Superficial Velocity – 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:

Superficial Velocity

Superficial velocity is a hypothetical flow velocity calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. The velocity of the given phase is calculated as if the second phase was ignored.

In engineering of multiphase flows and flows in porous media, superficial velocity (Vphase or jphase) is commonly used, because it is the value which is unambiguous, while real velocity is often spatially dependent and subject to many assumptions.

Superficial velocity can be expressed as:
superficial velocity - definition

For better understanding, let us consider pipe with a 0.1 m2 cross-section of  flow area. Assume that the flow rate is 1 m3/s. For single-phase fluid flow the superficial velocity will be equal to real fluid velocity and that will be 10 m/s.
For two-phase fluid flow (e.g. vapor-liquid flow) the situation will be different. Assuming the slip ratio is unity, both phases taken separately, will have superficial velocities of 5 m/s. The resulting real velocity will be then equal to 10 m/s. If the two phases will have different velocities (with slip), the situation will be more complicated.

flow patterns - horizontal flow
A flow regime map for the flow of an air/water mixture in a horizontal, 2.5cm diameter pipe at 25◦C and 1bar. Solid lines and points are experimental observations of the transition conditions while the hatched zones represent theoretical predictions. Source: Mandhane, J.M., Gregory, G.A. and Aziz, K.A. (1974). A flow pattern map for gas-liquid flow in horizontal pipes. Int. J. Multiphase Flow
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