Investigation of Thermal Hydraulics of a Nuclear Reactor Moderator
By
Araz Sarchami
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Mechanical and Industrial Engineering Department University of Toronto
© Copyright by Araz Sarchami 2011
ii
Investigation of Thermal Hydraulics of a Nuclear Reactor Moderator
Araz Sarchami
Doctor of Philosophy
Mechanical and Industrial Engineering Department University of Toronto
2011
Abstract
A three-dimensional numerical modeling of the thermo hydraulics of Canadian Deuterium
Uranium (CANDU) nuclear reactor is conducted. The moderator tank is a Pressurized heavy
water reactor which uses heavy water as moderator in a cylindrical tank. The main use of the
tank is to bring the fast neutrons to the thermal neutron energy levels. The moderator tank
compromises of several bundled tubes containing nuclear rods immersed inside the heavy
water.
It is important to keep the water temperature in the moderator at sub-cooled conditions, to
prevent potential failure due to overheating of the tubes. Because of difficulties in measuring
flow characteristics and temperature conditions inside a real reactor moderator, tests are
conducted using a scaled moderator in moderator test facility (MTF) by Chalk River
Laboratories of Atomic Energy of Canada Limited (CRL, AECL).
MTF tests are conducted using heating elements to heat tube surfaces. This is different than
the real reactor where nuclear radiation is the source of heating which results in a volumetric
heating of the heavy water. The data recorded inside the MTF tank have shown levels of
iii
fluctuations in the moderator temperatures and requires in depth investigation of causes and
effects.
The purpose of the current investigation is to determine the causes for, and the nature of the
moderator temperature fluctuations using three-dimensional simulation of MTF with both
(surface heating and volumetric heating) modes. In addition, three-dimensional simulation
of full scale actual moderator tank with volumetric heating is conducted to investigate the
effects of scaling on the temperature distribution. The numerical simulations are performed
on a 24-processor cluster using parallel version of the FLUENT 12. During the transient
simulation, 55 points of interest inside the tank are monitored for their temperature and
velocity fluctuations with time.
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To my dear mom and dad, Aziz and Giti
v
Acknowledgments
In the first place I would like to pay attribute to my supervisor, Dr. Nasser Ashgriz for his
supervision, advice, and guidance from the very beginning of this research as well as giving
me extraordinary experiences throughout this research. He is truly more than a scientific
supervisor who helped me through all my ups and downs during 5 years of my work in
MUSSL lab. He will always be my mentor and I will never forget his role in shaping my
future.
I also offer my regards and blessings to all my lab mates for their companionship and
greatly appreciate their patience and good attitude toward me.
My special thanks goes to all my family specially my dear parents, Aziz and Giti, whose
affection and support are immeasurable and unforgettable forever. They were beside me
whenever I needed and they never gave up in encouraging me to keep going. It would have
not been possible to pursue my PhD without them.
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Table of Contents
Acknowledgments ................................................................................................................... v
List of Tables .......................................................................................................................... ix
List of Figures .......................................................................................................................... x
1 Introduction ...................................................................................................................... 1
1.1 Nuclear Reactor ......................................................................................................... 1
1.2 Pressurized Heavy Water Reactor (PHWR) ............................................................. 2
1.3 Moderator .................................................................................................................. 3
1.4 Heavy Water ............................................................................................................. 5
1.5 CANDU Reactor ....................................................................................................... 6
1.6 Studies on moderator tank ......................................................................................... 9
1.7 Heat Exchangers ..................................................................................................... 14
1.8 Moderator Test Issues ............................................................................................. 17
1.9 Objectives ................................................................................................................ 19
2 Numerical Setup ............................................................................................................ 21
vii
2.1 MTF and Actual Tanks Geometry .......................................................................... 21
2.2 Operating Conditions .............................................................................................. 24
2.3 Heating Methods ..................................................................................................... 25
2.4 Mesh Construction .................................................................................................. 28
2.5 Computational Code ............................................................................................... 32
2.6 Solution Strategy ..................................................................................................... 32
2.7 Planes - Points ......................................................................................................... 35
2.8 Parallel Processing – Physical Run Time ............................................................... 41
3 Moderator Test Facility Simulation ............................................................................... 44
3.1 Temperature and Velocity Distributions ................................................................. 44
3.2 Temperature and Velocity Fluctuations .................................................................. 50
3.3 Asymmetry .............................................................................................................. 54
3.3.1 Main Flow Regimes ............................................................................. 54
3.3.2 Inlet Jets and Secondary Jet ............................................................... 60
3.3.3 Momentum versus Buoyancy .............................................................. 65
3.3.4 Asymmetry Effects .............................................................................. 67
4 Methods of Heating: Surface Heating and Volumetric Heating .................................... 75
5 Scaling Effects ............................................................................................................... 82
viii
6 Comparison of Two and Three Dimensional Simulations ............................................ 90
7 Summary and Conclusion .............................................................................................. 96
8 Future Work ................................................................................................................. 102
9 Reference ..................................................................................................................... 104
ix
List of Tables
Table 2-1 MTF and actual tank Shell and Core Dimensions ................................................. 21
Table 2-2 MTF and actual tank Tubes Array Dimensions .................................................... 21
Table 2-3 MTF and the actual tank operating conditions used here ...................................... 24
Table 2-4 Planes Coordinates ................................................................................................ 35
Table 2-5 Monitored points coordinates ................................................................................ 41
Table 2-6 Parallel processing time ........................................................................................ 41
Table 5-1 MTF and actual tank operating conditions ............................................................ 88
x
List of Figures
Figure 1-1 Heavy water moderator [51] ................................................................................. 5
Figure 1-2 CANDU reactor design [1] .................................................................................... 8
Figure 1-3 various moderator designs [10] .............................................................................. 8
Figure 1-4 The experimental data taken at the CANDU MTF .............................................. 18
Figure 2-1 The CAD data views of MTF tank and its Inlet Nozzles ..................................... 22
Figure 2-2 The CAD data views of Inlet Nozzle ................................................................... 23
Figure 2-3 The schematic drawing of the MTF tank (all dimensions are in mm) ................. 23
Figure 2-4 MTF heat generation map - surface heating ........................................................ 26
Figure 2-5 Mesh Generation - XY plane ............................................................................... 29
Figure 2-6 XY plane - mesh around tubes ............................................................................. 30
Figure 2-7 XY plane - mesh near the wall ............................................................................. 30
Figure 2-8 Inlet pipes ............................................................................................................. 31
Figure 2-9 Water outlet .......................................................................................................... 31
Figure 2-10 XY-Planes .......................................................................................................... 36
Figure 2-11 XZ-Planes .......................................................................................................... 36
Figure 2-12 YZ-Planes .......................................................................................................... 37
xi
Figure 2-13 Nozzle planes ..................................................................................................... 37
Figure 2-14 Outlet pipe plane ................................................................................................ 38
Figure 2-15 Temperature fluctuation - long range run for point 4 ........................................ 42
Figure 2-16 Velocity fluctuation - long range run for point 4 ............................................... 43
Figure 3-1 Temperature contours at two different times for plane S .................................... 44
Figure 3-2 Velocity contours at two different times for plane S ........................................... 46
Figure 3-3 Temperature contours at two different times for plane B2 .................................. 47
Figure 3-4 Velocity contours at two different times for plane B2 ......................................... 48
Figure 3-5 Temperature contours at two different times for plane D1 .................................. 49
Figure 3-6 Temperature contours at two different times for plane SX .................................. 49
Figure 3-7 Point 3 temperature and velocity fluctuations with time ..................................... 50
Figure 3-8 Point 12 temperature and velocity fluctuations with time ................................... 51
Figure 3-9 Point 20 temperature and velocity fluctuations with time ................................... 52
Figure 3-10 Point 50 temperature and velocity fluctuations with time ................................. 53
Figure 3-11 Comparison between simulation and experiment .............................................. 54
Figure 3-12 Temperature distribution on 4 planes on Z and Y directions ............................. 55
xii
Figure 3-13 Velocity vectors (colour by velocity magnitude) in two nozzle planes and
symmetry plane ...................................................................................................................... 58
Figure 3-14 Impingement point. ............................................................................................ 59
Figure 3-15 Effect of buoyancy force .................................................................................... 59
Figure 3-16 Inlet jets path. The marked points are used to record data on temperature and
velocity. ................................................................................................................................. 60
Figure 3-17 Secondary jet path. The marked points are used to record velocity and
temperature data ..................................................................................................................... 60
Figure 3-18 Temperature along the inlet jets penetration path. The x coordinate is angular
position with respect to positive X direction ......................................................................... 62
Figure 3-19 Velocity along the inlet jets penetration path. The x coordinate is angular
position with respect to positive X direction ......................................................................... 62
Figure 3-20 Temperature along the secondary jet penetration path. The x coordinate is
position along the penetration path with respect to impingement point ................................ 64
Figure 3-21 Velocity along the secondary jet penetration path. The x coordinate is position
along the penetration path with respect to impingement point .............................................. 64
Figure 3-22 Moderate buoyancy ............................................................................................ 65
Figure 3-23 Strong buoyancy ................................................................................................ 66
Figure 3-24 Asymmetrical flow. ............................................................................................ 67
xiii
Figure 3-25 Left and right nozzle planes. These planes are used to study the effect of jet on
jet impingement ..................................................................................................................... 68
Figure 3-26 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity
represents z-velocity .............................................................................................................. 70
Figure 3-27 Left nozzle plane. Y axis velocity represents x-velocity and Z axis velocity
represents z-velocity .............................................................................................................. 70
Figure 3-28 Right nozzle plane. Y axis velocity represents x-velocity and Z axis velocity
represents z-velocity .............................................................................................................. 71
Figure 3-29Right nozzle plane. Y axis velocity represents x-velocity and Z axis velocity
represents z-velocity .............................................................................................................. 72
Figure 3-30 Center plane in Z direction. this shows the transfer of symmetry plane effects to
the other planes along the Z-direction ................................................................................... 74
Figure 4-1 Location of compared points ............................................................................... 76
Figure 4-2 Temperature fluctuations ..................................................................................... 78
Figure 4-3 Temperature and velocity contours for t=150 s (three different simulations) ..... 81
Figure 5-1 Temperature contours for MTF and actual reactor .............................................. 84
Figure 5-2 Velocity contours for MTF and actual reactor ..................................................... 85
Figure 5-3 Temperature and velocity fluctuations plot for actual moderator and MTF ........ 86
xiv
Figure 6-1 Comparison between 2D and 3D temperature and velocity distributions ........... 92
Figure 6-2 Node 15 (located at top of the tank in XY plane) comparison between 2D and 3D
............................................................................................................................................... 94
Figure 6-3 Node 4 (located at the centre of the tank in XY plane) comparison between 2D
and 3D .................................................................................................................................... 95
1
1 Introduction
1.1 Nuclear Reactor
A nuclear reactor is a device to initiate, and control, a sustained nuclear chain reaction.
Nuclear reactors are commonly used in electrical power generation plants. It is usually
accomplished by methods that involve using heat from the nuclear reaction to power steam
turbines. When a large fissile atomic nucleus such as uranium-235 or plutonium-239 absorbs
a neutron, it may undergo nuclear fission. The heavy nucleus splits into two or more lighter
nuclei, releasing kinetic energy, gamma radiation and free neutrons; collectively known as
fission products [1]. A portion of these neutrons may later be absorbed by other fissile atoms
and trigger further fission events, which release more neutrons, and so on. This is known as
a nuclear chain reaction.
Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts
often producing free neutrons and photons (in the form of gamma rays), as well. Fission of
heavy elements is an exothermic reaction which can release large amounts of energy both as
electromagnetic radiation and as kinetic energy of the fragments (heating the bulk material
where fission takes place) [2]. The key to maintaining a nuclear reaction within a nuclear
reactor is to use the neutrons being released during fission to stimulate fission in other
nuclei. With careful control over the geometry and reaction rates, this can lead to a self-
sustaining reaction, a state known as "chain reaction".
Natural uranium consists of a mixture of various isotopes, primarily 238U and a much smaller
amount (about 0.72% by weight) of 235U. 238U can only be fissioned by neutrons that are
2
fairly energetic, about 1 MeV or above. No amount of 238U can be made "critical" to sustain
a chain reaction, since it will tend to parasitically absorb more neutrons than it releases by
the fission process. 235U, on the other hand, can support a self-sustained chain reaction, but
due to the low natural abundance of 235U, natural uranium cannot achieve criticality by itself
[3].
The "trick" to making a working reactor is to slow some of the neutrons to the point where
their probability of causing nuclear fission in 235U increases to a level that permits a
sustained chain reaction in the uranium as a whole. This requires the use of a neutron
moderator, which absorbs some of the neutrons' kinetic energy, slowing them down to
energy comparable to the thermal energy of the moderator nuclei themselves [3].
1.2 Pressurized Heavy Water Reactor (PHWR)
A pressurised heavy water reactor (PHWR) is a nuclear reactor, commonly using un-
enriched natural uranium as its fuel, which uses heavy water (deuterium oxide D2O) as its
coolant and moderator. The heavy water coolant is kept under pressure in order to raise its
boiling point, allowing it to be heated to higher temperatures without boiling. While heavy
water is significantly more expensive than ordinary light water, it yields greatly enhanced
neutron economy, allowing the reactor to operate without fuel enrichment facilities [3].
A great advantage of PHWR is that we are not required to use enriched Uranium. Enriched
Uranium has many complications. One would the requirement to build a uranium
enrichment facility, which is generally expensive to build and operate. They also present a
nuclear proliferation concern; the same systems used to enrich the 235U can also be used to
produce much more "pure" weapons-grade material (90% or more 235U), suitable for
3
producing a nuclear bomb. This is not a trivial exercise, by any means, but feasible enough
that enrichment facilities present a significant nuclear proliferation risk [3].
Pressurised heavy water reactors do have some drawbacks. Heavy water generally costs
hundreds of dollars per kilogram, though this is a trade-off against reduced fuel costs. It is
also notable that the reduced energy content of natural uranium as compared to enriched
uranium necessitates more frequent replacement of fuel; this is normally accomplished by
use of an on-power refuelling system. The increased rate of fuel movement through the
reactor also results in higher volumes of spent fuel than in reactors employing enriched
uranium; however, as the un-enriched fuel was less reactive, the heat generated is less,
allowing the spent fuel to be stored much more compactly [3].
1.3 Moderator
In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast
neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain
reaction involving uranium-235. Commonly used moderators include regular (light) water,
solid graphite and heavy water [1]. Beryllium has also been used in some experimental types,
and hydrocarbons have been suggested as another possibility [48].
Neutrons are normally bound into an atomic nucleus, and do not exist free for long in nature.
The unbound neutron has a half-life of just less than 15 minutes. The release of neutrons
from the nucleus requires exceeding the binding energy of the neutron, which is typically 7-
9 MeV. Whatever the source of neutrons, they are released with energies of several MeV
[48].
4
Water makes an excellent moderator. The hydrogen atoms in the water molecules are very
close in mass to a single neutron and thus have a potential for high energy transfer, similar
conceptually to the collision of two billiard balls. However, in addition to being a good
moderator, water is also fairly effective at absorbing neutrons. Using water as a moderator
will absorb enough neutrons that there will be too few left over to react with the small
amount of 235U in natural uranium. So, light water reactors require fuel with an enhanced
amount of 235U in the uranium, that is, enriched uranium which generally contains between
3% and 5% 235U by weight. In this enriched form there is enough 235U to react with the water-
moderated neutrons to maintain criticality [6, 7].
Use of enriched Uranium has several issues which are explained partially. An alternative
solution to the problem is to use a moderator that does not absorb neutrons as readily as
water. In this case potentially all of the neutrons being released can be moderated and used
in reactions with the 235U, in which case there is enough 235U in natural uranium to sustain a
chain reaction. One such moderator is heavy water, or deuterium-oxide. Although it reacts
dynamically with the neutrons in a similar fashion to light water, it already has the extra
neutron that light water would normally tend to absorb [6, 7]. The use of heavy water
moderator is the key to the PHWR system, enabling the use of natural uranium as fuel which
means that it can be operated without expensive uranium enrichment facilities. A schematic
of a heavy water reactor is shown in
Figure 1-1.
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6
1.5 CANDU Reactor
Canadian Deuterium Uranium (CANDU) nuclear reactor is a Pressurized Heavy Water
Reactor (PHWR) which uses a moderator tank to moderate the water temperature. The
moderator system in a CANDU reactor is a low-pressure system that is separate from the
primary heat transport system. The moderator-circulation system ensures that heat deposited
in the moderator is removed so that a certain amount of sub-cooling is maintained during
normal operation. Heavy water is used both as the moderator and as the primary heat
transport fluid. CANDU power reactor is comprised of several hundred horizontal fuel
channels in a large cylindrical Calandria (the reactor core of the CANDU reactor) vessel.
Each fuel channel consists of an internal pressure tube (containing the fuel and the hot
pressurized heavy water primary coolant), and an external Calandria tube separated from the
pressure tube by an insulating gas filled annulus. The Calandria vessel contains cool low-
pressure heavy-water moderator that surrounds each fuel channel. CANDU utilize natural
Uranium UO2 fuel. The fuel is in the form of half-metre-long cylindrical bundles, typically
containing 37 clustered elements. Twelve bundles sit end-to-end within the pressure tube,
roughly six metres long, through which pressurized heavy-water coolant is circulated [7].
CANDU is the most efficient of all reactors in using uranium: it uses about 15% less
uranium than a pressurized water reactor for each megawatt of electricity produced. Use of
natural uranium widens the source of supply and makes fuel fabrication easier. Most
countries can manufacture the relatively inexpensive fuel. There is no need for uranium
enrichment facility. Fuel reprocessing is not needed, so costs, facilities and waste disposal
associated with reprocessing are avoided. CANDU reactors can be fuelled with a number of
7
other low-fissile content fuels, including spent fuel from light water reactors. This reduces
dependency on uranium in the event of future supply shortages and price increases.
The CANDU reactor is conceptually similar to most light water reactors, although it differs
in the details. Like other water moderated reactors, fission reactions in the reactor core heat
pressurized water in a primary cooling loop. A heat exchanger transfers the heat to a
secondary cooling loop, which powers a steam turbine with an electrical generator attached
to it. Any excess heat energy in the steam after flowing through the turbine is rejected into
the environment in a variety of ways, most typically into a large body of cool water, such as
a lake, river or ocean. The schematic of the plant is shown in Figure 1-2. The main
difference between CANDUs and other water moderated reactors is that CANDUs use
heavy water for neutron moderation.
The large thermal mass of the moderator provides a significant heat sink that acts as an
additional safety feature. If a fuel assembly were to overheat and deform within its fuel
channel, the resulting change of geometry permits high heat transfer to the cool moderator,
thus preventing the breach of the fuel channel, and the possibility of a meltdown.
Furthermore, because of the use of natural uranium as fuel, this reactor cannot sustain a
chain reaction if its original fuel channel geometry is altered in any significant manner.
The CANDU product line, developed in Canada, includes the Generation III+ 1,200 MWe
class ACR (Advanced CANDU Reactor), known as the ACR-1000, and the 700 MWe class
CANDU 6 power reactor [9]. Each of these models varies in their geometry specifications
(as seen in Figure 1-3) as well as some other operating parameters and energy output.
F
Figure 1-2 C
Figure 1-3 var
8
CANDU react
rious moderat
tor design [1]
tor designs [100]
9
CANDU 6 is the smaller output reactor and it was designed specifically for electricity
production, unlike other major reactor types that evolved from other uses. This focused
development is one of the reasons that CANDU has such high fuel efficiency.
ACR is the latest model of CANDU series and it is offered with higher power output. The
other major differences in ACR as compared with CANDU are
The use of slightly enriched uranium fuel (2.1 % wt. U-235 in 42 pins of the fuel
bundle)
Light water (as opposed to heavy water D2O) as the coolant, which circulates in the fuel
channels
This result in a more compact reactor design (Calandria inside diameter 31.6 % less than that
for CANDU 6) and a reduction of heavy water inventory (72% less D2O mass inventory when
compared with CANDU 6)[57].
1.6 Studies on moderator tank
The specific studies on thermal hydraulics in CANDU reactors or in general term,
pressurized heavy water reactors are very limited in the open literature. This is due to the
fact that CANDU reactors are relatively new (since 1970s) and also due to limitation on
accessibility to existing studies due to sensitivity of the issue. Broader range of studies
which are physically similar to moderator tank can be considered as well. Studies on flow
over tubes and flow inside shell and tube heat exchangers are two examples of similar
devices.
10
Many of the references used here do not exist in open literature and are published only as
internal reports and presentations inside the nuclear industry. The studies are in two
categories of experimental and numerical.
Koroyannaski et al [12] experimentally examined the flow phenomena formed by inlet flows
and internal heating of a fluid in a Calandria cylindrical vessel of SPEL (Sheridan Park
Engineering Laboratory) experimental facility. They observed three flow patterns inside test
vessel and their occurrence was dependent on the flow rate and heat load. Carlucci and
Cheung [13] investigated the two-dimensional flow of internally heated fluid in a circular
vessel with two inlet nozzles at the sides and outlets at the bottom, and found that the flow
pattern was determined by the combination of buoyancy and inertia forces. Austman et al.
[14] measured the moderator temperature by inserting thermocouples through a shut-off rod
(SOR) guide tube in operating CANDU reactors at Bruce A and Pickering. Huget et al. [15]
and [16] conducted 2-dimensional moderator circulation tests at a 1/4-scaled facility in the
Stern Laboratories Inc. (SLI) in Canada. From these researches, three clearly distinct flow
patterns were observed according to certain operating ranges. Sion [17] measured the
temperature profile of the D2O moderator inside a CANDU reactor, within the calandria
vessel, by means of a specially instrumented probe introduced within the core.
Measurements were made under steady and transient reactor conditions using two different
sensors, resistance temperature detectors (RTD) and thermocouples. The results established
the feasibility of in-core moderator temperature measurement and indicated that the
thermocouples used were relatively not affected by the intense radiation.
Hohne et. al. [18] studied the influence of density differences on the mixing of a pressurized
water reactor. They presented a matrix experiments in which water with the same or higher
11
density was injected into a cold tank leg of the reactor with already established natural
circulation conditions at different low mass flow rates. Sensors measuring the concentration
of a tracer in the injected water were installed in the tank. A transition matrix from
momentum to buoyancy-driven flow experiments was selected for validation of the
computational fluid dynamics software ANSYS CFX. The results of the experiments and of
the numerical calculations show that mixing strongly depends on buoyancy effects: At
higher mass flow rates the injected slug propagates in the circumferential direction around
the core barrel. Buoyancy effects reduce this circumferential propagation with lower mass
flow rates and/or higher density differences.
Khartabil et al. [19] conducted three-dimensional moderator circulation tests in the
moderator test facility (MTF) in the Chalk River Laboratories of Atomic Energy of Canada
Limited (AECL). Along with separate phenomena tests related to the CANDU moderator
circulation, such as a hydraulic resistance through tube bundles, velocity profiles at an inlet
diffuser, flow development along a curved wall, and the turbulence generation by
temperature differences were measured. Based on these experimental works, a computer
code for a CANDU moderator analysis has been developed by Ontario Hydro and selected
as Canadian industry standard toolset (IST). This computer tool has been used for the design
of ACR and CANDU as well as a CANDU safety analysis. He also [20, 21] experimentally
studied the moderator tank and recorded its temperature in many points during the operation
using fixed thermocouples. He was able to create temperature maps on moderator cross
section plane. In order to perform the experiment, a scaled Calandria vessel was designed
and tested. The CANDU Moderator Test Facility (MTF) is a ¼ scale CANDU Calandria,
with 480 heaters that simulate 480 fuel channels. It is specifically designed to study
12
moderator circulation at scaled conditions that are representative of CANDU reactors. The
MTF was operated at various operating conditions that simulate moderator circulation in
CANDU reactors and temperatures were recorded. This study is initiated by these tests in
order to numerically simulate the same tank to have more in depth analysis and extract data
which are impossible to obtain using experimental devices. The comprehensive goals of this
study are mentioned in objective section of the thesis.
Quaraishi [22] simulated the fluid flow and predicted temperature distributions of SPEL
experiments computational codes. Collins [23, 24] carried out the thermal hydraulic analyses
for SPEL experiments and Wolsong units (Korea Republic nuclear power plant) 2, 3, 4,
respectively, using PHOENICS code using porous media assumption for fuel channels.
Yoon et. al [25] used a computational fluid dynamics model for predicting moderator
circulation inside the CANDU reactor vessel. It was to estimate the local sub-cooling of the
moderator in the vicinity of the calandria tubes. The buoyancy effect induced by the internal
heating is accounted for by the Boussinesq approximation. The standard k-e turbulence
model with logarithmic wall treatment is applied to predict the turbulent jet flows from the
inlet nozzles. The matrix of the calandria tubes in the core region is simplified to a porous
media. The governing equations are solved by CFX 4. They did a parametric analysis and
since their simulation was steady state, it was a base for future transient simulations. In their
next paper, Yoon et. al. [26] developed another computational fluid dynamics model by
using a coupled solver. They did the simulation for Wolsong Units 2/3/4. A steady-state
moderator circulation under operating conditions and the local moderator sub-cooling were
evaluated using the CFD tool. When compared to the former study in the Final Safety
Analysis Reports, the current analysis provided well-matched trends and reasonable results.
13
This new CFD model based on a coupled solver shows a dramatic increase in the computing
speed, when compared to that based on a segregated solver.
In addition, there have been several CFD models for predicting the thermal hydraulics of the
CANDU moderator. Yoon et al. [27] used the CFX-4 code (ANSYS Inc.) to develop a CFD
model with a porous media approach for the core region in order to predict the CANDU
moderator sub-cooling under normal operating conditions, while Yu et al. [28] used the
FLUENT code to model all the Calandria tubes as heating pipes without any approximation
for the core region. The analytic model based on CFX-4 has strength in the modeling of
hydraulic resistances in the core region and in the treatment of a heat source term in the
energy equations, but it faces convergence issues and a slow computing speed. It occurs
because CFX-4 code uses a segregated solver to resolve the moderator circulation.
There are some studies also on the future designs of the CANDU. These studies focus on
high temperature reactors with application in other areas such as hydrogen production.
Duffey et. al. [29] introduced the CANDU–Super Critical Water-cooled Reactor (SCWR)
concept. In this design the coolant outlet temperatures are about 625ºC. IT achieves
operating plant thermal efficiencies in excess of 40%, using a direct turbine cycle. In
addition, the plant has the potential to produce large quantities of low cost heat. It has
flexibility of range of plant sizes suitable for both small (400 MWe) and large (1200 MWe)
electric grids and the ability for co-generation of electric power, process heat, and hydrogen.
In the interests of sustainability, hydrogen production by a CANDU-SCWR is discussed as
part of the system requirements.
14
As mentioned in the beginning of this section, similarities of the moderator tank with heat
exchangers can be utilized to use more extensive available studies. The main function of the
moderator tank is cooling the pressure tubes which contain nuclear fuel. In other word, heat
is transferred from hot pressurized heavy water to cool, low pressure water. It is essentially
the same as heat exchanger’s function.
1.7 Heat Exchangers
A heat exchanger is a device built for efficient heat transfer from one medium to another.
The media may be separated by a solid wall, so that they never mix, or they may be in direct
contact [30]. There are two primary classifications of heat exchangers according to their
flow arrangement. In parallel-flow heat exchangers, the two fluids enter the exchanger at the
same end, and travel in parallel to one another to the other side. In counter-flow heat
exchangers the fluids enter the exchanger from opposite ends [31]. The counter current
design is most efficient, in that it can transfer the most heat from the heat (transfer) medium.
There are many types of heat exchangers for different applications. These types include:
shell and tube, plate heat, plate fin, and etc. the most relevant type to our moderator tank is
the shell and tube type. It is the most common type of heat exchanger in oil refineries and
other large chemical processes, and is suited for higher-pressure applications. As its name
implies, this type of heat exchanger consists of a shell (a large pressure vessel) with a
bundle of tubes inside it. One fluid runs through the tubes, and another fluid flows over the
tubes (through the shell) to transfer heat between the two fluids. The set of tubes is called a
tube bundle, and may be composed by several types of tubes: plain, longitudinally finned,
etc. [30] and [32].
15
There can be many designs for shell and tube heat exchangers based on their application.
The tubes may be straight or bent in the shape of a U, called U-tubes. Large heat exchangers
called steam generators are two-phase, shell-and-tube heat exchangers. They are used to boil
water recycled from a surface condenser into steam to drive a turbine to produce power [31].
Most shell-and-tube heat exchangers are 1, 2, or 4 pass designs on the tube side. This refers
to the number of times the fluid in the tubes passes through the fluid in the shell. In a single
pass heat exchanger, the fluid goes in one end of each tube and out the other.
Due to the similarities between design and application of this type of heat exchangers with
CANDU reactor moderator core, studies on these heat exchangers can be related to
moderator. In the following a brief overview of such studies are included.
Pekdemir et. al. [34] measured Shell side cross-flow velocity distributions and pressure
drops within the tube bundle of a cylindrical shell and tube heat exchanger using a particle-
tracking technique. In the context of modeling of the shell side flow, the experiments were
designed to study variation in the cross-flow component of the shell side flow within the
tube bundle. In addition, the results were used to test an empirical method of predicting
overall cross-flow in tube bundles. They [35] later on measured pressure distributions within
the tube bundle a shell-and-tube heat exchanger. Strategically placed tubes forming part of
the bundle were fitted with pressure tapings and were used to measure axial distributions of
cross-flow pressure drop. Comparison of the results with those obtained in the previous
study revealed the effect of various tubes configuration on the shell-side flow distribution.
Wang et. al. [36] performed an experiment of the heat transfer of a shell and tube heat
exchanger. For the purpose of heat transfer enhancement, the configuration of a shell-and-
16
tube heat exchanger was improved through the installation of sealers in the shell-side. The
gaps between the baffle plates and shell was blocked by the sealers, which effectively
decreased the short-circuit flow in the shell-side. The results of heat transfer experiments
showed that the shell-side heat transfer coefficient of the improved heat exchanger increased
by 18.2–25.5%, the overall coefficient of heat transfer increased by 15.6–19.7%. They
concluded that the heat transfer performance of the improved heat exchanger is intensified,
which is an obvious benefit to the optimizing of heat exchanger design for energy
conservation.
Kapale and Chand [37] developed a theoretical model for shell-side pressure drop. Their
study aimed to determine the overall pressure loss in the shell from the point of entry of the
fluid to the outlet point of fluid. It incorporated the effect of pressure drop in inlet and outlet
nozzles along with the losses in the segments created by baffles. The results of the model
matched more closely with the experimental results available in the literature compared to
analytical models developed by other researchers for different configurations of heat
exchangers. Vera-Garcia et. al. [38] presented a simplified model for the study of shell-and-
tubes heat exchangers. The model aimed to agree with the HXs when they are working as
condensers or evaporators. Despite its simplicity, the model proved to be useful to the
correct selection of shell-and-tubes HXs working at full and complex refrigeration systems.
The model was implemented and tested in the modeling of a general refrigeration cycle and
the results were compared with data obtained from a specific test bench for the analysis of
shell-and-tubes HXs. Ozden and Tari [39] numerically modeled a small heat exchanger. The
shell side design of a shell-and-tube heat exchanger; in particular the baffle spacing, baffle
cut and shell diameter dependencies of the heat transfer coefficient and the pressure drop
17
were investigated. The flow and temperature fields inside the shell were resolved using a
commercial CFD package. A set of CFD simulations was performed for a single shell and
single tube pass heat exchanger with a variable number of baffles and turbulent flow. For
two baffle cut values, the effect of the baffle spacing to shell diameter ratio on the heat
exchanger performance is investigated by varying flow rate.
1.8 Moderator Test Issues
The real time data recording at various locations inside the MTF tank have shown some
level of fluctuations in the moderator experimental temperatures (see Figure 1-4). The
observed frequency of the temperature fluctuations appear to be real and higher than the
sampling rate of the fixed thermocouples. Fluctuations in moderator temperatures are
believed to be due to the flow turbulence resulting from the interplay of local momentum
and buoyancy forces, inlet nozzle jet impingements, and the flow passing through the tube
bundle. The magnitude of the temperature fluctuations measured in the three-dimensional
moderator test facility (3D-MTF) depends on the test conditions and on the location in the
core.
Due to data sampling limitations in the experiments, the full spectrum of the fluctuations
could not be identified. Also, analysis of the experimental data could not identify any
dominant frequencies.
The purpose of the present study is to determine the causes for and the nature of the
moderator temperature fluctuations using three-dimensional simulation of MTF and actual
moderator tank. The results for two simulations will be compared to experimental data as
well as previously performed two-dimensional simulation. The results will be used to
iden
(MTF
temp
Two
the i
drive
inter
are f
heig
therm
well
tify the limit
TF versus ac
perature fluc
o-dimensiona
interaction o
en flows in
rmittent fluc
found to coe
ht of the do
mal boundar
-defined low
tations of tw
ctual tank).
ctuations.
Figure 1-4
al simulation
of momentum
n enclosure
ctuations, an
exist in the c
omain, and t
ry layers. An
w-frequency
wo-dimension
Suggestion
4 The experim
ns revealed t
m and buoy
es have spe
nd anomalou
convection c
the other is
n intriguing f
oscillation i
18
nal simulatio
ns also will
mental data tak
that the main
yancy driven
ecial feature
us scaling. T
cell. One is
intermittent
feature of tu
in the temper
on and the is
l be made
ken at the CA
n cause of th
n flows insid
es which i
There are tw
the large-sc
t bursts of th
urbulent conv
rature power
ssues with sc
to control a
ANDU MTF
he temperatu
de the MTF
include coh
wo coherent
ale circulati
hermal plum
vection is th
r spectrum.
caling of the
and enhance
ure fluctuatio
F tank. Buoy
herent struct
structures, w
on that span
mes from va
he emergence
e tank
e the
ons is
yancy
tures,
which
ns the
arious
e of a
19
The 2-dimensional isothermal modelling of the MTF tank revealed that the largest flow
fluctuations occurred outside the tube bank where the inlet jets flow, and around the top of
the tank where the two inlet jets impinge on each other. The high velocity gradients
between the inlet jets and the initially stagnant surroundings generate small vortices with
low fluctuation amplitude but high frequencies. As the vortices travels with the jets, their
fluctuation amplitudes amplify but their frequency recede. The impingement of the two inlet
jet results in a downward moving secondary jet which penetrated inside the tube bank. The
simulation concluded that the the source of flow fluctuations in the isothermal case is
outside of the tube bank, and the tubes dampen the fluctuations.
The thermal solution of the MTF model indicated that the buoyancy forces dominate at the
inner core of the tank, whereas, the inlet jet induced inertial forces dominate the outer edges
of the tank. The interaction between these two flows forms a complex and unstable flow
structure within the tank.
The most important issue in two-dimensional simulation which should be addressed is that
whether the 2-D model misses any major effects that may occur in the actual Calandria tank.
Therefore, the objective of the 3-D modelling is not only determining the thermo-fluid
behaviour inside the actual MTF, but also to check the applicability of 2-D model results.
1.9 Objectives
The main objectives of the present investigation is to study the temperature and velocity
fields inside the moderator tank, characterize the effects of inertia and buoyancy forces on
the flow and temperature distribution inside the tank, determine the nature and causes of the
temperature gradients in different zones inside the tank, determine the nature of the
20
temperature fluctuations in the moderator, and possibly give suggestions on how to modify
the geometry and/or operating conditions to improve mixing and make the temperature
distribution inside the calandria tank more uniform.
A three-dimensional simulation of the moderator tank is computationally expensive and time
consuming. In order to enhance the size of the simulation, parallel processing is employed.
The simulations are performed on a 24-processor cluster using parallel version of FLUENT
12.
Simultaneous calculation of the local flow velocity and temperature are carried out using
Reynolds Average Navier-Stokes (RANS). The simultaneous velocity and temperature
calculations fully characterize the spatial structure of the velocity and temperature
oscillations and allow us to answer some important open questions that are related directly
to the physical understanding of the convective turbulent flows. Detailed numerical methods
employed in the simulations are not mentioned here and can be found at Fluent help [41].
The simulations are conducted for both scaled down version of the calandria tank (MTF) for
which experimental data are available, and for a real full size actual mderator.
2
2.1
The
Tabl
1486
outle
The
vario
elem
Nume
MTF an
MTF tank i
le 2-1 and Ta
6 mm length
ets at the bot
MTF and th
ous views i
ments are sho
Lengt
Inside
SHE
Lengt
Inside
SHE
rical S
nd Actua
s a ¼ scale o
able 2-2, the
h, eight inlet
ttom of tank
he aactual ta
in Figure 2-
ows in Figure
Table 2-1
Table 2-
th of Calandria
e diameter of th
LL AND COR
th of Calandria
e diameter of th
LL AND COR
Setup
al Tanks
of actual Ca
e MTF tank
nozzles (fou
, and 48033
anks and the
-1 and Figu
e 2-3.
1 MTF and ac
-2 MTF and a
main shell: LC
he Calandria ma
RE DIMENSIO
main shell: LC
he Calandria ma
RE DIMENSIO
21
s Geome
alandria tank
comprises a
ur at each si
3 mm diame
eir inlet nozz
ure 2-2. Th
ctual tank Shel
ctual tank Tu
ain shell: DC
ONS
ain shell: DC
ONS
etry
k. As their m
a 2115 mm d
ide tank), tw
eter tubes.
zles (with flo
e dimension
ll and Core D
ubes Array Dim
5.
8.4
BrBr
1.486 m
2.115 m
MTFMTF
5.
8.4
BrBr
1.486 m
2.115 m
MTFMTF
main dimensi
diameter cyli
wo 152 mm d
ow splitters)
ns and arra
Dimensions
mensions
.94 m
458 m
ruce Bruce BScSc
BrucBruc
.94 m
458 m
ruce Bruce BScSc
BrucBruc
ions are show
indrical tank
diameter pip
) are shown
angements o
44
44
calecalece/MTFce/MTF
44
44
calecalece/MTFce/MTF
wn in
k with
pes as
from
of the
Fron
Top-Vie
nt-View
ew
Figure 2-1 T
The CAD data
22
views of MTF
F tank and its
Side
Isomet
Inlet Nozzles
e-View
ric-View
Top-Vie
Figur
ew
Fig
re 2-3 The sch
gure 2-2 The C
ematic drawin
23
CAD data view
ng of the MTF
ws of Inlet No
F tank (all dim
Isomet
zzle
mensions are in
ric-View
n mm)
24
2.2 Operating Conditions
During the normal operation of CANDU reactor, the cold moderator water enters the tank
through eight nozzles, four nozzles at each side, as shown in Figure 2-1, and heated fluid
exits from two outlet pipes at the bottom of the tank. Throughout the operation, two major
flow characteristics are identified inside the tank: Buoyancy driven fluid flows formed by
the internal heating, and momentum driven fluid flows by the jet flows through the inlet
nozzles, respectively. The flow behaviour depends on the operating conditions, such as,
moderator mass flow rate and its temperature, and the rate of heat influx to the moderator. In
addition, the method of adding heat to the moderator, i.e., volumetric (in the actual
moderator) or using heated channels (in MTF), can also have an effect on the flow and
temperature patterns inside the tank.
The operating conditions for the MTF and the actual moderator used in the simulations are
listed in Table 2-3.
Table 2-3 MTF and the actual tank operating conditions used here
11.4
51.5
40.1
2
8
22.9
14.74 kW/m2
1,090
MTFMTF
2Number of outlets
8Number of nozzles
16.2Temperature difference (ºC): T
61.0Outlet Temperature (ºC)
44.8Inlet Temperature (ºC)
948.0Moderator mass flow rate (kg/s)
277 kW/m3Average heat source
64,500Power (kW)
Bruce B, Bruce B, 50% FP50% FPNOMINAL CONDITIONS
11.4
51.5
40.1
2
8
22.9
14.74 kW/m2
1,090
MTFMTF
2Number of outlets
8Number of nozzles
16.2Temperature difference (ºC): T
61.0Outlet Temperature (ºC)
44.8Inlet Temperature (ºC)
948.0Moderator mass flow rate (kg/s)
277 kW/m3Average heat source
64,500Power (kW)
Bruce B, Bruce B, 50% FP50% FPNOMINAL CONDITIONS
25
2.3 Heating Methods
In the actual Calandria vessel of a CANDU reactor, the cold fluid is heated by direct heating
of neutrons, decay heat from fission products, and/or gamma rays in the vessel. However, in
many of the test models, electrically heated rods are used to replace the nuclear heating
process, as a result, two different methods of heat transfer inside the tank can be considered.
Surface heat transfer: In this method, similar to the experiments, heat source is at the
surface of the tubes (this method is used to simulate MTF).
Volumetric heat transfer: In this method, heat source is throughout the whole fluid
inside the tank (this method is used to simulate both MTF and the actual moderator
tank).
In numerical simulation, the first method is modeled through heat influx at the boundaries of
the tubes inside the calandria. Since the heat flux inside the actual tank is dependent on the
coordinate along the length of the tank, the heat influx in numerical model is divided into 24
zones along the tank length (each of 12 zones along the tank length is divided to inner and
outer sub zones) and every zone has a different influx of heat at its boundary. Figure 2-4
shows the heat influx for each zone along the tank length for MTF simulation.
The second method is represented through heat sources inside the tank. Similar to the
previous case, the tank volume is divided into 6 zones and each zone has its own volumetric
heat source. In this case although the total heat generation inside the tank is the same as
surface heating, but the method of heat generation distribution is different. Here we explain
the calculation method for MTF volumetric heating case.
Volu
heati
surfa
wher
umetric heat
ing method.
ace. The tota
re AT is the t
Figure
t flux for vo
Surface hea
al tube surfac
total tubes su
2-4 MTF hea
olumetric cas
ating generat
ce is:
urface inside
26
at generation m
se is calcula
tes 14,740
.
e the tank.
map - surface
ated based o
of heat in
heating
on heat gene
n average thr
.
eration in su
roughout its
.
(Eq 2-
urface
tubes
m2
-1)
27
Total heat generation inside the tank is:
, . . (Eq 2-2)
where QT is the total heat generation for surface heating case. As mentioned previously it
will be used for volumetric heating calculation. We need to calculate tank volume and net
fluid volume inside the tank:
.
. . (Eq 2-3)
. . . (Eq 2-4)
. . . (Eq 2-5)
Where VTA is total tank volume, VT is total tubes volume and VNT is the net fluid volume
inside the tank. for the purpose of numerical simulation and to have various heat generation
along the tank length, the tank domain is divided to 6 zones and each zone has its own
volumetric heat generation. Zone 1 is explained in the followings and the rest of the zones
will be calculated similarly.
Zone 1:
≡ 22164
28
≡ 19571
. . (Eq 2-6)
≡ . . (Eq 2-7)
≡ . . (Eq 2-8)
. . (Eq 2-9)
. . (Eq 2-10)
≡ . .
.
. (Eq 2-11)
This is the quantity which will be used in numerical simulation.
2.4 Mesh Construction
An unstructured non-uniform tetrahedral mesh was used to construct meshes in the MTF and
the actual tanks. A total of 3,200,000 meshes were generated using the commercial software
Gam
altho
sure
gene
mbit. The m
ough accurat
that the acc
erated meshe
mesh size wa
te measures
curacy of the
es are shown
as limited b
(i.e. mesh a
e simulation
n in Figure 2
Figure 2-5 M
29
by the capac
adaption and
ns are not co
-5 to Figure
Mesh Generatio
city of the
d gradient) h
ompromised
2-9.
on - XY plane
parallel com
have been em
by the mesh
e
mputing me
mployed to m
h resolution
emory
make
n. The
FFigure 2-6 XY
Figure 2-7 XY
30
Y plane - mesh
Y plane - mesh
h around tube
h near the wal
es
ll
The
of ce
meth
varia
solution dom
ells in each p
hod. Maxim
ation in num
main is divid
partition is 1
mum and mi
mber of cells
Figu
Figu
ded into 20
150,000 and
inimum num
will increase
31
ure 2-8 Inlet p
re 2-9 Water o
partitions fo
the maximu
mber of cel
e computatio
pipes
outlet
or parallel pr
um is 160,00
lls in partit
on efficiency
rocessing. M
00 with Carte
tioning is c
y.
Minimum nu
esian partitio
rucial since
umber
oning
e less
32
2.5 Computational Code
The fluid is assumed to be incompressible and single-phase. The flow is considered to be
time dependent and turbulent. The RNG k-ε turbulence model with non-equilibrium wall
treatment is chosen for turbulence modeling. Since the flow is strongly anisotropic,
especially in the near wall zones, the RNG k-ε turbulence modeling for this typical geometry
covers both, anisotropic turbulence and secondary flows. The surface heat flux is applied to
the tube walls and the inner wall surface of the tank is considered as an adiabatic boundary
condition. The buoyancy effects are accounted for the density changes using the Boussinesq
approximation.
Fluent solves the governing integral equations for the conservation of mass, momentum,
energy, and turbulence. The Pressure Implicit with Splitting of Operators (PISO) pressure-
velocity coupling scheme is used to approximate the relation between the corrections of
pressure and velocity. The second-order upwind scheme is employed for the momentum,
turbulence, and energy equations. This approach produced a higher order of accuracy.
In each time step, the inner iteration is progressed until the normalized residuals in the
numerical solution of governing equations reach less than 10-4. The physical properties of
water are used in MTF simulations. The time step in all transient simulations is equal to 0.01
sec.
2.6 Solution Strategy
Any transient solution of numerical modelling needs an approaching strategy. This strategy
can be set up based on the limitations of the numerical models or the physics of the real
33
operating conditions (e.g. the time dependent operating and boundary conditions). All these
approaches may affect the calculation convergences, simulation results, and the numerical
computational times. Two different methods can be employed in this case:
The Steady-Transient Solution Strategy: In this approach, three steps are taken. First,
we start with the steady state solution of the flow equations to form an initial flow
structure. Then, the steady state solution of the flow and the energy equations are
solved to form an initial flow and temperature structure. Finally, we switch to the
transient solution of the energy and flow equation solvers. This approach is
considerably faster in comparison with the next approach.
The Transient Solution Strategy: In this approach, the transient energy and flow
equations are solved right from the start. This approach is time consuming and takes
significantly longer time to finish.
Based on our initial assessment and considering the fact that due to the turbulent nature of
the problem and existence of the fluctuations, it will be faster and more stable to employ the
first method as our preferred method of solution.
The following Steps are taken for each of the MTF and actual tank simulations:
MTF
o Parallel, three-dimensional simulation of isothermal-steady state conditions,
o Parallel, three-dimensional simulation of steady state conditions with heat
transfer,
34
o Parallel, three-dimensional simulation of transient conditions with heat
transfer. (two different methods of heat transfer is considered; The methods
are explained in the following section).
Actual tank
o Parallel, three-dimensional simulation of isothermal-steady state conditions,
o Parallel, three-dimensional simulation of steady state conditions with heat
transfer,
o Parallel, three-dimensional simulation of transient conditions with heat
transfer (only one method of heat transfer which is volumetric heating is
considered).
Actual tank – long range run
o This includes near 1000 physical seconds of run to see if any significant
effect is missed in the short range simulations. This also will help to optimize
the minimum time chosen for short range simulations.
During the transient simulation, 55 points of interest inside the tank are monitored closely
for their temperature and velocity fluctuations with time. The data extracted from these
points are used along with other results to explain the flow processes that occur inside the
tank. In the coming sections, results for different simulations, their comparisons, and in
depth analysis will be presented. The main difference between simulations is their method of
heat generation inside the tank. The following section comprehensively explains different
methods and their difference.
35
2.7 Planes - Points
Total of 16 planes and 55 points with different orientations and coordinates are considered
for monitoring and result analysis. Figures 6-8 shows the corresponding planes. There are
seven planes in the X-Y, three in the X-Z and three in Y-Z planes. The exact location of
each plane and their names are shown in Table 2-4, Figure 2-10, Figure 2-11 and Figure
2-12 (the following coordinates corresponds to MTF geometry and for the actual tank, the
numbers are multiplied by 4 to get the equivalent coordinates).
Plane Name Location Plane Name Location
A1 Z = 0.6875 C2 Z = -0.1875
B1 Z = 0.375 B2 Z = -0.375
C1 Z = 0.1875 A2 Z = -0.6875
S Z = 0.0 D1 Y = 0.503246
Sy Y = 0.0 Sx X = -0.177461
D2 Y = -0.503246 E2 X = -0.638858
E1 X = 0.505763
Table 2-4 Planes Coordinates
Figu
Figu
36
ure 2-10 XY-P
ure 2-11 XZ-P
Planes
Planes
Ther
calle
calle
re are 3 mor
ed nozzle pla
ed outlet pipe
re planes wh
anes and the
e plane and
Figu
hich are show
ey pass throu
it passes ver
Figur
37
ure 2-12 YZ-P
wn in Figure
ugh the nozz
rtically throu
e 2-13 Nozzle
Planes
e 2-13 and F
zles at the inj
ugh outlet pi
planes
Figure 2-14.
njection plan
pes.
The first tw
ne. The last o
wo are
one is
Chos
fluct
simu
pene
for t
show
actu
sen points a
tuations wit
ulations) in
etration path
these points
wn in Table
al tank the n
Points
1
2
are monitor
h time. The
the regions
h as well as
will be pres
2-5 (the fol
numbers are
Figure 2
red througho
e point coo
with high t
deep inside
sented in res
llowing coor
multiplied b
X
0
0
38
2-14 Outlet pi
out the dom
ordinates are
temperature,
the tank. Th
sults section
rdinates cor
by 4 to get th
ipe plane
main for the
e chosen (b
cold and h
he temperatu
. The exact
rresponds to
he equivalen
Y
0
0
eir temperatu
based on pr
hot interactio
ure and velo
coordinates
o MTF geom
nt locations).
ure and vel
reliminary s
on zones, an
ocity fluctua
of the point
metry and fo
Z
-0.75
-0.60
locity
teady
nd jet
ations
ts are
or the
39
3 0 0 -0.45
4 0 0 -0.30
5 0 0 -0.15
6 0 0 0.00
7 0 0 +0.15
8 0 0 +0.30
9 0 0 +0.45
10 0 0 +0.60
11 0 0 +0.75
12 0 +0.5712 -0.75
13 0 +0.5712 -0.60
14 0 +0.5712 -0.45
15 0 +0.5712 -0.30
16 0 +0.5712 -0.15
17 0 +0.5712 0.00
18 0 +0.5712 +0.15
19 0 +0.5712 +0.30
20 0 +0.5712 +0.45
21 0 +0.5712 +0.60
22 0 +0.5712 +0.75
23 0 +0.713993 -0.75
24 0 +0.713993 -0.60
40
25 0 +0.713993 -0.45
26 0 +0.713993 -0.30
27 0 +0.713993 -0.15
28 0 +0.713993 0.00
29 0 +0.713993 +0.15
30 0 +0.713993 +0.30
31 0 +0.713993 +0.45
32 0 +0.713993 +0.60
33 0 +0.713993 +0.75
34 -0.357876 +0.713993 -0.75
35 -0.357876 +0.713993 -0.60
36 -0.357876 +0.713993 -0.45
37 -0.357876 +0.713993 -0.30
38 -0.357876 +0.713993 -0.15
39 -0.357876 +0.713993 0.00
40 -0.357876 +0.713993 +0.15
41 -0.357876 +0.713993 +0.30
42 -0.357876 +0.713993 +0.45
43 -0.357876 +0.713993 +0.60
44 -0.357876 +0.713993 +0.75
45 -0.624268 +0.682956 -0.75
46 -0.624268 +0.682956 -0.60
41
47 -0.624268 +0.682956 -0.45
48 -0.624268 +0.682956 -0.30
49 -0.624268 +0.682956 -0.15
50 -0.624268 +0.682956 0.00
51 -0.624268 +0.682956 +0.15
52 -0.624268 +0.682956 +0.30
53 -0.624268 +0.682956 +0.45
54 -0.624268 +0.682956 +0.60
55 -0.624268 +0.682956 +0.75
Table 2-5 Monitored points coordinates
2.8 Parallel Processing – Physical Run Time
Transient, three-dimensional simulations of MTF and the actual tank are performed for 150
physical seconds. As mentioned before, the simulation is run on a 24-processor cluster and
related information for MTF with surface heating is shown in Table 2-6. These are typical
numbers and similar quantities can be considered for other simulations as well.
AVERAGE WALL-CLOCK TIME PER 7.827 Sec
TOTAL WALL-CLOCK 346 hrs. 24 min 18 sec
TOTAL CPU TIME 6922 hrs. 56 min 15 sec
Table 2-6 Parallel processing time
The
large
simu
facil
for a
time
the m
show
for r
cann
acco
fluct
smal
experiments
er), but usin
ulation time
lity. As a res
about 1000
e frame for a
minimum tim
wn in Figure
reference pur
not be captu
ounted for in
tuations are
ll and they c
s have been
ng the same p
as well as
sult a more
physical sec
all simulation
me period w
e 2-15 and F
rposes. The
ured in 150
n FFT analy
not a concer
annot cause
Figure 2-15
n performed
period of sim
s considerab
practical ap
conds to fin
ns. The resul
which is prop
igure 2-16 a
figures show
seconds, bu
ysis. The lo
rn since their
sudden and
Temperature
42
for much lo
mulation is i
ble amount
proach is ch
d the proper
lts for long r
per for inves
and the rest o
w that althou
ut their freq
ng range ru
r amplitude
unpredicted
e fluctuation -
onger times
impossible s
of processi
hosen here. O
r time perio
run revealed
stigation. Ty
of the result
ugh some ve
quencies non
un also show
relative to h
d changes in
long range ru
(several ord
since it will r
ing power a
One simulat
od which can
d that 150 ph
ypical results
ts are in the
ery low frequ
ne the less
ws that thes
high frequen
tank temper
un for point 4
der of magn
require very
and data sto
tion is perfo
n be used a
hysical secon
s for long ru
appendix se
uency fluctu
are detected
se low frequ
ncy fluctuatio
rature.
nitude
y long
orage
ormed
as our
nds is
un are
ection
uation
d and
uency
ons is
Figure 2-16 Velocity flu
43
uctuation - lonng range run f
for point 4
3
Mod
expl
analy
3.1
Expe
tank
occu
effec
show
at tw
Moder
derator used
ained in pre
yzed using t
Tempe
erimental re
. This may o
ur on region
cts, causing
ws temperatu
wo different t
rator T
d in moderat
evious chapte
emperature
erature a
sults on MT
occur in the r
ns with high
velocity fluc
ure contours
times:
Figure 3-1 Te
Test Fa
tor test faci
ers. In this s
and velocity
and Velo
TF have reve
regions whe
h fluid velo
ctuations, an
s for plane S
emperature co
t= 2
44
acility S
ility is simu
section the r
y distribution
ocity Dis
ealed existen
ere hot and c
cities where
nd consequen
S, which is in
ontours at two
20 s
Simula
ulated using
result for the
ns throughou
stributio
nce of tempe
cold flows in
e the flow i
ntly, tempera
n the middle
o different tim
ation
g surface he
e simulation
ut the tank.
ons
erature fluctu
nteract. Fluct
is more pro
ature fluctua
e of the tank
mes for plane S
eating metho
n is presented
uations insid
tuations may
one to turbu
ations. Figur
k in the XY p
S
t= 150 s
od as
d and
de the
y also
ulence
re 3-1
plane
45
The lowest temperature in this plane is 40 oC, which is the inlet water temperature and the
highest temperature is 63 oC. The highest temperatures are at the top inner zone of the tank
and remain in the same zone as time proceeds. As we move from the inner to the outer zones
of the tank, temperature decreases due to the cold inlet jets flow near the outer wall. The
most intense fluctuations in temperature can be expected in the regions where the low
velocity hot fluid in the inner parts of the tank, referred to as the inner flow, mixes with the
cold high velocity flow on the outer regions, referred to as outer jet flow.
The hot region is shifted toward the left inlet resulting in asymmetric flow in the tank in this
plane. This asymmetry arises due to the competition between momentum and buoyancy
forces inside the tank. The detailed interaction of these forces and their effects on the
temperature distribution will be discussed later on this chapter. Figure 3-1 not only shows
that asymmetric flow in this plane but also an unsteady flow. In fact an unsteady flow is
observed throughout the whole tank and it is a particular nature of this moderator.
Figure 3-2 shows the velocity contours for the same plane and the same times as in Figure
3-1. The high velocity inlet fluid takes the path of least resistance and flows close to the
walls of the tank and outside the tube bundles. Inlet nozzles are designed to guide the fluid
toward the top of the tank. Therefore, the right and the left cold inlet fluids meet each other
somewhere close to the top of the tank. The flow generated by the impingement of these
fluids turns downward the core of the tube bundle opposing the upward moving buoyancy
flows. The bulk fluid velocity is almost 0.1 m/s, whereas the velocities close to the inlet
nozzle are around 1 m/s.
Figu
unste
inlet
Seve
heig
velo
regio
Figu
expe
is clo
ure 3-2 show
eady. This i
t nozzles.
eral other pla
ht, SX and
city distribu
ons where te
ure 3-3 show
ected the col
ose to 40 oC
ws that simil
s evident wh
Figure 3-2
anes are pres
the length,
ution is obser
emperature a
ws temperatu
ldest regions
C (same as th
lar to tempe
hen compari
Velocity cont
sented in Fig
, D1 of the
rved in all p
and velocity
ure contours
s shown in th
he inlet temp
t=
46
erature distr
ing flow con
tours at two di
gure 3-3 to F
e tank. Asym
planes. In ad
gradients are
in plane B2
he figure are
perature). Th
20 s
ribution, the
ntours at two
ifferent times
Figure 3-6. T
mmetric nat
ddition, segre
e large is vis
2 which pass
e near injecti
he temperatu
velocity di
o different t
for plane S
These includ
ture of the
egation betw
sible.
ses through
ion nozzles.
ure increases
stribution is
times close t
de plane alon
temperature
ween hot and
inlet nozzle
The temper
s to more tha
t= 150 s
s also
to the
ng the
e and
d cold
es. As
rature
an 50
oC a
as pl
Figu
bulk
The
impi
as 1
of th
s we proceed
lane S (top s
F
ure 3-4 show
k of the tank
flow velocit
inging jets w
m/s. The im
he tank and t
d to the inne
section of the
Figure 3-3 Te
ws the velocit
is under 0.4
ties are relat
which penetr
mpingement z
his side rem
er core. Alth
e tank), but i
mperature co
ty contours
4 m/s. the fl
tively large
rates into the
zone for the
mains cooler t
t=
47
hough the gen
it is moved t
ntours at two
for the same
low velocity
close to the
e core. In th
inlet jets is
than the left
20 s
neral locatio
toward one s
different time
e plane as Fi
y is the highe
e outlet pipe
hese regions
clearly visib
side of the t
on of the hot
side of the ta
es for plane B
igure 3-3. Th
est close to
as well as i
the velocitie
ble on the to
tank.
t zone is the
ank.
B2
he velocity i
the inlet noz
in the path o
es can be as
op right-hand
t= 150 s
same
in the
zzles.
of the
s high
d side
Figu
It cl
and
or le
porti
obse
velo
grad
Figu
SX.
arou
comp
ure 3-5 show
early shows
it is more to
ess similar to
ion of the tan
erved at the
cities in the
dients near th
ure 3-6 show
This particu
und them. Ba
pared to the
Figure 3-4 V
ws the temper
that the ho
oward the lef
o the previou
nk, specifica
front (left)
ese zones k
he walls resu
ws the tempe
ular plane p
ased on the i
e lower or u
Velocity conto
rature contou
t zone is no
ft side. The h
us planes. Th
ally in the m
and back (
keep the flui
ult in a relativ
erature conto
passes throu
input conditi
upper tubes.
t=
48
ours at two dif
urs in a plan
ot extended t
high velociti
he result sho
middle far fro
(right) sides
id cooler th
vely large m
ours for a p
ugh the tube
ions, the tub
Temperature
20 s
fferent times f
ne along the
throughout t
ies for plane
ows almost u
om the walls
s of the tan
han the othe
mixing betwe
plane along t
es and show
bes in the mi
es are as hig
for plane B2
length of th
the whole le
e D1 are in th
uniform velo
. Large velo
nk near the
er zones. Th
een the hot a
the height o
ws the temp
iddle have h
gh as 63 oC
he tank, plane
ength of the
he range of
cities in the
city gradien
walls. The
he large vel
and cold fluid
of the tank, p
perature vari
higher heat f
C in some re
t= 150 s
e D1.
e tank
1 m/s
main
nts are
large
locity
ds.
plane
iation
fluxes
gions
near
those
temp
the tubes. T
e close to
peratures as
F
F
The velociti
the water
shown in Fig
Figure 3-5 Tem
Figure 3-6 Tem
ies close to
outlet. Low
gure 3-6.
mperature con
mperature con
t=
t=
49
the tube wa
w velocitie
ntours at two
ntours at two
20 s
20 s
alls are low
s result in
different time
different time
and below
lower mix
es for plane D
es for plane SX
t=
1 m/s excep
xing and h
D1
X
t= 150 s
= 150 s
pt for
higher
3.2
This
temp
fluct
Sinc
oC a
can
with
Figu
porti
char
fluct
2 Tempe
s section pre
perature and
tuations for p
ce this point
at t=78 s. Th
be categoriz
hin 0.03 m/s
ure 3-8 show
ion of the t
acteristics s
tuations star
erature a
sents results
velocity var
point 3, whi
is not in the
e temperatur
zed as low
to 0.06 m/s.
Figure 3-7 Po
ws the fluctu
tank near th
since it is a
rt with high
and Velo
s for several
riation with
ich is located
high temper
re variation
frequency w
oint 3 tempera
uations for
he end wall
at the end o
amplitude, b
50
ocity Flu
points insid
time. Figure
d on the tan
rature zone,
is as high as
with high a
ature and velo
point 12. A
l, but it is
of the tank,
but it quickl
uctuation
de the tank w
e 3-7 shows
nk centerline
the highest
s 6 oC. The
amplitude. T
ocity fluctuati
Although this
not affected
, far from h
ly damps to
ns
which are m
the tempera
e close to the
temperature
frequency o
The velocity
ions with time
s point is lo
d by high t
high temper
o a low ampl
onitored for
ature and vel
e end of the
e observed is
of the fluctua
y fluctuation
e
ocated at th
temperature
rature zone.
litude fluctu
r their
locity
tank.
s 59.9
ations
ns are
he top
zone
. The
uation
arou
fluct
the t
decr
Afte
the p
Figu
regio
decr
tank
low
und 53 oC. T
tuations are
temperature
ease at early
er t=20 s, the
previous poin
ure 3-9 show
on. Tempera
eases every
, but these s
velocity bul
This point is
located. It s
to decrease
y times whi
e velocity se
nt. This is du
Figure 3-8 Po
ws the tempe
atures fluctu
20 to 30 se
sudden chang
k flow and p
s far from th
starts with hi
significantly
ich can be a
eems relativ
ue to its loca
oint 12 temper
erature and v
uate close to
econds. Alth
ges indicate
periodically
51
he jet penetr
igh temperat
y and stay at
associated w
vely stable bu
ation being a
rature and vel
velocity fluc
o 60 oC. Ve
hough this p
that the out
reaches to p
ration path,
ature but as t
t that level. T
with the initi
ut having hi
at generally h
locity fluctuat
ctuations for
elocity plots
point is loca
ter high velo
point 20 caus
where the l
time proceed
The velocitie
ial flow dev
igher mean
high velocity
tions with time
r point 20, l
show sudd
ated in the i
ocity flow p
sing sudden
large temper
ds, mixing f
es show a su
velopment p
temperature
y zone.
e
ocated in th
den increases
inner zone o
enetrates int
changes.
rature
forces
udden
phase.
e than
he hot
s and
of the
to the
Figu
and
one
one
frequ
zone
poin
The
are p
betw
ure 3-10 show
exactly at th
is the high
is a much
uency fluctu
e, as well as
nt does not g
low frequen
partially cau
ween inlet no
ws the fluctu
he center of
frequency w
lower freq
uations are d
being at the
go higher tha
ncy is the re
used by the
ozzles and ou
Figure 3-9 Po
uations for p
it. Two diff
which exists
quency whic
due to the lo
e interface o
an 56 oC sin
esult of large
mixing of
utlet pipe.
oint 20 temper
52
point 50, loc
ferent pattern
throughout
ch complete
cation of the
f the cold an
nce it is in c
er flow patte
hot and col
rature and vel
cated at the t
ns of fluctua
the whole
es every 12
e point bein
nd the hot w
contact with
erns inside t
ld water and
locity fluctuat
top left-hand
ations are ob
simulation t
0 seconds
ng close to th
water. The te
low temper
the tank. Th
d partially b
tions with time
d side of the
bserved. The
time. The se
or so. The
he jet penetr
emperature a
rature inlet w
ese flow pat
by the fluid
e
e tank
e first
econd
high
ration
at this
water.
tterns
flow
The
Atom
expe
expe
the e
simu
than
acco
also
F
simulations
mic energy
eriments. Fig
erimental me
experimenta
ulation result
10% variati
ount for the
the chaotic
Figure 3-10 Po
s are perform
of Canada L
gure 3-11 s
easurements
al results: Ho
t at almost t
ion with resp
errors from
and unpredic
oint 50 tempe
med based o
Limited. He
shows a qua
s in symmetr
ot, Medium,
the same coo
pect to the ex
experimenta
ctable nature
53
rature and ve
on the exper
ere the simu
alitative com
ry plane. Th
, and cold z
ordinates. Th
xperimental
al results as
e of the flow
elocity fluctuat
riments cond
ulation resul
mparison be
hree distinct
zones. Simila
he temperatu
results. This
well as num
w inside the t
tions with tim
ducted in th
lts are comp
tween simu
tive zones a
ar zones can
ure in differe
s is consider
merical simu
tank.
me
he laboratori
pared to tho
ulation result
are determin
n be identifi
ent point ha
red accurate
ulation error
ies of
ose of
t and
ned in
ied in
s less
if we
rs and
3.3
3.3.
Simu
tank
plan
direc
Gene
the u
since
injec
tank
flow
Thes
3 Asymm
.1 Main F
ulations show
. Figure 3-1
es essential
ction.
erally, high
upper parts o
e it will redu
cted at the to
with high te
w which pas
se two factor
Figure 3-1
metry
Flow Regi
w an asymm
12 shows th
lly cover th
temperature
of the tank.
uce the cooli
op of the tan
emperature.
ses through
rs greatly red
11 Compariso
imes
metry in temp
hree planes i
he entire tan
e areas are c
It also shou
ing efficienc
nk; the flow p
But what oc
the tubes d
duce the coo
54
n between sim
perature dist
in Z directio
nk and it c
concentrated
ld be noted
cy. The ideal
passes throu
ccurs in real
does not pa
oling effects
mulation and e
tribution in a
on and one
clearly show
d close to th
that, current
l condition i
ugh a large n
ity is that th
ass through
inside the ta
experiment
all three dire
plane in Y
ws the asym
e symmetry
t distribution
s than when
number of tu
he hot zone l
maximum n
ank. If we ca
ections insid
direction. T
mmetry in e
y plane (z=0)
n is not desi
n the cold wa
ubes and exit
lies at the top
number of t
an find the re
de the
These
every
0) and
irable
ater is
ts the
p and
them.
eason
behi
symm
nd the asym
metry at all
Fi
mmetry, we c
directions.
igure 3-12 Tem
can suggest
mperature dis
55
a solution w
tribution on 4
which will m
4 planes on Z
make the dist
and Y directio
tribution clo
ons
ose to
56
In order to reveal the causes behind the asymmetry, it is necessary to analyze the flow
regimes inside the tank. Figure 3-13 shows velocity vectors (which are shown with constant
length and coloured by their velocity magnitude) for three different planes parallel to the XY
plane. These planes include the symmetry plane in the middle and two inlet planes. The first
inlet plane contains two nozzles and the second inlet plane contains two nozzles and an
outlet pipe.
The flow pattern in the inlet planes show that the injected fluid from the left and the right
nozzles goes through the outer edges of the tank at a high velocity. These two flows impinge
on each other at some point close to the top of the tank. This impingement forms a
secondary downward moving flow which passes through the tube bundle (mostly on the
right hand side of the tank) and exits through the outlet pipe. This pattern is the strongest in
the plane with inlet and outlet and weakens in the plane with only-inlet nozzle and in the
symmetry plane (z=0). On the plane having only-inlet nozzle, although there is strong trace
of the above pattern, but upward flow is also strong and it dominates the left hand side of the
tank. A substantially clock-wise flow circulating the outer edges of the tank is noticeable in
this plane. This substantially clock-wise flow is the strongest on the symmetry plane. This
flow has certain effects which will be explained in the remainder of this chapter.
Three different flow regimes can be identified inside the tank. These flows are:
Inlet jet impingement flows: these are the flows generated due to the inlet nozzle
flows which go through the upper edge of the tank, impinge on each other, and form
downward moving flows, which goes through the tube bundle (Figure 3-14).
As
nozz
the t
are,
Buoyanc
through t
(from inl
buoyancy
Clock-w
almost ¾
comes fr
second su
explained in
zle and the h
tank. The re
will be expla
cy-driven fl
the tubes but
let to the ou
y forces insi
wise flow: thi
¾ of the ou
rom the righ
ub-flow runs
n the previo
hot zone is p
eason behind
ained in the
lows: there
t toward the
utlet) and as
de the tank (
is flow regim
uter edge per
ht nozzle w
s from the le
us chapters,
pushed to the
d the asymm
coming line
57
is a strong
top of the ta
will be exp
(Figure 3-15
me is the stro
riphery. It c
which goes t
eft nozzle to
, the imping
e left. It resu
metry and ho
es.
flow at the
ank. This is
plained later
5).
ongest in sym
consists of t
through the
the top of th
gement poin
ults in a high
ow it occurs
left hand si
against the b
r is mainly d
mmetry plan
two sub-flow
bottom of t
he tank.
nt is yielded
hly asymme
s and what t
ide which p
bulk flow re
due to the s
ne and it occ
ws. The firs
the tank an
toward the
etrical flow i
the conseque
passes
egime
strong
cupies
st one
d the
right
inside
ences
Figgure 3-13 Veloocity vectors (ccolour by velo
Inject
Inj
58
ocity magnitud
tion plane -2
ection plan
de) in two noz
2
e -1
zzle planes andd symmetry plane
Figure 3-
Figure 3-15
59
-14 Impingem
5 Effect of buo
ment point.
oyancy force
3.3.
Clos
help
path
prese
meas
Figu
alon
Figur
Fig
.2 Inlet Je
se investigati
us in expla
used for m
ented with re
sured agains
ure 3-16. Th
g the second
re 3-16 Inlet je
gure 3-17 Seco
ets and S
ion of inlet j
aining the ph
monitoring th
espect to the
st the positiv
he results fo
dary jet path
ets path. The
ondary jet pat
Secondar
ets and the s
henomenon
he inlet jets
e angular pos
ve X directi
or the second
as shown in
marked point
h. The marke
60
ry Jet
secondary je
in the tank.
and the sec
sition of the
ion and it in
dary jet are
n Figure 3-17
ts are used to r
d points are u
et reveals val
. Figure 3-1
condary jet.
presented p
ncreases cou
e presented f
7.
record data on
used to record
luable inform
6 and Figur
The results
oints. The an
unter clock-w
from the im
n temperature
d velocity and t
mation whic
re 3-17 show
for inlet jet
ngular positi
wise as show
mpingement
e and velocity
temperature d
h can
w the
ts are
ion is
wn in
point
y.
data
61
Figure 3-18 and Figure 3-19 show temperature and velocity along the inlet jets. The
impingement point is indicated with a red line in the middle and the points on the right side
attribute to the right nozzle and vice versa. The temperature plot shows that temperature
increases from the inlet toward the impingement point. This is expected since as flow passes
through the tubes and interacts with hot water inside the tank, its temperature increases more
than 15 oC for the left jet and less than 10 oC for the right jet. The average temperature is
also higher for the left jet compared with the right jet. This is due to two main factors:
The impingement point is on the right side of the tank and the left jet travels a large
distance to the impingement point. Therefore, it heats up more.
The hot zone is pushed to the left and therefore, the left jet passes through a hot
boundary, which will cause an increase in its temperature comparing to the right jet.
The velocity plot shows that the inlet jets lose their momentum as much as 90% once they
reach to the impingement point. The velocity decreases from more than 1 m/s at the nozzle
inlet to less than 0.5 m/s at the impingement point. It is not desirable since very low
impingement velocity will produce low-momentum secondary jet that cannot penetrate the
tank efficiently and will affect cooling efficiency of the tubes inside the tank.
Figu
Fi
Tem
per
atur
e (o C
) V
eloc
ity
(m/s
)
ure 3-18 Temp
igure 3-19 Vel
erature along
locity along th
g the inlet jetsrespect
he inlet jets perespect
62
penetration pto positive X d
netration pathto positive X d
Tetha (De
Tetha (Deg
path. The x coodirection
h. The x coorddirection
egree)
gree)
ordinate is an
dinate is angu
ngular position
ular position w
n with
with
63
Figure 3-20 and Figure 3-21 shows the temperature and velocity for the secondary jet.
Temperature variation shows an oscillatory nature. The penetration path for the secondary
jet lies at the boundary of cold and hot zones and as a result their mixing will affect the
temperature on the penetration path, forcing it to show an oscillatory behaviour. As the flow
passes through more tubes inside the tank, we expect the temperature to increase as shown
in the plot. The variation between the highest and the lowest temperature on the secondary
jet penetration path is close to 12 oC. This large variation in a short distance is a driving
force behind buoyancy force inside the tank. Its presence changes the temperature
distribution inside the tank while competing with the momentum force.
The velocity of the secondary jet also decreases by distance from the impingement point. It
is expected since the secondary jet has to penetrate into the bulk flow inside the tank which
has very low velocity. The secondary jet only carries 10% of the initial momentum injected
by the inlet nozzles. This amount reduces further significantly. Half way through its path,
the secondary jet has lost 80% of its already small initial momentum. It is a problem since it
greatly reduces the mixing inside the tank and by the time the flow is near the exit, the
inertia is not the driving force anymore and flow becomes buoyancy driven.
Fig
Fig
This
decr
gure 3-20 Tem
gure 3-21 Velo
s effect is a
eases as the
Tem
per
atur
e (o C
) V
eloc
ity
(m/s
)
mperature alonthe pen
ocity along thepenet
also shown
secondary j
Initial increa
Clo inl
ng the secondanetration path
e secondary jetration path w
in detail in
jet goes tow
Distance fr
Distanc
ase
Hw
ose to let jet
64
ary jet penetra with respect t
et penetrationwith respect to
n Figure 3-1
ward the outl
rom Imping
ce from Imp
Hot boundary warming effect
ation path. Thto impingeme
n path. The x co impingement
15. Tempera
et pipes. Ne
ement (m)
pingement (
Clock-wis
he x coordinatent point
coordinate is pt point
ature increa
ear the outlet
(m)
se cooling effect
e is position a
position along
ases and vel
t the flow st
t
along
the
locity
tream
has v
mom
of th
3.3.
In o
first
buoy
impi
the t
the t
This
insid
very low vel
mentum turns
he tank at the
.3 Momen
rder to anal
a symmetri
yancy is com
inge on each
tank. The bu
tank. These
s is called m
de the tank.
locity and hi
s around (cre
e left hand si
ntum ver
lyze the mai
ical distribut
mpeting with
h other exac
uoyancy forc
circulations
moderate buo
igh temperat
eating circul
ide instead o
rsus Buoy
in reason be
tion is consi
h momentum
tly at the ce
ce creates tw
prevent the
oyancy sinc
Figure 3-
65
ture. Most o
lation zone a
of going to th
yancy
ehind the as
idered in Fig
m forces due
enter line. A
wo hot tempe
e secondary j
ce it has not
-22 Moderate
f The hot flo
at the bottom
he outlet pip
symmetrical
gure 3-22. I
e to inlet jet
A secondary j
erature circu
jet to go dir
t enough str
buoyancy
ow which ha
m)) and mov
pes.
distribution
In these con
ts penetratio
jet forms an
ulating zone
rectly toward
rength to do
as lost most
ves toward th
n inside the
nditions mod
on. Two inle
nd penetrates
e at the botto
d the outlet
ominate the
of its
he top
tank,
derate
et jets
s into
om of
pipe.
flow
The
high
circu
inne
finds
of th
In th
exter
from
and
the m
distr
second scen
her heat flux
ulations due
r core and p
s its way to
he tank as sh
he third situ
rnal disturba
m symmetric
the moment
moderator re
ributed asym
nario is to ha
x or higher
to buoyancy
prevent the s
the exit pipe
own in Figu
uation, stron
ances which
al to asymm
tum driven s
eactor. It is a
mmetrically d
ave stronger
temperature
y force expa
secondary je
e by going a
ure 3-23.
Figure 3
ng buoyancy
affects the f
metrical. The
secondary je
a mix of stro
due to variou
66
r buoyancy f
e gradient in
and to the to
et from pene
around the ci
3-23 Strong b
y exists insi
flow inside t
e buoyancy c
et occupies th
ong buoyancy
us disturbanc
force inside
nside the ta
op of the tan
etrating into
irculation zo
uoyancy
ide the tank
the tank, the
circulation o
the other sid
y and mome
ces in the flo
the tank. It
ank. In these
nk. They oc
o the tank. T
one through
k but due to
e flow distrib
occupies one
de. This is w
entum force
ow.
can occur d
e conditions
cupy most o
The secondar
the outer su
o turbulence
bution transf
e side of the
what occurs i
which have
due to
s, the
of the
ry jet
urface
e and
forms
e tank
inside
been
3.3.
Whe
their
flow
insid
left,
.4 Asymm
en the asymm
r existence c
ws is called “
de the tank.
which we ar
metry Eff
metrical dist
contributes t
“3D effect” f
These are c
re looking at
Figure 3-
ects
tribution dev
to more asym
flow. To ful
called nozzle
t them from
67
-24 Asymmetr
velops inside
mmetry insi
ly understan
e planes and
top position
rical flow.
e the tank, it
ide the tank
nd it, we hav
d there is on
n.
t generates o
k. One of the
ve to look in
ne at the righ
other flows w
e most impo
nto to new p
ht and one a
which
ortant
planes
at the
Figu
left h
3-29
borro
prese
wise
Ther
respe
othe
symm
Figure 3-25 L
ure 3-26 and
hand side. T
9 are special
owed from
ents Z-veloc
e in left plane
re are four n
ect to symm
r on symm
metry plane
Left and right
Figure 3-27
he vectors a
lly sketched
another pla
city. In this w
e and counte
ozzles on ea
metry plane
etry plane.
. The same p
t nozzle planes
7 shows velo
and streamlin
. The planes
ane. The Y
way the vect
er clock-wise
ach plane (lef
(z=0). The i
They form
phenomenon
68
s. These planeimpingement
ocity vectors
nes at these f
s are in YZ
Y-component
tors which a
e on the righ
ft plane and
inlet flows f
a secondar
n occurs bet
es are used to st
s and stream
figures as w
plane, but
t present X
are toward p
ht plane.
d right plane)
from nozzle
ry jet which
tween nozzle
study the effe
m lines for no
well as Figure
the velocity
X-velocity an
positive Y, ar
) which are s
es 2 and 3 im
h rotates cl
es 1 and 2 a
ct of jet on jet
ozzle plane a
e 3-28 and F
y component
nd Z-compo
re rotating c
symmetrical
mpinges on
lock-wise on
and nozzles 3
t
at the
Figure
ts are
onent
clock-
l with
each
n the
3 and
4. T
plan
from
clock
betw
dow
his is visibl
e, vectors in
m nozzles 2 a
k-wise on th
ween nozzles
nward push
e on both v
n negative Y
and 3 imping
he symmetry
s 1 and 2 an
from the sec
1
Zoom
vector and st
direction ar
ge on the sy
y plane. Sim
nd nozzles 2
condary jet w
2m Area
69
tream line p
re rotating cl
mmetry and
milar to the
and 3. The
which is form
Symmet
3
presentations
lock-wise in
d again form
left plane, t
reason for
med at the ri
try Plane
4
s. In the cas
n symmetry p
m a secondary
the same ph
being clock
ight hand sid
4
se of right n
plane. Here f
y jet which r
henomena ha
k-wise flow i
de of the tank
nozzle
flows
rotate
appen
is the
k.
Fi
Fi
igure 3-26 Lef
igure 3-27 Lef
ft nozzle plane
ft nozzle plane
e. Y axis veloc
e. Y axis veloc
70
ity representsvelocity
ity representsvelocity
Sym
Zoom Area
s x-velocity an
s x-velocity an
mmetry Plan
a
nd Z axis veloc
nd Z axis veloc
ne
city represents
city represents
s z-
s z-
Figgure 3-28 Righht nozzle plan
1
ne. Y axis veloc
2
71
city representvelocity
Symmet
3
Zoom Area
ts x-velocity an
try Plane
4Zo
a
nd Z axis velo
oom Area
ocity represent
ts z-
Fig
The
flow
symm
para
3-30
will
The
inlet
poin
effec
gure 3-29Righ
sum of thes
w inside the t
metry plane
llel plane by
0. As observe
transfer any
large scale c
t jet on the
nt to right sid
ct” because
ht nozzle plane
e clock-wise
tank on three
e between 3
y means of fl
ed, there are
ything on the
clock-wise fl
left hand si
de and contri
it cannot
e. Y axis veloc
e flows on th
e planes: sym
and 4. The
flows in YZ d
e two large s
e symmetry p
flow results i
ide. This in
ibutes to the
be captured
72
city representsvelocity
he left and r
mmetry plan
ese clock-wi
direction. Fl
scale rotation
plane to the o
in weaker in
turn, will i
asymmetry
d in two d
Symme
s x-velocity an
right creates
ne, symmetry
ise rotations
lows in YZ d
ns with resp
other paralle
nlet jet on the
intensify mo
inside the ta
dimensional
etry Plane
nd Z axis veloc
an overall s
y plane betw
s are transfe
direction are
ect to symm
el planes.
e right hand
ovement of
ank. This eff
simulations
city represent
strong clock
ween 1 and 2
erred to the
e shown in F
metry plane w
side and stro
the impinge
ffect is called
s. Although
ts z-
-wise
2, and
other
Figure
which
onger
ement
d “3D
h this
phen
acco
nomenon do
ounted for in
oes not initi
our analysis
iate the asy
s.
73
ymmetry buut since it ccontributes
to it, shoulld be
Fig
ure 3-30 Centter plane in Z direction. thisplanes
74
s shows the tralong the Z-d
ansfer of symdirection
metry plane e
effects to the oother
75
4 Methods of Heating: Surface Heating and Volumetric Heating
Moderator test facility simulation is carried out using two methods of heating which are
explained in previous sections: MTF with surface heating, and MTF with volumetric
heating. The volumetric heating occurs in actual reactor whereas surface heating is the
method employed in test facility due to practical reasons. It is beneficial to compare the
results of these simulations to fully understand the effect of different heating method on
temperature and velocity distributions as well as fluctuations inside the tank.
From 55 points which are monitored in each of the simulations, three points have been
chosen (17, 39, and 50), along with the temperature and velocity contours in the several
planes, to show difference between heating methods and the effects they will have on final
results. Locations of These three points are shown in Figure 4-1. They are located inside the
hot zone, near the interaction between hot and cold, low velocity and high velocity flows.
First, temperature fluctuations with time for three points are compared with each other
(Figure 4-2). The first plot corresponds to point 17 which is located deeper inside the tank
comparing to other points. The general trend shows that the volumetric actual tank
simulation has the highest temperature. This is expected since the actual tank has higher
influx of heat comparing to MTF simulations (surface heating and volumetric heating).
MTF surface heating has a lower temperature than MTF volumetric heating. Volumetric
heating results in a better heat distribution throughout the tank. This results in a better
mixing of hot and cold flows which in turn results in lower overall temperature. The other
advantage of the volumetric heating over surface heating is lower fluctuation amplitudes.
Poin
surfa
beha
itself
heati
close
figur
and
patte
nt 39 is close
ace heating
aviour at this
f fully in the
ing due to b
est to the ou
re, the fluctu
MTF volum
ern. The mai
er to the out
model with
s point due t
e surface he
better mixing
uter wall an
uations are
metric heatin
in driving fo
Figure 4-1 Lo
ter wall and
h volumetric
to its approx
eating simula
g and less te
nd it is at th
more intens
g are very c
rce for the m
Point 50
76
ocation of com
lies just bes
c model reve
imate distan
ation while i
emperature
he heart of j
se and with
close to each
mixing in thi
Poi
Point 39
mpared points
side the jet
eals that the
nce to the mi
it is dampen
gradient ins
jet penetrati
higher frequ
h other and
is zone is the
int 17
s
penetration
e temperatur
ixing zone. T
ned in the ca
side the tank
on path. As
uency. MTF
they almost
e flow mome
path. Comp
re shows ch
This effect s
ase of volum
k. Point 50 i
s observed i
F surface he
t follow the
entum rather
paring
haotic
shows
metric
is the
in the
eating
same
r than
buoy
effec
mixi
inter
temp
heati
that
distr
yancy effect
ct on the tem
ing occurrin
resting point
perature in t
ing (althoug
in critical z
ributed in the
ts inside the
mperature flu
ng here is d
t is the comp
the case of
gh in some o
zones where
e case of vol
flow. As a
uctuation. T
due to the
parison betw
MTF surfa
occasions it
e interaction
lumetric hea
77
result diffe
The flow has
incoming fl
ween average
ace heating
drops below
n between ho
ating which r
erent method
s high veloc
fluid from i
e temperature
is visibly h
w surface v
ot and cold
results in low
ds of heating
city in this r
injection no
es in each po
higher than
volumetric h
zones occu
wer average
g have mini
egion and a
zzles. The
oint. The av
MTF volum
eating). It s
urs, heat is b
temperature
imum
all the
other
erage
metric
shows
better
e.
Figure 4-2 T
78
Temperature fluctuations
79
Comparison between temperature and velocity distribution in symmetry plane of S is
presented in Figure 4-3. Temperature in the MTF-volumetric is distributed more uniform
and mixing is stronger. Therefore, MTF-volumetric compared with MTF-surface heating has
less temperature gradient. The hot zone is almost in the middle in the case of MTF surface
heating. But it has moved toward the left hand side in MTF-volumetric, although the
temperature variation inside the tank is less in the latter case. The jet penetration into the
tank is stronger in MTF-volumetric. This is due to the fact that temperature is more uniform
in volumetric which results in weaker buoyancy force. The weaker the buoyancy, the
stronger the effect of momentum and more is the jet penetration into the tank. It will cause
better cooling inside the tank since the cold jet will pass through more tubes on its way to
the exit pipe.
The volumetric simulation for the actual reactor shows that the hot zone has moved further
to the left and temperatures are generally higher due to higher heat influx. Temperature
gradient is more intense in this case. Although the heat generation method here is
volumetric, but due to higher heat generation, buoyancy forces play more important role in
shaping flow regimes inside the tank. As a result the final temperature distribution more
looks like MTF-surface heating rather than MTF-volumetric.
The velocity contour comparison reveals that in the case of MTF-volumetric, jet penetrates
into the tank with higher velocity in comparison with MTF-surface heating. The jet
impingement point is closer to the center line in the case of MTF-volumetric. This confirms
why the hot zone is leaning more toward the left hand side in MTF-volumetric. The
velocities in actual tank-volumetric are 30-40% higher due to higher mass flux injected from
the nozzles. The high velocity zone is wider in this case and many regions on the jet
pene
to th
furth
etration path
he center line
her to the lef
Temperature
Temperature
h have veloci
e compared w
ft hand side o
e –MTF – Sur
e –MTF – Volu
ities higher t
with both M
of the tank.
face Heating
metric Heating
80
than 1 m/s.
MTF simulatio
g
The jet imp
ons. This wi
Velocity
Velocity –
ingement po
ill force the h
y –MTF – Surfa
–MTF – Volum
oint is also c
hot zone to m
ace Heating
metric Heating
closer
move
Gene
grad
temp
aver
is pr
heati
in vi
T
Figure 4-
erally, volum
dient inside
perature dist
age tempera
ractical due
ing result sin
isibly less gr
Temperature –A
-3 Temperatur
metric heatin
the tank. T
tributions in
ature is gener
to experime
nce the resu
radient in tem
Actual tank – V
re and velocity
ng results in
This can be
n different
rally lower.
ental limitat
lt in this cha
mperature an
Volumetric Hea
81
y contours for
better temp
e observed
planes. The
This shows
tions, but on
apter shows
nd lower ave
ating
r t=150 s (thre
perature distr
from the f
e fluctuation
that althoug
ne should b
that the actu
erage temper
Velocity –Ac
ee different sim
ribution and
fluctuation p
ns are less
gh the surfac
e cautious u
ual method o
rature throug
ctual tank – Vo
mulations)
d less temper
plots as we
intense and
e heating me
using the su
of heating re
ghout the tan
olumetric Heatin
rature
ell as
d the
ethod
urface
esults
nk.
ng
82
5 Scaling Effects
The Experimental and numerical results for MTF are used to analyze the flow regimes in
MTF tank and draw conclusions to be used to analyze the actual reactor moderator. Due to
practical limitations it is impossible to do experiment in actual reactor environment but the
advantage of the numerical simulation is that there is no limit in the simulation conditions
and we are able to simulate actual reactor moderator. This is crucial case to simulate since it
will determine two issues:
Actual case simulation: it will help us to assess the situation based on the real
operating geometry and condition. It will enable us to analyze flow regimes inside
the tank more accurately.
Comparison between MTF and actual tanks: If MTF and actual tank are simulated
with the same operating conditions, their results can be compared and the effect of
scaling can be investigated.
The results for temperature and velocity distributions along with fluctuations are presented
here and compared for both cases. Figure 5-1 shows the temperature distribution inside the
moderator tank for both MTF and the actual reactor tank. It presents a plane which passes
through two inlet nozzles and one outlet. This is one of the most important planes inside the
tank since it shows the interaction between inlet jets, bulk fluid inside the tank, and the exit
flow.
Temperature contours are shown for two different times. The first one is the initial phase
simulation at t = 20 s and the second one is for t = 150 s which is considered the end of the
simu
actua
inlet
oppo
almo
max
MTF
locat
jets a
The
obse
hot a
here
diffe
the a
the s
ulation. The
al moderator
t temperature
osite side of
ost the same
imum tempe
F is close to
tion of the h
are located o
temperature
erved betwee
and cold flow
are the m
erence inside
actual reacto
scaling meth
M
upper row c
r simulation
e of 40 oC. T
f the impinge
e location a
erature betw
55 oC while
hot zone is a
on the top rig
e distribution
en high and l
ws in the cas
momentum o
e the tank. Si
or, this signi
hod employe
MTF
corresponds t
. Two inlet n
The highest t
ement locati
as MTF) for
een to cases
e in the case
almost the sa
ght hand side
n is more uni
low tempera
se of MTF co
of the inlet
ince the met
ificant varia
d in modelin
t=
83
to MTF sim
nozzles are v
temperature
ion while th
r the actual
. The averag
e of actual re
ame in both
e of the tank
iform in the
ature zones.
omparing to
jets and th
thod of heat
ation in temp
ng the actual
20 sMTF
mulation and
visible at tw
observed fo
he high temp
reactor. It i
ge temperatu
eactor it incr
cases as the
k.
case of MTF
This can be
o the actual r
he buoyancy
generation i
perature dist
l reactor.
F
the lower ro
o sides of th
or MTF is aro
perature is c
is close to 3
ure in bulk fl
reases by 18
e impingeme
F and less se
the result of
reactor. The
y force due
is the same f
tribution can
t= 150
ow is the resu
he outer wall
ound 55 oC a
close to 73 o
35% variatio
low in the ca
8% to 65 oC
ent point for
egregation c
f better mixi
competing f
e to temper
for both MTF
n be attribut
0 s
ult of
l with
at the
oC (at
on in
ase of
C. The
r inlet
an be
ing of
forces
rature
F and
ted to
Figu
insta
case
max
inlet
bund
pene
ure 5-2 show
ances. The im
s. The velo
imum veloc
t jets imping
dles and goe
etrates more
A
M
Figure 5-1
ws the velo
mpingement
ocities are n
city as high
ge on each o
s toward the
in the case o
Actual react
MTF
Temperature
ocity contou
t point is loc
nearly 45%
as 1.3 m/s
other a seco
e exit pipe. T
of actual rea
t=or
t=
84
e contours for
urs for the s
cated at the
higher in t
comparing t
ondary jet is
The velocity
ctor compar
20 s
20 sMTF
Actua
r MTF and act
same plane
top right ha
the case of
to only 0.9
s formed wh
distribution
ring to the M
F
al reactor
tual reactor
as Figure
and side of t
the actual
m/s for the
hich passes
ns show that
MTF simulati
t= 150
t= 150
5-1 at the
the tank for
reactor with
MTF. After
through the
the seconda
ion.
0 s
0 s
same
r both
h the
r two
e tube
ary jet
As
temp
iden
most
actua
more
expe
these
explained b
perature and
tified for th
t points as s
al reactor co
e temperatu
eriences mor
e two flows
Ac
Figure 5
before, seve
d velocity.
e frequency
shown in Fig
omparing to
ure gradient
re segregatio
are more int
ctual reacto
5-2 Velocity co
eral points
Considering
and amplitu
gure 5-3, the
the MTF si
visible in t
on between
tense and res
t=or
85
ontours for M
inside the
g all monit
ude of temp
e frequency
imulation. T
the case of
high and lo
sults in highe
20 sActua
MTF and actua
tank have
tored points
perature and
is higher an
The higher fr
the real rea
ow temperatu
er frequency
al reactor
al reactor
e been mon
s, no gener
velocity flu
nd amplitude
requency can
actor. Since
ures, the int
y fluctuation
t= 150
nitored for
ral trend ca
uctuations. B
e is lower fo
n be attribut
e the real re
teraction bet
ns in tempera
0 s
their
an be
But in
or the
ted to
eactor
tween
ature.
Base
by tw
com
caus
of ho
Figure 5-
ed on the res
wo forces: m
es from den
ses the bulk f
ot zone on th
-3 Temperatu
sults presente
momentum a
nsity variati
flow motion
he top left co
re and velocit
ed, it can be
and buoyanc
on (due to
n from the inl
orner of the t
M
86
ty fluctuations
concluded t
cy. The first
temperature
lets to the ou
tank.
MTF
MTF
s plot for actu
that the flow
is due to th
e gradient)
utlets and bu
al moderator
w inside the t
he inlet jets a
inside the t
uoyancy cau
A
Ac
and MTF
tank is domin
and the latte
tank. Mome
uses the form
Actual react
ctual reacto
nated
er one
entum
mation
tor
or
87
In order to be able to quantify the phenomena, two non-dimensional numbers are considered
in the open literature for similar cases. These numbers are Archimedes and Rayleigh
numbers. The definitions for these numbers are as follow:
Δ (Eq 5-1)
Δ (Eq 5-2)
Where g is the acceleration of gravity, V is the inlet average velocity, β is the thermal
expansion coefficient, is thermal diffusivity, ΔT=Tout – Tin , is kinematic viscosity, and
D is the tank diameter. Archimedes number shows the ratio between buoyancy and
momentum forces which are the main competing forces here and the Rayleigh number adds
to this ratio the effect of heating method inside the tank. Khartabil et. al. [20] (the
experiments which this research is based on) used Archimedes number as the basis of their
experiments. They wanted to scale down their experiment tank 4 times smaller in each
direction comparing to the actual reactor (64 times smaller in volume). They assumed
constant Archimedes number for both cases and then scaled down both the volume and the
heat input by a factor of 64.
Comparing the simulation results for the actual reactor and the scaled down MTF model
shows that the differences between the two are noticeable and can be attributed to the
method of scaling. The temperature distributions, maximum and minimum temperatures,
velocity distributions, and the fluctuations frequency and amplitude vary in the two cases in
88
a way that cannot be ignored or being associated with numerical errors. Table 5-1 shows the
comparison between Archimedes, Rayleigh, and Grashof numbers for MTF and the actual
reactor. It is clear that although the Archimedes numbers match, but the Rayleigh numbers
vary by 2 orders of magnitude. This can be the main reason behind the differences observed
between two cases which are supposed to present each other with an acceptable accuracy.
Ar Ra Gr
MTF 0.1027 3.6×1012 1186.7×108
Actual Tank 0.1131 4.6×1014 9060.65×108
Table 5-1 MTF and actual tank operating conditions
The main issue which triggered the experimental and numerical investigation of the
moderator tank was the fluctuation observed in temperature and velocity inside the tank. The
result presented here, clearly shows that the fluctuation for the same points inside the MTF
and the actual tank are noticeably different. Although one may expect to see different
fluctuations at the same point (since the nature of the fluctuations is random and
unpredictable), but their frequency and amplitude and also the average quantity should be
similar which is not the case in comparing several points between the two cases.
There are several papers [63, 64, 65] which suggest that the fluctuations inside the tank have
direct relation with Rayleigh number. In fact, they suggest that Rayleigh number is the
determining factor for the fluctuations and higher than a critical Rayleigh number the
fluctuations are initiated. For example cheng et. al. [63] suggests that for air convective flow
inside a bottom heated cylinder, flow is chaotic for Rayleigh number higher than 105. All
89
other papers also suggest similar ranges for the initiation of fluctuation and chaotic flow.
The Rayleigh number for our specific case is much higher than critical Rayleigh number and
we are well inside the chaotic zone which will cause unsteady fluctuations in temperature
and velocity. As a result, Rayleigh number becomes an important part of our conditions and
should be considered in scaling procedure from the actual reactor moderator to the MTF
tank.
90
6 Comparison of Two and Three Dimensional Simulations
Two dimensional simulations are essential for the initial assessment of the problem. Its
computational time is significantly less than three dimensional simulations and as a result it
can be used to obtain an initial analysis of the issues involved. A brief section here is
presented for two dimensional simulation results and their comparison with three
dimensional simulation results.
Two-dimensional simulations revealed that the main cause of the temperature fluctuation is
the interaction of momentum and buoyancy driven flows inside the tank. Buoyancy driven
flows in enclosures have special features which include coherent structures, intermittent
fluctuations, and anomalous scaling. There are two coherent structures, which are found to
coexist in the convection cell. One is the large-scale circulation that spans the height of the
domain, and the other is intermittent bursts of thermal plumes from various thermal
boundary layers. An intriguing feature of turbulent convection is the emergence of a well-
defined low-frequency oscillation in the temperature power spectrum.
The 2-dimensional isothermal modelling of the MTF tank revealed that the largest flow
fluctuations occurred outside the tube bundle where the inlet jets flow, and around the top of
the tank where the two inlet jets impinge on each other. The high velocity gradients
between the inlet jets and the low velocity surroundings generate small vortices with low
fluctuation amplitude but high frequencies. As the vortices travels with the jets, their
fluctuation amplitudes amplify but their frequency recede. The impingement of the two inlet
jet results in a downward moving secondary jet which penetrated inside the tube bank. The
91
simulation concluded that the the source of flow fluctuations in the isothermal case is
outside of the tube bank, and the tubes dampen the fluctuations.
The thermal solution of the MTF model indicated that the buoyancy forces dominate at the
inner core of the tank, whereas, the inlet jet induced inertial forces dominate the outer edges
of the tank. The interaction between these two flows forms a complex and unstable flow
structure within the tank.
The most important issue in two-dimensional simulation which should be addressed is that
whether the 2-D model misses any major effects that may occur in the actual Calandria tank.
This question was answered in the previous sections. As observed, many three dimensional
effects were missing especially along the tank length. For example in 2D, we only have one
XY plane whereas in 3D there are several XY planes. Each of these planes, as explained
(depending on their location), has distinctive flow regimes and they interplay with each
other through flows running along the tank length. None of these effects can me captured in
two-dimensional simulation. These are game changing phenomenon and should be
considered in full detail.
Figure 6-1 compares temperature and velocity distributions in two and three dimensional
simulations. Since 2D simulation has only one plane to present, it is compared to one
arbitrary plane in 3D which has similar geometry. The temperatures are in the same range
spanning from 40 oC (inlet temperature) to above 60 oC. The hot zone in 2D is more
concentrated and toward the top middle while it is more scattered in 3D and toward middle
centre. Although the high temperatures in both cases are close to each other, but they vary in
low temperatures. While 2D has a large zone close to inlet temperature, the 3D has confined
the i
most
The
regim
pipe
Gene
dime
inlet tempera
tly near outl
velocities a
mes. 2D has
, while 3D h
erally, flow
ensional sim
Figure
ature to thei
let pipe. Vel
are almost in
s a strong fl
has less stron
s are better
mulation.
6-1 Comparis
Ho
ir vicinity an
ocity distrib
n the same
low going fr
ng flow goin
distributed
son between 2D
3D
3D
ot Zone
92
nd lowest vi
utions are co
range. Two
rom the left
ng from the r
in three di
D and 3D tem
isible temper
ompared in
simulations
t nozzle cou
right nozzle
imensional s
mperature and
ratures are a
the second p
s mainly dif
unter clock-w
clock-wise t
simulation c
d velocity distr
H
around 50 oC
part of the fi
ffer in their
wise to the o
to the outlet
compared to
ributions
2D
2D
Hot Zone
C and
igure.
flow
outlet
pipe.
o two
D
D
93
Temperature and velocity fluctuations are the next items to be compared. One-on-one
comparison is difficult here since one should make sure that the same point in 2D and 3D
are compared together. Two points are chosen for comparison. Point 15 which is located at
top of the tank (Figure 6-2) and point 4 which is located at the center of the tank (Figure
6-3). Simulation in 2D can be run for much longer period of time comparing to 3D, as a
result, the plots for 2D are over 700 physical seconds while the plots for 3D are over 150
physical seconds. Top node (node 15) is located near the hot zone. Although the plots shows
the same trend up to 150 seconds, but the temperature for 3D is higher in the order of 2-3 oC.
The amplitude of fluctuations in 2D is noticeably higher than 3D. It can be the effect of less
mixing and more segregation (between hot and cold zones) which will make the flow
unstable and prone to fluctuations.
The same phenomenon is occurring for node 4 which is a center node. The temperatures in
2D and 3D are close with higher temperatures in 3D. The fluctuations in 2D have higher
amplitude comparing to 3D. a general conclusion one might draw from these figures is that
while 2D and 3D compare almost the same temperature range at each node, but they are
quite different in the fluctuation behaviour and its amplitude and consequently the
fluctuation frequencies.
Figure 6-2 N
Tem
per
atu
re (
C)
Node 15 (locat
40
45
50
55
60
65
0 10
2D –
ted at top of th
0 200
– Node 15
94
he tank in XY
300 4
Arbitrary Time
Y plane) compa
400 500
(sec)
3D – Node
arison betwee
600
15
en 2D and 3D
700
F
Figure 6-3 Nod
Te
mp
erat
ure
(C)
de 4 (located a
40
45
50
55
60
65
0 10
Te
mp
erat
ure
(C
)
at the centre o
00 200
95
of the tank in X
300 4
Arbitrary Time
XY plane) com
400 500
(sec)
2D – No
3D – Nod
mparison betw
600 7
de 4
de 4
ween 2D and 3
700
3D
96
7 Summary and Conclusion
A three-dimensional numerical modeling of thermal hydraulics of Canadian Deuterium
Uranium (CANDU) nuclear reactor is conducted. The moderator tank is a Pressurized heavy
water reactor which uses heavy water as moderator in a cylindrical tank. The main use of the
tank is to bring the fast neutrons to the thermal neutron energy levels. It consists of several
hundred horizontal fuel channels. Each fuel channel consists of an internal pressure tube and
an external tube separated from the pressure tube by an insulating annulus. The tank
contains cool low-pressure heavy water that surrounds fuel channels.
There have been several studies on the operation of CANDU reactors. Three-dimensional
moderator circulation tests have been conducted in the moderator test facility (MTF) in
Chalk River Laboratories (CRL) of Atomic Energy of Canada Limited (AECL). The
CANDU Moderator Test Facility (MTF) is a ¼ scale of CANDU Calandria, with 480
heaters that simulate 480 fuel channels.
The data recorded inside the MTF tank have shown levels of fluctuations in the moderator
temperatures. The frequency of the fluctuations is higher than the sampling rate of the fixed
thermocouples. Fluctuations in temperature are believed to be due to the interaction between
local momentum and buoyancy forces, inlet jet impingement, and the flow passing through
the tube bundle. Because of the limitation in data sampling, full range of the fluctuations
could not be identified. Also, analysis could not identify any dominant frequencies.
The purpose of the current investigation is to determine the causes for, and nature of the
temperature fluctuations using three-dimensional simulation of MTF with two different
97
heating methods (surface heating and volumetric heating) and three-dimensional simulation
of actual tank with volumetric heating.
The simulations are carried out for two geometries (different in size), two heating methods,
and two solution strategies. These simulations include: MTF with surface heating, MTF with
volumetric heating, actual tank with volumetric heating. The numerical modeling is
performed on a 24-processor cluster of computers using parallel version of the FLUENT 12.
During the transient simulation, 55 points of interest inside the tank are monitored for their
temperature and velocity fluctuations with time. These data along with temperature and
velocity distributions in different planes inside the tank are used to analyze the phenomena
occurring inside the tank. The result for MTF simulation is presented in extended length and
the main flow regimes inside the tank are identified. Asymmetry in temperature and velocity
distribution is presented in different spatial planes and the causes behind the issue are
explained and discussed. The after effects for asymmetry is identified and explained. Two
different heating methods are compared and their differences are identified. The effect of
scaling on the temperature and velocity distributions is studied and at the end a quick
comparison between two and three dimensional simulations is presented. Based on all the
assessment in various phases of the study, the following conclusions are made:
Temperature contours in various planes show the hot region at the top and left-hand
side (close to the center line) of the tank for the case of MTF-surface heating.
Hot region moves further to the center in MTF-volumetric and temperature
distribution is more uniform and less temperature gradient is observed.
Actual moderator has the highest temperature recorded due to higher heat influx. The
hot region is also at the left side of the tank.
98
The general trend is that the inner zones of the tank are higher in temperature
specifically at the middle of the tank (close to z=0). It means that the flow is colder
near the walls at both ends of the tank.
Temperature increases to 65 oC in hot zone for MTF-surface heating while it is
below 60 oC and near 55 oC in most parts of the tank. Temperature drops from the
inner zones to the outer wall of the tank due to the close distance to the jet
penetration path.
In the case of MTF-volumetric, maximum temperature is near 58 oC and the
minimum is 46 oC.
Temperatures are lower in MTF-volumetric comparing to MTF-surface heating. This
is mainly due to the different method of heating. Volumetric heating encourages
mixing of cold and hot flows and results in more uniform temperature inside the
tank. In the volumetric method, the heat is distributed as a heat source throughout the
domain while in the surface heating, local heating occurs, which makes the heat
transfer concentrated to specific sections.
The buoyancy effects in the tank are more visible in the case of MTF-surface heating
and the actual moderator. In the case of MTF-surface heating, the method of heat
generation through the surface of the tubes discourages better flow mixing and
creates segregated hot and cold zones, which in turn boosts the buoyancy effects
inside the tank. In the actual moderator, although the heat generation method is
volumetric, but since the heat influx is higher in comparison with other cases,
powerful temperature gradients exist inside the tank, causing strong buoyancy forces
as opposed to inertia forces.
99
Depending on the location of the monitored point, the behaviour of the fluctuations
is different. Points which are located near the hot and cold boundaries have higher
frequencies and, depending on the conditions (e.g. level of mixing) high or low
amplitudes.
The impingement point of inlet jets lies at the left hand side of the tank. A secondary
jet is formed after jet impingement which goes to the outlet pipes passing through the
heated tubes, cooling them down along the way.
The inlet jets lose 90% of their momentum upon reaching to the impingement point.
The velocity of the secondary jet further reduces once it reaches bottom of the tank.
It only carries 20% of its initial momentum.
The impingement point is important in temperature distribution inside the tank. It
affects flow mixing and its location can strongly influence the location of hot region.
The best case scenario is to have the impingement point on the center line. In that
case, the secondary jet will pass through a maximum number of tubes along its way
resulting in maximum cooling. This also will result in a uniform temperature
distribution.
The asymmetry inside the tank is severe and has many after effects. It is the result of
competition between strong buoyancy and momentum flows. The buoyancy has
occupied most of the core region while the momentum driven flow goes through the
edges. A small disturbance from turbulence or any other involved parameter forces
out the temperature and velocity distributions from symmetry, resulting in current
distributions inside the tank.
100
Investigation of the nozzle planes revealed the existence of a jet impingement effect
on the symmetry plane (in XY). It creates a clock-wise rotating flow in the symmetry
plane (which is transferred to the other planes through flows in the YZ plane). The
rotating flow is strongest in the symmetry plane, then the nozzle plane without exit
pipe and it is the weakest in the nozzle plane with the exit pipe, which is mainly
dominated but by the bulk flow from the inlet nozzles to the outlet pipe.
The rotating flows weaken the right inlet flow, contributing to the movement of the
impingement point to the right hand side of the tank.
The asymmetry in the jet impingement point causes many issues such as:
o The hot zone lies asymmetrically at the left, which forces the left inlet jet to
the outer walls, decreasing its X-section and increasing its velocity
furthermore. This eventually results in a stronger left inlet jet, which in turn,
intensifies the asymmetry and causes less efficiency in the cooling process.
o Since the hot zone is at the left hand side, it heats up the left hand side jet.
The temperature in the right hand side jet is on the average, about 18%
higher. This will cause a higher temperature at the impingement point, which
reduces the cooling effect of the secondary jet.
Velocity contours show relatively small velocities throughout the tank. The bulk
flow moves with a steady and slow pace and most of the momentum action is
observed near the inlet nozzles, penetration path of the inlet jets, and the boundaries
between the low and the high velocity currents.
Comparison between two heating method shows that the surface heating results in
more temperature gradient as the heat is distributed on the surface of the tubes
101
through conduction while in the volumetric method; the heat is distributed as a
source term throughout the domain.
The comparison between MTF and actual moderator result revealed the effect of
scaling on the temperature and velocity distributions. The method of scaling
becomes important and it is concluded that Rayleigh number should be used along
with Archimedes number for scaling purposes. The Rayleigh number is a crucial
parameter in fluctuation analysis as it is suggested in the literature that beyond a
critical Rayleigh number, the fluctuations are initiated inside the tank and
temperature and velocity show a chaotic, unsteady and un-periodic behaviour.
102
8 Future Work
Flow inside actual calandria tank is very complicated and it is dependent on many factors
including operating conditions and heat generation inside the fuel bundles. Simulations so
far have indicated that buoyancy and inertia forces are the determining factors in the flow
regime inside the tank. The fluctuations in the temperature and the velocity are strongly
location dependant and vary significantly in hot and cold zones.
The phenomenon and its causes and consequences have been comprehensively explained in
this research, but what remains is the cure for the problem and how actually, the fluctuations
and segregation in hot and cold zones can be utilized to achieve more stable and distributed
flow inside the tank. Based on this assessment the followings are suggested for the future
works:
Long range run: The experimental results are performed in the range of 3000 to
4000 physical seconds. Moreover, there are some practical evidences that the hot and
cold zones will change sides in time. But this is in the range of 2000 to 5000 physical
seconds. It is suggested to carry out a very long run in the range of 3000 to 4000
physical seconds to see the effects in long range and also detect any possible changes
in the flow temperature distribution inside the tank.
Mass flux modifications: flow distribution inside the tank is explained here
comprehensively and it is observed that most of the occurrences inside the tank are
due to asymmetrical injected jet penetration. Practically it is possible to change the
mass influx through the inlet nozzles as explained in the followings. Several
103
simulations should be carried out to be able to draw conclusive results and to
quantify the improvement in the flow versus the changes in the mass flux:
o It is possible to vary the mass flux in one side nozzles with respect to the
other side as much as 5% (for practical reasons).
o The total mass influx to the nozzles can be increased as much as 10% (for
practical reasons) to achieve stronger injection which will encourage the
mixing inside the tank.
Geometry modifications: although it is practically very difficult due to the
limitation with nuclear safety and restrict regulations, but it is a proper theoretical
pilot project to observe the effects of geometry change on the flow and temperature
distributions inside the tank. It can include changes in the nozzle locations, nozzle
angle and changes in the outlet pipe location.
Start-up phase modeling: at the moment, all solution strategies start from a filled
tank with an initial velocity and temperature distribution. One more realistic scenario
will be to start the simulation right from the start-up phase. In this method, the
simulation will start from quiescent flow with zero velocity and temperature all over
the domain. In this way we will be able to capture the physics involved in its entire
entirety showing the initial phases which lead to asymmetry in the tank.
104
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