s

u gj :

Drift parameter, m/s

V z :

Axial component of velocity, m/s

x :

Vapor quality, non-dimensional

Fr:

Froude number

We:

Weber number

X tt :

Martinelli parameter

α :

Void fraction, non-dimensional

β :

Volumetric gas fraction, non-dimensional

ε :

Mean absolute deviation, non-dimensional

γ 10 :

Fraction of data predicted within ± 10 %

λ :

Capillary length, m

μ :

Dynamic viscosity, kg/m s

ρ :

Density, kg/m3

σ :

Surface tension, N/m

θ :

Inclination relative to horizontal plane, degrees

ξ :

Shedd [21] parameter, non-dimensional

g:

Relative to gas phase

H :

Horizontal

HM:

Homogeneous model

i :

Liquid or gas phase

l:

Relative to liquid phase

m :

Relative to mixture

R:

Rouhani [10]

V :

Vertical

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Acknowledgments

The authors gratefully acknowledge a research Grant and scholarships awarded to the first author by FAPESP (São Paulo Research Foundation, Brazil) under Contract Numbers 2010/20670-2, 2014/06902-9, 2015/00854-5 and 2011/50176-2. The second author is also grateful to CNPq (National Council for Scientific and Technological Development, Brazil) for a Grant under Contract Number 303852/2013-5.

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  1. Heat Transfer Research Group, Mechanical Engineering Department, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São Carlense, 400, Parque Arnold Schmidt, São Carlos, São Paulo, CEP 13566-590, Brazil

    Fabio Toshio Kanizawa & Gherhardt Ribatski

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  1. Fabio Toshio Kanizawa
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Correspondence to Fabio Toshio Kanizawa.

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Technical Editor: Jose A. dos Reis Parise.

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Kanizawa, F.T., Ribatski, G. Void fraction predictive method based on the minimum kinetic energy. J Braz. Soc. Mech. Sci. Eng. 38, 209–225 (2016). https://doi.org/10.1007/s40430-015-0446-x

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