RENSSELAER POLYTECHNIC INSTITUTE
Modeling Subcooled Boiling in
a Nuclear Reactor Core
Matthew P. Wilcox
2/17/2012
The purpose of this paper is to propose my thesis idea to the faculty of Rensselaer Polytechnic Institute
to become a Master of Mechanical Engineering. The goal of this thesis is to analytically calculate the
amount of subcooled boiling that occurs in a nuclear reactor core under various fluid conditions. Using
the analytical results a set of equations or tables will be produced to allow for quick calculation of
voiding at different axial heights based on temperature, pressure, mass flux and heat flux. All analysis
results will be determined using ANSYS Fluent and a population boundary equation model.
Table of Contents
Introduction .................................................................................................................................................. 2
Problem Description ..................................................................................................................................... 2
Methodology................................................................................................................................................. 3
Required Resources ...................................................................................................................................... 3
Outcome ....................................................................................................................................................... 3
Deadlines....................................................................................................................................................... 4
References .................................................................................................................................................... 5
Introduction
Nuclear reactors have been used for commercial electricity production since 1958. They provide roughly
20% of the electricity in the United States and about 13% world-wide. There are two distinct types of
nuclear reactors, Pressurizer Water Reactors (PWR) and Boiling Water Reactors (BWR). The more
common of the two types is the PWR which heats water that flows over nuclear fuel rods and then uses
that heated water to produce steam. The goal of the pressurized system is to heat the water to the
greatest temperature possible to improve efficiency and prevent bulk boiling which could lead to fuel
failure. The heat is removed from the fuel through and efficient heat transfer process known as nucleate
boiling. During nucleate boiling, the heated surface temperature is hotter than the saturation temperature
of the fluid causing localized boiling in the subcooled bulk fluid. Where in the core and to what extend
subcooled boiling occurs is generally unknown.
The power in a nuclear reactor is held constant by keeping the reactivity balanced at zero. Positive
reactivity leads to a power increase while negative reactivity leads to a power decrease. Some of the
components that make up the reactivity balance equation are water temperature, water density, fuel
temperature and voiding in the core. The accuracy at which each parameter can be measured impacts
the ability to calculate core power during a transient. Being able to accurately measure the core power
during a transient removes uncertainty in the safety analyses performed. Currently there are methods
to accurately calculate the reactivity components listed above except for voiding in the core. If a more
accurate method was developed to calculate voiding under varying conditions, there would be less
uncertainty in the power calculation and more safety analysis margin could be gained thus allowing
plants to increase power and produce more electricity.
The purpose of this thesis is to develop a better understanding of subcooled boiling in a nuclear reactor
and generate a more accurate method to measure voiding at different axial locations in the core.
Problem Description
Currently there are only crude methods to measure the amount of subcooled boiling that occurs in a
nuclear reactor. The amount of voiding that occurs has a direct impact on fission power. If a better
understanding of the level of voiding due to subcooled boiling was developed, the accuracy at which
fission power is calculated during a transient could be improved and the amount of uncertainty reduced.
Fluid properties such as temperature, pressure, mass flux and heat flux will be varied and their impact
on the amount of subcooled boiling at different axial locations in a nuclear reactor will be determined.
Methodology
A portion of a fuel bundle will be modeled using ANSYS Fluent. The traditional models available (energy
equation, turbulence, two-phase, etc.) in Fluent will be implemented along with a Population Balance
Equation (PBE) model. Population balance equations have been introduced in several branches of
modern science, mainly in branches with particulate entities. Population balance equations define how
populations of separate entities develop in specific properties over time. They are nothing more than
a balance on the number of particles in a particular state. The PBE model will be used to determine the
number of steam bubbles in the core, reveal how they develop over time and decide if the bubbles
shrink and collapse or coalesce and grow in size.
Ten models will be created, each more advanced than the previous. The final model will be threedimensional, use multiple heated rods, allow for turbulent, two-phase flow and have the PBE model
implemented. For more information about the model progression and development, see the Deadlines
section.
After each model is developed, it will be compared to known experimental data whenever possible in
order to validate the information generated by ANSYS Fluent. After the models have been validated and
the final model developed, the initial conditions, temperature, pressure, mass flux and heat flux, will be
altered so that the voiding at different axial locations can be determined for the various initial
conditions.
Once the data has been collected, it will be analyzed to produce either a set of equations or a set of
tables that will allow the user to quickly determine how much voiding occurs based on the known
conditions.
Required Resources
A number of resources will be necessary to complete this thesis. First and foremost, access to ANSYS
Fluent software and a computer powerful enough to run the software will be needed. Help with
creating the models may be necessary if they do not meet expectations. Various technical papers
explaining nucleate boiling, two-phase flow, turbulence and population balance equations and how they
can be modeled are necessary. Additionally, experimental data will be required to validate the models
developed. Lastly, Wikipedia.org will be utilized as a reference since it provides helpful information,
diagrams and pictures, and resources that could prove vital support.
Outcome
The expected outcome of this thesis is a set of equations or tables that will let the user determine how
much voiding occurs at an axial location in the core for a given set of conditions (temperature, pressure,
mass flux and heat flux).
Deadlines
Documentation / Analysis Deadlines:
Thesis Proposal – 2/15/12
Data/Results Collection – 8/1/12
Initial Draft – 10/1/12
Final Draft – 12/01/12
Finish Thesis – 12/15/12
Submit Final Report – 12/16/12
Model Deadlines:
Model 1: Single heated rod, no flow, 2-D, one-phase – 12/28/11
Model 2: Multiple heated rods, no flow, 2-D, one-phase – 1/8/12
Model 3: Single heated rod, perpendicular laminar flow, 2-D, one-phase – 1/22/12
Model 4: Single heated rod, parallel laminar flow, 2-D, one-phase – 2/5/12
Model 5: Single heated rod, perpendicular turbulent flow, 2-D, one-phase – 2/15/12
Model 6: Single heated rod, parallel turbulent flow, 2-D, one-phase – 2/22/12
Model 7: Single heated rod, parallel turbulent flow, 2-D, two-phase – 3/15/12
Model 8: Single heated rod, parallel turbulent flow, 2-D, two-phase, PBE model – 4/15/12
Model 9: Single heated rod, parallel turbulent flow, 3-D, two-phase, PBE model – 5/15/12
Model 10: Multiple heated rods, parallel turbulent flow, 3-D, two-phase, PBE model – 6/6/12
References
Tong, L. S., “Boiling Heat Transfer and Two Phase Flow,” 1975.
Eckert, E. R. G., “Introduction to the Transfer of Heat and Mass,” McGraw-Hill Inc., 1950.
Wallis, Graham B., “One-dimensional Two-phase Flow,” McGraw-Hill Inc., 1969.
Kays, W. M., et al., “Convective Heat and Mass Transfer,”4th edition, McGraw-Hill Inc., 2005.
Kaminski, Deborah A., Jenson, Michael K., “Introduction to Thermal and Fluids Engineering,” 1st edition,
Wiley, 2004.
Hinze, J. O., “Turbulence: An Introduction to Its Mechanism and Theory,” McGraw-Hill Inc., 1959.
Tennekes, H. & Lumley, J. L., “A First Course in Turbulence,” Massachusetts Institute of Technology,
1972.
ANSYS Fluent, “User’s Guide,” Release 13.0, 2010.
ANSYS Fluent, “ANSYS FLUENT Population Balance Module Manual,” Release 13.0, 2010.
Basu, Nilanjana; et. al., “Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1-Model
Development,” Journal of Heat Transfer, February 2005, Vol. 127, p. 133-140.
Kodama, S.; Kataoka, I., “Critical Heat Flux Prediction Method Based on Two-Phase Turbulence Model,”
Journal of Nuclear Science and Technology, October 2003, Vol. 40, No. 10, p. 725-733.
Sakashita, H., et. al., “Critical Heat Flux and Near-Wall Boiling Behaviors in Saturated and Subcooled Pool
Boiling on Vertical and Inclined Surfaces,” Journal of Nuclear Science and Technology, 2009, Vol. 46, No.
11, p. 1038-1048.
Morales-Ruiz, S.; et. al., “Numerical Analysis of Two-Phase Flow in Condensers and Evaporators with
Special Emphasis on Single-Phase/Two-Phase Transition Zones,” Applied Thermal Engineering, 2009, p.
1032-1042.