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UNIVERSITÀ DEGLI STUDI DI PERUGIA

Dipartimento d’Ingegneria

Corso di Laurea Magistrale in Ingegneria Meccanica

TESI DI LAUREA MAGISTRALE

The silicon strip modules of the outer tracker of the CMS

(Compact Muon Solenoid) experiment at LHC (Large Hadron

Collider): thermal studies

Relatori Candidato

Ing. Giorgio Baldinelli Cristiano Turrioni

Prof. Claudia Cecchi

Ing. Francesco Bianchi

Anno Accademico 2016/2017

“ Per tutti quelli

che continuano a lottare …”

I

SUMMARY

INTRODUCTION IV

THE LHC – LARGE HADRON COLLIDER 1

1.1 The Large Hadron Collider 1

1.2 Scientific Purposes 4

1.3 Discoveries and Social Impact 4

THE CMS – COMPACT MUON SOLENOID 8

2.1 General layout of the Experiment 8

2.2 The CMS Phase-2 Upgrade 9

2.3 The Interaction Point 10

2.4 The Tracker 10

2.5 The Electromagnetic Calorimeter 16

2.6 The Hadronic Calorimeter 16

2.7 The Superconducting Solenoid 17

2.8 The Muon System 17

THE 2S - 2 STRIPS MODULE OF THE OUTER SILICON

TRACKER IN CMS 19

3.1 Operating Fundamentals of Silicon Sensors 19

3.2 Components and General Layout of the Module 21

3.3 Cooling and Thermal Requirements 26

3.4 Module Assembly 29

II

HEAT TRANSFER ELEMENTS 34

4.1 Heat Exchange Mechanisms 34

4.2 Conduction Heat Transfer 35

4.3 Convection Heat Transfer 37

4.4 Thermal Radiation Heat Transfer 39

4.5 Treatment of Cavities 41

THE FINITE VOLUME METHOD 42

5.1 Equations of Conservation 42

5.2 Outline of the Finite Volume Method 44

5.3 Boundary Conditions 46

5.4 Sensitivity of the Solution to Errors 46

5.5 The Grid Convergence Index 48

FINITE VOLUME METHOD MODEL OF THE OUTER

TRACKER 2S MODULE 51

6.1 Introduction to the Software 51

6.2 Geometry of the Model 52

6.3 Meshing Procedure 56

6.4 Boundary Conditions 61

EXPERIMENTAL VALIDATION 67

7.1 Introduction to the Validation Procedure 67

7.2 The 2S Module for Tests 69

7.3 Peltier Cells 70

7.4 Heatsink System 74

7.5 Thermocouples 77

III

7.6 Test Number 1 80

7.7 Test Number 2 84

ANALYSIS OF RESULTS 89

8.1 Simulation N°1 compared with Test N°1 89

8.2 Simulation N°2 compared with Test N°2 98

8.3 Simulation of the module in operative conditions 103

FUTURE WORKS 107

9.1 Developments for the FVM model. 107

9.2 Developments for the test bench. 108

9.3 New tests for the module 109

CONCLUSIONS 112

REFERENCES 113

APPENDIX 116

IV

INTRODUCTION

“Somewhere, something incredible is waiting to be known.”

This thesis opens with a famous sentence attributed to Sharon Bagley, which sums up the

reasons that led to the work. One of the highest ambitions of the human beings is to question

about what happens in the world around it, trying to give answers to its insatiable desire of

knowledge. Curiosity and ambition have driven human society to dedicate a big part of its

resources to science, and the maximum expression of this is the creations of big research

organizations as the “Conseil européen pour la recherche nucléaire”, better known as CERN.

But science, over the years, has always gone hand in hand with technique. In this context

started the cooperation between the Italian National Institute for Nuclear Physics research

(INFN) and the Engineering Department of University of Perugia. The work described in

this thesis, born from the mentioned collaboration, is focused on the study of characteristics

of one of the components of a big particle detector that could help humans to know more

about what is happening in nature. This component, from here called “2S module” or just

“module”, is a silicon device that can detect the passage of subatomic particles: it is used in

atomic and nuclear physics. It is the basic part of the Outer Tracker of the Compact Muon

Solenoid (CMS) particle detector at the Large Hadron Collider (LHC) at CERN. The CMS

detector will be upgraded for the so called Phase2 of the LHC during the Long Shutdown 3

(LS3) scheduled to last from 2024 to mid 2016, and is now in the research and development

phase, in collaboration with thousand scientists and engineers from all over the world. A

particle detector is a device that can recognise particles that passing through it as well as

reconstruct the trajectories of some of them. In the first two chapters a description of CMS

will be presented, as well as the context in which it is inserted (i.e. the Large Hadron Collider

machine). CMS is already operative since 2008, but an upgrade is planned for the High

Luminosity phase. The 2S module, main component of the Outer Tracker, is part of this

upgrade. It is a silicon sensor which exploits the properties of doped semiconductors to

operate. Its description is given in chapter 3. In the context of particles detection, temperature

plays a key role because, in order to work, some sensors need a cooling system to make their

temperature low. The thermal studies conducted in this thesis are aimed at contributing to

fulfil this task. In order to describe the thermal behaviour of the module, a Finite Volume

V

Method model (FVM) has been implemented, starting from the study of its geometry and

operative conditions. To understand what is a FVM model and how it works, some basic

notions of heat transfer mechanism and numerical methods are described respectively in

chapters 4 and 5. In chapter 6, the procedure followed to create a computational model for

the module analysis is explained, and some results of simulations are reported. It is known

in the engineering sector that every numerical model needs an experimental validation to be

considered reliable. In order to obtain some experimental data to make a comparison with

the results of simulations, a test bench system has been constructed: its functioning is linked

to the needs of the module under study. The guidelines followed to build this system are

reported in chapter 7, as well as the experimental tests that have been executed. Comparison

of results obtained both from simulations and tests are shown in chapter 8, where once the

model has been validated, the simulation of the module under its operative conditions at

CMS is reported. During the process of study, some other tests and simulations have also

been planned for future works: these are included chapter 9.

1

Chapter 1

THE LHC – LARGE HADRON COLLIDER

1.1 The Large Hadron Collider

The Large Hadron Collider (LHC) is described [1] as the world newest and most powerful

particle accelerator for Physics research. It is designed to collide proton beams with a centre-

of-mass energy of 14 TeV (teraelectronvolts) and an unprecedented luminosity that is

1034cm-2s-1. It can also produce collisions between heavy (Pb) ions with an energy of 2.8

TeV per nucleon and a peak luminosity of 1027 cm-2s-1. It was built at CERN (European

Organization for Nuclear Research) between 1998 and 2008 (as described in [2]) in

collaboration with over 10.000 scientists and engineers from over 100 countries, as well as

hundreds of universities and laboratories. It is financed by European public funds and its

products belong to humanity. Its first physics run took place from March 2010 to early 2013

at an energy of 3.5 to 4 TeV per beam (7 to 8 TeV centre of mass energy), about 4 times the

previous world record for a collider. It is installed in a tunnel of 27 kilometres in

circumference, as deep as 175 metres beneath the France–Switzerland border near Geneva,

in a region between Geneva airport and the Jura mountains, originally excavated to build the

Large Electron-Positron Collider (LEP). A very simplified geographical map of the tunnel

is shown in Figure 1.1. The Large Hadron Collider relies on superconducting magnets that

are at the frontier of the present technology. Other large superconducting accelerators

(Tevatron-FNAL, HERA-DESY and RHICBNL) all use classical NbTi superconductors,

cooled by supercritical helium at temperatures slightly above 4.2 Kelvin (K), with fields

below or around 5 Tesla (T). LHC magnets work at 1.9 K (-271°C) which makes the machine

the coldest point in the known universe. At the same time the energy of the collisions

corresponds to a temperature of 1016 K. So we can both find very low temperatures and very

high temperatures in the same machine. The LHC magnet system, while still making use of

the well-proven technology based on NbTi Rutherford cables, cools the magnets to the

setpoint temperature using superfluid helium, and operates at fields above 8 T. One


2

detrimental effect of reducing the temperature by more than a factor of two is the reduction

of the heat capacity of the cable by almost an order of magnitude.

Figure 1.1 - Map of the Large Hadron Collider at CERN [3].

As a result, for a given temperature margin (difference between the critical temperature of

the superconductor and the operating temperature), the energy deposition that can trigger a

quench is substantially reduced. This means that the temperature margin must be

significantly larger than that used in previous accelerators and that a tighter control of

movements and heat dissipation inside cables is needed. Since the electromagnetic forces

increase with the square of the field, the structures retaining the conductor motion must be

mechanically much stronger than in earlier designs. In addition, space limitations in the

tunnel and the need to keep costs down have led to the adoption of the “two-in-one” or “twin-

bore” design for almost all of the LHC superconducting magnets. The two-in-one design

accommodates the windings for the two beam channels in a common cold mass and cryostat,

with magnetic flux circulating in the opposite sense through the two channels. This makes

the magnet structure complicated, especially for the dipoles, for which the separation of the

two beam channels is small enough to reach both the magnetic and mechanical coupling.

The machine accelerates two beams of particles that circulate in opposite directions, each

contained in a vacuum tube. When proton beams turn around there are 200.000 billion


3

protons in each beam and these beams collide 40 million times per second. These collisions

occur at four points along the orbit, in correspondence with caverns where the tunnel widens

to make space for large experimental rooms. These stations include the four main particle

physics experiments shown in Figure 1.2: ATLAS (A Toroidal LHC ApparatuS), CMS

(Compact Muon Solenoid), LHCb (LHC-beauty) and ALICE (A Large Ion Collider

Experiment). These are huge devices made up of numerous detectors using different

technologies and operating around the point where the beams collide. Many particles are

produced in the collisions, thanks to the transformation of a part of the very high energy in

mass, and their properties are measured by the detectors.[4]

Figure 1.2 - The LHC accelerator with its largest pre-accelerator, the SPS, and its four experiments: ATLAS (access point 1), ALICE (point 2), CMS (point 5) and LHC-B (point 8). This picture is taken by “Design ,

Construction and Commissioning of the CMS Tracker at CERN and Proposed Improvements for Detectors at the Future International Linear Collider” [5]

Several pre-accelerators like the Linear Accelerator 2 (Linac2), the Proton Synchrotron

Booster (PSB), the Proton Synchrotron (PS) and the Super Proton Synchrotron (SPS) are

necessary to accelerate protons up to an energy of 450 GeV. At this energy, they are filled

into the LHC in up to 2808 bunches, each consisting of up to 1.15x1011 protons. The particles

are then brought to their nominal energy during an approximately 20 minutes long phase of

acceleration, which is continued by several hours, when the machine operates as a storage

ring. During this time the protons are focused to intersect and collide every 25 ns in four

distinct locations, the interaction points (IPs). Around them, the four large detector systems

have been built to measure the particles produced by the collisions.


4

1.2 Scientific Purposes

The main goal of LHC was is to help answering some of the fundamental open questions in

physics, concerning the basic laws governing the interactions and forces among the

elementary objects, the deep structure of space and time, and in particular the interrelation

between quantum mechanics and general relativity. LHC allows scientists to study the

fundamental constituents of matter, and then to obtain information on the structure of the

universe. The study of the infinitely small is strictly related to the infinitely large. The most

discussed questions are about supersymmetry, one of the possible extension of the Standard

Model, extra dimensions, Dark Matter and the generation mechanism of the property "mass"

of the elementary particles. There are also other open questions that may be explored using

high-energy particle collisions: for example, it is already known that electromagnetism and

the weak nuclear force are different manifestations of a single force called the electroweak

force. The LHC may clarify whether the electroweak force and the strong nuclear force are

similarly just different manifestations of one universal unified force, as predicted by various

Grand Unification Theories. Moreover, scientists would like to answer the question about

why is the fourth fundamental force (gravity) so many orders of magnitude weaker than the

other three fundamental forces. Furthermore, there are also many other questions, such as:

are there additional sources of quark flavour mixing, beyond those already present within

the Standard Model? Why are there apparent violations of the symmetry between matter and

antimatter? What are the nature and properties of quark–gluon plasma thought to have

existed in the early universe and in certain compact and strange astronomical objects today?

This will be investigated by heavy ion collisions, mainly by the ALICE experiment, but also

in CMS, ATLAS and LHCb. First observed in 2010, findings published in 2012 confirmed

the phenomenon of jet quenching in heavy-ion collisions.

1.3 Discoveries and Social Impact

Alongside the previous questions, which are the engine of scientific research carried out at

CERN, over the years there have been also numerous scientific discoveries of considerable

importance. The first relevant physics results from the Large Hadron Collider, involving 284

collisions which took place in the ALICE detector, were reported on 15 December 2009.


5

After the first year of data collection, the LHC experimental collaborations started to release

their preliminary results concerning searches for new physics beyond the Standard Model in

proton-proton collisions. As a result, bounds were set on the allowed parameter space of

various extensions of the Standard Model, such as models with large extra dimensions,

constrained versions of the Minimal Supersymmetric Standard Model, and others. On 24

May 2011, it was reported that quark–gluon plasma (the densest matter thought to exist

besides black holes) had been created in the LHC. Between July and August 2011, results of

searches for the Higgs boson and for exotic particles, based on the data collected during the

first half of the 2011 run, were presented in conferences in Grenoble and Mumbai. In the

latter conference it was reported that, despite hints of a Higgs signal in earlier data, ATLAS

and CMS exclude with 95% confidence level (using the CLs method) the existence of a

Higgs boson with the properties predicted by the Standard Model over most of the mass

region between 145 and 466 GeV. The searches for new particles did not yield signals either,

allowing to further constrain the parameter space of various extensions of the Standard

Model, including its supersymmetric extensions. On 13 December 2011, CERN reported

that the Standard Model Higgs boson, if it exists, is most likely to have a mass constrained

to the range 115–130 GeV. Both the CMS and ATLAS detectors have also shown intensity

peaks in the 124–125 GeV range, consistent with either background noise or the observation

of the Higgs boson. On 22 December 2011, it was reported that a new composite particle

had been observed, the χb (3P) bottomonium state. On 4 July 2012, both the CMS and

ATLAS teams announced the discovery of a boson in the mass region around 125–126 GeV,

with a statistical significance at the level of 5 sigma each. This meets the formal level

required to announce a new particle. The properties of the observed particle were consistent

with the Higgs boson, but scientists were cautious as to whether it is formally identified as

actually being the Higgs boson, pending further analysis. On 8 November 2012, the LHCb

team reported on an experiment seen as a "golden" test of supersymmetry theories in physics,

by measuring the very rare decay of the Bs meson into two muons (Bs0 → μ+μ−). The results,

which match those predicted by the non-supersymmetrical Standard Model rather than the

predictions of many branches of supersymmetry, show the decays are less common than

some forms of supersymmetry predict, though could still match the predictions of other

versions of supersymmetry theory. The results as initially drafted are stated to be short of

proof but at a relatively high 3.5 sigma level of significance. The result was later confirmed


6

by the CMS collaboration. In August 2013 the LHCb team revealed an anomaly in the

angular distribution of B meson decay products which could not be predicted by the Standard

Model; this anomaly had a statistical certainty of 4.5 sigma, just short of the 5 sigma needed

to be officially recognized as a discovery. It is unknown what the cause of this anomaly

would be, although the Z' boson has been suggested as a possible candidate. On 19

November 2014, the LHCb experiment announced the discovery of two new heavy

subatomic particles: both of them are baryons that are composed of one bottom, one down,

and one strange quark. They are excited states of the bottom Xi baryon. The LHCb

collaboration has observed multiple exotic hadrons, possibly pentaquarks or tetraquarks, in

the Run 1 data. On 4 April 2014, the collaboration confirmed the existence of the tetraquark

candidate Z(4430) with a significance of over 13.9 sigma. On 13 July 2015, results consistent

with pentaquark states in the decay of bottom Lambda baryons were reported. On 28 June

2016, the collaboration announced four tetraquark-like particles decaying into a J/ψ and a φ

meson, only one of which was well established before (X(4274), X(4500) and X(4700) and

X(4140)). In December 2016, ATLAS presented a measurement of the W boson mass,

researching the precision of analyses done at the Tevatron. On 15 December 2015, the

ATLAS and CMS experiments both reported a number of preliminary results for Higgs

physics, supersymmetry (SUSY) searches and exotics searches using 13 TeV proton

collision data. Both experiments saw a moderate excess around 750 GeV in the two-photon

invariant mass spectrum, but the experiments did not confirm the existence of the

hypothetical particle in an August 2016 report [6][7][8][9].

In addition to scientific successes, CERN has contributed to the development of the society

with important innovations and discoveries that found space in common life. It is the place

where the scientific objectives consist of developing cutting-edge technologies in many

sectors that are transferred to society: an example of this is the World Wide Web, born in

1989, from an idea of Tim Berners-Lee and Robert Cailliau. The first computer arrived at

CERN in 1959, since then physicists began to use computer tools. For physics, a new era of

research began, where experiments produced a large amount of data, impossible to process

by human beings alone. Physicists resigned themselves to the use of computers and software

to filter and process the mountain of data in search of events deemed significant for the

outcome of the experiments. Subsequently, the connection of several computers was

experimented with each other: it was the turn of the first computer network. One of the most


7

powerful computing centers was born at CERN, dedicated to the increasingly demanding

requirements of new experiments and the ever-increasing capacity for data acquisition of the

instruments connected to the new accelerators. Another important use of particle accelerator

is the hadronic therapy based on targeting tumors with ionizing particles. These particles

damage the DNA of the tissue cells, causing them to die. Because of their reduced ability to

repair damaged DNA, the cancer cells are particularly vulnerable to these attacks. The dose

(expressed in MeV) given by the protons to the tissue is maximum in an area of a few

millimeters, unlike electrons or X-rays. The electron beams, X-rays of different energy and

protons penetrate human tissue differently. The path taken by electrons is very short and are

useful only in areas close to the skin. X-rays penetrate more deeply but the dose absorbed

by the tissue has a typical exponential decay with increasing thickness. For protons and

heavier ions, however, the dose increases with increasing thickness up to the peak of Bragg,

which occurs just before the end of the journey. Once this peak is exceeded, the dose drops

to zero (in the case of protons) or almost to zero (in the case of heavy ions). The advantage

in the use of the latter is in the lower energy deposit in the healthy tissue surrounding the

targeted one, saving it from unnecessary damage.

8

Chapter 2

THE CMS – COMPACT MUON SOLENOID

2.1 General layout of the Experiment

The Compact Muon Solenoid (CMS) experiment is one of the physics detectors built on the

Large Hadron Collider (LHC) at CERN. CMS is designed as a general-purpose detector,

capable of studying many aspects of proton collisions between 0.9-13 TeV, the center-of-

mass energy of the LHC particle accelerator. The CMS detector is built around a huge

solenoid magnet and consists of several concentric layers. It takes the shape of a cylindrical

coil of superconducting cable that generates a magnetic field of 4 T, about 100.000 times

greater than the Earth magnetic field. The CMS magnetic field is confined by a steel 'yoke'

that forms the bulk of the whole detector weight of 12.500 tonnes. A schematic

representation of the CMS detector is presented in Figure 2.1, where its sizes are also

compared to those of a human.

Figure 2.1 - Schematic representation of the various layers forming the CMS detector. In the lower left area some characteristic data of the detector are reported, such as weight, diameter, length and magnetic field.

This picture is taken from [10].


9

An unusual feature of the CMS detector is that (instead of being built in-situ underground,

like the other giant detectors of the LHC experiments) it was constructed on the surface,

before being lowered underground in 15 sections and reassembled. It contains subsystems

designed to measure the energy and momentum of photons, electrons, muons, and other

products of the collisions. The innermost layer is a silicon-based tracker. The surrounding is

occupied by a scintillating crystal electromagnetic calorimeter, which is in turn surrounded

by a sampling calorimeter for hadrons. The tracker and the calorimetry are compact enough

to fit inside the CMS Solenoid which generates a powerful magnetic field of 3.8 Tesla.

Beyond the magnet, externally, there is a large muon detector, that has inside iron plates

which allow the return for the magnetic field lines. It is interesting to note that this detector

is heavier than the Eiffel Tower and it has a higher iron content than it.

2.2 The CMS Phase-2 Upgrade

An upgrade program is planned for the LHC which will smoothly bring the luminosity up to

or above 5x1034 cm-2s-1, to possibly reach an integrated luminosity of 3000 fb-1 (inverse

femtobarns). In particle physics the luminosity indicates the number of events per cross

section per unit time. This upgrade will start after 2020. In this scenario, called Phase-2,

when LHC will reach the High Luminosity phase (HL-LHC), CMS has to upgrade too, and

it will need a completely new Tracker detector, in order to fully exploit the highly-

demanding operating conditions and the delivered luminosity. The present Tracker was

designed to operate with high efficiency at an instantaneous luminosity of 1.0x1034 cm-2s-1,

with an average pileup of 20-30 collisions per bunch crossing, and up to an integrated

luminosity of 500 fb-1. The new Tracker should have also Trigger capabilities. To achieve

such goals, research and development activities are ongoing to explore options and develop

solutions. The original pixel detector has already been replaced with a new device, the Phase-

1 pixel detector, during the extended year-end technical stop of 2016/2017. The Phase-2

Tracker will have more radiation tolerance to be fully efficient up to the target integrated

luminosity, and more granularity, in order to ensure efficient tracking performance with a

high level of pileup. Other goals will be reducing material in the tracking volume, contribute


10

to the L1 trigger and extend tracking acceptance. In section 2.4, the Tracker is presented as

it is designed for the Phase-2 Upgrade.

2.3 The Interaction Point

The interaction point represents the accelerator region where proton-proton collisions occur

between the two beams circulating in the LHC. At the collision point each beam has a radius

of 17 μm and the crossing angle between the beams is 285 μrad. At full design luminosity

each of the two LHC beams will contain 2.808 bunches of 1.15×1011 protons. The interval

between crossings is 25 ns, although the number of collisions per second is only 31.6 million

due to gaps in the beam as injector magnets are activated and deactivated. To record and

save every single event, a memory with a huge capacity would be necessary. At full

luminosity each collision will produce an average of 20 proton-proton interactions. The

collisions occur at a centre of mass energy of 14 TeV. Neverless, it is worth noting that for

studies of physics at the electroweak scale, the scattering events are initiated by a single

quark or gluon from each proton, and so the actual energy involved in each collision is lower

as the total centre of mass energy is shared by these quarks and gluons.

2.4 The Tracker

Momentum of particles is crucial in the process of building up a picture of events at the heart

of the collision. To calculate the momentum of a particle it is necessary to track its path

through a magnetic field; the more curved the path, the less momentum the particle had. The

CMS tracker records the paths taken by charged particles by finding their positions at a

number of different layers. The tracker can reconstruct the paths of high-energy muons,

electrons and hadrons (particles made up of quarks) as well as see tracks coming from the

decay of very short-lived particles such as beauty or “b quarks” that will be used to study

the differences between matter and antimatter. Once the data coming from the tracker is

collected, it is possible to reconstruct 3D images of the trajectories followed by the particles

produced in the interaction, as shown in Figure 2.2 below.


11

Figure 2.2 - This image represents the photograph of a collision event taken by the CMS detector. The yellow curved lines represent the set of particle trajectories from the collision point to the outside. These

trajectories are reconstructed by the Tracker, and they present a helicoidal pattern as the particles are diverted in their motion by the Lorentz force produced by the magnetic field. The image has been obtained

from [11].

The tracker needs to reconstruct the tracks of charged particles with very high accuracy and

has to be as thin as possible in order to minimise the multiple scattering in the material. This

is implemented by taking position measurements so accurate that tracks can be reliably

reconstructed using just a few measurement points. Each measurement has an accuracy

around 10 µm, a fraction of the width of a human hair. As the tracker represents the

innermost layer of the detector it receives the highest volume of particles: the construction

materials were therefore carefully chosen to resist radiation. The CMS tracker is made

entirely of silicon: the pixels, at the very core of the detector and dealing with the highest

intensity of particles, and the silicon microstrip detectors that surround it. As particles travel

through the tracker the pixels and microstrips produce tiny electric signals that are amplified

and detected. The tracker is equipped with sensors covering an area that has the same size

of a tennis court, with 75 million separate electronic read-out channels. The tracker is in turn

divided into two parts: Inner Tracker and Outer Tracker.


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2.4.1 The Inner Tracker

The Inner Tracker [12] is equipped with sensors called “pixel modules”, or PS modules. The

high-luminosity operation implies extreme challenges for the design of the Inner Tracker in

terms of radiation tolerance of sensors and readout electronics, as well as data volume to be

stored in the front-end pipelines and sent out at high trigger rates. Thin silicon sensors with

thickness of 100–150 mm, segmented into pixel sizes of 25 x 100 mm2 or 50 x 50 mm2, are

expected to exhibit the required radiation tolerance and to deliver the desired performance

in terms of detector resolution, occupancy, low mass and two-track separation. Figure 2.3

shows the general layout of the modules disposal in the pixel detector.

Figure 2.3- Sketch of one quarter of the pixel detector layout in the r-z view. Green lines correspond to modules made of two readout chips and orange lines represent larger modules with four chips [12].

Consequently a readout chip with a small cell size and low detection threshold is required.

ATLAS and CMS are carrying out a common development in the framework of RD53 to

design a pixel chip with 2500 mm2 cell size, in 65 nm CMOS technology. With such a

configuration the detector resolution is much more robust with respect to radiation damage

than previous detectors, where the precision relies on the ability to reconstruct the tails of

the charge deposit in a 300 mm thick sensor. The Inner Tracker is composed of a barrel part

with four cylindrical layers (referred to as Tracker Barrel Pixel detector – TBPX), eight small

double discs (Tracker Forward Pixel detector – TFPX) plus four large discs (Tracker End

cap Pixel detector) in each forward direction. The design of the Inner Tracker will allow to


13

replace degraded parts over an extended year-end technical stop, which requires the

possibility to extract and insert the detector without removing the CMS beam pipe. This is

achieved by inserting the detector on inclined rails, necessitating a step in the radial boundary

between the Outer Tracker and the Inner Tracker. The last three double-discs of the Outer

Tracker endcap have three rings less than the first two double-discs. The Phase-2 Inner

Tracker uses all the available volume up to the mechanical structures (bulkheads) enclosing

the tracker, except for a small space close to the bulkheads that is reserved for a beam

condition monitoring device. The measurement of the luminosity will be integrated as

additional functionality in the four large double-discs forming the high z extension. A 3D

CAD model of the inner tracker is shown in Figure 2.4:

Figure 2.4 - Perspective view of one quarter of the Inner Tracker, showing the TBPX ladders and TFPX and TEPX dees inside the supporting structures. The pixel modules are shown as orange elements in TBPX and as

green elements in TFPX and TBPX. The dees are depicted as red and orange surfaces. Picture taken from [12].

2.4.2 The Outer Tracker

The Outer Tracker is populated with silicon modules. The concept of these modules relies

on the fact that they have two sensors: the strips of the top and bottom sensors of a module

are parallel to each other. Two versions of these modules have been realized: modules with

two strip sensors (2-strip or 2S modules), that are exactly the topic of study of this work, and

modules with a strip and a macro-pixel sensor (pixel-strip or PS modules). The strips in the

2S modules have a length of about 5 cm, while those in the PS modules are about 2.4 cm

long. In PS modules one of the two sensors is segmented into macro-pixels of about 1.5 mm


14

length, providing the z(r) coordinate measurement in the barrel (endcaps), where z is the

axial coordinate and r is the radial coordinate of the cylinder. The PS modules are deployed

in the first three layers of the Outer Tracker, in the radial region of 200–600 mm, i.e. down

to radii at which the stub resolution remains acceptable and the data reduction effective. The

2S modules are deployed in the outermost three layers, in the radial region above 600 mm.

In the endcaps the modules are arranged in rings on disc-like structures, with the rings at low

radii, up to about 700 mm, equipped with PS modules, while 2S modules are used at larger

radii. So we can distinguish three macro regions in this layer: the Tracker Barrel with PS

modules, or TBPS; the Tracker Barrel with 2S modules, or TB2S; and the Tracker Endcap

Double-Discs, or TEDD. They are shown in Figure 2.5 below.

Figure 2.5 - Sketch of one quarter of the Outer Tracker in r-z view. Blue (red) lines represent PS (2S) modules. The three sub-detectors, named TBPS, TB2S, and TEDD, are indicated. All overlapping layers are shown separately. This picture is taken from [12].

The precision on the z coordinates provided by the three PS barrel layers constrains to put

the origin of the trigger tracks to a portion of the luminous region of about 1 mm, which is

sufficiently precise to partially discriminate particles coming from different vertices. The

concept of the mentioned modules implies that both their the top and the bottom silicon

sensors of a module must be connected to the readout electronics that performs stub finding.

In order to implement the connectivity between the upper and lower sensors with reliable

and affordable technologies, the two halves of each module are read out independently by

front-end hybrids on the two ends, which prevents communication between the sensor halves

and thus the reconstruction of stubs when particles cross the module near the centre with a


15

large incident angle. In a flat barrel layout the effect translates into a geometrical inefficiency

of stub finding, which is larger than 30% at the edge of the first barrel layer.

Figure 2.6 - Drawing of the innermost layer of the TBPS, showing the central flat section and the two (identical) tilted sections. The length of each section varies between the three TBPS layers, as indicated by the ranges of dimensions given below the arrows. The layer 1 integrates also the central part of the Inner

Tracker support tube, as visible inside. This picture is also taken from [12].

To overcome this limitation, CMS has developed an innovative layout where the first three

barrel layers, that are populated with PS modules, feature progressively tilted modules,

nearly perpendicular to incident particles over the entire barrel length. In the outer three

layers of the barrel the effect of stub finding inefficiency is much less severe because of the

smaller incidence angles (the incidence angle is measured with respect to the sensor normal),

the smaller sensor spacing at those radii, and the double length of the 2S modules along z.

In order to provide a visual image of some layers of the outer tracker, some 3D CAD

drawings are shown in Figure 2.6 and Figure 2.7. They represent, respectively, the

innermost layer of the TBPS, the innermost layer of the TB2S and in addition the two

identical TEED units.


16

Figure 2.7 – On the left there is the ladders structure of the innermost layer of TB2S as installed in the support wheel. On the right there are the two identical TEDD units, each consisting of five double-discs. Each

double disc consists of four dees.

2.5 The Electromagnetic Calorimeter

The Electromagnetic Calorimeter (ECAL) [5] is placed around the vertex detector and the

Silicon Strip Tracker (described in more detail in the next section). Its aim is to measure the

energy of electromagnetically interacting particles like electrons and photons by stopping

them in an absorber of dense matter. The emerging electromagnetic shower creates photons

which are amplified and detected by silicon Avalanche Photo Diodes (APDs) and Vacuum

Phototriodes (VPTs). Lead tungstate (PbWO4) has been chosen as dense absorbing and

scintillating material [6]. It is arranged in brick-shaped crystals with a size of 23 x 2.2 x 2.2

cm3. It has excellent properties for calorimeters like a short radiation length of 0.89 cm and

a small Moliere radius of 2.2 cm; it is also radiation hard over the levels expected within 10

years of full LHC collision rate. The electromagnetic calorimeter plays an important role for

the Higgs decay mode H → γγ by detecting two photons. It is also essential for the

measurement of electrons with large transverse momenta, since these particles are clear

signatures for many interesting decays.

2.6 The Hadronic Calorimeter

The Hadronic Calorimeter (HCAL) surrounds the ECAL. It consists of an inner barrel

region, located inside the superconducting solenoid, an outer barrel part inside the iron return


17

yoke of the magnet, two end caps and two very forward calorimeters. The latter ones are

called Hadron Forward (HF) calorimeters and they are placed outside the magnet return yoke

at about 12 m from the interaction point. In contrast to the homogeneous ECAL, the HCAL

is a sampling type calorimeter made of copper as absorber material and mostly plastic

scintillators in between as light emitting active material. Devices to shift wavelength are

used to guide the signals from the scintillators to the endcap region, where APDs and

Proximity Focused Hybrid Photo Diodes (PFHPD) are converting and amplifying them to

electrical signals. In the HF, quartz fibres embedded into copper absorbers are used as

scintillators. Hadrons strongly interact with nuclei in the copper absorbers creating hadronic

jets. The energy of these jets is determined, as well as missing transverse energy which is

possible to reconstruct the hermetic design of the HCAL.

2.7 The Superconducting Solenoid

The superconducting magnet surrounds the tracking detectors, the ECAL and most parts of

the HCAL. It plays an essential role for the momentum measurement of charged particles by

deflecting their track while they are produced at the interaction point. Most parts of the

calorimeters are also placed inside the solenoid to reduce the absorbing material in front of

them, which increases their energy resolution. The magnet coil has a length of about 12.5 m,

a diameter of about 6 m and it is made of superconducting Niobium Titanium (NiTi) wires,

powered by an electrical current of 20,000 Amperes to reach the nominal magnetic field of

4 Tesla. The solenoidal shape of the field lines is closed by an iron return yoke surrounding

the coil, in which the muon detectors are installed.

2.8 The Muon System

The outermost detectors are embedded into the iron return yoke of the superconducting

magnet. This contributes to make this layer much more radial in relations to the others. The

muon System occupies a considerable volume percentage in the detector, as it is shown in

Figure 2.8, where it is possible to find, through a sectional view, the general summary layout

of the previous layers. Three different gaseous detector systems are used for the detection of


18

muons: a barrel region is based on Drift Tubes (DT), while strong magnetic field variations

in the end cap regions require the use of cathode strip chambers (CSC). In both parts,

Resistive Plate Chambers (RPCs) are used in addition for fast signals needed for the trigger.

Muons are the only particles (except the almost non-interacting neutrinos) which are not

absorbed by the calorimeters in the inner detector region. Since they are decay products of

many interesting physics processes like the Higgs decay cascade to two Z-bosons, their

detection is a clear signature that something interesting happened. Thus, signals from the

RPCs are taken into account for building the first-level global trigger decision for the

experiment.

Figure 2.8 - Cross-sectional view of the CMS detector. It is possible to observe, moving from left to right: the detection point, the Silicon Tracker, the ECAL, the HCAL, the superconducting solenoid and the muon system.

Here there is also a representation of how different kind of particles interact (or not) with each layer. This picture is taken from [11].

19

Chapter 3

THE 2S - 2 STRIPS MODULE OF THE

OUTER SILICON TRACKER IN CMS

3.1 Operating Fundamentals of Silicon Sensors

Semiconductor sensors are electronic devices widely used in the field of high-energy

experimental physics in order to detect the passage of a particle and to measure its energy.

The operating principle is based on the collection of charges inside a depleted region of a p-

n junction due to the ionization caused by the passage of particles through the semiconductor.

A peculiarity of these devices is that they are particularly suitable for carrying out precision

measurements relating to the determination of the average life of short-lived subnuclear

particles and the trajectory they travel; this is made possible by the high spatial resolution of

these sensors. Another advantage is their compactness, their ability to work well at low

temperatures and in presence of strong magnetic fields, a feature that makes their use

desirable inside the particle detectors placed along the LHC. Moreover, only 3.66 eV are

needed to generate an electron-hole pair, by comparison with the 30 eV of a gas detector. It

should also be remembered that they exhibit good resistance to damage and degradation of

performance when subjected to massive doses of radiation. The CMS detector is equipped

with single-sided semiconductor p+ n- sensors that allow the application of high substrate

bias voltages. This is necessitated due to the inversion effect of the substrate type due to high

radiation doses; therefore, to ensure that the device works properly over time, it must be

over-saturated. Moreover, since the sensors have to maintain their functionality over time, it

is also necessary that they work at an operating temperature of -10° C or less. Single-sided

sensors are less sensitive to radiation damage than double-sided detectors; they are also much

cheaper. From the back-to-back approach of two single-sided detectors, rotated 90° with

respect to each other, it is possible to reconstruct two coordinates. The sensor is made on a

wafer of material n with a thickness of 300 microns. On one face of this structure (n-side) a

n+ layer is made, while on the other (p-side) microstructures p+ implants are present. Above

these microstructures, separated by a thin insulator, polysilicon tracks are deposited and

THE 2S – 2 STRIPS MODULE OF THE OUTER SILICON TRACKER IN CMS

20

subsequently metallized. The distance between a microstrip and the other ("pitch") is one of

the factors determining the spatial resolution, which obviously improves as spacing

decreases. However, this distance cannot be excessively reduced, otherwise there may be

unwanted phenomena of capacitive coupling between the adjacent microstrips. An electric

field for reverse polarization (reverse bias) is applied to the substrate in order to empty the

entire structure. In fact, under standard operating conditions, free carriers in the substrate

must be absent. In Figure 3.1 a scheme showing the depleted zone is showed.

Figure 3.1 - Scheme showing the sectional view of a silicon module, and the mechanism for collecting the charge when a particle passes through the depleted area. Picture taken from [13].

The polarization of the sensor occurs by applying a d.d.p. between the substrate n+ and the

guard ring on the p side, which is connected to the p+ implants by polysilicon resistors. When

a particle passes through the sensor, it gives energy to the lattice atoms, so that some

electrons acquire energy to pass from the valence band to the conduction band. The electron-

hole pairs thus created migrate because of the applied electric field and the motion of the

holes, dragged towards the microstrips, induces on them a signal of the type:

𝑞(𝑡) = 𝑄 (1 −

𝑥0

𝑑) (1 − 𝑒

−1

𝜖𝜌) (3.1)

where d is the thickness of the sensor and x0 the distance between the point of production of

the charge Q and the microstrip that collects it. The 300 microns thick sensors are used as


21

vertex detectors, i.e. they operate the reconstruction of the trajectory of the particles. They

have an efficient spatial resolution, since in this way the charge is collected by a limited

number of microstrips, allowing to determine with good precision the point of passage of

the particle. However, due to the reduced thickness of the substrate, all particles give the

same energy to the material and therefore the same amount of charge is generated by

ionization. While this is unimportant to determine the passage point, this does not allow to

distinguish the type of particle that has passed through the sensor. The information collected

from these sensors must be available for reading and interpretation by a front-end reading

architecture. From an electrical point of view, the single microstrip is seen at the input of the

reading electronics as a capacitive network.

3.2 Components and General Layout of the Module

The module studied in this paper, which functioning principle is based on silicon sensor

theory, is one of the fundamental constituents of the Outer Silicon Tracker of CMS. It is used

both in the TB2S layer, where it is the only constituent, and in the TEDD, where it covers

about an half of the sensible area. The total number of 2S modules needed for the detector

is 15,360 elements. The module is generally indicated by the abbreviation "2S", which means

"2 strips", since the active part of the sensor consists of two identical facing silicon plates.

At each side of the sensor there are 1,016 strips which are read out by eight CBC chips,

resulting in a total of 2,032 channels. Each sensor has an active area of 90 cm2 and a thickness

of 320 microns. The gap between them is fixed and can take two different values: 1.8 mm

and 4 mm. It follows that the 2S modules are generally called "2S 1.8 mm" or "2S 4 mm".

To guarantee this gap, spacers made of aluminum/carbon fibre composite (AL-CF) are used.

In each module three spacers are present. Two of them are specular and they are called "main

bridges": they longitudinally cover the whole length of the silicon sensors and they are

placed on two opposite sides of the module. A third spacer, smaller than the previous ones,

takes the name of "stump bridge" and it is placed on the third side of the structure, in a central

position with respect to the other two. It is inserted primarily for heat transport from a service

board called Service Hybrid to the cooling system, although it does help to remove some


22

heat from the sensors as well. To better clarify the structure indicated so far, a 3D CAD

model is shown in Figure 3.2.

Figure 3.2- 3D CAD representation of the silicon sensor of the 2S Module (yellow) and its support spacers (grey). The drawing is managed with SolidWorks [37].

The spacers provide also mechanical support to the structure and an efficient heat removal,

as they are characterised by a high thermal conductivity (this is particularly true, considering

anisotropy, for the components of thermal conductivity parallel to the plane where carbon

fibres are positioned), and a coefficient of thermal expansion well matched to the silicon

one. Spacers are fixed to silicon with a two-components epoxy glue. In order to guarantee

the correct functioning of the silicon sensor, it is necessary to electrically isolate the spacers

from the silicon plates: a 25 microns sheet of kapton is used to achieve this goal; the kapton

is glued between the spacers and the silicon. Each module houses also its own electronic

data reading, peripherally hosted on three sides of the sensor; it is composed of three parts,

two of which are called "front-end hybrids", while the third is called "service Hybrid". The

front-end hybrids are realized in a flexible (flex) technology and they are laminated onto

CFRP (Carbon Fibre Reinforced Polymer) supports, also referred to as stiffeners. The

hybrids are folded around spacers matching the thickness of the assembly of the two sensors,

in order to minimize the length of the wirebonds between hybrids and sensors, or between


23

hybrids and MPA periphery in the case of PS modules. One 2S front-end hybrid carries eight

CMS Binary Chips (CBCs) reading out the strips of the top and bottom sensors at one sensor

end, plus the Concentrator Integrated Circuit (CIC), which serves as interface between all

the CBCs of the hybrid and the readout link. The role of the CIC is mainly to aggregate and

serialize the data of the readout chips and to distribute them clock, trigger, and control

signals. One PS front-end hybrid houses eight Short Strip ASICs (SSAs) reading out the strip

sensor, and the same CIC as used for 2S hybrids. All the front-end chips implement binary

readout. At the aim of fully exploiting the achievable hit position resolution in the on-module

stub finding, which compares cluster positions, in both module types one extra bit is added

to the hit address, so that in the case of clusters with an even number of fired channels, the

coordinate is set in the centre of the cluster, in between the two channels (“half-strip

resolution”). The auxiliary electronics for powering and optical readout is integrated on

service hybrids realized in the same flex technology as the front-end hybrids. The service

hybrids are also laminated onto stiffeners. In 2S modules one single service hybrid is located

at one end of the sensor assembly. The overall design of the 2S module is shown in Figure

3.3.

Figure 3.3 - 3D CAD of the 2S Module including the "Hybrids" electronic boards on three sides of the Silicon sensor.

All the components constituting the module are summarized in Table 3.1 below; each one

of the three hybrids is considered as a single sub-assembly part, as in this work we focus

on the mechanical and thermal aspect of the module, and not exactly on the electrical


24

behaviour. However, it has to be remembered that each of the hybrids has its characteristic

components that are in turn assembled together.

Component N° of elements

per module

Colors in Figure13

Silicon Sensor 2 Yellow

Main bridge 2 Dark Gray

Stump Bridge 1 Dark Gray

Left Hybrid 1 Orange/Red

Right Hybrid 1 Orange/Red

Service Hybrid 1 Light gray/Red

Kapton sheet 6 Light Orange

Glue Layers 12 Not Visible

Wire bonding - Encapsulation 8 Medium Gray

Table 3.1 - Types of components that make up a single 2S module and their respective quantities. The last column on the right also shows the colours with which they are represented in the CAD drawing of Figure 12.

Each module is therefore housed in a linear ladder structure (in the case of TB2S detector)

or disc shaped supports (in TEDD). The TB2S ladders are made of two parallel carbon fibre

C-shaped profiles, joined by several orthogonal elements (referred to as cross pieces), also

made of carbon fibre. The modules are supported by machined inserts, built in aluminium

carbon fibre composite material, supported by the C-shaped profiles. These inserts also

provide a connection to the cooling pipe that transits the full length of the ladder and back,

forming a U-shaped circuit. The ladder structure is shown in Figure 3.4a. On the other hand,

in TEDD, modules are mounted in discs, which for assembly reasons, are split in half-discs,

or “dees”. Two discs are grouped to form one double disc, which provides one hermetic

detector plane. In this case the cooling circuitry is made in sectors. The cooling pipes are up

to 8 m long and have many bends in order to reach every module in the sector. Carbon foam

blocks and aluminium inserts are used to provide thermal contacts between the modules and

the cooling pipes. This second type of use and positioning for the 2S module in the outer

Tracker is presented in Figure 3.4b.


25

Figure 3.4 – 3D CAD model of the structures on which the Modules will be installed. On the left (Figure a) the ladder structure, in addition to providing structural support, includes the cooling system and the channels

for the wiring of the power supply and data reading cables of the modules. In each ladder, two rows of modules are arranged. On the right (Figure b) there is one dee of the TEDD.

The module design was largely driven by the choice of making it self-contained, such that

the power conversion, opto-components, and control electronics are all on-board and not

shared with other modules. In addition, it is desirable to keep the 2S and PS module designs

as similar as possible for the different sensor spacing versions, so that for each module type

only a minor change in components is required for the different versions. Other general

principles [12] for the module design that apply to both 2S and PS modules include:

• Use of aluminium / carbon fibre (Al-CF) composite material as a spacer between

sensors and for hybrid fold-over. This material has both high thermal conductivity

and a low coefficient of thermal expansion (CTE) of 4 parts per million (ppm) per

C° along the two axes. These properties allow a good heat conduction from the sensor

and hybrids as well as a low stress on the glue joints between sensors, spacers, and

CFRP (carbon fibre reinforced polymer) parts.

• The use of glue layers as thin as possible to permit good heat conduction while

providing the necessary structural strength.

• Use of a flex hybrid circuit folded around a spacer allowing connection of sensors to

the ASICs via wire bonding with optimal geometric conditions. In addition, the fold-

over of the hybrids will be part of the hybrid assembly, built in industry.

• Direct sensor to hybrid wire bonding connections eliminating the need for pitch

adapters.


26

The bond pad pitch of the hybrid is identical to that of the sensor, simplifying the

wire bonding. The electrical lines are routed further to the bump bond pads on the

hybrid, where the chips are connected via bump bonding.

• Use of high reliability connectors, where possible, between service hybrids and front-

end

Hybrids, as well as for the connection to the backplane bias circuit. As a fall-back

solution, connectivity between hybrids would be realized through wire bonding.

• Encapsulation of all wire bonds to reduce risk of handling damage and damage due

to possible resonant vibrations in the magnetic field.

• The HV isolation requirement is 1,000 V between any conductive structures at high

voltage

and those at ground potential. This gives a safety margin of 400 V with respect to the

nominal bias voltage of 600 V, and still 200 V margin with respect to the maximum

sensor bias voltage of 800 V, considered to be used in order to increase the signal, if

it shall ever be required.

• Use of kapton MT polyimide films of 25 mm thickness for HV isolation between

sensors

and Al-CF spacers. It provides a reliable barrier and it has a relatively high thermal

conductivity.

• The HV bias connection to the 2S strip sensors will use a small flex circuit glued to

the back of the bare sensor before assembly. Then, it will be wire bonded to the

sensor backplane and encapsulated to protect the wires. One thermistor, read out by

the LpGBT, is also mounted on a kapton flex circuit and it will be glued to the top

sensor in each module. Both the HV bias and the thermistor circuit will have a

connector tail so they can be connected to the service hybrid (temperature sensors

and bias circuit in 2S modules) or the front-end hybrid.

3.3 Cooling and Thermal Requirements

Temperature plays a fundamental role in the functioning of semiconductor devices: it is

directly connected to the vibration of particles, and the higher it is, the higher is the

probability that the particles move from one energy band to the other. The ideal condition

for the particles not to pass spontaneously from one band to another, is to have an operating

temperature of 0 K, but this constitutes a theoretical limit for physics. However, it is


27

nevertheless true that lower is the working temperature, the better is the functioning of

devices. Silicon sensors, being semiconductor materials, require a temperature not higher

than -20 °C for their optimal functioning. However, there are multiple sources of thermal

power in each module, which tend to increase their temperature. The first source of heat is

the silicon sensor itself, because by applying the reverse bias voltage, leakage currents

always appear. It is possible to provide an estimate of this current with the formula obtained

by [14]:

𝑃𝑠𝑒𝑛𝑠𝑜𝑟(𝑇, ∆𝐸) ≈ 𝑃0

𝑇2

𝑇02 𝑒𝑥𝑝 (−

∆𝐸

2𝑘𝐵(

1

𝑇−

1

𝑇0)) (3.3)

Moreover, given the need to insert a reading electronics in each sensor, it is necessary to

consider the fact that each of the inserted electronic components produces heat. The values

of these main thermal powers [12], considered constant during time, are shown in the Table

3.2.

Component Power consumption

(mW)

2 x 8 CBCs 2,188

2 CICs 625

LpGBT 500

VTRx+ 306

DC-DC converters 1,770

Table 3.2 -Thermal power produced by main electronic components of each single module.

We can therefore summarize the total power generated by each sub-assembly, considering

for the silicon an operating temperature of -20 °C and at standard operating bias voltage (see

Table 3.3).

Sub-Assembly Power (W) Number per module

Sensor 0.6 2

Front-end-Hybrid 1.4 2

Service Hybrid 2.6 1

Table 3.3 - Thermal power produced by main subassembly of each single module.


28

A total thermal generation of 6.6 W per module is so obtained. In order to cool the module

and take away the heat produced, a liquid CO2 cooling system has been built, connecting

each module of the array in series. The heat is transferred by conduction from the module to

the CO2 tube through the spacers, which play therefore a key role in thermal management.

The pipe system is inserted directly into the ladder structure that supports all the modules,

as shown in the CAD drawing of Figure 3.5.

Figure 3.5 - Detail of the assembly of a single module on the support structure. It is possible to notice in light blue the pipes that transport CO2 for cooling, which are distributed longitudinally to the structure and are in

contact with the module in the five end points of the spacers.

The thermal performance of a module and its corresponding cooling structure is

characterised in terms of the temperature at which the module undergoes thermal runaway

(i.e. when the cooling power is insufficient to remove all the heat from the module and the

sensor temperature rises in a positive feedback loop, since the leakage current increases

exponentially with temperature) when the coolant temperature is increased. The nominal

value of the CO2 temperature flowing in the pipes is -35 °C. The temperature of the

environment is regulated by a cooling shield, in the range -20 °C to +20 °C. The whole set-

up can be kept in vacuum or in a dry nitrogen atmosphere to avoid condensation and to

control convection [15].


29

3.4 Module Assembly

The module construction consists basically on the assembly of the following elements: two

sensors, three spacers, and three hybrids for the 2S modules; they are realised by various

suppliers who collaborate with CMS. The construction of 2S modules is based primarily on

manual jig-based assembly techniques. Each Jig is made with machine tools and has very

tight tolerances, in order to guarantee the necessary precision. Each of its dimensions is

subjected to quality control by means of metrology machines before it is applied for

assembly. A robot-based module assembly, as was used in the existing CMS silicon strip

tracker, is not adopted for two reasons. First, the back-to-back sensor arrangement poses

numerous problems for placement, precision alignment and retaining the positioning during

glue curing. Second, even in a robotic assembly a very large amount of human intervention

is needed: unpacking, inventory, visual inspection, component selection and placement,

programming and surveillance of the robot, inspection of assembly results, handling, testing,

storing, and packing. The specifications for the sensor to sensor alignment during assembly

are: a distance perpendicular to the strips of Dx < 50 mm, a distance along the strips of Dy <

100 mm, and a tilt angle between the strips smaller than 400 mrad in 2S modules. Kapton

isolation foils are used to isolate the spacers, which are at ground potential, against the

backplane of the sensors, where the bias voltage is applied. The first step in 2S module

assembly is thus the gluing of the kapton isolation foils to the backplane of the sensors. The

three kapton foils will be stamp cut in industry with a high precision, using kapton MT sheets

of 25 mm thickness. At the same time, the HV bias circuit, produced by a qualified flex

circuit manufacturer, can be glued. This assembly step will require two assembly jigs. One

jig is used to accurately position the very small and thin kapton parts for vacuum pick-up,

used to transfer the foils to the second jig, which holds the sensor in a precise and stable

position. The glue used for the kapton to sensor joint can be distributed with a dispensing

robot in order to provide a precise volume of glue on the backplane of the sensor. The glue

to be used is a low viscosity, two parts epoxy adhesive with a long working time and suitable

for room temperature curing. It must be electronics grade since it will be in contact with the

back side of the sensors, it has not to degrade the HV isolation between the parts of the sensor

at bias voltage and the nearby parts at ground potential. After mixing the two components of


30

the epoxy glue and before putting it on the foils, the mixture is kept in a vacuum chamber to

remove any air bubbles trapped in the glue as shown in Figure 3.6

Figure 1 -On the left side it is possible to see the two-component Polytech Ep-601 epoxy adhesive used for kapton gluing. On the right is the device with which the vacuum is obtained: it is a vessel consisting of two

shells between which a gasket is placed, which through a small tube can be connected to a centralized laboratory vacuum system.

The next step is the gluing of the sensors to the Al-CF bridges. This step uses the sensor

assembly jig, which has a vacuum baseplate to hold the bottom sensor in place. This jig

features precise stops machined to micron accuracy so that the top and bottom sensors, when

pushed up against the stops, will have the required alignment precision.

Figure 3.7 – On the left, the jig for Kapton gluing built in the INFN section of Perugia laboratories. On the right, metrology of jig for Silicon gluing, made with Mitutoyo A776


31

After gluing Kapton on sensors using a gluing Jig (Figure 3.7), the steps for sensor assembly

are following described: placement of the bottom sensor, application of vacuum, application

of glue to the two sides of the Al-CF bridges using a glue transfer jig. Glue is painted or

rolled onto the surface of the glue transfer jig, which is designed so that only the part of the

bridge needing glue receives it when the piece is guided down onto the surface using

precision pins. Then, the bridges can be lowered onto the bottom sensor, again using

precision pins. The top sensor can then be placed on the top of the bridges, pushing the sensor

against the stops to achieve alignment with the bottom sensor. Then, a weight plate is placed

on the top sensor to apply a uniform force over the gluing zones, so that the glue will be

squeezed to a thin layer. This plate has foam bars glued to the bottom so that the contact to

the sensor is compliant and will not damage the sensor active surface. The whole jig can go

into a vacuum chamber, with the purpose of removing air bubbles if formed. All the

mechanical assembly phases are followed by a strict tolerance control through metrology

measuring machines, such as the Mitutoyo A776 (see Figure 3.8), available at the INFN

laboratory in Perugia, where the module studied was assembled.

Figure 3.8 - On the left the Silicon sensor installed on a specific measuring jig. The Jig holds the sensor creating a vacuum on the interface. The Jig in turn has holes in the lower part that allow it to be placed on

the granite surface of the Mitutoyo A776 measuring machine, shown on the right.


32

The following step is to glue the hybrids to the Al-CF bridges using another gluing jig

(shown in Figure 3.9). Glue is applied to the zones of the Al-CF bridges that will be in

contact with the CF hybrid stiffeners. The FE hybrids are lowered in place and pushed

against the sensor package with a spring pusher, to avoid a gap between sensor and hybrid

which would make encapsulation of the bond wires difficult. The service hybrid is lowered

in place using guide pins that match the holes in the hybrid. Weight bars are then placed on

all hybrids to achieve uniform and thin layers of glue. Once the glue is cured, the module is

moved to the wire bonding jig. This jig uses six suction cups to safely hold the bottom sensor

against the jig surface, which is covered with an anti-static plastic film. The jig has two

hybrid support bars which can be raised and lowered using a screw system. These bars will

support the hybrid during bonding.

Figure 3.9 - Photo of 2S module jigs designed to glue Hybrids.

Guide pins corresponding to the alignment holes in the Al-CF bridge feet will allow to

accurately position the module when lowering it onto the jig. Once the module is placed on

the jig, the vacuum can be activated, so pulling down the module onto the jig surface. Top

side bonding will include the two rows of readout connections between sensors and hybrids,

the top side ground bias connections, and potentially the connections between service hybrid

and the two FE hybrids. Once the top side bonding is finished, the module can be lifted off

and turned over for the bottom side bonding. The jig has been designed in a way that, after

wire bonding, the module can still be placed on the jig without damaging the existing wires,


33

to assure that repairs can be made. After bonding is completed, the module is moved to the

module carrier plate. The latter has been designed to protect the module wires but

guaranteeing that the module can be tested electrically and the wires on the module can be

encapsulated using a dispenser robot, all without removing the module from the carrier. The

module will be tested to be certain that all electronics is working correctly and that the wire

bonding of the input channels is complete and without short circuits. Once the module has

passed this test, it can go for wire encapsulation. Wire encapsulation will be performed on a

glue dispensing robot with a volumetric dispenser system. The goal is to completely

encapsulate the row of bond wires with an elastic, tough and transparent material and without

trapped air bubbles. The dispensing of the encapsulant results difficult because of the fine

pitch of the wires, which requires a low viscosity fluid that yet must not flow out to cover

other areas of the sensor or hybrid. The encapsulation will first be performed on the top side

of the module. After curing, encapsulation will be performed on the bottom side. Afterwards,

the module will again be electrically tested to check that no new problems have arisen from

the encapsulation step. If the module passes this test, the assembly work is complete.

34

Chapter 4

HEAT TRANSFER ELEMENTS

4.1 Heat Exchange Mechanisms

Heat is defined [16] as the form of energy that is transferred between two systems or between

two parts of the same system. Since it is a form of energy, it is measured in Joules. The

energy exchanged per unit of time, be defined thermal power; it is measured in Watts. Heat

is a form of transiting energy and it is generally distinguished from internal energy. In some

cases, it is a consequence of a temperature difference, in others it can be produced by

chemical or nuclear reactions. The temperature distribution in a body and the thermal flux

that propagates through it are controlled by the combined effects of different transmission

mechanisms. These mechanisms are conduction, convection and irradiation (also ebullition

and condensation in some cases). Conduction is an exchange of energy by direct interaction

between the molecules of a continuum in the presence of temperature gradients. It occurs in

gases, liquids, and solids and it is based on the molecular kinetic theory. Irradiation is a

transfer of thermal energy in the form of electromagnetic waves emitted as a result of atomic

agitation at the surface of a body, due to the fact that it is at a temperature higher than 0 K.

Like all electromagnetic waves, thermal radiation propagates at the speed of light and it does

not necessarily require the presence of matter to propagate: it can also travel in the vacuum.

However, when it propagates in matter, it interacts with this one, and it can be partly

absorbed, partly transmitted and partly reflected. Conduction and irradiation are fundamental

physical mechanisms, while convection is actually a combined process due to conduction

(and irradiation) and the movement of fluid particles: for what have been said, convection is

a heat exchange enhanced by a velocity field. It intervenes in numerous practical applications

and is rather complex to describe, as it is influenced by many parameters such as geometry,

fluid properties, motion regimes, etc. The three mechanisms just exposed can exist

simultaneously, and the presence of all three is the most general model possible. However,

when one mechanism is predominant over others, the effects of the other two may be

overlooked, and this in many cases greatly simplifies the analysis of the thermal problem.


35

At the base of the heat transmission mechanisms, there are the principles of thermodynamics

and the laws of conservation of mass, momentum and energy. Regarding the study of the 2S

module object of this work, all three heat exchange mechanisms listed are present. However,

special attention will be given to the conduction mechanism, as it is primarily responsible

for module cooling and heat transfer in general. As it will be shown later, also the convection

and boiling mechanisms are present because the module interacts with fluids, both aeriform

as regards the environment, and evaporating liquids such as carbon dioxide that flows into

cooling pipes. We will consider these other mechanisms as boundary conditions of the

system. Furthermore, talking about heat transmission, it is important to consider the regime

under which the study is done. The regime is called stationary if the value of the studied

quantities is constant over time. Instead it is called transitory if a temporal variation is

observed. Since machines like particle detectors remain in operation for long periods of time

without being switched off, the stationary approach is chosen for this treatment. This

approach is not entirely exhaustive, since the event of detection of a particle introduces a

purely transitory discontinuity, which alters the values the quantities establishing a temporal

variation. However, the stationary approach is considered significant for a first rough and

conservative analysis of the structure.

4.2 Conduction Heat Transfer

The heat conduction mechanism occurs in all the states of matter, and it is due to the

propagation of energy by direct contact of the particles. In gases conduction takes place by

atomic and molecular diffusion, while in dielectric solids and liquids it occurs by means of

elastic waves. In metals the phenomenon is dominated by the diffusion of free electrons, and

this effect is predominant compared to elastic waves. The mathematical formulation of the

phenomenon is due to Jean Baptiste Fourier (1768, 1830), who first noticed that the

transmission of heat by conduction through an isothermal surface in the normal direction to

it, is proportional to the variation of temperature per unit of length in same direction. The

equation that describes this concept is called “Fourier equation”, and it is shown below.

𝑑𝑄𝑛 = −𝑘𝑑𝐴

𝜕𝑇

𝜕𝑛𝑑𝜏 (4.1)


36

The proportionality constant k takes the name of thermal conductivity; it is measured in

[𝑊

𝑚𝐾] and it is a characteristic property of the material. It is a function not only of the material

but also of the pressure and the temperature itself. The thermal conductivity of solid

materials, especially metals, is much higher than that of liquids and solids. If we consider

only the exchange by conduction accordingly, solid materials are the main protagonists.

However, if the liquid and gaseous materials are not still but they have a field of motion, the

convective exchange could play a significant role. Starting from the Fourier equation, it is

possible to carry out an energy balance on an infinitesimal element of matter. If it is also

considered that the solid is opaque with a stationary centre of gravity, then assuming its

physical properties independent of time, and the volume variations negligible compared to

the volume itself, the general equation of heat conduction can be expressed as shown in Eq.

(4.2).

𝑎∇2𝑇 +

𝜌𝑐=

𝜕𝑇

𝜕𝑡 (4.2)

The quantity 𝑎 = 𝑘/𝜌𝑐 takes the name of thermal diffusivity and represents the propagation

velocity of a temperature variation inside a body. The second term on the left represents the

internal heat generation of the body. At this point, some simplifications are introduced: first

of all, stationary state can be considered, as it was mentioned before; the consequence of this

is that the temporal derivative becomes zero. Considering also the one-dimensional problem

and ignoring the internal heat generation, the equation can be written as (4.3):

𝜕2𝑇

𝜕𝑥2= 0 (4.3)

Integrating this equation two times in x, and considering an imposed temperature as

boundary condition (T1 in x=x1 and T2 in x=x2, with ∆𝑥 =x1-x2), the mathematical

formulation of the temperature field is obtained:

𝑇(𝑥) = 𝑇1 −

𝑇1 − 𝑇2

∆𝑥𝑥 (4.4)

By deriving this equation again and inserting it into the Fourier equation, the thermal flow

that passes through a wall in the unit of time is obtained:


37

𝑞 = −𝑘𝐴

𝑇2 − 𝑇1

∆𝑥 (4.5)

In this equation 𝑞 = 𝜕𝑄/𝜕𝜏 is the thermal power, measured in Watts. By making an analogy

between heat flux and flow of electrical charges, the second member of the previous relation

can be interpreted as the ratio between a potential difference and a resistance to flow

propagation. So a new quantity called thermal resistance is defined as:

𝑅 =

∆𝑥

𝑘𝐴 (4.6)

This equation allows to facilitate the treatment in case of a multi-layer wall, that is a wall

made up of several plane layers of different characteristics; in this case temperatures on the

external faces of each wall are considered always known. With this reasoning the total

resistance of the wall is calculated as the sum of the resistances of each single layer:

𝑞 = −1

𝑅𝑇𝑂𝑇(𝑇𝑗 − 𝑇1) = − ∑

𝑘𝑖𝐴

∆𝑥𝑖(𝑇𝑗 − 𝑇1)

𝑗

𝑖=1

(4.7)

This arrangement, as it will be seen later, is particularly useful when working with thin layers

composed of several parts, because generally they can be treated as one single wall with the

equivalent thermal conductivity. However, it is important to remember that this equation is

valid only if the flow is completely mono dimensional; if a real two-dimensional or three-

dimensional flow is treated with such writing, an error will inevitably be committed, and the

thermal flux will be underestimated.

4.3 Convection Heat Transfer

The transport of heat by convection in fluids is very often associated with movements of

parts of fluid that substantially modify the nature of the phenomenon. Fluid motions can be

caused by an external action such as pumps and fans: in this case the convection is called

forced convection. It can also happen that the fluid is set in motion by buoyancy forces due

to a temperature difference combined with a field of gravity: in this second case it is called

natural convection. In other words, the first type is present when the fluid is moving with

respect to the surface of the body under the thrust of an external propeller, or more generally,


38

when it has a velocity field independent on the body itself and therefore on its temperature.

In natural convection, on the other hand, the movement of the fluid is due solely to the

combined effect of differences in local density due to, for instance, body temperature, and

to the action of a mass force field, such as gravity in the most common problems. In both

cases, to express the global effect of convection between a solid surface and a fluid we refer

to a very simplified relationship introduced since 1701 and known as Newton's law of body

cooling:

𝑞 = ℎ𝐴(𝑇𝑤𝑎𝑙𝑙 − 𝑇𝑓𝑙𝑢𝑖𝑑) (4.8)

Where A is the surface area of the interaction wall-fluid and h takes the name of convective

coefficient; its unit of measure is [𝑊

𝑚2𝐾]. The coefficient h is actually a very complex function

to define, and it depends on the geometry of the system, on the physical properties of the

fluid and on the thermo-fluid-dynamic conditions of the process.

As far as concern the module studied in this thesis, forced convection intervenes only inside

cooling pipes that transport CO2. However, for the purposes of this study, it is considered

only the cooling effect of CO2 and not its whole physics. Many practical problems

concerning natural convection refer to geometries and conditions of motion so complicated

that it is preferable to use experimental data rather than to solve the problem analytically.

However, in absence of experimental data or just to have a value for a first attempt of

calculation, the literature provides a series of empirical correlations, obtained for common

geometries, which allow to obtain the quantities of interest; among these quantities the most

important is the convection coefficient h. In order to find a way to obtain a numerical value

for h, a dimensionless parameter that takes the name of Nusselt Number can be introduced:

𝑁𝑢 =

ℎ𝐿

𝑘 (4.9)

In this equation h is the convective coefficient, L is a characteristic geometrical quantity of

the problem and k is the thermal conductivity. This value represents the relationship between

the effect of convective heat exchange and the effect of conductive heat exchange: for

example, if Nu has the order of the unity, the convection does not have a preponderant effect

in relation to conduction. If, on the other hand, Nu is much higher than unity, heat transport

is mainly enhanced by the motion of the fluid, and therefore cannot be described in only


39

conductive terms. The correlation of McAdams [17] correlate the number of Nusselt to the

number of Rayleigh (𝑅𝑎), in the case of natural convection on a rectangular flat plate, with

a descending thermal flow; i.e.:

𝑁𝑢 = 0,27𝑅𝑎

14 (4.10)

This correlation is valid for 3 ∗ 105 < 𝑅𝑎 < 1010.

The Rayleigh number is another dimensionless parameter used in fluid dynamics and

indicates the relationship between inertial forces and viscous forces. In the case of natural

convection, it can be written as follows:

𝑅𝑎 =

𝑔𝛽𝐿3(𝑇𝑝 − 𝑇∞)

𝜐𝑎 (4.11)

In this equation, g represents the gravitational acceleration, β the volumetric coefficient of

thermal expansion, L the characteristic length of the problem, 𝜐 the viscosity and 𝑎 the

thermal diffusivity of the fluid. Furthermore, Tp is the wall temperature, and 𝑇∞ is the

temperature of the fluid. Therefore, once temperatures, the geometric characteristics of the

system and the thermodynamic properties of the fluid are known, it is always possible to

calculate the Rayleigh number, and proceeding backwards, finding h with analytical

considerations.

4.4 Thermal Radiation Heat Transfer

Radiant heat, also known as thermal radiation, is the transfer of electromagnetic radiation

which describes the heat exchange of energy by photons. All bodies emit energy by radiation

in relation to their thermodynamic state. Two types of emission can be distinguished:

volumetric emission, proper of the gases, and superficial emission, which characterizes the

behaviour of most liquids and solids. In the latter, the radiation emitted by the internal

molecules is strongly absorbed by the adjacent ones, so the radiation coming from them is

only that emitted by the molecules that are within the distance of 1 µm from the exposed

surface. Regarding the nature of thermal irradiation, two theories are possible: the first

interprets radiation as a mix of electromagnetic waves, while the second describes it through


40

the propagation of particles, in particular photons. In both cases it is possible to define a

wavelength λ and a frequency ν, linked together by equation (4.12).

𝜆 =𝑐

ν

(4.12)

C is the velocity of propagation of the wave. The range corresponding to the thermal

radiation is the part of spectrum included between wavelengths of [0,1; 100] µm; within this

range visible radiation is included. The transmission of heat by radiation between two bodies,

respectively at temperatures T1 e T2, occurs as a consequence of two successive

transformations of energy. In fact, a part of the internal energy of the first body is emitted

by its surface as electromagnetic waves and, impressing on the surface of the second body,

is in part absorbed and converted in internal energy again. At the same time, this second

body emits, and its radiation arrives in the first body again. In other words, there are two

fluxes of energy in transit, and the net transport of heat is equal to the difference between

them. Next to these considerations, an ideal element called black body can be defined. Its

absorbs the whole energy that hit it, and it emits the maximum quantity of energy in relation

to other bodies, in the same conditions. So, when two black bodies exchange heat for

radiation, the net flux will be the one showed in equation (4.13).

𝑞′′ = 𝜎(𝑇14 − 𝑇2

4) (4.13)

This equation derives directly from the Stefan-Boltzman equation, and σ is a constant of

proportionality that takes the name of Stefan-Boltzman constant, and its value is

σ=5.66910-8 W/m2K4. Real surfaces do not emit the same power of the ideal body, showed

in previous equation, but their total radiation emitted is still proportional to T4. In order to

characterize this new behaviour of real surfaces, a parameter called emissivity is introduced.

This parameter links the thermal power of real bodies to the one of the black body. So its

definition is given by equation (4.13) below:

𝜖 =𝑞𝑟𝑒𝑎𝑙

𝑞𝑏𝑙𝑎𝑐𝑘 𝑏𝑜𝑑𝑦 (4.14)

In addition, it should be noted that not all energy coming from a body affects the other

surface: a part of it will be dispersed in the ambient. Considering these other effects, the

equation (4.12) can be generalized as the following:


41

𝑞′′ = 𝑓(𝜖)𝑓(𝑔)𝜎(𝑇14 − 𝑇2

4) (4.15)

In this equation, 𝑓(𝜖) is a function of the emissivity and 𝑓(𝑔) a function of geometrical

configuration of the system and the ambient.

4.5 Treatment of Cavities

When a cavity containing a fluid has to be modelled, the inner fluid inside it can be

considered in movement or standing still. In general, if the cavity is small and the

temperature gradient is not high enough, the absolute value of the velocity field is very low

and can therefore be neglected. This also allows to consider the only effect of conduction

(and possibly irradiation) without considering convection. In the literature [18], air cavities

are considered unventilated if they are completely closed or connected either to the exterior

or to the interior by a slit with a width not exceeding 2 mm. The heat flow rate in these

cavities shall be represented by an equivalent thermal conductivity 𝑘𝑒𝑞 that includes the heat

flow by conduction, by convection and by radiation; it depends also on the geometry of the

cavity and on the adjacent materials. The equivalent thermal conductivity is given by the

equation (4.12):

𝑘𝑒𝑞 =

𝑑

𝑅𝑠 (4.16)

Where d is the dimension of the cavity in the direction of heat flow, and 𝑅𝑠 is the thermal

resistance of the cavity given by:

𝑅𝑠 =

1

ℎ𝑎 + ℎ𝑟 (4.17)

In this second equation, ℎ𝑎 is the convective heat transfer coefficient and ℎ𝑟 is the radiative

heat transfer coefficient, both obtained by the correlation given by normative UNI EN ISO

10077-2.

42

Chapter 5

THE FINITE VOLUME METHOD

5.1 Equations of Conservation

Problems of heat exchange present an analytical solution only in very few cases, generally

characterised by simple geometries, not complex boundary conditions and heavy

simplifications. In reality, most of the time irregular geometries have to be solved, as well

as non-linearity and combined boundary conditions. This means that many practical

problems cannot be solved analytically, except through simplifications that can often

compromise the reliability of the results. However, over the year numerical methods have

been developed and, thanks to the growing development of computational power, they allow

to deal with complex problems. Numerical methods always provide approximate results, but

if they are used correctly, they allow to provide an estimate of the error committed, in order

to obtain a valid result for the purpose of the study. In the field of thermal fluid dynamics,

the most common numerical methods are the finite difference method, the finite volume

method and the finite element method. With regard to this document, some basic notion of

the finite volume method alone will be described, without any claim of completeness, but

simply with the aim to introduce the calculation software used for the study of the 2S module

(which is ANSYS Fluent 17.1 [36]); this software is based on the finite volumes method.

Generally, all the aforementioned approaches are based on the numerical solution of the

conservation equations, so this chapter starts with a brief description of these. The first

equation is the mass conservation one, which, for an open system with various inputs and

outputs, can be expressed in the form:

𝜕𝜌

𝜕𝑡+ ∇ ∙ (𝜌𝒗) = 0 (5.1)

In this equation 𝜌 is the density of the material and 𝒗 is the velocity vector. In many cases

of studies, including this one, the regime is considered stationary, i.e. the descriptive physical


43

quantities are independent on time t. The mass conservation equation (5.1) is therefore

simplified in the following:

∇ ∙ (𝜌𝒗) = 0 (5.2)

Beyond this relation, there is the energy conservation equation. It can be written for open

systems, in the case of low velocities and neglecting the changes in kinetic and potential

energy, in the form shown below:

𝜕

𝜕𝑡(𝜌𝑐𝑝𝑇) + ∇ ∙ (𝜌𝒗𝑐𝑝𝑇) = ∇ ∙ (k∇T) + + ∅ +

𝜕𝑝

𝜕𝑡 (5.3)

Beyond the terms of the previous equation, now the following appear: 𝑐𝑝, the specific heat

at constant pressure; T, the thermodynamic temperature, the thermal conductivity k, and the

pressure p. The first term on the left represents the temporal variation of the energy in the

control volume. Considering the stationary regime, this term is null. The other terms are the

balance between the incoming energy and the outgoing energy of the system; in particular

the second term on the left and the first term on the right, represent respectively the advective

transport and the conductive transport. Finally represents the internal heat generation

related to the conversion of chemical, electrical and nuclear energies and ∅ is the energy

relative to the work performed by the forces of friction. Also this term for the purposes of

this analysis can be neglected. Under the aforementioned hypotheses, the energy

conservation equation (5.3) takes the form:

∇ ∙ (𝜌𝒗𝑐𝑝𝑇) = ∇ ∙ (k∇T) + (5.4)

This formulation of the equation is called conservative. If the specific density and heat

remain constant in the process, they can be taken out of the operator ∇, and thus the equation

is said to be non-conservative. In analytical terms, for incompressible fluids with constant

specific heats, the two forms lead to the same solutions. In numerical terms, however, the

discretization based on the finite element method do not generally guarantee mass

conservation. As a consequence, the non-conservative form of the energy equation allows

us to ignore spurious enthalpy parts that involve mass fictitious local creations or

destructions. With regard to the finite volume method, on the other hand, conservative

expression is preferred as said by G. Comini, G. Croce, and E. Nobile in [19]. The third and


44

last conservation equation useful for modelling the thermal fluid dynamic is the conservation

of momentum, which directly derives from Newton's second law. The latter, in its most

general formulation, takes the form:

𝑭 = 𝑚𝑑𝒗

𝑑𝑡+ 𝒗

𝑑𝑚

𝑑𝑡 (5.5)

By developing this equation for a generic volume of control, and by distinguishing at first

member between surface forces and volume forces, the Navier equations are obtained.

−∇𝑝 + ∇ ∙ 𝑻 + 𝜌𝒈 =𝜕

𝜕𝑡(𝜌𝒗) + ∇ ∙ (𝜌𝒗𝒗) (5.6)

In (5.6), T is the tensor of viscous stresses and g is gravitational acceleration. It is noted that,

unlike the other two scalars equations, the latter is a vector equation. Generally, this equation

is further developed by inserting the explicit expression of T (constitutive equation) and

highlighting in p the contributions of the hydrostatic pressure (neutral with respect to motion)

and of the pure pressure 𝑝 . It is then obtained the most common form of the momentum

conservation equation, also known as the Navier-Stokes equation. It is in the conservative

form, and it is also used in the natural convection problems treated.

𝜕

𝜕𝑡(𝜌𝒗) + ∇ ∙ (𝜌𝒗𝒗) = −∇𝑝 + ∇ ∙ (𝜇∇𝒗) − 𝜌𝛽(𝑡 − 𝑡0)𝒈 (5.7)

In this equation, 𝜇 is the dynamic viscosity and 𝛽 is the coefficient of volume expansion.

5.2 Outline of the Finite Volume Method

Looking at the equations in the previous chapter, it is evident that they can all be written in

a same form as shown in equation (5.8):

𝜕

𝜕𝑡(𝜌∅) + ∇ ∙ (𝜌𝒗∅) = ∇ ∙ (Γ∇∅) + 𝑠 (5.8)

∅ is a generic scalar (e.g. temperature, velocity component, etc.) and Γ represents the

molecular transport property for scalar itself. In other words, this equation says that the sum

of an accumulation term plus a convection term is equal to the sum of a diffusion term plus


45

a source term, s. Based on this observation, it will be sufficient to develop a method for the

solution of this general equation, then move on to the particular solution of each single

conservation equation. The basic idea of the finite volume method is to use the integral

formulation of the equation (5.8), written for a generic volume of control V. It takes the

form:

∫ [𝜕

𝜕𝑡(𝜌∅) + ∇ ∙ (𝜌𝒗∅) − ∇ ∙ (Γ∇∅) − 𝑠] 𝑑𝑉 = 0

𝑉

(5.9)

Using the Gauss theorem it is therefore possible to develop two of the four integral quantities

in surface integrals, calculated on the generic surface contour A of the volume. The (5.9) can

therefore be expressed as follows:

∫𝜕

𝜕𝑡(𝜌∅)𝑑𝑉 + ∫ 𝑝∅𝒗 ∙ 𝒏𝑑𝐴

𝐴

= ∫ Γ∇∅ ∙ 𝒏𝑑𝐴 + ∫ 𝑠𝑑𝑉𝑉𝐴𝑉

(5.10)

The conservation equation (5.10) can be applied to any volume of arbitrary control. At this

point it is therefore sufficient to divide the continuous object of study into many small

elements of finite volume, and to resolve in each of them. By summing the equations

obtained for all the control volumes that make up the entire computational domain, it is

obtained again the global conservation equation, since the flows on each internal face are

cancelled, as they are evaluated with a different sign in two volumes of adjacent control. To

ensure that this is true, the volumes must not intersect each other, and must completely cover

the whole domain. The operation of dividing the body into many small elements of finite

volume takes the name of meshing procedure, where for each element it is possible to

recognize faces and nodes. The most common approach consists of positioning the nodes in

the control centre of volumes. This procedure is no longer carried out manually, but there

are dedicated software that can be used. The meshing operation can take up most of the time

required to create a Finite Volume Method (FVM) model and it is a key point, as it will be

seen below, for the success of the entire work. For some of the terms of the general equation

of conservation it is necessary to integrate on the volume of the element. The simplest

approximation for this integral is given by the product of the average value of the integrand

function, assumed equal to the value of the centre of the element, for the volume of the

element itself. For example, in the case of the source term:


46

𝑆𝑝 = ∫ 𝑠𝑑𝑉 = ∆𝑉 ≈ 𝑆𝑝∆𝑥𝑖∆𝑦𝑗∆𝑧𝑘𝑉

(5.11)

This quantity is easy to evaluate because all the variables are defined at the centre of the

control volumes and, therefore, no interpolation is necessary. As far as the calculation of

surface integrals, on the other hand, it would be necessary to know the value of the integrand

function on each point of the surface, but this is not possible because the quantities are known

only at the centre. The simplest approximation to calculate these integrals equally is based

on the rule of the midpoint: the integral is approximated with the product of the integrand

function evaluated in the centre of the face and the area of the face, that is for example:

∫ 𝑝∅𝒗 ∙ 𝒏𝑑𝐴 = 𝑝∅𝒗 𝐴 = 𝑝∅𝒗 ∆𝑥𝑖∆𝑦𝑗 ≈ 𝑝∅𝒗∆𝑥𝑖∆𝑦𝑗𝐴

(5.12)

It can be shown that the approximation thus obtained if the subdivision of the domain is

sufficiently fine, is reduced to the square of the characteristic dimension of the face.

5.3 Boundary Conditions

The boundary conditions must be applied before assembling, and then solving, the equation

system. Two approaches are possible for this purpose: in the first approach, a node is inserted

on the boundary surface of each boundary element, which therefore will have two nodes, the

internal one and the border one. In the second case, a so-called ghost cell is used, which is a

fictitious cell imagined adjacent to the boundary element, which has no physical meaning,

but facilitates the imposition of the boundary conditions.

5.4 Sensitivity of the Solution to Errors

The numerical simulation of a thermal fluid dynamic system, as already mentioned above,

represents only an approximation of the real phenomena, which implies that whatever the

solution is, an error E is always present. In order to obtain a meaningful and useful result, it

is necessary to be able to estimate this error and make it non-significant for the purpose of

the analysis to be carried out. This error can be separated in two parts: an error that derives


47

from the choice of the equations (and respective boundary conditions) that describe the

phenomenon under examination, as they may be more or less suitable for the description of

physical reality. It is called modelling error, 𝐸𝑚𝑜𝑑. Then, the numerical error is the error

that derives from the solution of the aforesaid equations, since they are solved numerically

and not in a mathematically exact way. For what has been said so far, it can be written:

𝐸 = 𝐸𝑚𝑜𝑑 + 𝐸𝑛𝑢𝑚 (5.13)

The effects due to the intrinsic limitations of the codes, such as the types of boundary

conditions available or limitations in the assignment of the properties of the materials, as

well as explicit modelling choices made by the user contribute to the modelling error. The

numerical error, instead, can be decomposed in turn into three components:

𝐸𝑛𝑢𝑚 = 𝐸𝑖 + 𝐸𝑟 + 𝐸𝑑 (5.14)

The first term in the second member 𝐸𝑖 represents the convergence error and it derives from

the linearization of the differential equations: as a consequence, the solution is searched

iteratively, as a subsequent correction of a solution of first attempt solution. During the

iterative procedure, the error component 𝐸𝑖 is subsequently reduced and can be monitored

by the control of residuals. The error 𝐸𝑟 is then called round-off error, as it derives from the

fact that the calculator reserves, for the representation of the numerical quantities, memory

allocations of finite size. However, this error can be limited by adopting appropriate

normalized forms of the variables or by using a double precision numerical representation;

this second solution was adopted in our work. Finally, always referring to the equation

(5.14), 𝐸𝑑 represents the error of discretization; it derives from the fact that the differential

equations, defined on the continuum, are represented in discrete form in the domain of space

and time. Since our analysis is performed in steady state conditions, only spatial

discretization is of particularly important. In the field of computational fluid dynamics, if the

numerical solver is well designed, the discretization error is the predominant component of

the numerical error and it may be sometimes significant, depending on the mesh and the time

step used [19] . In the next paragraph a method used to estimate and eventually reduce the

discretization error will be reported. The modelling error control process is called validation

of the specific type of simulation, and it involves the comparison between the numerical

result and the experimental physical data. The control of the numeric origin error instead


48

takes the name of verification, and it concerns purely the mathematical-numerical field,

regardless of any physical feedback [20].

5.5 The Grid Convergence Index

The grid convergence index (GCI) provides a discretization error estimate. This method

assumes that a relationship exists between the exact solution 𝑓𝑒𝑥𝑎𝑐𝑡 and the approximate

solution 𝑓(ℎ) of computational fluid dynamic model expressed as:

𝑓𝑒𝑥𝑎𝑐𝑡 = 𝑓(ℎ) + 𝐴ℎ𝑝 + 𝐻𝑂𝑇(ℎ) (5.15)

In this relation, h is a parameter that represent the mesh spatial discretization, A is a constant

and p is the order of convergence. With the acronym HOT is then indicated the terms of a

higher order, also dependent on h. In this equation, it is necessary to know the exact solution

to calculate the error, but in most problems the exact solution is not known. If the mesh is

sufficiently refined, i.e. the results are in the asymptotic region and do not change rapidly,

the term HOT can be neglected [21]. The discretization error can therefore be written as:

𝐸𝑑(ℎ) = 𝑓𝑒𝑥𝑎𝑐𝑡 − 𝑓(ℎ) ≈ 𝐴ℎ𝑝 (5.16)

It is often convenient to write this result in logarithmic terms:

log 𝐸𝑑(ℎ) = log(𝐴) + 𝑝 log(ℎ) (5.17)

Looking at the equations (5.16) and (5.17) there are 3 unknowns ( 𝑓𝑒𝑥𝑎𝑐𝑡, A , P) and two

known quantities (h, 𝑓(ℎ) ) for each simulation. The three unknown quantities can be

obtained by doing three different simulations where h can be varied, and by putting the

results into a system. So ℎ1, ℎ2, ℎ3 are defined, standing respectively for the measurement

of the discretization of the mesh in the simulation 1, 2 and 3, with the convention that it is

ℎ1 < ℎ2 < ℎ3. From three simulations also the quantities 𝑓(ℎ1) = 𝑓1, 𝑓(ℎ2) = 𝑓2, 𝑓(ℎ3) =

𝑓3 can be estimated. By writing the equation (5.17) three times, it is possible to derive the

relation for p:


49

𝑝 =|ln |

𝑓32

𝑓21|| + 𝑞(𝑝)

ln (𝑟21)

(5.18)

In this relation a quantity q is needed, which is a function of p, to calculate p:

𝑞(𝑝) = ln (𝑟21

𝑝 − 𝑠

𝑟32𝑝 − 𝑠

) (5.19)

So the problem has to be solved in an iterative way. The other quantities that appear in the

formula are shown below:

𝑟𝑖+1,𝑖 = ℎ𝑖+1/ℎ𝑖 (5.20)

𝑓32 = 𝑓3 − 𝑓2 (5.21)

𝑓21 = 𝑓2 − 𝑓1 (5.22)

𝑠 = 𝑠𝑖𝑔𝑛 (𝑓32

𝑓21) (5.23)

Given these quantities, it is therefore possible to calculate the GCI, which is an estimate of

the discretization error, as follows [22]:

𝐺𝐶𝐼12 = 𝐹𝑠

|𝑓2 − 𝑓1

𝑓1|

𝑟𝑝21 − 1

(5.24)

Finally, it is also possible to provide an estimate of the exact numerical convergence

solution:

𝑓∗ =𝑟21

𝑝 𝑓1 − 𝑓2

𝑟21𝑝 − 1

(5.25)

It can be shown that the exact solution lies in a range:

[𝑓1(1 − 𝐺𝐶𝐼12 ) , 𝑓1 (1 + 𝐺𝐶𝐼12)] (5.26)

With a 95% confidence level.


50

In order to facilitate the study of the Grid Convergence Index, a short Matlab script was

developed, which was also used for the GCI calculations of this work. This script is

showed in Appendix.

51

Chapter 6

FINITE VOLUME METHOD MODEL OF

THE OUTER TRACKER 2S MODULE

6.1 Introduction to the Software

The software used for the finite volume analysis is Fluent 17.1 [36], by the Ansys company.

The platform provided by Ansys for the management of computational fluid dynamic models

is called Workbench. It is based on a block system and provides the user with a very easy

file and information management. It also puts the Fluent software in communication with

other programs such as the one for the management of geometry, the one for the construction

of the grid of volumes or the one for the presentation of results. Starting a new project in

Workbench, a block like the one below in Figure 6.1 will appear in the workspace:

Figure 6.1 - Diagram of the operations to be carried out to develop a Finished Volume Model (FVM) with the Ansys fluent 17.1 solver. It is available in the Workbench platform.

The block is designed to provide the user with a division of the work in successive steps;

each of them is represented by a line; all the lines have to be sequentially executed from top

to bottom. This division into parts of the work is what it will be followed step by step in each

one of the next paragraphs. Moreover, at each step of the modelling process the platform

FINITE VOLUME METHOD MODEL OF THE OUTER TRACKER 2S MODULE

52

opens a different software, designed and optimized to best perform the single stage that have

to be executed. The first operation to be performed is the implementation of the geometry:

the system component that makes this possible is called Design Modeler. It is a tool that

allows to import a 3D model from an external CAD software and to process it in order to

guarantee the user's needs. It also allows to create a new geometry starting from scratch.

After this step of processing the geometry, the division of the continuum into elements of

finite volume is needed. This operation is carried out by an appropriate meshing tool made

available by workbench. The following procedure, that goes under the name of model setup,

is the one where the boundary conditions are set to the model, as well as the characteristics

of the materials to be used. All of those parameters are chosen by the user to make the model

as similar as possible to the real case. This section, like the one called solution, is entrusted

to Fluent software. Last step is represented by the reading of the results, that can always be

entrusted to the same Fluent or to an external software that takes the name of CFD-post. In

the case of this thesis, where not differently specified, tools made available by the same

fluent software will be used to present the results. In the following chapters, for each step,

the development of a model for the 2S module of the external tracker with 1.8 mm thickness

will be explained in more detail.

6.2 Geometry of the Model

As it was mentioned in the previous paragraph, the first operation to be performed to build

a computational fluid dynamic (CFD) model is to create a 3D digital model of the object to

be studied. In this case, the 3D CAD design of the module is provided by the CMS working

group (mechanical section) and it is shown in the Figure 6.2:

To better understand the shape and position of each component of the model, an exploded

view of it is also provided in Figure 6.3.


53

Figure 6.2 -3D CAD model of the 2S module with a thickness of 1.8 mm realized by the mechanical working group of the CMS Outer Tracker, approved on 2016.12.02. The file containing the model is a step file (.stp)

and it is opened with SolidWorks 2014.

Figure 6.3 - Exploded view of the 3D CAD drawing of the 2S module with 1.8 mm thickness. In the central area, from top to bottom the following components can be seen: the top sensor, the first three glue layers, the three Kapton strips, the second glue layers, the three spacers, the third glue layers, other three Kapton

strips, the fourth glue layers, the bottom glue layers. Externally on three sides of sensors there are the three “hybrids” electronic boards.


54

In this model there are three dedicated electronic boards disposed on the three edges: as

mentioned in chapter 3, they produce heat. In this study these boards are excluded from the

model to simplify the geometry. In order to reproduce their heating effect on the silicon

sensor particular boundary conditions will be imposed. Wire bond connections between

sensor and boards are also excluded, as happens for the respective encapsulations. By

operating in this way, a leaner model is obtained, and the calculation time is reduced, as the

number of elements used to discretize the domain. In the exploded drawing there is also the

possibility to see how spacers are glued to the sensor: there is a first layer of glue that binds

the face of the spacer to the Kapton sheet, and then a further layer of glue that binds the latter

to the Silicon sensor. The thickness of each layer is presented in Table 6.1. A sandwich

structure is thus obtained, as shown in Figure 6.4.

Figure 6.4 - Detail of the transversal stratification of the module, focused in the area of only one spacer. It is possible to notice, from top to bottom: the top sensor, the first glue layer, the first kapton strip, the second

glue layer, the AL-CF spacer, the third glue layer, the second kapton strip, the fourth glue layer and the bottom sensor.

Layer Note Thickness (μm)

Al-CF bridge whole component 1220

Glue layer single layer 25

Kapton sheet single layer 25

Silicon sensor single sensor 320

Table 6.1 - Thicknesses of each individual layer.


55

Glue and Kapton layers, as it will be seen in the next section, result very critical with regard

to the meshing phase. In fact, if they have to be divided into elements, they should have a

very high number of divisions, which make the numerical model considerably heavier.

However, they play a key role in thermal flux, since they introduce a non-negligible thermal

resistance, so they cannot be excluded from the model. Taking into account both these

reasons, the best way to treat these components is to physically exclude them from the

geometry, so as not to divide them into elements, and to simulate their effect with a contact

resistance, i.e. to introduce a mathematical relationship that can compensate for the choice

of exclusion. Therefore, the idea is to slice the model complete of layers, to cancel the 75

micrometres inclusive of the layer of the layer of the glue-kapton-glue, both on the top and

of the bottom of the Al-CF bridge, and to reattach the silicon directly to the spacer.

Looking again at the CAD drawing in Figure 6.2, if electronic boards are excluded, it appears

to be symmetrical with respect to a plane perpendicular to that on which the module lies, and

parallel to the two spacers. So the strategy of cutting the geometry of the module in half and

putting a symmetry plan on the cutting edge is adopted. In this way the number of elements

is halved, and the calculation times is lowered as the dimensions of the model are greatly

reduced. Another consideration to be made concerns the fluid that is present in the cavities

of the spacer: they are the chambers where the air is entrapped during assembly and remains

internally confined until the module enters into operative conditions as well as for the whole

life of it. Therefore, as it is generally air at atmospheric pressure, it is generally not

conductive, but since the layer is very thin, it gives a contribution to the thermal exchange

of interest. Moreover, between the two silicon plates, a fluid is present under operating

conditions (air or nitrogen): although this fluid is not able to develop a field of motion due

to natural convection, being the thickness being very thin so offering a contribution to the

exchange by conduction. The 3D CAD model does not foresee the physical presence of these

fluid layers between the components: for these reasons they are inserted in the Design

Modeler mode. At the end of this phase of geometry processing, the model appears as shown

in Figure 6.5:


56

Figure 6.5 - 3D model developed by the Workbench Design Modeler. It can be noted that only half of the module is considered, and solid (coloured in blue, green, yellow, red and light blue) bodies are inserted

between the cavities of the spacer.

The file containing this model is then passed to the meshing software. For the sake of clarity,

the processing of the geometry carried out on the original model is summarized below:

• Exclusion of electronic boards and respective connections.

• Excluding the glue-Kapton-glue layers for a total shortening of the model of

2x75=150 μm.

• Halving the module and insertion of the symmetry plane

• Insertion of material simulating the entrapped fluid in the internal cavities

6.3 Meshing Procedure

With meshing procedure is intended the process of division of a body into finite volume

elements. This procedure is entrusted to a specific meshing tool software provided by

Workbench. Sizes of element are the crucial quantity to define in this phase: if elements are

not small enough, an error of discretization occurs, as well as difficulties in solving equation

in regions where important gradients are presents. On the other way, if elements have too

small sizes, a big number of elements is needed to divide the whole body, and, in many


57

cases, the power of the calculator may not be enough to handle the model. So it is necessary

to find the right compromise between times of calculation, power of the calculator, and level

of discretization of the model. Another factor to take in account during meshing operations

is the quality of each element. A square is an ideal geometrical shape, and error connected

in solving equations in this kind of volumes will be minimum. It follows from this that a

body has to be discretized in elements which shapes are much close to the ideal ideal. In

many practical cases, this is not achievable, because bodies have complex geometries, and

the only way is using volumes with not ideal shapes. The quantity called element quality

helps to judge how much elements are close to the shape of squares or cubes. The element

quality function of the Workbench meshing tool provides a composite quality metric that

ranges between 0 and 1. This metric is based on the ratio of the volume to the sum of the

square of the edge lengths for 2D quadrilateral or triangular elements, or the square root of

the cube of the sum of the square of the edge lengths for 3D elements. A value of 1 indicates

a perfect cube or square while a value of 0 indicates that the element has a zero or negative

volume. For three-dimensional brick elements:

𝑄𝑢𝑎𝑙𝑖𝑡𝑦 = 𝐶𝑣𝑜𝑙𝑢𝑚𝑒

√[∑(𝐸𝑑𝑔𝑒 𝐿𝑒𝑛𝑔ℎ𝑡)2]32 (6.1)

where C is a constant defined for each type of elements. After some attempts, the selected

value for elements medium size is imposed 1.21x10-4 m. The size function is computed when

meshing begins. When the Adaptive size function method is used, the mesher uses the value

of the Element seed size property to determine a starting point for the mesh size. The value

of the Element seed size property can be user-defined, or it can be automatically computed

by the mesher (defaulted based on the bounding box). When meshing begins, edges are

meshed with this size initially, and then they are refined for curvature and 2D proximity.

Next, mesh-based defeaturing occurs. The final edge mesh is then passed into a least-squares

fit size function, which guides face and volume meshing. For all other size function methods,

the mesher examines the size sources and, based on the smallest size obtained at the location

of the sources, the distance to each source, and the growth rate, the smallest size at each

point is selected and stored in a background grid. The mesher uses the sizes from the

background grid to generate a mesh. The background grid is refined automatically to provide

size distribution to the mesher. About the meshing procedure of the 2S module, the most


58

critical elements to divide in finite volume elements are the layers of glue and Kapton. The

problem is that if the layers of glue and Kapton have to be meshed, a huge number of

elements is necessary to guarantee acceptable element quality. This happens because the

sizes of this layers are very different to each other, in particular, the thickness of 25 µm

compared with the other two dimensions. In order to have a good element quality, i.e. correct

solution of equations, every volume element that composes a body must have dimensions as

similar as possible. Furthermore, for each dimension of the body, at least three rows of

volume elements are necessary to guarantee correct solution. An example of elements with

good and bad quality is shown in Figure 6.6.

Figure 6.6 – On the left, a body divided in volume elements with good quality of shape. On the right, the same body is divided in elements with not good quality. The body meshed as in the right way has a much

smaller number of elements and needs a lower computational power, but results may be affected by errors.

If the only Kapton layer should be divided in volume elements with best quality, we estimate

that 11,867,136 elements are necessary. This implies that, for the whole module made of six

Kapton layers, as well as twelve glue layers with same dimensions, the number of element

necessary is huge. This problem can be overcome by inserting an equivalent thermal

resistance instead of modelling the whole geometry of layers, as mentioned in Section 6.2.

Operating on this way, glue and Kapton are substituted by a thermal equivalent resistance,

inserted between spacers and silicon sensor. However, the thermal resistance allows to

reconstruct only mono-dimensional flows, perpendicular to the surface where it is inserted.

Heat fluxes parallel to these surfaces are neglected. In the thin layers of 2S module, Kapton

and glue planar dimensions are sensibly higher than the thickness, so also a planar flux of

heat occurs, and it can be significant. If an estimation of the error introduced by inserting the


59

equivalent thermal resistance instead of mashing all layers is searched, the only way is

meshing layers and comparing results. In this way some studies have been executed. In

particular, some 2D simulation of the sectional view have been done. In two dimensions, the

number of elements is maintained low even if glue and Kapton layers are meshed. The study

consisted of imposing a cold temperature on the spacer and a hot temperature on the edge of

the silicon sensor, in both configurations of insertion of equivalent thermal resistance and of

meshing all layers. Thermal fluxes entering in the system have been calculated and

compared: a deviation around 3% between the two cases has found. In Figure 6.7 is shown

a detail of the 2D study, where the difference between meshing all layers or inserting thermal

resistance is presented.

Figure 6.7 – Effect of small layers in 2D simulations, in the case of meshing all the layers (on the left) and in the case of inserting a thermal resistance (on the right). Thermal resistance does not allow to evaluate heat

fluxes on the horizontal direction.

Inserting thermal equivalent resistance in the model, the result of meshing procedure is

shown in Figure 6.8. It is very difficult to appreciate graphically the division in volume

elements, as they are very small compared with the geometry.


60

Figure 6.8 – Details of module geometry divided in finite volume elements.

In this model, there are a total of 5,867,070 elements and 2,009,418 nodes. Applying the

element quality function, the graph showed in Figure 6.9 is created by the software:

Figure 6.9 – Graph showing on x axe the element quality levels, from 0 to 1, and on y the number of elements which have a certain element quality.

Meshing software offers also the possibility to colour each element with a different rgb level

proportional to its quality, on the base of a user defined scale. The result of this is shown in

Figure 6.10.


61

Figure 6.10 – Volume elements coloured in different way as function of their element quality. Blue colour corresponds to a perfect quality.

6.4 Boundary Conditions

After meshing procedure, data have been loaded in Fluent solver. The first parameter to be

set in this ambient is the type of analysis that is wanted. In this case only a thermal analysis

is desired, and, as fluids in motion are not considered, the only equation to be solved is the

energy one. From this, it follows, considering also the steady state of the system, that the

only parameter characterising materials that is needed is the thermal conductivity. For solid

bodies, (silicon, spacers, air) values taken from Fluent database are used (see Table 6.2).

Material Thermal conductivity [W/mK]

Silicon 180

Aluminium 202.4

Air 0.0242

Table 6.2 – Material characteristics for materials.

For equivalent thermal resistances inserted in bodies interfaces (where needed), values are

calculated using equation (4.7). The software asks as input data the equivalent thermal


62

conductivity, and not the thermal resistance. In this way, the equation to calculate it becomes

the (6.2) as follows, in the case of a wall composed of two layers:

𝐾𝑒𝑞 =(𝑆1 + 𝑆2)𝑘1𝑘2

𝑘1 + 𝑘2 (6.2)

In case of a wall made of three layers, the equation used is the (6.3):

𝐾𝑒𝑞 =(𝑆1 + 𝑆2 + 𝑆2)𝑘1𝑘2𝑘3

𝑘1 + 𝑘2 + 𝑘3 (6.3)

Where 𝑆1, 𝑆2, 𝑆3 and 𝑘1, 𝑘2, 𝑘3 are, respectively, the thickness and the thermal conductivity

of each layer. The values to be put in these equations are showed in Table 6.3 below, and

they are taken from datasheets of materials:

Material Thermal conductivity [W/mK] Thickness [µm]

Glue – Polytech 601 EP 0.2 25

Kapton - 50 0.8 50

Kapton - 25 0.12 25

Table 4.3 – Characteristics of materials inserted in equations (6.2) and (2.3).

It follows that values for interfaces coming from the application of (6.2) and (6.3) that are

inserted in Fluent are the following of Table 6.4:

Material Thermal conductivity [W/mK] Thickness [µm]

Glue - Kapton 25 - Glue 0.163 75

Glue – Kapton 50 - Glue 0.15 100

Thermal Grease 4 500

Nickel 83 200

Glue-Kapton 0.32 50

Table 6.4 – Equivalent thermal conductivity of thin layers.


63

Glue-Kapton25-glue layers are inserted in the area between spacer and silicon sensor. Glue-

Kapton50-glue layers are the ones between the heating resistances and the silicon sensor.

Glue and Kapton, on the other hand, is inserted on the area of the silicon sensor where there

is glued foil of Kapton, but the shadow of the spacer is not present. Nickel is the material of

the thermal resistance, and Thermal grease is inserted in area where spacers are in contacts

with cold faces of Peltier cells (see Section 7.3 for more details). In latter areas, also

temperatures are also imposed: they are selected respecting temperatures of Peltier cells (see

sections 7.6 and 7.7). These values for temperatures are resumed in Table 6.5:

Area T in simulation N°1 [°C] T in simulation N°2 [°C]

Stump Bridge area -0.17 -4.24

Lower Spacer area -2.95 -4.19

Upper Spacer area 1.18 -2.94

Table 6.5 – Imposed temperatures.

In all the remaining external surfaces of the model, convective and radiative boundary

conditions are set. As far as convection, a convective coefficient of 7 W/m2K is imposed.

This value is found to refine and to adjust results after experimental simulations. For what

concerns radiation, the emissivity of sensor surfaces has been evaluated by an emissometer,

as shown in Figure 6.11:

Figure 6.11 – Pictures representing the measurement of emissivity: on the left, the calibration process of the instrument, on the right the measurement on the silicon sensor surface.


64

The first step to use this instrument, is to calibrate it by measuring emissivity of reference

objects of known values: one of them has high emissivity, and the other has low emissivity.

After calibration, the measurement on the sensor areas was done. Values to be inserted in

the Fluent software are reported in Table 6.6.

External surfaces Emissivity (measured) Convection coefficient

Top sensor face 0.45 7

Bottom sensor face 0.03 7

Other surfaces 0.9 7

Table 6.6 – Reference values for boundary conditions on the external surfaces of the module.

It can be noted that the emissivity on the top face of the sensor is higher than the one of the

bottom surface: this happens because of the effect of thermocouples and relative thermal

paste. The temperature of the ambient is set to 23 °C.

Two kinds of simulations are done: in the first one, only the cooling effect of refrigerators is

simulated. A preview of this simulation is presented in Figure 6.12, with details of the

spacers in Figure 6.13:


65

Figure 6.12 – Contour Plot of temperature obtained inserting previous boundary conditions in simulation. Temperature are expressed in K.

Figure 6.13 – Detail of temperature field on spacers, in simulation type number one. Temperatures are expressed in Kelvin.


66

In the second type of simulation, next to the same boundary conditions of the previous case,

the heating effect of hybrids is inserted. This is done by identifying two areas in the opposite

sides of the upper face of the sensor: a heat generation of 1.5x107 W/m3 is imposed for these

regions. The contour plot of temperature obtained is presented in Figure 6.14, ad details of

the temperature of spacers are shown in Figure 6.15.

Figure 6.14 – Contour plot of temperature in simulation number two; temperatures are higher than before as a consequence of heating elements. Temperatures are expressed in Celsius.

Figure 6.15 – Details of temperature field on the spacers. Temperatures are expressed in Celsius.

67

Chapter 7

EXPERIMENTAL VALIDATION

7.1 Introduction to the Validation Procedure

The validation process is always necessary to evaluate the quality of the model, and in

particular to estimate the modelling error. This process consists in reproducing the operating

conditions of the model in laboratory, in the same way they have been simulated in the

software: doing so, the main physical quantities of interest can be monitored experimentally

and then compared with those that come out from the numerical model. The result of this

comparison is exactly the modelling error. At this stage it is not necessary to reproduce the

real operating conditions of the module as they are in real functioning, but it is sufficient to

reproduce a condition reasonably similar. What is needed instead, is that the condition tested

experimentally is exactly the same simulated by the FVM. Once this validation process is

completed, the real operating condition can be simulated through the software alone, being

confident that the model has already been validated. This is particularly useful when it is

necessary to validate models that are characterised by extreme real operating conditions

which are difficult to reproduce in laboratory. In the case of this thesis, it was very onerous

to reproduce the actual operating conditions of the 2S module, in particular with respect to

the cooling temperatures (first of all the liquid C02 at -35 ° C). For these reasons it has been

adopted a different technique of cooling, based on Peltier cells. Therefore, a cooling system

for thermal study of the 2D module has been constructed, whose components are

summarized in Table 7.1. In next paragraphs, the various components used to set up this

experimental test bench will be presented, as well as their sizing procedure. The 2S module

assembled to carry out the experimental tests is also presented. It presents slight changes

compared to the theoretical version. These changes were made to allow consistency between

the test conditions and the boundary conditions of the finished volume model. In Figure 7.1

an image of the overall system as used for the experimental tests is reported.


68

Components Quantity

Peltier cell 5

Heatsink 5

Centrifugal fan 5

ABS ducts 5

Heater strip 2

Thermocouples 32

Baseplate 1

Cable terminal block 1

9 V fan power supply 1

Adjustable power supply for cells 5

Adjustable power supply for heaters 1

Data acquisition system for thermocouples 1

Table 7.1 - Components used for the assembly of the test bench for the experimental thermal analysis of the 2S Module. For each component the quantity needed is also presented.

Figure 7.1 - Picture of the test bench for the 2S Module thermal analysis during a test run.


69

7.2 The 2S Module for Tests

The module where the tests were carried out is a two strips prototype module with 1.8 mm

thickness, assembled ad hoc for these studies by the INFN (Istituto Nazionale di Fisica

Nucleare) section of Perugia. The module is a prototype because the production phase of 2S

sensors for CMS phase-2 has not started. The silicon sensor that constitute the module was

produced directly from the official manufacturer Hamamatsu [28]. Since in the prototyping

phase it is very difficult to find original sensors, the module has been built with only one

silicon sensor (the only one on the top) instead of two; this does not create particular

problems in the validation process because the planar symmetry of the module can be

exploited, in addition to the transversal one shown in Section 6.2. Obviously, it is necessary

to modify the 3D CAD geometry of the simulated model in order to take into account this

exclusion. The kapton sheets used has been purchased from RS [29], and it has the exactly

required thickness of 25 μm as well as mechanical, electrical and thermal characteristics

compatible with those of theoretical use. The glue used is the two-component epoxy

Polytech 601 [30], with low viscosity. The two components were resin (part A) and hardener

(part B) and their quantity in proportion were respectively 100 and 35. The spacers were

instead produced directly in the mechanical workshop of the Physics Department of Perugia.

They were made with a computerized numerical control milling machine. The material used

was pure aluminium, and not aluminium carbon fibre. Two terminals have also been

connected to the module, through wire bonding; one on the upper face of the sensor, and one

on the bottom. They allow to provide power supply for the Bias Voltage. The machine for

wire bonding, available in the clean room of the department of physics of Perugia, is showed

in Figure 7.2. In addition to the thermal power generated by the leakage currents due to this

voltage, the heat generation of the electronic boards has been reproduced through the effect

of heating resistance. Two resistive strips of Nickel were glued on two opposite sides of the

silicon sensor using Loctite glue. The two strips are then connected in series to a bench

power supply which allows the circulation of current necessary for heating by Joule effect.

The measured electrical resistance of the two strips is 0.18 Ω. The two strips are used as heat

generators to reproduce the effect of the two Front-ends Hybrids.


70

Figure 7.2 – On the left the wire bonding machine of the Perugia INFN section laboratory used to connect the strips of the silicon sensor to the Bias Voltage Pins. On the right the silicon module for tests is presented.

These are in fact connected to the module by wire bonding and encapsulation, and then

provide a bridge for the heat to move from the board to the silicon. The Service Hybrid is

not directly connected to silicon with wire bonding, so no heat source has been arranged to

reproduce its effect. To ensure electrical insulation between the heating strip and the upper

face of the sensor, a strip of 50 µm thickness Kapton is inserted between the two. A new

“sandwich“ structure made by glue, Kapton and glue is then created.

7.3 Peltier Cells

Peltier cells are thermoelectric devices. The thermoelectric effect is the direct conversion of

temperature difference to electric voltage and vice versa. A thermoelectric device creates

voltage when there is a different temperature on each side. Conversely, when a voltage is

applied to it, it creates a temperature difference [23]. The thermoelectric effect therefore

includes three different physical phenomena that go under the name, respectively, of

Seebeck effect, Peltier effect, and Thomson effect. We have the first effect when we join

two dissimilar metals in two different points, and we put them at different temperatures:

inside the circuit formed by the two metals will flow an electric current. This principle is

used for the construction of thermocouples. We have the Thomson effect when an electric

current is passed through a conductor having a temperature gradient over its length: heat will

be either absorbed by or expelled from the conductor. The Peltier effect, on the other hand,

mirrors the Seebeck effect, and it occurs when a current flow in a circuit consisting of two


71

different conductive or semiconductor materials: in one junction a lowering of temperature

occurs while in the other junction the temperature increases. Therefore a device that works

by exploiting the Peltier effect acts as an electric heat pump. These devices are called Peltier

cells, and are made up of arrays of doped semiconductor materials, alternatively of type p

and type n. They are connected electrically in series, and thermally in parallel. The scheme

of functioning is shown in Figure 7.3.

Figure 7.3 – Peltier cooling by multiple pellets of N and P type semiconductors.

The whole device is completed by creating a matrix with many arrays of this type and placing

a ceramic substrate on the upper and lower faces of this matrix. What is obtained is a device

that in very little space is able to absorb heat from a cold side and transfer it to a hot side.

The cold wall of this device can be used to simulate the cooling system of the 2S module. In

order to select the most suitable Peltier cell for our purposes, we have developed a

mathematical cell model based on the studies [24] [25] [26]. Generally, Peltier cell

manufacturers report four characteristic parameters to describe cells: 𝐼𝑚𝑎𝑥, 𝑉𝑚𝑎𝑥, 𝑄𝑚𝑎𝑥 e

𝐷𝑇𝑚𝑎𝑥 that are respectively, the maximum current allowed, the maximum voltage allowed,

the maximum heat absorbed from the colder face and the maximum temperature difference

between the two faces obtainable. Given these quantities, formulas are proposed [27] to find

some characteristic quantities of the cell, which are the Seebeck coefficient S𝑚, the electric

resistance R𝑚 and the thermal conductivity K𝑚:

S𝑚 = 𝑉𝑚𝑎𝑥

𝑇𝑎 (7.1)


72

R𝑚 =(𝑇𝑎 − 𝐷𝑇𝑚𝑎𝑥)𝑉𝑚𝑎𝑥

𝑇𝑎𝐼𝑚𝑎𝑥 (7.2)

K𝑚 =(𝑇𝑎 − 𝐷𝑇𝑚𝑎𝑥)𝑉𝑚𝑎𝑥𝐼𝑚𝑎𝑥

2𝑇𝑎𝐷𝑇𝑚𝑎𝑥 (7.3)

In equations (7.1) (7.2) and (7.3), Ta is the temperature of the ambient. These three quantities

are very useful as they allow to evaluate directly the heat absorbed by the cold face 𝑄𝑐 and

the one taken off by the hot face 𝑄ℎ:

𝑄𝑐 = 𝑆𝑚𝐼𝑇𝑐 −𝐼2𝑅𝑚

2− 𝑘𝑚𝐷𝑇 (7.4)

𝑄ℎ = 𝑆𝑚𝐼𝑇𝑐 +𝐼2𝑅𝑚

2− 𝑘𝑚𝐷𝑇 (7.5)

In equations (7.4) and (7.5), I is the current flowing in the cell circuit and DT the temperature

difference between hot and cold faces of the cell. The conceptual scheme of the Peltier cell

is shown in Figure 7.4 below:

Figure 7.4 -Schematic of the Peltier cooling module with a heatsink on the top and a fan for ventilation. On the right there is the corresponding mono dimensional thermal resistance network: Rha is the thermal

resistance of the heatsink, and Rjc the one relative to the interface between the cold side of the cell and the object to be cooled. The arrows indicate the heat flows.


73

In order for the heat Qc to be absorbed by the cold face, it is necessary that the heat Qh is

dissipated in the hot face: this is the key point for the operation of the cell. At the aim of

dissipating the heat Qc, a finned metallic heatsink is inserted in contact with the hot wall,

and some thermal paste is interposed between them to ensure correct thermal coupling.

Knowing the temperature of the ambient, the temperature of the hot face Th and the heat to

be dissipated Qc, it is possible to calculate the dissipation system thermal resistance

necessary to guarantee operation. The equation for calculating the thermal resistance suitable

for the heatsink is the following:

Rℎ𝑎 =(𝑇ℎ − 𝑇𝑎)

𝑄ℎ

(7.6)

In order to automatically manage all the calculations to choose the best Peltier cell for the

purposes of this thesis, a Matlab program was created. The script of this program is reported

in Appendix. By inserting in this program the parameters related to a lot of commercial

Peltier cells, the most suitable one turns out to be the ET-071-10-13 cell from the

manufacturer Adaptive [31]. The aforementioned cell has the characteristics of Table 7.2:

Peltier Cell ET-071-10-13

Imax 3.9 [A]

Vmax 8.8 [V]

Qcmax 18.7 [W]

DTmax 74 [°C]

Table 7.2 - Characteristic parameters of the selected Peltier cell, in the order: maximum current allowed, maximum voltage allowed, maximum heat absorbed from the colder face and maximum temperature

difference between the two faces obtainable

In addition, the following operating conditions of Table 7.3 are hypothesized and chosen to

maximize performance of the cell and to obtain an achievable and not too powerful

dissipation system:

Imposed operative conditions

Tc 267 [°C]

DT 46 [°C]

Qc 5 [W]

Ta 296 [°C]

Table 7.3 – Boundary conditions imposed for the Peltier cell


74

The Matlab program then returns the following output data of Table 7.4.

Table 7.4 – Parameters of the cooling module obtained from the Matlab script.

Dimensions of the selected Peltier cell are resumed in Figure 7.5.

Figure 7.5 - Peltier Cell ET-071-10-13. Referring to the image on the right, the dimensions of the cell are A=20 mm, B=20 mm, H=3.6 mm and L=100 mm.

7.4 Heatsink System

The Peltier cell presented in the previous section has to be connected to a heat sink with a

lower thermal resistance than Rha=1.5812 K/W, in order to function correctly. Moreover, the

dimensions of the heat sink have to comply some criterion of choice: in fact they have to be

comparable with the dimensions of the cell in order to guarantee a correct coupling. After

Cell Parameters

Sm 0.02953

Rm 1.6961

Km 0.17431

Z 0.0029496

COP 0.46548

Temperatures

[°C]

Th 40

Tc -6

Tj -4.44

Powers [W]

Qc 5.0008

Qh 15.7485

Qe 10.7434

Heatsink Resistance

[k/w]

Rha 1.5812


75

consulting several product catalogues then, the heatsink ICK S 25x25x18.5 was chosen,

produced by Fischer Elektronik [32]; some characteristics are show in Figure 7.6.

Figure 7.6 - Geometrical dimensions in [mm] of the heatsink ICK S by Fischer Elektronic (on the left) and variation of its thermal resistance with the velocity of the forced air flow (on the right).

The hot face of the Peltier cell is placed in contact with the flat side of the heat sink (see

Figure 7.7); a high conductivity thermal grease RS is put to ensure a correct thermal coupling

between the two interfaces. In the whole system, five Peltier cells and five heat sinks are

used: each of them will cool the five protruding parts of the spacers.

Figure 7.7 – Coupling scheme of a Peltier cell with the respective heatsink. Between the two contact faces some thermal paste with high thermal conductivity is inserted.


76

The heat sink has a thermal resistance greater than 4.5 K/W if it works in natural convection

conditions. To reach the suitable thermal resistance Rha=1.5812 K/W is necessary to make it

working under forced convection conditions, with a velocity of the air higher than 4 m/s. To

make so, a fan is needed. For this cooling system a Sunon GB1205PKV1-8AY centrifugal

fan [33] is used, generating an air flow of 9.68 m3/h is used. Its geometrical sizes are shown

in Figure 7.8. The size of its outlet nozzle is 23x16 cm, so it produces velocity equal to:

𝑣 = 9,68

3600 ∙ 0.023 ∙ 0.016= 7.3 𝑚/𝑠 (7.7)

The found speed value is higher than the required one, then this fan is suitable for this project.

Figure 7.8 – Geometrical dimensions of the Sunon GB1205PKV1-8AY fan

In order to conduct the flow of air from the fan to the heat sink, special ducts have been

ideated, which have a rectangular opening on one side, where the fins of the heat sink can

be inserted. These ducts are long enough to release the exhaust air in an area far from the

module, such that it does not affect the natural convection conditions on the sensor faces.

They have been designed to make the structure as symmetric as possible. The ducts also

provide structural support for the fans and Peltier cells. They were modelled with Solidworks

2016 and realized by additive manufacturing in ABSplus-P430. The 3D printer was made

available by the mechanical workshop of the Physics Department of the University of

Perugia. The system is then placed on a flat square wooden slab, on which the electrical


77

connections of the fans and the cells have also been joint into, which flow into a single

terminal board (see Figure 7.9). The five fans are connected in parallel, and they are powered

to 9 Volts direct current. The Peltier cells, on the other hand, are connected each one to a

different power supply, which allows a voltage regulation from 1 to 30 Volts and a current

regulation from 1 to 5 A. The regulation of each Peltier cell is then done manually.

Figure 7.9 - 3D CAD drawing of the ducts for the cooling system (on the right), with the silicon sensor aligned in correct position and picture of the whole cooling system (on the left).

7.5 Thermocouples

In order to measure the temperature at various points in the system, thermocouples are used.

These devices consist of two wires of different materials joined together on two ends: one

of the two joints is called the measuring joint, and it is put in contact with the target, the

other is the reference joint, which temperature is known. The device thus created exploits

the Seebeck effect, and it produces a current proportional to the temperature of the hot joint.

In order to guarantee a correct coupling between the thermocouples and the object to be

measured, RS thermal paste is used. On each Peltier cell, a thermocouple is used to measure

the temperature of the cold face, and another one to measure the temperature of the hot face,

for a total of 10 thermocouples for cells only. Three thermocouples were then used to


78

measure the air temperature at the plug of three fans: two of them are related to the conduits

of the cells that will host the main bridge spacers, and one is attached the cell hosting the

stump bridge. For the same conduits, three more thermocouples are placed at the outlet, to

detect the temperature of outlet air flow after it has cooled the heat sink. The thermocouples

described above are used only to control the cooling system. In order to perform

measurements on the sensor of the module, 16 thermocouples are used, arranged on the

upper surface of the silicon, to form a 4x4 matrix (see Figure 7.10).

Figure 7.10 - Details of the thermocouples placement. On the right the matrix of 4x4 thermocouples to measure the temperature field on the silicon sensor. On the left a lateral view of the system is presented:

sensors for the silicon module are suspended from the above.

They are attached to the silicon sensor with a small piece of adhesive tape, and at the

interface a small drop of thermal paste is placed to improve thermal contact. These

thermocouples are supported by a rod placed above the module, in order to keep the wires

suspended, falling from above. A total of 32 thermocouples are used in this system. In Figure

7.11 is presented a schematic view of thermocouple dispositions on the silicon sensor.


79

Figure 7.11 – Schematic view of thermocouples disposition on the upper face of the silicon sensor.

They are connected to an acquisition system based on Hardware National Instruments and

Software Labview 2014 [34]. This system allows real-time display of the temperature values

of each individual thermocouple: the user interface is in Figure 7.12. It also permits to carry

out temporal signal acquisitions on time intervals chosen by the user.

Figure 7.12 – Details of the data acquisition system: thermocouples are connected to the National Instrument data acquisition system (on the right) which converts the signal from analogue to digital. This

hardware is then connected to a desktop PC through ethernet cable, where signal is read by LabView software. On the left there is its frontal panel layout, where the user can read or record the value of each

thermocouple.


80

7.6 Test Number 1

In the first test the module is cooled by the five Peltier cells; no heat sources are introduced.

Before placing the module on the cooling system, some thermal grease with high thermal

conductivity is put on the bottom surfaces of the spacers which are in contact with Peltier

cells. When the module is placed on the test bench, particular attention has been made to

make each end of the spacers adhering perfectly to the respective cold face of the cell. Then

the cells and the fans are switched on. Checking in real time the temperature of the cold faces

of the cells, the supply voltage has been manually in order to obtain the setpoint value for

them. It was decided to supply each cell separately regulated because it was observed from

previous tests that they have a different response with same input. This is probably due to

different performance of each cell, because of the manufacturing process or assembly of the

cooling system. The cells are regulated up to a voltage of V=3 Volts. After this step, the

system has been left running for several minutes in order to stabilize the transients and to

reach the stationary regime. With the same voltage, the temperatures of the cold faces do not

reach the same value, as expected from previous tests. However, since the amplitude of the

temperature oscillations is not so high, a more refined regulation to have same temperatures

has not been made in this first test. Once acceptable stabilized conditions are reached, data

acquisition has begun for a period t of 3,800 seconds.

Figure 7.13 – Scheme of Peltier cells numbering. The corresponding temperatures of cold faces are, in the order, from left to right and from top to bottom: T4, T2, T5, T1 and T3


81

For this test and next, the enumeration criterion presented in Figure 7.13 has been adopted

to identify cell cold temperatures. Data have been exported to Microsoft Excel where

temporal trends for each temperature signal have been plotted. They are shown from Figures

from 7.14 to 7.18.

Figure 7.14 – Temperature variation of the cold face for cell n° 1, in test n°1.

Figure 7.15 Temperature variation of the cold face for cell n° 2, in test n°1

Figure 7.16 – Temperature variation of the cold face for cell n° 3, in test n°1

-0,5

-0,3

-0,1

0,1

0,3

0,5

0 500 1000 1500 2000 2500 3000 3500 4000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°1

-1

-0,8

-0,6

-0,4

-0,2

0

0 500 1000 1500 2000 2500 3000 3500 4000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°2

-3,5

-3,3

-3,1

-2,9

-2,7

-2,5

0 500 1000 1500 2000 2500 3000 3500 4000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°3


82


Figure 7.18 Temperature variation of the cold face for cell n° 5, in test n°1

A certain oscillation values around the measurement range can be observed. A time range

has been extracted between 1,500 and 2,000 seconds, where all the temperature values are

more stable; and then an average temperature has been calculated. In this interval the

amplitude oscillation of temperatures is smaller than in other intervals: in Figure 7.19 the

temperature trend of a thermocouple measuring the silicon surface is shown.

1

1,1

1,2

1,3

1,4

1,5

1,6

0 500 1000 1500 2000 2500 3000 3500 4000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°4

-3,5

-3,3

-3,1

-2,9

-2,7

-2,5

0 500 1000 1500 2000 2500 3000 3500 4000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°5


83

Figure 7.19 – Temperature signal of one thermocouple limited on the set time range of [1,500 -2,000] seconds. It is scaled to 0. The amplitude oscillation is around 0.2°C.

Processing the temperature of each thermocouple of the silicon top face, a 4X4 matrix is

obtained. Each element of the matrix is an average value of temperature on the corresponding

measuring point. The matrix has the shape of (7.8):

T(I,J)test 1=[

11.39 13.4512.56 13.34

13.71 12.6414.24 13.67

12.21 12.8210.32 10.67

13.65 13.1711.49 10.85

]

(7.8)

I and J are respectively the x and y coordinate of thermocouples. These values are then

interpolated through software Surfer 9 [35]. What is obtained is a thermal map of the silicon

top face; this map is shown in Figure 7.20.

11

11,2

11,4

11,6

11,8

12

0 50 100 150 200 250 300 350 400 450 500

Tem

per

atu

re [

T]

Time [s]

Termocouple S1 Temperature


84

Figure 7.20 - Thermal contour plot T (x, y) of silicon sensor upper face obtained with experimental test number 1.

7.7 Test Number 2

For the test number 2, in addition to activating cooling as in test number 1, a heat generation

is provided through thermal heating strips glued on two sides of the silicon sensor. The

heating effect of electronic boards is so introduced. In order to obtain a set point value for

the supply current to give to the strip, the equation (7.9) is used:


85

𝑄 = 𝑅𝐼2 (7.9)

R is the electrical resistance of the strip, and its measured value is R=0.18 Ω. After giving

1.9 Amperes current to heating circuit, Peltier Cells are switched on. In this case they are

regulated manually in order to reach a common temperature of -3.5°C. However, after

stabilization, each cell reaches a different temperature close to -3.5°C. With a manual

adjustment of the cooling system is very difficult to ensure simultaneously stationary

conditions and setpoint temperature for cells. The implementation of an electronic PID

(Proportional-Integrative-Derivative) control on the system would be useful to fix this issue.

In the case of this test, priority is given to the condition of stationary regime, in order to

guarantee the stationary conditions also in the FVM simulation. To make this achievable,

temperatures with a certain deviation from the setpoint are accepted, as long as they are

stationary. Data have been recorded for a time interval of 8,000 seconds. Temperature data

of cold faces of Peltier cells have been reported in Figures from 7.21 to 7.25.

Figure 7.21 - Temperature variation of the cold face for cell n° 1, in test n°2

-5

-4,5

-4

-3,5

-3

-2,5

-2

0 1000 2000 3000 4000 5000 6000 7000 8000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°1


86

Figure 7.22 -- Cold face temperature variation for cell n° 2, in test n°2

Figure 7.23 - Temperature variation of the cold face for cell n° 3, in test n°2


-5

-4,5

-4

-3,5

-3

-2,5

-2

0 1000 2000 3000 4000 5000 6000 7000 8000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°2

-5

-4,5

-4

-3,5

-3

-2,5

-2

0 1000 2000 3000 4000 5000 6000 7000 8000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°3

-5

-4,5

-4

-3,5

-3

-2,5

-2

0 1000 2000 3000 4000 5000 6000 7000 8000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°4


87

Figure 7.25 -- Temperature variation of the cold face for cell n° 5, in test n°2

In this test, as the previous one, a time range where the signal is more stable is extracted.

The chosen values are included between 7,500 and 8,000 seconds. The temperature signal

of one thermocouple measuring the silicon surface is proposed in Figure 7.26. It can be

seen that the amplitude of temperature oscillation is well included in a maximum range of

0.2 °C.

Figure 7.26 – Temperature variation of the thermocouple S1 on the silicon surface, in the selected interval of time [7500-8000] seconds, scaled to 0.

For each thermocouple, the mean value is calculated in the selected time interval. A 4x4

matrix is obtained: each element of it is the temperature on a point on the surface of the

silicon, where the thermocouple is present. This matrix is shown below in (7.10):

-5

-4,5

-4

-3,5

-3

-2,5

-2

0 1000 2000 3000 4000 5000 6000 7000 8000

Tem

per

atu

re [

°C]

Time [s]

Cold face N°5

13,5

13,7

13,9

14,1

14,3

14,5

0 50 100 150 200 250 300 350 400 450 500

Tem

per

atu

re [

°C]

Time [s]

Termocouple S1 Temperature


88

T(I,J)test 2=[

14.05 15.0015.17 15.19

15.64 15.2415.82 16.29

15.53 14.5112.44 11.28

14.86 16.0112.36 12.44

]

(7.10)

I and J are respectively the x and y coordinate of thermocouples. These values are

interpolated as the previous test with Surfer 9. The interpolation algorithm used is based on

the Kriging method. This spatial interpolation is based on the assumption that the quantity

varies in the space with continuity: and it uses the autocorrelation function. The thermal map

of the silicon top face obtained is shown in Figure 7.27. Comparing Figure 7.20 with Figure

7.27, it is evident that the second one has higher temperature, as a consequence of the thermal

sources introduced by the heating strips. In addition, also lines of equal temperatures have a

different positioning in space.

Figure 7.27 - Thermal map T(x,y) of silicon sensor upper face obtained with experimental test number 2.

89

Chapter 8

ANALYSIS OF RESULTS

8.1 Simulation N°1 compared with Test N°1

The FVM simulation number 1 made with Fluent and test number 1 are developed to be

compared to each other. By comparing thermal map of silicon sensor upper surface obtained

with Fluent and the thermal map obtained by experimental test number 1, a difference of

results is evident, even if they have been set with same conditions. The two contour plots are

resumed in Figure 8.1.

Figure 8.1 - Comparison between thermal fields of the upper face of the silicon sensor obtained by Fluent simulation (on the left) and experimental test (on the right).

It should be noted that the comparison has to be made between the whole area of the

experimental contour plot and the area of the Fluent one enclosed in the rectangular line.

This is due to the fact that thermocouples in tests are placed only in the central area of the

sensor and not in edges, so the related chart is about the area where sensors are present. By

analysing data, a region on the upper right side of the experimental data presents

ANALYSIS OF RESULTS

90

temperatures higher than the simulation ones. This trend was detected in all the tests carried

out in laboratory. In order to give an evaluation of this difference, data have been exported

from Ansys to Matlab, where a particular script has been made to select temperature data at

user defined coordinates. This script is presented in Appendix. In this way, temperature data

corresponding to measurement points can be selected from the simulated model and

compared directly with experimental data. After calculating the module of difference

between the two set of data, the bar diagram of Figure 8.2 is obtained.

Figure 8.2 – Module of temperature difference between experimental test number one and corresponding Ansys simulation.

The maximum value of the temperature difference revelated is DTmax=0.790 °C. The mean

value of the difference on the whole sensor is 𝐷𝑇 =0.478 °C. It can be noted from the latter

diagram that in the right region the error committed is higher than the other. Instead of doing

this, if only the eight thermocouples of the left half of the module are considered, and their

values are mirrored on the right half, the similarity of results is greatly increased.

Considering the symmetry of model and boundary conditions, it is reasonable to expect a

symmetrical thermal field. The process followed was to take data from the first two columns

of matrix (7.8) and mirror them on the other two columns. What is obtained is the (8.1):

0

0,2

0,4

0,6

0,8

1

Y

Tem

per

atu

re d

iffe

ren

ce [

°C]

X

ANALYSIS OF RESULTS

91

T(I,J)mirror=[

11.39 13.4512.56 13.34

13.45 11.3913.34 12.56

12.21 12.8210.32 10.67

12.82 12.2110.67 10.32

]

(8.1)

Data have been interpolated with Kriging algorithm and the new contour plot obtained is

compared with the Fluent one, in Figure 8.3:

Figure 8.3 - Comparison between thermal fields of the upper face of the silicon sensor obtained by Fluent simulation (on the left) and mirrored values of temperatures of experimental data (on the right).

In this case the similarity is better than before. In order to evaluate the deviation of results

between the real case and the simulation model, which is proportional to the modelling error,

the punctual difference of the two thermal fields has to be calculated. Values of temperature

on the upper face of the silicon are exported from Ansys to Matlab. A specific script has been

written to find temperatures from the Ansys file at a desired (x, y, z) spatial coordinate. Whit

this algorithm, it was easy to find temperature values in the FVM in the corresponding points

where thermocouples were placed in tests. More precisely, for each coordinate (x, y, z) of

searched point, not only one value of temperature has been taken, but all the temperatures

enclosed in a square area of 2 mm. Then, for each selection, the mean value has been

calculated as reference value. This was made because the thermocouple with thermal paste,

does not provide a punctual measurement, but an average value on a very small area.

Operating in this way, sixteen values are obtained from Fluent simulations, that are directly

ANALYSIS OF RESULTS

92

comparable with the ones derived from experimental data. The module of difference between

values of tests and simulation has been calculated by:

𝐷𝑇 = |𝑇𝑡𝑒𝑠𝑡 − 𝑇𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛| (8.2)

Results of this calculation for each one of the sixteen points of measurement are shown in

Figure 8.4:

Figure 8.4 – Temperature difference between discrete values obtained in Fluent and values measured in test number 1.

The maximum value of the temperature difference is DTmax=0.559 °C. The mean value of

the difference on the whole sensor is 𝐷𝑇 =0.407 °C. Values found by equation (8.2) are then

interpolated with Kriging algorithm and plotted with Surfer 9, to have a map distribution of

the differences. The contour plot is shown in Figure 8.5.

0

0,2

0,4

0,6

0,8

1

Y

Tem

per

atu

re d

iffe

ren

ce [

°C]

X

ANALYSIS OF RESULTS

93

Figure 8.5 – Interpolated module of temperature difference on the measuring area of silicon sensor.

Calculations made so far are executed considering only the left side of the module. But what

happened to the right side has to be discussed. After the tests, the module has been removed

from the test bench and analysed with a microscope, thanks to the help of the Physics

Department of Perugia. In Figure 8.6 a picture of the module during the check is provided.

Figure 8.6 -Picture of microscope used to analyse the module after the thermal tests.

By inspecting the module, it has observed that on the top right corner (looking from above,

as it is presented on Figure 12), there is a region on the spacer-Kapton interface were the

ANALYSIS OF RESULTS

94

glue is absent. In other words, in this area, the spacer and the silicon sensor are not well

matched together. Instead of glue, air is present in the layer, and air has a thermal

conductivity that is an order of magnitude lower respect to the glue. This means that heat

flux from silicon to spacer is reduced considerably in that region, so the resulting temperature

is higher. By the microscope it is evident that in this area the spacer is detached from the

sensor as shown in Figure 8.7

Figure 8.7 -Two images of interfaces between spacer and silicon sensor taken by microscope. On the left, a part of the module where the two components are well matched; on the right there is the investigated

region on the north-east area of the module where spacer and silicon sensor are detached.

This gap is due to the mechanical manufacturing process of the spacer: its surface was not

planar, and this out of tolerances made the glue not to adhere. In order to estimate the

amplitude of the gap, a thin Kapton foil of 50 µm thickness is inserted through it as reported

in Figure 8.8. The next step consisted of simulating this issue with the Fluent software and

check if the new configuration is closer to the reality coming from tests. To introduce the

effect of the deflection of spacer, the geometrical shape of the 3D CAD model has not been

modified, but different conditions of thermal resistances have been given to the interface.

First an area has been identified in the common surface between spacer and sensor. This area

has then been divided in three parts. In each part, a different value for thickness is set as

boundary condition.

ANALYSIS OF RESULTS

95

Figure 8.8 – Picture showing a Kapton foil of 50 µm thickness passing through the interface. The amplitude of the gap is estimated about 100 µm.

In order to reproduce the deflection of spacer, its deformed edge has been considered as a

half sine wave. The area subtended by this curve is the air layer infiltrated between the spacer

and the silicon sensor. This area is than discretized in three parts as shown in Figure 8.9: the

central rectangle has the thickness of 100 µm, and double length in comparison with the

others.

Figure 8.9 – Discretization of air gap between the spacer and the silicon sensor, on the right upper side corner of the module

ANALYSIS OF RESULTS

96

The problem in this reasoning is that the Fluent model made represents only a half of the

module, so it can’t be used to simulate different boundary conditions from one half to the

other: they are just specular.

Figure 8.10 – Temperature plot obtained by matching results of two Fluent simulations, one for the well glued spacer-sensor interface (on the left) and one for the bad glued one (on the right). Horizontal axe is the

X coordinate, and the vertical one is Y, both in mm. Temperature is expressed in Kelvin.

In order to reproduce in a single plot of temperature the asymmetry found in tests, two

different simulations have to be done with the software, one for the left side (that is the same

already done) reproducing the effect of a well-matched spacer, and another one for the right

side, that reproduces the effect of the bad glued spacer. The results of the two simulations,

each one reproducing a half, are then matched together to obtain the whole field, the

drawback of this procedure is that on the line of matching, boundary conditions are not

correlated, and a discontinuity of the field in the middle is present. The simple operation of

matching together two half simulations produced the temperature field of Figure 8.10,

plotted in Matlab after exporting data from Fluent: analysing this is not completely correct.

The way to solve this issue is taking the temperature value of some points of the field, with

a Matlab algorithm, and then to interpolate data of both the left side and the right side

together. The results of the interpolation are compared with test number one data in Figure

8.11. Now the two contour plots are visibly more similar.

ANALYSIS OF RESULTS

97

Figure 8.11 – Comparison between test number one interpolated data (on the right) and data coming from Fluent (on the left), after the insertion of the effect of badly matched interface spacer-sensors.

In this case the difference between temperature values on corresponding points of the two

graphs are calculated. They are still proportional to the modelling error, but they also take

into account the error of interpolations and the error due to discontinuity of boundary

conditions in simulations. Module of temperature differences are reported in Figure 8.12.

Figure 8.12 - Temperature difference between discrete values obtained by matching two Fluent simulations and values measured in test number 1.

0

0,2

0,4

0,6

0,8

1

Y

Tem

per

atu

re d

iffe

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ce [

°C]

X

ANALYSIS OF RESULTS

98

The maximum value calculated is DTmax=0.66 °C and the average is 𝐷𝑇 =0.354 °C. It can be

noted that on the right side of the module, the temperature difference between experimental

test and simulation has lowered compared to previous cases. In the middle, a certain error is

still present, due to interpolations of two Fluent simulations. Data of module temperature

difference have been also interpolated on the measuring area, as shown in Figure 8.13.

Figure 8.13 - Interpolated module of temperature difference on the measuring area of silicon sensor, in the case of comparison between data of test number 1 ad data reconstructed by matching two Fluent

simulations.

Interpolated data of temperature difference show that in the vertical axe which splits the

area in two halves, a bigger deviation is present. This confirms that merging two fluent

simulations, it is difficult to guarantee continuity.

8.2 Simulation N°2 compared with Test N°2

The thermal map of the upper face of the silicon sensor is presented in Figure 8.14, both the

one obtained by Fluent software and the one coming from test number 2.

ANALYSIS OF RESULTS

99

Figure 8.14 - Comparison between thermal fields of the upper face of the silicon sensor obtained by Fluent simulation (on the left) and experimental test (on the right).

In this case the effect of the heaters is evident, and the temperature is higher than before. The

bad connection between the spacer and the silicon sensor on the right-upper side, makes the

temperature of the experimental test higher than the simulated one. Difference in module

between temperatures of two sets of data (experimental and simulation) is plotted in Figure

8.15. Following the same procedure described in the previous section, data of the first two

columns of experimental data (representative of the well-matched interface) are mirrored on

the other side, obtaining the matrix (8.3) below:

T(I,J)mirror2=[

14.05 15.0015.17 15.19

15.00 14.0515.19 15.17

15.53 14,5112.44 11.28

14,51 15,5312.28 12.44

]

(8.3)

ANALYSIS OF RESULTS

100

Figure 8.15 - Module of temperature difference between experimental test number two and corresponding Ansys simulation.

These data are interpolated, and what is obtained is the map of Figure 8.16, compared with

the one obtained with Fluent.

Figure 8.16 - Comparison between thermal fields of the upper face of the silicon sensor obtained by Fluent simulation (on the left) and mirrored values of temperatures of experimental data type 2 (on the right).

The temperature difference in module between two cases (experimental and simulations) is

reported in the bar diagram of Figure 8.17.

0

0,3

0,6

0,9

1,2

1,5

Y

Tem

per

atu

re d

iffe

ren

ce [

°C]

X

ANALYSIS OF RESULTS

101

Figure 8.17 - Temperature difference between discrete values obtained in Fluent and values measured in test number 1.

The maximum value of the temperature difference calculated is DTmax=0.84 °C and the

average is 𝐷𝑇 =0.290 °C. At this point, the same reconstruction of the bad matched interface

between spacer and silicon sensor in made using Fluent. Two simulations are necessary also

in this case, one for the right side, and one for the left side of the spacer, as the model can

simulate only one half of the module at each time.

Figure 8.18 - Comparison between test number two interpolated data (on the right) and data coming from Fluent (on the left), after the insertion of the effect of badly matched interface spacer-sensors.

0

0,3

0,6

0,9

1,2

1,5

Y

Tem

per

atu

re d

iffe

ren

ce [

°C]

X

ANALYSIS OF RESULTS

102

With this procedure, we reconstruct again the thermal field on the whole face of the sensor

by interpolating data of two simulations. The results of reconstruction are showed in Figure

8.18, in comparison with the original thermal field obtained with the experimental test

number 2. The temperature differences between the two cases are then calculated and plotted

in Figure 8.19. The maximum value of the temperature difference calculated is DTmax=0.964

°C and the average is 𝐷𝑇 =0.288 °C.

Figure 8.19 - Temperature difference between discrete values obtained by matching two Fluent simulations and values measured in test number 2.

In this second last comparison it is evident that the insertion of the effect of bad gluing

between spacer and silicon has brought benefits, has happened in previous section: the

difference between temperature of test and simulation have lowered in comparison to Figure

8.15. These values are then interpolated on measuring area, and their map is the subject of

Figure 8.20, that confirms what has been said.

0

0,3

0,6

0,9

1,2

1,5

Y

Tem

per

atu

re d

iffe

ren

ce [

°C]

X

ANALYSIS OF RESULTS

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Figure 8.202 - Interpolated module of temperature difference on the measuring area of silicon sensor, in the case of comparison between data of test number 2 ad data reconstructed by matching two Fluent

simulations.

8.3 Simulation of the module in operative conditions

Once the Fluent model has been validated, a simulation in operative conditions can be

executed. In this case, the temperature of the ambient is set to -20°C, and the cooling effect

is obtained by imposing convective heat exchange with CO2 at -35°C, with a convective

coefficient h=5,000 W/m2K. These values are taken from [14]. The heating effect of Front

End Hybrids is quantified as Q=1.4 W, for the sake of safety. In this case configuration the

whole power produced by the two lateral electronic boards is transferred to the silicon sensor.

Heat produced inside the sensor due to leakage currents is also inserted: this value is

considered constant and set to Q=0.6 W [12]. The result of this simulation is showed in

Figure 8.21.

ANALYSIS OF RESULTS

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Figure 8.21 – Thermal contour plot of the module obtained by fluent, in the case of operative conditions of the module. Temperature is expressed in °C.

In this analysis both the top and the bottom sensors are present, as well as the air entrapped

between them and inside cavities.

Figure 8.22 – Thermal map on the silicon upper surface in operating conditions, in case of bad glued interface between sensor and spacer in the upper right side.

ANALYSIS OF RESULTS

105

Air is considered as a solid, i.e. its velocity field is negligible. Inserting in the simulations

the effect of bad interface between silicon sensor and spacer: a map of temperature T(x, y)

for this case is obtained and showed in Figure 8.22. Dividing the sensor in four quadrants,

the upper-right one, in the case of bad glued spacer with a maximum gap of 0.0001 mm in a

length of 3.2 cm, is 0.968°C hotter than in the case of perfect gluing. The maximum punctual

difference is exactly on the right upper corner of the module, were it reaches the value of

3.87°C.

In operative conditions, the heat produced inside the sensor is not a constant value, but it is

function of leakage current and temperature. An estimate of this dependence is provided by

the relation (8.4) taken from [12]:

𝑃𝑠𝑒𝑛𝑠𝑜𝑟 ∝ 𝑃0

𝑇2

𝑇02 𝑒𝑥𝑝 [−

∆𝐸

2𝑘𝐵(

1

𝑇−

1

𝑇0)]

(8.4)

In this equation, P0 is the constant value of thermal power generated, T is the temperature on

sensor, T0 is a reference value for temperature, ∆𝐸 is the amplitude of the band gap for a

semiconductor at 0 K and 𝑘𝐵 is the Boltzman constant. The values of these quantities are

reported in Table 8.1.

Quantity Value Unit

P0 0.6 W

T0 253 K

∆𝐸 1.93863x10-19 J

𝑘𝐵 1.28x10-23 J/K

Table 8.1 – Values for equation 8.4

The equation (8.4) is plotted in Matlab for a range of temperature of [233, 273] K, as

shown in Figure 8.23.

ANALYSIS OF RESULTS

106

Figure 8.23 -Power generated by silicon sensor as function of temperature.

In case of perfect gluing, the mean value of temperature on the upper-right quadrant of the

module is -13.5317°C. Inserting this value on equation (8.4), a power generation of 1.26 W

is obtained. In case of bad gluing, the mean value of temperature of the same quadrant is

-12.42 °C. Inserting this value on equation (8.4), a power generation of 1.43 W is obtained.

Therefore, the effect of heating observed in the upper-right quadrant, leads to an increase of

thermal power produced inside the silicon of about 0.17 W. This contribute is not considered

in simulations, so in real conditions the increase of temperature due to bad gluing can be

even higher than the simulated one.

107

Chapter 9

FUTURE WORKS

9.1 Developments for the FVM model.

The model proposed so far brings to good results, but it can be improved in order to reduce

the modelling error and to include more components, such as electronic boards. In various

simulations showed in this thesis, only the indirect effect of electronic heating on silicon

sensor has been modelled. Anyway, as discussed in previous sections, heat generation effect

on two sides of the module is only an approximation of reality, and it is not so easy to find

the correct value of thermal flux to insert in that point. Instead, if Front End Hybrids and

Service Hybrid are modelled, heat generation can be set exactly inside the electronic

components that are present, and the propagation of thermal fluxes will be closer to reality.

For sure, this will lead to have a higher number of elements to be simulated, and the

computational power necessary to manage them will be higher too. The same reasoning

stands for the support of the spacers: modelling CO2 cooling pipes junctions at the ends of

the spacers will bring to more confident results. Another improvement that can be done is to

simulate the whole model, and not only a half: in this way it should be possible to set

different boundary conditions from left to right in the same simulation. This development

permits to avoid the necessity of implementing two simulations, one for each half, to make

asymmetrical boundary conditions. Operating in this way, continuity of boundary conditions

in the mirroring plane are always granted and the error of interpolation is excluded. Working

on this way will also have some disadvantages, linked to the fact that the number of volume

elements will double. Furthermore, it was said that glue and Kapton have not been meshed

in the model and they have been substituted by an equivalent thermal resistance, as explained

in Section 6.3. This implies that a refinement in the treatment of the glue-Kapton-glue layers

can be done. Than, the problem of thermal runaway has to be studied more in detail, and

equation (8.4) can be implemented directly in the computational model, in order to consider

automatically this phenomenon in simulations.

FUTURE WORKS

108

Summing up, the main developments to be made on the FVM model are:

• Modelling and simulating front end hybrids, service hybrids and CO2 pipelines

junctions.

• Modelling whole module and not only a half, in order to give the possibility to set

non symmetrical boundary conditions.

• Evaluating the effect of thermal resistance, and trying to refine the coupling area

between spacers and sensors.

• Inserting the dependence of temperature on the internal heat generation of the silicon

sensor.

9.2 Developments for the test bench.

Doing tests in the bench built for experimental validation, some suggestions for

improvement have been designed. First of all, as mentioned in Section 7.6, there is the

necessity to install an electronical control (PID) for the regulation of the setpoint value for

Peltier cells. In this way, we are confident that cells stabilize exactly on the target

temperature, and not to a temperature close to it. Doing this, a new power supply system has

to be designed, in order to disengage from the five bench power supplies, which are bulky

and difficult to manage. A second update of the system is to make the pipelines of air cooling

heatsink longer, in order to eject hot air as far as possible from the fan suction. In this way

fans will not be influenced by hot air coming from other conducts. In the actual

configuration, an influence of 1°C higher than ambient temperature has been detected in fan

suction. Another implementation that can be made is creating a room around the measuring

area where the vacuum is created: fans and conducts of air cooling will pull and eject air out

from this room. In this way, the effect of convection can be excluded from measurements,

FUTURE WORKS

109

as well as the uncertainty linked to the convection coefficient. Another advantage of the

controlled room is that we exclude humidity from the measuring area: during tests in

ambient, when temperature went under 0°C, the sublimation of water vapor occurred. A

layer of ice was created on the cold surfaces of Peltier cells as well as terminal parts of the

spacer, as shown in Figure 8.24: this fact can influence measurements and has to be avoided.

Figure 8.24 – Formation of ice on the colder surface of Peltier cell when temperature go down 0°C.

9.3 New tests for the module

Other kind of tests for the module have been foreseen. The first of these is supplying the

module with the bias voltage in order to establish leakage currents that produce heat. This

new condition can be added to the others of test number 2. The module has already been

provided with terminals to attach clamps for bias voltage. This configuration will help to

study the thermal runaway [14]. Then, the test bench inclusive of Peltier cells could be

postioned inside the cold box of the Thermotechnic Laboratory of the Rngineering

Department of the University of Perugia: in this way the temperature of the ambient can be

set down to -20°C, simulating operative conditions closer to CMS room. Peltier cells will

reproduce the effect of CO2 cooling as well. This will help to investigate if the effect of the

bad gluing of the spacer will be equal to the one at ambient temperature or it will be modified

by different temperatures. More than this, tests with infrared thermal camera are already

planned. Infrared cameras have some advantages compared with thermocouples:

FUTURE WORKS

110

• They are not in contact with the object that has to be measured. They do not influence

the measurement introducing a thermal contact.

• They do not introduce electromagnetic interactions with the object as well.

Thermocouples, being in contact with bodies, can conduct electricity if a difference

of voltage is present.

• They record directly a thermal map of the object, so values have not to be

interpolated. Actually, they still furnish a discrete matrix of values, but the spatial

gap between to detected values is so small that the field can be considered continuum.

However, the main problem linked to thermal cameras is the emissivity of surfaces.

Materials of the module components are very different to each other, so emissivity can vary

a lot. More than this, the silicon surface is very reflective, so it is influenced by the external

environment. To solve this, the module can be painted with a high-emissivity paint, before

starting the tests. Some preliminary images with an infrared camera made to check the

functioning of the cooling system have been already taken and shown in Figure 8.25. In the

upper picture is shown the cooling system working without the module on the top. Peltier

cells upper faces are visibly colder than ambient. Conduits of air are hotter than ambient

from the place where heatsink of Peltier cells is inserted, as a consequence of air worming

up after flowing through fins. Motors of fans are other hot points. In the picture on the

middle, the silicon is placed in its wright position for tests. The thermal field observed on

the surface of the silicon is very similar to that of simulations. However, in this case the

stump bridge on the centre of the lower edge was not in contact with Peltier cell, and it had

not benefited from the cooling effect. This is confirmed from the fact that its colour (related

to temperature) is different from other spacers. In last picture on the bottom, is shown the 2S

module during test number 2. The heating effect of Nickel strips on the left and right edge

is visible. In this picture it is also visible the different emissivity between the adhesive tape

that fix thermocouples to sensor and the upper face of it.

FUTURE WORKS

111

Figure 8.25 – Pictures taken with a thermal camera in order to check the functioning of the system and fix issues. These pictures are not taken into account for measurements yes because studies about emissivity are

still in progress.

112

CONCLUSIONS

The path followed to create a Finite Volume Method model for the 2 Strips module of CMS

experiment has been shown. The model has been realised with Ansys Fluent 17.1 software,

importing a 3D CAD model of the geometry given by the CMS research group. It has been

modified in order to make it suitable for the requirements of the study, and then it has been

meshed in the best way to find the better compromise between good discretization and

available calculation power. Boundary conditions have been set with reference to

experimental tests for validation, and, after that, to respect the operative conditions of the

module. The experimental validation of the model has been realised by a test system

originally ideated and built. The guidelines of this project, as well as the selection of

components have been showed. The prototype module used in tests has been built in

collaboration with the INFN (Istituto Nazionale di Fisica Nucleare) section of Perugia. The

assembly process starting from components has been presented. Two tests have been made,

each one regarding a particular set of boundary conditions: in the first one only the effect of

cooling has been analysed, while the second one has been characterised by the simultaneous

presence of cooling and heating. During tests, an unexpected result for the thermal field has

been found. This was followed by a work aimed at finding the problem, which ended

discovering an issue happened during the fabrication process. In order to understand the

nature of this issue, first a manipulation of data between simulation results and test data has

firstly been made, and, after this, the Fluent model has been modified in order to take in

account this aspect. This analysis constituted a starting point to realise some studies about

the problem found, and to see what will happen if this problem will occur during operative

conditions. After solving this issue and validating the Fluent model, the module has been

simulated in its operative conditions. A functional FVM model is now available and it can

be used for many other studies.

113

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116

APPENDIX

In this section some Matlab scripts used to take calculations for the thesis are reported.

• PROGRAM NUMBER 1

% PROGRAM TO CALCULATE GRID CONVERGENCE INDEX % IN GENERAL CASE OF r NOT COSTANT %________________________________________________________________________ %________________________________________________________________________ %Eseguire prima di questo programma 3 simulazioni in Ansys %Stabilire un parametro h indice della dimensione della mesh %Deve essere h1<h2<h3 %Il rapporto r=h(i+1)/h(i) deve essere r>1.3 %Calcolare in ciascuna delle tre simulazioni la grandezza di interesse f clc clear all close all

%Dati iniziali h1=5*10^(-6); %m h2=7.5*10^-6; %m h3=1.125*10^-5; %m

f1=317.916528; %W f2=317.82146036; %W f3=317.6528457; %W

%Algoritmo di calcolo r21=h2/h1; r32=h3/h2; if r21<1.3 disp(['Warning: il rapporto r21 è ' num2str(r21)]) disp([' ']) elseif r32<1.3

disp(['Warning: il rapporto r32 è ' num2str(r32)]) disp([' ']) end

f21=f2-f1; f32=f3-f2; s=sign(f32/f21); q=0; errore=0.00000001; %impostare errore desiderato e=100; while e>errore p=abs(log(abs(f32/f21))+q)/log(r21); qq=log((r21^p-s)/(r32^p-s)); e=qq-q; q=qq; end

e21=abs((f2-f1)/f1);

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e32=abs((f3-f2)/f2);

%Calcolo valori di interesse f0=f1+((f1-f2)/(r21^p-1)); GCI12=1.25*e21/(r21^p-1)*100; GCI23=1.25*e32/(r32^p-1)*100; inf=f1*(1-GCI12); sup=f1*(1+GCI12); as=GCI23/(r21^p*GCI12);

disp([' GCI12= ' num2str(GCI12) ' %' ]) disp([' GCI23= ' num2str(GCI23) ' %' ]) disp([' ']) disp(['Intervallo confidenza 95% [ ' num2str(inf) ' ; ' num2str(sup) '

]'])

disp(['Soluzione estrapolata: f0=' num2str(f0)]) disp([' ']) disp(['Verifica convergenza: ' num2str(as) ' (circa 1)'])

% % Se desidero avere un certo GCI % GCIdesiderato=0.01; % GCI percentuale desiderato % % rd=(GCIdesiderato/GCI12)^(1/p); % disp([' ']) % disp([ 'Per avere GCI=' num2str(GCIdesiderato) ' devo avere r21 pari a:

' num2str(rd)])


% PROGRAM TO CALCULATE PARAMETERS FOR PELTIER CELLS %STARTING FROM DATASHEET %________________________________________________________________________ %_______________________________________________________________________ clc clear all close all %________________________________________________________________________ %Dati di fabbrica Cella Imax=3.9; %A , corrente che produce il DTmax Vmax=8.8; %V , voltaggio DC massimo a DTmax DTmax=74; %K ,massima differenza di temperatura ottenibile tra le

duefacce Th0=298; %K ,temperatura parete calda a cui si realizza il DTmax Qcmax=18.7;%W ,massimo calore assorbito alla parete fredda a I=Imax e

DT=0 %________________________________________________________________________ %Parametri calcolati cella Sm=Vmax/Th0; Rm=(Th0-DTmax)*Vmax/(Th0*Imax); Km=(Th0-DTmax)*Vmax*Imax/(2*Th0*DTmax);

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Z=(Sm^2)/(Rm*Km); %Parametri del caso operativo %LEGENDA % Ta=temperaura ambiente % Th=temperatura faccia calda cella % Tc=temperatura faccia fredda cella % Tj=temperatura "junction",temberatura fredda sul corpo da raffreddare %________________________________________________________________________ %PARAMETRI DA SCEGLIERE Tc=267; DT=46; Qc=5; Ta=296;

Th=Tc+DT; %__________________________________________________ %Algoritmo per il calcolo della corrente i=0; I=0.001; QQc=0; while QQc<Qc QQc=Sm*I*Tc-I^2*Rm/2-Km*DT; I=I+0.001; i=i+1; if I>Imax disp([' ']) disp(['ATTENZIONE!!!!! superato il limite di corrente ']) disp([' ']) disp(['Premere ctrl+c']) pause end end Qc=QQc;

%__________________________________________________ %RESISTENZA DELLA GIUNZIONE Kpt=4; % W/mK Conducibilità pasta termica ss=0.0005; % spessore pasta termica Acont=20*20*10^(-6);%mm^2,area contatto cella spacer Rjc=ss/(Kpt*Acont); %resistenza termica giunzione %________________________________________________________________________ %CALCOLI Tj=Tc+Qc*Rjc; Qh=Sm*I*Th+I^2*Rm/2-Km*DT; Qte=Sm*I*DT+Rm*I^2; COP=Qc/Qte; %Verifica:deve venire come il cop sceltro

R=(Th-Ta)/Qh; %formula semplificata Rha=((Sm*I*Rjc+Km*Rjc+1)*Qc+Km*Ta-

(Sm*I+Km)*Tj+(Rm*I^2/2))/(((Sm^2*I^2*Rjc+Sm*I)-Km)*Qc-

(Sm*I)^2*Tj+Rm*I^2*(0.5*Sm*I-Km)); %correlazione

%Rjc=((-Sm*I*Rha+Km*Rha+1)*Qc+Km*Ta+((Sm*I)^2*Rha-Sm*I-Km)*Tj+(Rm*Km*I-

0.5*Sm*Rm*I^3)*Rha+(Rm*I^2/2))/(((Sm*I)^2*Rha-Sm*I-Km)*Qc); %DDT=((Sm*I*Rha-1)*Tj+(1+Sm*I*Rjc)*Ta+Rm*I^2*(0.5*Rha-

0.5*Rjc+Sm*I*Rjc*Rha))/(Km*(Rjc+Rha)-(Sm*I*Rha-1)*(Sm*I*Rjc+1)); %Calcolo Tminima ottenibile in condizioni ideali di Rha=0

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Tjj=Tj; RRha=Rha; while RRha>0 Tjj=Tjj-1; RRha=((Sm*I*Rjc+Km*Rjc+1)*Qc+Km*Ta-

(Sm*I+Km)*Tjj+(Rm*I^2/2))/(((Sm^2*I^2*Rjc+Sm*I)-Km)*Qc-

(Sm*I)^2*Tjj+Rm*I^2*(0.5*Sm*I-Km)); end

disp([' ']) disp(['PARAMETRI CELLA SCELTA: ' ]) disp(['C. Seebeck Sm=' num2str(Sm) ]) disp(['Res. elettrica Rm=' num2str(Rm) ]) disp(['Cond. Termica Km=' num2str(Km) ]) disp(['Z factor cella Z=' num2str(Z) ]) disp([' ']) disp(['TEMPERATURE SISTEMA: ' ]) disp(['Ta=' num2str(Ta-273) ' °C' ]) disp(['Th=' num2str(Th-273) ' °C' ]) disp(['Tc=' num2str(Tc-273) ' °C' ]) disp(['Tj=' num2str(Tj-273) ' °C' ]) disp([' ']) disp(['POTENZE: ' ]) disp(['Qc=' num2str(Qc) ' W' ]) disp(['Qh=' num2str(Qh) ' W' ]) disp(['Qelettrica=' num2str(Qte) ' W' ]) disp([' ']) disp(['Corrente assorbita: I=' num2str(I) ' A' ]) disp([' ']) disp(['Resistenza termica del dissipatore (correlazione) ' num2str(Rha)

]) disp(['Resistenza termica del dissipatore (formula semplificata) '

num2str(R) ]) disp([' ']) disp(['COP ricalcolato: COP=' num2str(COP) ]) % disp(['Con questi I, Qc, DT posso arrivare idealmente a Tjmin= '

num2str(Tjj+1-273) ' °C' ]) %________________________________________________________________________


%PROGRAM TO MANAGE EXPORTATION OF RESULTS FROM ANSYS %________________________________________________________________________ %________________________________________________________________________ %Data have to be present on the Matlab Workspace clc clear all close all %Part 1 - load Ansys ASCII output file on workspace and create A matrix A(:,1)=xcoordinate;

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A(:,2)=ycoordinate; A(:,3)=temperature; scatter(A(:,1),A(:,2),5,A(:,3)) %Part 2 - rescale matrix A to allign the coordinate system A(:,1)=10000*A(:,1); A(:,2)=10000*A(:,2); A(:,1)=ceil(A(:,1)); A(:,2)=ceil(A(:,2)); A(:,1)=0.1*A(:,1); A(:,2)=0.1*A(:,2);

A(:,1)=-A(:,1); %mirror x axe A(:,2)=-A(:,2); %mirror y axe A(:,1)=A(:,1)+95.5; %translate x axe A(:,2)=A(:,2)+62.6; %Translate y axe %Part 3 - Algorithm to find characteristic quantity in a known point [L,C]=size(A);

X=23; %set x coordinate of the target point Y=81; %set y coordinate of target point %delta=0.5; %set resolution

t=1; i=1; while t==1 c=A(i,1); if c==X b=A(i,2); if b==Y T=A(i,3)-273 t=0; end end i=i+1; end

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