# Pressure Drop – Homogeneous Flow Model

## Pressure Drop – Homogeneous Flow Model

The simplest approach to the prediction of two-phase flows is to treat the entire two-phase flow as if it were all liquid, except flowing at the two-phase mixture velocity. The two-phase pressure drops for flows inside pipes and channels are the sum of three contributions:

The total pressure drop of the two-phase flow is then:

∆ptotal = ∆pstatic + ∆pmom + ∆pfrict

The static and momentum pressure drops can be calculated similarly as in case of single-phase flow and using the homogeneous mixture density:

The most problematic term is the frictional pressure drop ∆pfrict, which is based on the single-phase pressure drop that is multiplied by the two-phase correction factor (homogeneous friction multiplier – Φlo2). By this approach the frictional component of the two-phase pressure drop is:

where (dP/dz)2f is frictional pressure gradient of two-phase flow and (dP/dz)1f is frictional pressure gradient if entire flow (of total mass flow rate G) flows as liquid in the channel (standard single-phase pressure drop). The term Φlois the homogeneous friction multiplier, that can be derived according to various methods. One of possible multipliers is equal to Φlo2 = (1+xglg – 1)) and therefore:

As can be seen this simple model suggests that the two-phase frictional losses are in any event higher than the single-phase frictional losses. The homogeneous friction multiplier increases rapidly with flow quality.

Typical flow qualities in steam generators and BWR cores are on the order of 10 to 20 %. The corresponding two phase frictional loss would then be 2 – 4 times that in an equivalent single-phase system.

Martinelli-Nelson Friction Multiplicator
Example: Pressure Drop - BWR

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.
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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

Two-phase dP