Slip Ratio – Velocity Ratio

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:

Slip Ratio – Velocity Ratio

In two-phase fluid flow it is convenient to use the slip ratio. The slip ratio (or velocity ratio) in two-phase flow is defined as the ratio of the velocity of the vapor phase to the velocity of the liquid phase. The slip ratio in a two-phase fluid flow is defined as:

In the homogeneous equilibrium model (HEM) of two-phase flow, the slip ratio is by definition assumed to be unity (there is no slip). However, most industrial two-phase flows have different velocity of the gas and liquid phases, these can differ significantly. The models that account for the existence of the slip are called separated flow models.

slip ratio - definition
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

The reason for defining the void fraction and the slip ratio is that they also make it possible to calculate the pressure drop of the two-phase flow. Several correlations for calculation the slip ratio, S, and the void fraction are presented in literature. The following correlations are given in order of increasing accuracy.

homogeneous flow model
Zivi slip correlation
Chisholm slip correlation
smith void correlation

 
References:
Reactor Physics and Thermal Hydraulics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
  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