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.

iv

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 

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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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