Void Fraction – Two-phase Flow

Basic Parameters of Two‐phase Fluid Flow

In this section we will consider the simultaneous flow of gas (or vapor) and liquid water (as encountered in steam generators and condensers) in concurrent flow through a duct with cross-sectional area A. The subscripts “v” and “ℓ” indicate the vapor and liquid phase, respectively. Fundamental parameters that characterize this flow are:

Void Fraction

The void fraction, α, is one of the most important parameters used to characterize two-phase fluid flow, especially the gas-liquid flow.
Various geometric definitions are used for specifying this parameter. The void fraction in a two-phase fluid flow may be defined as:

  1. The fraction of the channel volume that is occupied by the gas phase. This void fraction is known as the volumetric void fraction.
  2. The fraction of the channel cross-sectional area that is occupied by the gas phase. This void fraction is known as the cross-sectional void fraction.
  3. The local void fraction refers to that at a one single point or very small volume. Therefore it takes the values of 1 or 0.

For further purposes, we will assume a void fraction to be the fraction of the channel cross-sectional area that is occupied by the gas phase (i.e. cross-sectional void fraction) defined as:
void fraction definition
The void fraction is of importance is the two-phase flow, because it influences key physical parameters, such as viscosity, pressure drop and heat transfer.

The relations between x, α, and S can be deducted and the result is:

relations between quality, void fraction and slip

Effect of S on α vs x for water at 7 MPa. Source: Buongiorno Jacopo, MIT Department of Nuclear Science and Engineering, NOTES ON TWO-PHASE FLOW
Effect of S on α vs x for water at 7 MPa. Source: Buongiorno Jacopo, MIT Department of Nuclear Science and Engineering, NOTES ON TWO-PHASE FLOW
 
References:
Reactor Physics and Thermal Hydraulics:
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  6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
  7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
  8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
  9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
  10. White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Two-phase Flow