Lockhart-Martinelli correlation - Separated Flow Model

An alternate approach to calculating two-phase pressure drop is the separated-phases model.

In this model, the phases are considered to be flowing separately in the channel, each occupying a given fraction of the channel cross-section and each with a given velocity. It is obvious the predicting the void fraction is very important for these methods. Numerous methods are available for predicting the void fraction.

The method of Lockhart and Martinelli is the original method that predicted the two-phase frictional pressure drop based on a friction multiplicator for the liquid-phase or the vapor-phase:

∆p_frict = Φ_ltt² . ∆p_l (liquid-phase ∆p)

∆p_frict = Φ_gtt² . ∆p_g (vapor-phase ∆p)

The single-phase friction factors of the liquid f_l and the vapor f_g are based on the single-phase flowing alone in the channel, in either viscous laminar (v) or turbulent (t) regimes.

∆p_l can be calculated classically but with an application of (1-x)² in the expression and ∆p_g with an application of vapor quality x^2, respectively.

The two-phase multipliers Φ_ltt² and Φ_gtt² are equal to:

where X_tt is the Martinelli’s parameter defined as:

and the value of C in these equations depends on the flow regimes of the liquid and vapor. These values are in the following table.

The Lockhart-Martinelli correlation has been found to be adequate for two-phase flows at low and moderate pressures. Martinelli and Nelson’s (1948) and Thom (1964) revised models are recommended for applications at higher pressures.

separated flow model - Lockhart-Martinelli correlation — Correlations for void fraction and frictional pressure drop (Lockhart and Martinelli, 1949)

References:

Reactor Physics and Thermal Hydraulics:

J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.
White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN: 978-0077422417

See above:

Two-phase dP