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Flow Patterns, Void Fraction and Pressure Drop in Gas-Liquid Two Phase Flow at Different Pipe Orientations

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Book cover Frontiers and Progress in Multiphase Flow I

Part of the book series: Frontiers and Progress in Multiphase Flow ((FPMF))

Abstract

This chapter presents an insightful discussion on flow patterns, void fraction and phenomenon of two phase frictional pressure drop in gas-liquid two phase flow. The flow structure of different flow patterns observed in gas-liquid two phase flow at various pipe orientations are described with the aid of flow visualization. This chapter is helpful in understanding the impact of varying flow patterns, pipe diameter and pipe orientation on the void fraction and two phase pressure drop. Additionally, a brief overview of the void fraction, its dependency on the flow patterns and its influence on the hydrostatic pressure drop is presented. A brief synopsis of the two phase void fraction and frictional pressure drop correlations available in the literature is presented. The performance of these correlations is assessed against a comprehensive database for air-water and refrigerant two phase flow conditions. Based on this detailed analysis, the top performing void fraction and pressure drop correlations are identified and recommended for use for these fluid combinations in different two phase flow situations. Finally, application of the recommended correlations is presented in the form of solved problems. It is expected that these solved problems will give readers an idea of selection and implementation of appropriate correlations for different two phase flow conditions.

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Abbreviations

BCh :

Variable in (Chisholm [20]) correlation

Co :

Distribution parameter

D:

Pipe diameter (m)

f:

Friction factor

Fr:

Froude number (\( Fr = {{G^{2} } \mathord{\left/ {\vphantom {{G^{2} } {(gD\rho^{2} )}}} \right. \kern-0pt} {(gD\rho^{2} )}} \))

g:

Acceleration due to gravity (9.81 m/s2)

G:

Mass flux (kg/m2 s)

Ku:

Kutateladze number as defined by Takeuchi et al. [97]

L:

Pipe length (m)

La:

Laplace number (\( La = {{\sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma {g(\rho_{l} - \rho_{g} )}}} \right. \kern-0pt} {g(\rho_{l} - \rho_{g} )}}} } \mathord{\left/ {\vphantom {{\sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma {g(\rho_{l} - \rho_{g} )}}} \right. \kern-0pt} {g(\rho_{l} - \rho_{g} )}}} } D}} \right. \kern-0pt} D} \))

Nμf :

Viscosity number \( \left( {N_{\mu f} = {{\mu_{l} } \mathord{\left/ {\vphantom {{\mu_{l} } {\left( {\rho_{l} \sigma \sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma {g\Delta \rho }}} \right. \kern-0pt} {g\Delta \rho }}} } \right)^{0.5} }}} \right. \kern-0pt} {\left( {\rho_{l} \sigma \sqrt {{\sigma \mathord{\left/ {\vphantom {\sigma {g\Delta \rho }}} \right. \kern-0pt} {g\Delta \rho }}} } \right)^{0.5} }}} \right) \)

P:

Pressure (Pa)

Re:

Reynolds number (\( \text{Re} = {{\left( {GD} \right)} \mathord{\left/ {\vphantom {{\left( {GD} \right)} \mu }} \right. \kern-0pt} \mu } \))

S:

Slip ratio

U:

Phase velocity (m/s)

Ugm :

Drift velocity (m/s)

We:

Weber number (\( We = {{(G^{2} D)} \mathord{\left/ {\vphantom {{(G^{2} D)} {(\sigma \rho )}}} \right. \kern-0pt} {(\sigma \rho )}} \))

x:

Two phase quality

X :

(Lockhart and Martinelli [66]) parameter

α:

Void fraction

β:

Gas volumetric flow fraction

ρ:

Phase density (kg/m3)

μ:

Phase dynamic viscosity (Pa-s)

θ:

Pipe orientation (degrees)

σ:

Surface tension (N/m)

Φ2 :

Two phase frictional multiplier

a:

Accelerational

atm:

Atmospheric

crit:

Critical

f:

Frictional

g:

Gas

go:

Gas only

h:

Hydrostatic

in:

Inlet

j:

Phase

l:

Liquid

lo:

Liquid only

m:

Mixture

out:

Outlet

s:

Superficial

sys:

System

t:

Total

tp:

Two phase

tt:

Turbulent-turbulent

w:

Water

*:

Non-dimensional parameter

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Acknowledgements

The authors are thankful to Dr. John Thome (EPFL, Switzerland), Dr. Josua Meyer (University of Pretoria, South Africa), Dr. Somchai Wongwises (KMUTT, Thailand) and Dr. Neima Brauner (Tel Aviv University, Israel) for sharing void fraction and pressure drop data.

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  1. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK, 74078, USA

    Afshin J. Ghajar & Swanand M. Bhagwat

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  1. Afshin J. Ghajar
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  2. Swanand M. Bhagwat
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Correspondence to Afshin J. Ghajar .

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  1. Department of Engineering Faculty of Science and Technology, Aarhus University, Aarhus C, Denmark

    Lixin Cheng

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Ghajar, A.J., Bhagwat, S.M. (2014). Flow Patterns, Void Fraction and Pressure Drop in Gas-Liquid Two Phase Flow at Different Pipe Orientations. In: Cheng, L. (eds) Frontiers and Progress in Multiphase Flow I. Frontiers and Progress in Multiphase Flow. Springer, Cham. https://doi.org/10.1007/978-3-319-04358-6_4

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