Faculty of Technology & ScienceDepartment of Physics and Electrical Engineering

Henrik Jackman

Surface temperature measurement ona Yankee cylinder during operation

Engineering PhysicsMaster Thesis

Date/Term: 2009-06-10Supervisors: Prof. Kjell Magnsson,

Jonas Cederlöf, Hans Ivarsson, Karl-Johan Tolfsson

Examiner: Prof. Lars JohanssonSerial Number: X-XX XX XX

Karlstads universitet 651 88 KarlstadTfn 054-700 10 00 Fax 054-700 14 60

Information@kau.se www.kau.se

Abstract

The Yankee cylinder is used in most of Metso Paper's machines. It is used in the drying andcreping process. Since the outcome of these processes largely aect the paper's nal quality it isimportant that the Yankee cylinder behaves in a controlled fashion. One important parameteraecting the behaviour of the Yankee cylinder is its surface temperature. The objective of thisthesis was to search for and evaluate methods for measuring the surface temperature of a Yankeecylinder during operation. Metso Paper is looking for a method having an accuracy of ∆T = 1C,a response time of t < 10 ms, and being portable. Three dierent instruments were tested duringthe thesis:

• Thermophone, a contact measurement device currently used by Metso Paper.

• RAYNGER MX4, a pyrometer from Raytek.

• FLIR P640, a thermographic camera with a 640x480 focal plane array from FLIR.

The instruments were tested by performing measurements on Metso Paper's pilot machine inKarlstad during operation. The measurements revealed drawbacks for all three instruments. Thebiggest drawbacks of the Thermophone was its response time, t ≈ 5 min, and its dependence onthe frictional heating of the teon cup. The frictional heating causes the measured temperature toincrease even after 15 min making it hard to know when to stop the measurement. How much thefrictional heating aects the measured temperature was dicult to analyse, making it a suggestionfor future studies.The biggest drawback of the pyrometer and the thermographic camera is the measurement errordue to emissivity errors. Since the Yankee cylinder have a varying surface nish the emissivityvaries a lot along the surface introducing temperature errors as large as ∆T = 30C.Two methods that claim to be emissivity independent were investigated; double-band and gold cuppyrometers. Double-band pyrometers require the target to be a grey body and for it to have largetemperatures, T > 300C, making this method unsuitable for measuring the surface temperatureof the Yankee cylinder. Gold cup pyrometers require the gold hemisphere to have a reectance ofρ = 1. Because of the environment surrounding the Yankee cylinder it would be dicult keepingthe gold hemisphere as clean as required making this method unsuitable as well.

Acknowledgements

I would like to thank my supervisor at Karlstad University Prof. Kjell Magnusson for guiding methrough this work. I would also like to thank my examiner Prof. Lars Johansson for giving meuseful advices on how to improve this paper. Last but not least I would like to thank my supervisorsat Metso Paper: Jonas Cederlöf, Hans Ivarsson, and Karl-Johan Tolfsson for answering all of myquestions and making this project fun and challenging.

Contents

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Metso Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Yankee dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Heat transfer and temperature measurement 82.1 Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Emissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Absorptivity, reectivity and transmissivity . . . . . . . . . . . . . . . . . . 13

2.4 Temperature measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 The Yankee dryer 163.1 Inside the Yankee dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Nip load & Hood dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Creping process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Sensors 214.1 Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Thermopiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Sensors similar to thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.1 Resistance thermometer & bolometer . . . . . . . . . . . . . . . . . . . . . 264.3.2 Pyroelectric sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Thermal IR sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.5 Photonic IR sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.6 Techniques using IR sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Experimental 345.1 Thermophone measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2 Pyrometer measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.3 Thermographic camera measurements . . . . . . . . . . . . . . . . . . . . . . . . . 355.4 Thermophone specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.4.1 Couette ow in Thermophone . . . . . . . . . . . . . . . . . . . . . . . . . . 385.5 RAYNGER MX4 specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.6 FLIR P640 specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.6.1 Measurement error due to incorrect emissivity . . . . . . . . . . . . . . . . 43

6 Results 456.1 Thermophone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.2 Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486.3 Thermographic camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7 Discussion & Conclusions 57

A MATLAB code 61

List of Figures

1.1 Examples of tissue products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Examples of tissue paper machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Dierent processes involving the Yankee dryer . . . . . . . . . . . . . . . . . . . . . 31.4 Steam inside the Yankee dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Magnication of the Yankee headers . . . . . . . . . . . . . . . . . . . . . . . . . . 51.6 Crowning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.7 Resulting temperature distribution after FEM calculations . . . . . . . . . . . . . . 61.8 Crowning curves from FEM calculations . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Thermal conductivity vs. temperature for three dierent phases. . . . . . . . . . . 92.2 Proles for the uid velocity and temperature in the boundary layer. . . . . . . . . 102.3 Spectrum of electromagnetic radiation. . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Projection of dA1 normal to the direction of radation. . . . . . . . . . . . . . . . . 122.5 The Planck distribution for a black body at dierent temperatures as well as the

Wien displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.6 Comparison between the emission of a black body and a real body. . . . . . . . . . 132.7 Radiation from and irradiation on a surface. . . . . . . . . . . . . . . . . . . . . . . 142.8 An information system consisting of a sensor, a signal processor, and an actuator. . 153.1 How the steam condensate assemblies on the inside of the Yankee dryer. . . . . . . 173.2 How the saturated steam temperature varies with pressure. . . . . . . . . . . . . . 173.3 Coating nozzles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Pictures of the Yankee surface with and without a coating layer. . . . . . . . . . . 183.5 Hood dryer operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.6 The creping process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1 Seebeck's experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 A simple thermocouple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 A simple thermopile conguration . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 A schematic diagram of a thermopile detector structure. . . . . . . . . . . . . . . . 244.5 The transmissivity for air over a 300 m distance. . . . . . . . . . . . . . . . . . . . 254.6 A schematic sketch of the structure of a micro bolometer. . . . . . . . . . . . . . . 274.7 A general image of a thermal IR sensor . . . . . . . . . . . . . . . . . . . . . . . . 274.8 A general image of a photonic IR sensor . . . . . . . . . . . . . . . . . . . . . . . . 294.9 Spectral detectivities of commercially available photonic sensors. . . . . . . . . . . 314.10 Schematic of a gold-cup pyrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.11 Plot of εeff versus ρ for ve xed emissivities. . . . . . . . . . . . . . . . . . . . . 335.1 How the Thermophone was held against the Yankee dryer during the measurements. 345.2 Bad and good way to hold the Thermophone. . . . . . . . . . . . . . . . . . . . . . 345.3 The pyrometer measurement setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.4 The setup of how the thermographic pictures was taken. . . . . . . . . . . . . . . . 365.5 A sketch of the Thermophone geometry. . . . . . . . . . . . . . . . . . . . . . . . . 375.6 Photos of the Thermophone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.7 The parameters of the Couette ow. . . . . . . . . . . . . . . . . . . . . . . . . . . 395.8 The calculated response of the brass piece. . . . . . . . . . . . . . . . . . . . . . . . 415.9 RAYNGER MX4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.10 FLIR P640 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.11 Showing how the fractional errors δε and δT are related. . . . . . . . . . . . . . . . 446.1 Thermophone graph 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.2 Thermophone graph 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.3 Thermophone graph 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.4 Thermophone graph single stove plate. . . . . . . . . . . . . . . . . . . . . . . . . . 476.5 Surface nish and measured temperatures. . . . . . . . . . . . . . . . . . . . . . . . 486.6 Thermographic image to determine the background radiation. . . . . . . . . . . . . 506.7 Thermographic image 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.8 Thermographic image 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.9 Thermographic image 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.10 Thermographic image 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.11 Thermographic images on the Thermophone. . . . . . . . . . . . . . . . . . . . . . 556.12 Thermographic image on the Thermophone after measurement. . . . . . . . . . . . 556.13 Graph comparing the temperature measured by the Thermophone to the tempera-

ture of the Thermophone viewed by the FLIR P640. . . . . . . . . . . . . . . . . . 567.1 Two ways of making the contribution from the background radiation smaller. . . . 58

1 Introduction

This paper is the result of a master thesis project (30 hp) on the temperature measurementof a Yankee cylinder surface during operation. The work was performed at the department ofCalculation at Metso Paper, Karlstad in 2009. It completes the author's studies for a M.Sc degreein Engineering Physics at the Faculty of Technology and Science at Karlstad University, Sweden.

1.1 Background

1.1.1 Metso Paper

Metso Paper is a world leading supplier of technology for pulp and paper industry. The branch inKarlstad is specialised in designing and constructing tissue machines. Examples of tissue productsinclude: napkins, handkerchiefs, industrial wipers, kitchen towels, and bathroom paper. Some ofthe mentioned examples can be viewed in Fig. 1.1.

Figure 1.1: A few examples of tissue products.

The products are manufactured using dierent machines specialised for dierent qualities. Eachmachine that is produced is unique, but they make use of one of the following techniques:

• Dry Creped Tissue (DCT)

• New Tissue Technology (NTT)

• Structured Tissue Technology (STT)

• Trough Air Drying (TAD)

DCT and TAD is the two most common techniques since NTT and STT are still very new. Itshould be noted that the names of the techniques are Metso Paper's own. Examples of machinesusing three of these techniques can be viewed in Fig. 1.2.

To get a picture of how the paper goes from pulp to nished product one can point out vesteps in the production line:

• A slurry of pulp, water, and chemicals is dispersed uniformly on a moving wire by an unitcalled the headbox. This dispersion is made by a jet through an opening called the slice.When introduced on the wire the slurry contains of about 99% water.

• The slurry continues on the wire and is formed in a number of steps. In the forming processMetso use two main designs: Crescent and C-wrap forming. In this process most of the waterin the slurry is removed.

• In the next step the slurry is pressed onto a drying cylinder called the Yankee dryer by oneor two pressure rolls. This is called the nip and also removes some of the water.

1

Figure 1.2: Examples of tissue paper machines. The topmost machine uses the DCT technology,the middle one STT, and the bottom one TAD. As can be seen machines using dierent techniqueslook quite dierent, but there are similarities. One component that is used in all machines aboveis a dryer cylinder called the Yankee dryer (marked red in the images). The Yankee dryer is usedin nearly all of Metso Papers machines.

• The paper continues on the Yankee dryer, which, together with a drying hood, dries thepaper from 40% dryness to 90-98% dryness. [1]

• In the last step the paper is removed from the Yankee dryer. The removal is made by acreping doctor that scrapes the paper of the Yankee dryer. The paper then continues and isnally reeled onto big paper rolls.

2

Figure 1.3: The dierent processes involving the Yankee dryer. The paper is forced onto the Yankeedryer in the nip where the paper together with a felt is pressed between a suction press roll and theYankee dryer. Since the Yankee dryer is covered with a coating that acts as a glue the paper sticksto the Yankee dryer. During the nip water is pressed out of the paper. The paper then continueon the Yankee dryer and enter the drying hood. In the drying hood water is evaporated from thepaper partly because of the high Yankee dryer temperature and partly because of the hot air fromthe hood dryer. After the hood dryer the paper continue to the doctors. The rst doctor is thecut-o doctor and is used to cut o the paper and guiding it to a pulper. This doctor is only usedwhile the next doctor, the creping doctor, is substituted due to maintenance. The creping doctorscrapes the paper o the Yankee cylinder and while doing this the paper is creped (explained inmore detail later). The task of the cleaning doctor is to scrape of remainders of coating and paper.After the cleaning doctor a new layer of coating is sprayed onto the Yankee dryer.

1.1.2 Yankee dryer

As was said in the previous section the Yankee dryer is used in most of Metso Papers machines.The Yankee dryer has typically two tasks; drying the paper and being part of the creping process.

The drying of the paper is made in two dierent ways by the Yankee dryer. Firstly the wa-ter is pressed out of the paper when the paper is forced onto the Yankee dryer in the nip bya press roll. Secondly the water is evaporated from the paper partly because of the high Yankeedryer temperature and partly because of the hot air that is blown on the paper from the hood dryer.

In the creping process the paper is creped of the Yankee dryer by a creping doctor. In theseprocesses much of the paper's nal quality is determined. Therefore it is very important that theYankee dryer behaves in a controlled fashion. An image of the dierent processes can be viewedin Fig. 1.3

3

The Yankee dryer is heated from the inside by overheated steam that keeps a pressure of 6-9 bardepending on what type of paper that is produced. Because the steam transfer some of its energyto the Yankee dryer and the paper the steam condensate on the inside of the Yankee cylinder. Thiscondensate is removed by by a number of condensate headers that acts as straws and suck out thecondensate out of the Yankee dryer. A more detailed picture of how the steam is introduced andremoved is seen in Fig. 1.4 and Fig. 1.5.

Figure 1.4: Showing how the steam enters the Yankee dryer and how the condensate is removed.

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Figure 1.5: Showing a cross-section of the Yankee dryer as well as a magnication of a condensateheader. The inside of the Yankee dryer is made of internal grooves which purpose is to collect thecondensate. The straws of the headers run inside these grooves and suck away the condensate.

One big aspect in designing the Yankee dryer is the crowning. The crowning is made in orderto get an evenly distributed pressure on the paper in the nip. Because of the high temperatureand pressure inside the Yankee dryer it expands while in operation. The paper cools the Yankeedryer but close to the edges no paper is on the cylinder. Therefore the Yankee dryer is hotterclose to the edges and the thermal expansion is larger in these regions. By knowing the operatingtemperatures and pressures it is possible to make up for this uneven thermal expansion by makingthe Yankee dryer thicker in the middle than close to the edges. In Fig. 1.6 three cases of crowningare shown, one successful, one too small, and one too big.

Figure 1.6: Showing three kinds of crowning, one correct, one too small, and one too big.

To get a correct crown, as seen in the left image in Fig.1.6, careful calculations are made beforethe Yankee dryer is ground. Two dierent types of nite element method (FEM) simulationsare made; one 2D axi-symmetric model and one 3D model. In the 2D model the inner pressure,centrifugal, and thermal loads are considered to be axi-symmetric. In the 3D model the nipload isconsidered which cannot be considered to be an axi-symmetric load.The inner pressure and centrifugal loads are rather straightforward to apply to the FEM modelsince they are constant while the machine is running. The temperature is however not constantsince the paper cools the Yankee dryer and the hood dryer heats it. Instead of trying to inputthis cumbersome temperature variation, a revolution mean value is used in the 2D model. At thepaper edge, where the paper ends, no cooling eect from the paper is present. Here a convectionboundary condition is set depending on how fast the Yankee dryer is rotating. An example ofthe resulting temperature distribution at running conditions after a 2D FEM calculation can beviewed in Fig.1.7. After the two FEM (2D and 3D) calculations, a resulting total deection curveof the Yankee dryer is achieved. An example of such a curve can be viewed in Fig. 1.8. This curveis then inverted and used as a template for the ground of the Yankee dryer.

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Figure 1.7: Showing the resulting temperature distribution at running conditions after a 2D FEMcalculation. In reality the transition in the sheet edge is probably not as sharp as the one picturedin the right image. More complex transitions have been tried, but the result does not deviate muchfrom the sharp transition, which is why the sharp transition is used.

Figure 1.8: Showing the resulting curves from the FEM calculations. The pressure curve is achievedfrom measurements since the Yankee dryer rst is pre-ground while kept at its running pressure.This pressure causes the middle of the Yankee dryer to expand more than the ends, which is whythe ends is ground more. The nip as well as the temperature load causes the ends of the Yankeedryer to expand more than the middle of it. Adding together the nip, temperature, rotation, andpressure curves one end up with the nal crown curve. This crown curve is inverted and used asa template when making the nal ground of the Yankee dryer.

1.2 Objective

As has been said much of the nal quality of the paper is determined by the Yankee dryer be-haviour. Therefore it is of great importance that the Yankee dryer behaves uniformly along theaxial direction. The nip needs to be uniform in order to press away equal amounts of water alongthe paper. If the nip is non-uniform it can lead to dierences in moisture of the paper which canresults in an unstable process.

Metso Paper have a method to measure the surface temperature of the Yankee dryer which iscalled the Thermophone. This instrument consists of a thermocouple attached on a thin circularbrass piece. This brass piece is kept inside a teon cup and held in place by four metal wires. Theteon cup is used to protect the brass piece and thermocouple from the surrounding air. Duringmeasurements the brass piece is kept as close to the Yankee surface as possible without coming in

6

contact with it.

The measured temperatures are believed, by people at Metso Paper, to be dependent on theperson who performs the measurement. This dependence is probably due to how the Thermophoneis pressed against the Yankee cylinder and how close the brass piece comes to the Yankee dryer.Apart from these diculties it is a dicult task to analyse what temperature the Thermophone isshowing, since it exchanges heat through conduction (metal wires), convection (air ow in teoncup) as well as radiation.

Because of the diculties regarding the Thermophone and the importance of knowing thetemperature of the Yankee dryer, Metso Paper are looking for alternative methods. The objectiveof this thesis work was to look for and to investigate alternative temperature measurement methods.

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2 Heat transfer and temperature measurement

Temperature and heat are two closely related concepts. Heat, often referred to as thermal energy,can be considered as the internal kinetic energy of the atoms and molecules in a body. In a monoatomic gas the heat is directly related to the average of the absolute velocity of all atoms. Forother gases, and liquids, the vibrations and rotations of the molecules also contribute to the heat.In solids the atoms and molecules are not free to move. So for solids heat is the vibrations of theatoms and molecules about their equilibrium position.

Temperature is related to heat through the zeroth law of thermodynamics which states: "Iftwo thermodynamic systems are each in thermal equilibrium with a third, then they are in ther-mal equilibrium with each other". This means that if two systems are put in contact with eachother heat will ow between them until they are in thermal equilibrium. When two bodies arein thermal equilibrium they have, by denition, the same temperature. The exchange of heatis called heat transfer and can be accomplished through three dierent mechanisms: conduction,convection and radiation. These mechanisms are discussed in sections 2.1, 2.2, and 2.3 respectively.

The rst law of thermodynamics states that: "The increase in the internal energy of a systemis equal to the amount of energy added by heating the system, minus the amount lost as a result ofthe work done by the system on its surroundings", and put in an equation:

dU = δQ− δW (2.1)

With dU being a small change of the internal energy, δQ being a small amount of heat addedto the system, and δW being a small amount of work done by the system. This law is related tochanges in temperatures through the specic heat, Cp, which is a measure of the amount of energyneeded to increase the temperature of a body. The specic heat for a body at constant pressure isdened as:

Cp =∂U

∂T+ p

∂V

∂T=(∂H

∂T

)p

(2.2)

With ∂V∂T being the partial derivative of the volume of the body with respect to the temperature,

and H being the enthalpy dened as H = U +pV . The specic heat can also be dened for a bodyat constant volume:

Cv =(∂U

∂T

)V

(2.3)

In most cases when increases the temperature of a solid or liquid they expand which is why thespecic heat at constant pressure is usually used for these matters. For a gas kept at a constantvolume the specic heat at constant volume is more appropriate.

Rearranging Eq. 2.2 one see that if the temperature increases it results in an increase in internalenergy or an increase in volume, or both:

Cp∂T = ∂U + p∂V (2.4)

In the following three sections the three mechanisms of heat transfer will be discussed.

2.1 Conduction

Conduction is due to atomic and molecular activity. When looking at a gas the particles, which thegas is composed of, constantly and in a random fashion collide with each other. In these collisionsenergy and momentum are transferred between the particles. Particles with a higher free energytransfer some of their energy to particles with lower energy. The distance over which an individualparticle can transfer its energy is equal to its mean free path, `. Assuming a temperature gradientin the x-direction, dTdx , the particle heat transport is proportional to `

dTdx , while the heat transport of

the gas as a total is also proportional to the density, specic heat, and the average particle velocity.

The picture of the conduction in liquids is similar if there are no free charge carriers (electronsor ions) which if present contribute to the conduction. Since liquids have a larger density than

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gases their particles interact more frequently and as a consequence they conduct heat better.

In solids the particles are not as free to move as the particles in uids. Instead their motion isrestricted to vibrations about their equilibrium position. Because of the periodic nature of crys-talline solids these vibrations create vibrational modes in the crystal lattice. These modes can beseen as a particle with a wavelength and a velocity but with no mass, called a phonon (cf. photon).The velocity of a phonon equals the velocity of sound in the solid. Phonons play a big role in theconduction of heat in solids but a more thorough discussion about their nature is out of the scopefor this paper. Apart from phonons, charge carriers also play a part in the conduction of heat inelectrical conducting solids.

Heat transfer through conduction in one dimension is described by the equation:

q′′ = −k∂T∂x

(2.5)

Where q′′ is the heat ux and k the thermal conductivity. The thermal conductivity variesbetween materials and is, as mentioned, dependent on the phase of the matter. A schematicpicture of how the thermal conductivity varies with temperature for the dierent phases can beviewed in Fig. 2.1.

Figure 2.1: Showing how the thermal conductivity varies with temperature for the three phases.[2]

2.2 Convection

Convection is similar to conduction since heat is transferred through the motions of atoms andmolecules. The thing that dierentiate convection from conduction is the macroscopic uid motionassociated with convection. The heat transfer through convection is made between a solid surfaceand a uid in motion. When the uid moves a lot of molecules are moving collectively or as ag-gregates. If there is a temperature dierence between the uid and the surface this bulk motioncontribute to the heat transfer. The molecules still have a random motion in the aggregates. Soconvection can be seen as a superposition of the heat transfer due to the random motion and thebulk motion of the uid.

Convection can be described by looking at a boundary layer for the uid. When looking at aboundary layer one looks at a layer in which the heat transfer is active and disregard the rest of theuid motion. In the boundary layer two proles can be identied: the velocity and the temperatureprole of the uid. The velocity goes from the surface velocity us, zero for a stationary surface,to the uid velocity u∞ and the temperature goes from the surface temperature Ts to the uidtemperature T∞. Since the temperature and velocity goes asymptotically from their surface valuesto their uid values it is hard to make a distinct edge of the boundary layer. Since the mechanisms

9

governing momentum and heat transfer are not identical, though related, the extent of the prolesneed not to be equal. The extent of the proles are not constant along the surface since theydevelop and grow which further complicate the determination of their magnitude. In Fig. 2.2 thetwo proles are shown.

Figure 2.2: Proles for the uid velocity and temperature in the boundary layer. In this case thesurface temperature Ts is higher than the uid temperature T∞ i.e Ts > T∞, which is the reasonfor the direction of q′′. The velocity of the uid is zero near the surface, since the surface is notmoving, and its temperature is Ts near the surface as indicated in the gure. The extent of thetwo proles in the y-direction is in general not equal to each other.

At the surface the heat is transferred solely through conduction since the velocity of the uidis zero with respect to the surface. Further away from the surface the heat is transferred with theuid motion which is the origin of the boundary layer. Heat transfer from a surface by convectionis described by the equation:

q′′ = h(Ts − T∞) (2.6)

With h being the convection heat transfer coecient which depends on surface geometry, the na-ture of the uid motion, and the thermodynamical and transport properties of the uid. Sincethe boundary layer changes along the ow and the properties depend on parameters that changesalong the ow an exact determination of h is in most cases impossible. Therefore approximatevalues of h are assumed when performing calculations.

The nature of the motion of the uid can either be forced or natural. Natural convection iswhen the motion of the uid is caused by temperature or pressure dierences in the uid. It iscommon knowledge that warm air rises because of the density reduction with temperature. Thisis an example of natural convection. An example of forced convection is a fan that forces the airto ow.

2.3 Radiation

All matter that has a temperature higher than 0 K emit electromagnetic radiation. The source ofthis radiation is energy transitions in the atoms and molecules of the body. These transitions aremaintained by the free energy of the body, i.e in close relation to the temperature. With higher freeenergy the probability for transitions increase and as a consequence more radiation are emitted.In Fig. 2.3 the electromagnetic spectra is shown where the thermal radiation part is highlighted.

Since the energy is transferred by electromagnetic radiation this transfer mechanism does notrequire any medium between the two bodies exchanging energy. This is however necessary forconduction and convection. Thermal radiation between two bodies are actually most ecient ifthere is vacuum between the bodies. If there is gas between the bodies the atoms and molecules in

10

Figure 2.3: Spectrum of electromagnetic radiation. Note that thermal radiation extends into thevisible spectra. [3]

the gas also emit and absorb radiation which must be taken into account when studying thermalradiation. The heat transfer between two bodies is accomplished through that the hotter surfaceemits more radiation than it absorbs and the opposite for the colder surface. When the two sur-faces are in thermal equilibrium they emit and absorb equal amount of radiation.

In 1879 Jozef Stefan deduced the relation between the heat ux q′′, due to thermal radiation,and the temperature of the emitting surface Ts on the basis of experimental results. In 1884 LudwigBoltzmann derived the same relation from theoretical considerations using thermodynamics. Thisrelation is called the Stefan−Boltzmann law and reads:

q′′ = σT 4s (2.7)

With σ = 5.67 ∗ 108 W/(m2 K4) being the Stefan−Boltzmann constant. This relation how-ever only holds for a perfect black body. A blackbody is an ideal surface that has the followingcharacteristics [3]:

• A blackbody absorbs all electromagnetic radiation independent on the wavelength and direc-tion.

• For a prescribed temperature and wavelength no surface can emit more energy than a black-body.

• The blackbody is a diuse emitter, i.e it emits radiation independent of direction.

As mentioned in the list above radiation from a black body also depends on the wavelength λ.This relation was deduced by Max Planck in 1901 and reads:

Iλ(λ, Ts) =2hc20

λ5[exp(hc0/λkBTs)− 1](2.8)

With h = 6.6256 ∗ 10−34 Js being the Planck constant, c0 = 3 ∗ 108 m/s being the speed oflight, and kB = 1.805 ∗ 10−23 J/K the Boltzmann constant. The spectral intensity, Iλ(λ, Ts), isthe radiated energy intensity for a blackbody at absolute temperature T per unit solid angle andper unit wavelength about the wavelength λ.Integrating this spectral intensity over all solid angels one obtains the spectral hemispherical emis-sive power Eλ(λ, Ts), also known as the Planck distribution:

Eλ(λ, Ts) =∫Iλ(λ, Ts) cos θdΩ =

∫ 2π

0

∫ π/2

0

Iλ(λ, Ts) cos θ sin θdθdφ = πIλ(λ, Ts) (2.9)

11

The cos θ factor arises because one is only interested in the projection of the radiation from adierential small surface dA1 normal to the direction of radiation. This term is easier understoodfrom Fig. 2.4.

Figure 2.4: Projection of dA1 normal to the direction of radation. [3]

Integrating Eλ(λ, Ts) over all wavelengths one obtain the Stefan−Boltzmann law:∫ ∞0

Eλ(λ, Ts)dλ =∫ ∞

0

2πhc20λ5[exp(hc0/λkBTs)− 1]

dλ = σT 4s (2.10)

Derivating Eq. 2.9 with respect to λ and putting the derivative equal to zero one get thewavelength at which Eλ(λ, Ts) peaks:

d

dλEλ(λ, Ts) = 0 ⇒ λmaxTs = C (2.11)

With C being a constant equal to C = 2897.8 µmK. This relation between the peaking wave-length and the surface temperature is called Wien's displacement law. In Fig. 2.5 the Wiendisplacement along with the Planck distribution are shown for dierent temperatures.

Figure 2.5: The Planck distribution for a black body at dierent temperatures as well as the Wiendisplacement. Only black bodies with a temperature over ∼800 K emit radiation in the visiblespectra. Black bodies with lower temperatures emit radiation in the infrared spectra. [3]

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2.3.1 Emissivity

Wien's displacement law, the Planck distribution, and the Stefan−Boltzmann law are only validfor perfect black bodies. In reality no material has the exact characteristics of a black body. Whenlooking at emitting thermal radiation, all real bodies emit less (or equal) amount of radiation thana black body would do at the same temperature. A real body possess a property called emissivity,ε, that describes how well, compared to a black body, it emits thermal radiation. Emissivitydepends on the wavelength and the direction of the radiation, as well as on the temperature, i.eε = ελ,Ω(λ, θ, φ, T ). This makes the temperature dependence of the thermal radiation less trivialsince the spectral directional emissivity of a real body is dened as:

ελ,Ω(λ, θ, φ, T ) ≡ Iλ,real(λ, θ, φ, T )Iλ,black(λ, T )

(2.12)

The reason Iλ,black(λ, T ) do not depend on the space angles is simply because the black body isa diuse emitter. Depending on the situation there are alternative ways of dening the emissivity.When looking at the total wavelength spectra, the total directional emissivity is dened as:

εΩ(θ, φ, T ) ≡ Ireal(θ, φ, T )Iblack(T )

(2.13)

When looking at the total hemispherical radiation the spectral hemispherical emissivity isdened as:

ελ(λ, T ) ≡ Eλ,real(λ, T )Eλ,black(λ, T )

(2.14)

The total hemispherical emissivity is dened as:

ε(T ) ≡ Ereal(T )Eblack(T )

=

∫∞0ελ(λ, T )Eλ,black(T )dλ

Eblack(T )(2.15)

In Fig. 2.6 a comparison between the emission of a real surface and a black body is shown.

Figure 2.6: Comparison between the emission of a black body and a real body. (a) shows thespectral distribution and (b) shows the directional distribution. [3]

2.3.2 Absorptivity, reectivity and transmissivity

Radiation leaving a surface is not only emitted radiation, but also transmitted and reected,see Fig. 2.7. So in addition to emissivity, ε, real surfaces also have the properties absorptivity(α), reectivity (ρ), and transmissivity (τ). By looking at the radiation from a surface one getscontributions from the surrounding. This makes it more dicult to relate the radiation from asurface to its temperature.

13

Figure 2.7: a) shows the origin of radiation leaving a surface. b) shows what happens at anirradiated surface. Where α is the absorptivity of the surface, τ the transmissivity, ρ the reectivity,and ε the emissivity. In general α are not equal to ε, but they can be equal under specic conditions.

The properties for an irradiated surface α, ρ, and τ depend on the wavelength, λ and one thesolid angle, Ω. They are dened as:

αλ,Ω(λ,Ω) ≡ Iλ,i,abs.(λ,Ω)Iλ,i(λ,Ω)

(2.16)

ρλ,Ω(λ,Ω) ≡ Iλ,i,refl.(λ,Ω)Iλ,i(λ,Ω)

(2.17)

τλ,Ω(λ,Ω) ≡ Iλ,i,trans.(λ,Ω)Iλ,i(λ,Ω)

(2.18)

They can also be dened as the total directional, the spectral hemispherical, and total hemi-spherical α, ρ, and τ in a similar way that the emissivity was in Eq. 2.13 - 2.15. As mentioned inFig. 2.7 α 6= ε in general but there are exceptions.

1. αλ,Ω = ελ,Ω is always true, since αλ,Ω and ελ,Ω are inherent surface properties.

2. αλ = ελ if the irradiation is diuse or if the surface is diuse.

3. α = ε if 1. and 2. are true and if irradiation correspond to emission from a black body atthe same temperature as the surface. Or if 1. and 2. are true and if the surface is grey, i.eαλ and ελ are independent of λ.

For the proof of these postulations the reader is referred to section 12.7 in [3].

αλ is dependent on the irradiation of the surface whilst ελ is independent of it. This meansthat for point 3 in the list above to be true ελ and αλ does not have to be independent of λ forall wavelengths, but only over the spectral range of the irradiation. This is the denition of a greysurface that says: "a surface is a grey surface if αλ and ελ are independent of λ over the spectralregion of the irradiation".

For the irradiation the following function holds:

α+ ρ+ τ = 1 (2.19)

But since α 6= ε in general the equation: ε+ ρ+ τ = 1 does not hold, in general. By knowingρ and τ one does not necessarily know ε.

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2.4 Temperature measurement

Measuring the temperature of a system involves a complex interaction between the sensor andthe system. The sensor changes its behaviour with temperature or with a property related to thetemperature. This change produces a signal that is processed by a signal processor and is fromthere sent to an actuator. This course of event is shown in Fig. 2.8.

Figure 2.8: Showing an information system consisting of a sensor, a signal processor, and anactuator.

The physical signal in temperature measurement is usually related to the heat transfer betweenthe sensor and the system changing the temperature of the sensor. In most thermal sensors heatis transferred between the sensor and the system of interest until they are at thermal equilib-rium, i.e have the same temperature. This temperature depend on the initial thermal propertiesand the mass of the system and the sensor, since the heat transfer goes two ways. If the factorcp,sensormsensor is comparable to cp,systemmsystem than there is risk that the temperature of thesystem changes. For a system's temperature not to be aected by the heat transfer with the sensorthe equality cp,sensormsensor cp,systemmsystem must hold. This is achieved by using a smallsensor with a small specic heat. It is also an advantage that the thermal conductivity of thesensor is large so that it fast reaches thermal equilibrium. Some sensors measures the heat uxbetween the sensor and the target and can from there achieve the temperature of the target. Butin order to achieve the temperature of the target a reference temperature must be known, i.e thetemperature of the sensor. The reason for this is that heat ux is dependent on the temperaturedierence between the bodies exchanging heat.

As discussed heat transfer is accomplished through three dierent mechanisms: conduction,convection and radiation. For the two rst mechanisms the sensor needs to be in contact with, orin close proximity to the system of interest. Otherwise the heat transfer will be between the sensorand another system and the temperature felt by the sensor is not the one of interest. Sensorsthat exchange heat through radiation need not to be in close proximity to the target. But as thedistance between the target and the sensor grows so does the sources of error. With increasingdistance the atmosphere, i.e the medium between the target and the sensor, aects the radiationmore as well as the background radiation. More of how dierent sensor works will be discussed inchapter 4.

15

3 The Yankee dryer

The objective of this project was to investigate methods for measuring the temperature of theYankee dryer. In order to get a better picture of the system this section will be devoted todescribing the Yankee and the environment around it. The Yankee dryer was explained shortlyin section 1.1.2 so some references will be made to this section. Fig. 1.3 shows an overview ofthe dierent processes involving the Yankee cylinder. To follow the Yankee one revolution one canpoint out four dierent processes:

1. Coating shower

2. Nip process

3. Hood dryer

4. Creping process

These processes will be discussed more thoroughly in the following subsections. But rst itcan be useful to get a picture of the dimensions of the Yankee. As many of the machines thatMetso Paper manufacture are custom made so are the Yankee dryers. Some of the Yankee dryer'sconstructional parameters are listed in table 1 below.

Parameter Min. value Max. valueLength (mm) 3 380 6 500Diameter (mm) 3 660 5 500Mass (kg) 65 000 133 000Machine speed (m/min) 200 2 000

Table 1: Some of the constructional parameters of the Yankee dryer. These values are taken fromstandard Yankee dryers. So for the custom made ones parameters can be outside the range of thetabulated values.

The Yankee dryer is made of cast iron that is highly polished on the shell surface so that thepaper is dried on a smooth and uniform surface. To achieve this ne surface the Yankee dryer isworked upon in two steps. In the rst step the Yankee dryer is turned in a lathe so that almost theright shape is achieved. In the second step a ner grind is made to achieve the polished surface.The crowning, as discussed in 1.1.2, is made in both steps. Having such a polished cast ironsurface makes it sensitive to oxidation. In the following sections the dierent processes involvingthe Yankee dryer will be discussed, beginning with the inside of the Yankee.

3.1 Inside the Yankee dryer

As was shown in Fig. 1.4 the Yankee dryer is heated from the inside by overheated steam. As arule of thumb the steam pressure varies between 6-9 bar depending on the process. Since the papercools the cylinder from the outside thermal energy is transferred from the steam which causes thesteam to condensate. Depending on the rotational speed the condensate is assembled dierently onthe inside of the Yankee dryer. In Fig. 3.1 three dierent assemblies are shown. As the rotationalspeed seldom is lower than 600 m/min the condensate is in general assembled as a ring on theinside shell (the image to the right in Fig. 3.1).

Because condensate is covering the inside of the Yankee dryer the maximum temperature thatcan be achieved here is given by the saturated steam temperature at the appropriate pressure. Agraph showing how the saturated steam temperature varies with pressure is shown in Fig. 3.2. Assaid above the pressure varies between 5-9 bar which corresponds to a maximum inside tempera-ture variation of ∼160-180C.

The steam is removed from the shell surface by headers, see Fig. 1.5. The headers consist ofsmall metal pipes that acts as straws and suck up the condensate. The headers rotates along withthe Yankee dryer. This imply that the condensate layer inside is not uniform since it is thinner near

16

Figure 3.1: Showing how the steam condensate assemblies on the inside of the Yankee dryer.

Figure 3.2: Showing how the saturated steam temperature varies with pressure. For a givenpressure this temperature corresponds to the maximum temperature on the inside of the Yankeedryer.

the headers. The behaviour of the condensate layer aects the inner temperature of the Yankeedryer. A thicker condensate layer reduces the heat ux between the steam and the paper. Thismeans that higher steam pressures must be used which demands more energy resulting in highercosts for the paper manufacturer. In order to maximize the heat transfer between the steam andthe paper the inside walls are covered with grooves. The grooves are 25-32 mm deep, 12 mm wideand separated by 30 mm. The condensate assemblies inside these grooves which makes it easierfor the headers, that run in the grooves, to remove it.

If the headers do not function properly, i.e remove too little condensate, this will change thetemperature prole of the Yankee dryer. Since an uneven temperature prole will cause an uneventhermal expansion, a malfunctionning header will cause a number of problems in the processesinvolving the Yankee dryer. A fast and dependable temperature measurement method woulddetect an uneven temperature prole and help nding the errors in a process.

3.2 Coating

Just before paper is pressed onto the Yankee cylinder the cylinder is sprayed with a aqueoussolution. This solution contains of adhesives and release agents. Their task is to optimize theadhesion of the paper on the Yankee dryer, as well as protecting the cylinder from corrosion andthe wear caused by the doctor blades. The solution is sprayed through a number of nozzles attached

17

to a boom situated just before the nip. The boom oscillates in order to avoid streaks on the Yankeedryer surface. A picture of this process is shown in Fig. 3.3. The chemicals are most commonlydierent polymers as adhesives and dierent oils as release agents [1]. Depending on the tissuegrade that is being manufactured a lot of dierent combinations of coating solutions are used.

Figure 3.3: The aqueous solution is sprayed onto the surface from the nozzles. While spraying theboom is oscillating to avoid streaks on the Yankee cylinder surface. [1]

When the aqueous solution hits the Yankee cylinder the water is evaporated leaving the chemi-cals on the cylinder. The chemicals form a tacky coating on the cylinder that changes the surface'sadhesive properties as well as its appearance. A clean Yankee dryer, without any coating or paperrests on it, is a polished cast iron surface, making it highly reective. The coating makes thesurface look white and dull. A thick coating layer seems opaque to the eye. A picture of how thecoating layer changes the appearance of the surface is seen in Fig. 3.4.

Figure 3.4: Showing how the Yankee dryer's surface appearance changes when the coating isintroduced. a) and c) shows a clean Yankee before the coating was introduced. b) and d) showsthe surface after the coating was introduced but before any paper was pressed on the Yankee dryer.It is obvious that the reectance of the surface decrease when the coating is introduced.

18

3.3 Nip load & Hood dryer

As described in section 1.1.2 the paper is pressed onto the Yankee dryer in the nip process. MetsoPaper produces machines that use a single nip as well as machines that use a double nip. Theadvantage of using a double nip is that more water can be pressed out of the paper before it isattached to the Yankee dryer. Having a higher dryness percentage before the Yankee dryer savesenergy since less water has to be evaporated by the Yankee dryer. Depending on the dryness ofthe paper and the speed of the machine the paper cools the cylinder dierently.

The heat from the Yankee dryer is not sucient to dry the paper which is the reason for theuse of a hood dryer. The hood dryer operates by blowing hot air jets through nozzles onto thepaper. As is seen in Fig. 1.2 the hood dryer covers much of the Yankee dryer's surface, in order toblow as much hot air as possible on the paper. A picture of how the hood dryer operates is seenin Fig. 3.5.

Figure 3.5: Showing how the hood dryer operates (left image) and the dierent heat uxes in thepaper while on the Yankee dryer (right image). The heat ux in the paper comprise conductionof heat from the Yankee dryer and forced convection of heat from the air jets. If much water isremoved the Yankee dryer is heated by the air jets.

The temperature of the air blown from the hood dryer varies, depending on the process, andcan be up to 700C. The impingement speed is also varied and can be up to 185 m/s. If too muchof the water is removed the hood dryer warms up the Yankee dryer surface instead of drying thepaper. Since the size of the nozzles can be varied, so can the jet streams. An uneven temperaturedistribution of the Yankee dryer surface can be corrected by changing the size of the nozzles.As discussed earlier uneven temperature distributions can cause problems in the manufacturingprocess.

3.4 Creping process

The creping process is simply scraping the paper o the Yankee dryer with the doctor blades. Inthis process much of the papers nal quality is determined. When the paper reach the doctorblade it begins to wrinkle which breaks the physical structure of the sheet. So called microfolds(wrinkles) are created and pile up on top of each other on the doctor blade. When a critical num-ber of microfolds have been stacked on each other the pile collapses and a new pile of microfoldsbegins to grow. These piles of microfolds are called macrofolds, see Fig. 3.6. The structure ofthese microfolds and macrofolds determine the smoothness of the paper surface [1].

The structure of the micro- and macrofolds can be varied by changing the impact angle of thedoctor blade, see Fig. 3.6. Using a large impact angle, the crepes fall o the blade easier. Thisaects the macrofolds in such way that the number of microfolds per macrofold decreases with anincreasing impact angle. A sheet with a large number of microfolds per macrofold has a high basisweight as well as high smoothness. This is a very simple picture of the creping process since it alsodepends on adhesion, geometry, and presence of a coating layer to name a few [1]. A more detaileddiscussion on this process is however outside the scope of this work.

19

Figure 3.6: The creping process. a) shows creping with a large impact angle. b) shows crepingwith a small impact angle. With a larger impact angle the crepes fall of the blade easier whichdecrease the number of microfolds per macrofold.

In an ideal paper machine the doctor blade would only crepe o the paper leaving the Yankeecylinder and the coating layer unchanged. With the high speeds of these machines (up to 2000m/min) this is a dicult task. During the creping process there are three doctor blades, see Fig.1.3. The doctor blade that comes rst in the process is the cut-o doctor that scrapes o thepaper while the creping doctor is being substituted. The next doctor is the creping doctor whichcrepes the paper and the last is the cleaning doctor. The cleaning doctor scrapes much of thepaper residues as well as some coating. Without the cleaning doctor the surface would not be assmooth as required due to the paper residues. Since some of the coating is removed, new coatingis constantly sprayed on the Yankee dryer.

As mentioned the crepe doctor is changed fairly often since it experiences big wear duringoperation which worsens its performance. Due to this wear the coating thickness varies with timesince a fresh doctor scrapes of more coating and paper residues. It is not unusual that the doctorsscrapes uneven in the cross machine direction leading to an unevenly coating layer. This aectsthe heat transfer and the appearance of the surface.

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4 Sensors

4.1 Thermocouples

In 1821 Thomas Johann Seebeck discovered the thermoelectric eect when he observed a magneticneedle move when being close to a circuit consisting of two metals, copper and bismuth. The circuithad two junctions, where the metals connected, which was held at dierent temperatures. Sincethe theory of the relation between electric and magnetic elds was still being investigated, Seebecknever recognized that an electric current was owing in the circuit. Instead Seebeck believed thatthe metals got directly magnetized by the temperature gradient and therefore called his discoverythermomagnetism. Later the discovery was renamed to the thermoelectric eect. An image of theexperiment made by Seebeck can be viewed in Fig. 4.1.

Figure 4.1: Showing the set-up of Seebeck's experiment that unveilled the thermoelectric eect.[4]

Since its discovery the thermoelectric eect has found many practical applications, one of thesebeing a thermocouple. In its simplest form a thermocouple consists of two wires consisting ofdierent materials that are connected to each other at one end. In the other end the two wires areconnected to a voltmeter. The set-up of a simple thermocouple is better understood from Fig. 4.2.

Figure 4.2: A simple thermocouple. Two metal, or semiconducting, wires forms a junction atone end and are connected to a voltmeter at the other end. Since the two end are at dierenttemperatures a voltage is created in the circuit which can be sensed by the voltmeter.

The voltage, ∆V , that the voltmeter senses is due to a temperature dependence of the Fermilevel, EF , in the two materials. This dependence is described by the Seebeck coecient [5]:

αs(T ) =1q

dEFdT

(4.1)

Where q is the electron charge. Rearranging Eq. 4.1 the voltage dierence of a single wire in atemperature gradient that varies along the wire in the interval T ∈ [T1, T2] can be written as [6]:

∆V = ∆EF = q

∫ T1

T2

αs(T )dT (4.2)

21

Now combining two wires, as in Fig. 4.2, the measured voltage becomes:

∆V = q

∫ T0

T1

αs,1(T )dT−q∫ T0

T1

αs,2(T )dT = q

∫ T0

T1

αs,1(T )−αs,2(T )dT = q

∫ T0

T1

αs,12(T )dT (4.3)

Where αs,1(T ) is the Seebeck coecient of metal 1. It is clear from Eq. 4.3 that if the two wiresconsist of the same material, i.e αs,1 = αs,2, no voltage would be produced in the circuit. Themagnitude of the voltage is on the order of µV/K, so one need to use a quite sensitive voltmeter.A table of absolute Seebeck coecients of a number of metals can be viewed in Table 4.1, thistable is taken from [5].

Metal 273 K 200 KChrome (Cr) 18.8 17.3Gold (Au) 1.79 1.94Copper (Cu) 1.70 1.83Silver (Ag) 1.38 1.51Rhodium (Rh) 0.48 0.4Lead -0.995 -1.047Aluminium (Al) - -1.7Platinum (Pt) -4.45 -5.28Nickel (Ni) -18.0 -

Table 2: Absolute Seebeck coecients, αs, for a number of metals. Notice that some metals havenegative values of αs.

As is shown in Table 4.1 some metals have positive αs and some have negative. By conventionthe sign of αs represents the voltage dierence between the cold and warm end of the conductor.The sign of αs is determined by how charges accumulate in the materials due to the temperaturedierence. What happens in the metal is that charge carriers at the hot end get more energetic,due to the higher temperature, than the charge carriers at the cold end. The more energetic chargecarriers therefore diuse towards from the hot end to the cold end. This diusion continues un-til a voltage dierence between the hot and cold end is built up, ∆V , that prevents further diusion.

From this discussion all metals, having only electrons as charge carrier, should have the samesign on αs. But an increased temperature also aects the mean free path and the scattering timeof the charge carriers. If the mean free path increases much or if the scattering time decreasesmuch with temperature the high energetic charge carriers gets trapped at the hot end. This leadsto an accumulation of charge carriers at the hot end which, having only one charge carrier, wouldhave the opposite sign of the voltage than in the previous case.

This situation gets more complicated for semiconductors where there are two charge carriers,electrons and holes. Holes diusing from the hot to the cold end would give the same sign of thevoltage as electrons diusing from cold to hot.

In order to measure the temperature with a thermocouple either the thermoelectric junctiontemperature or the terminus connection must be known. This is because the produced voltagedepends on the temperature dierence as stated in Eq. 4.2. One can solve this problem by keep-ing one of the temperatures constant or by measuring one of the temperatures with an externaldevice. One way of keeping the temperature constant can be by keeping the terminus connectionimmersed in ice water which keeps the temperature constant at 0C. This makes the temperaturemeasurement device rather dicult to use since one always need a bucket of ice water. A morecommon way is to measure the temperature at the terminus connection with an external device.

Since any two conducting materials with dierent αs can form a thermocouple, the number ofpossible thermocouples are numerous. In order to get the behaviour of the thermocouples stan-dardized eight standard types of thermocouples have been characterized that can be divided into

22

three groups. An overview of the standard types and groups can be viewed in Table 4.1.

Group Types ApplicationRare-metal B,R and S Suitable for high temperature

measurements. Are more expen-sive than the other groups.

Nickel-based K and N Suitable to use in the tempera-ture interval between the othergroups.

Constantan negative E,J and T Suitable for measuring low tem-peratures since they have a highSeebeck coecients at low tem-peratures.

Table 3: The three standard groups and eight types of thermocouples.

The standardized types have stringent guidelines on their behaviour. There are reference ta-bles where the thermoelectric voltage versus temperature is listed for the dierent types. Thesetables relates the thermoelectric voltage to the temperature of the thermoelectric junction for athermocouple with the terminus connection kept at 0C. The values in these tables were obtainedfrom polynomial functions on the form.

∆V =n∑i

ai(t90)i (4.4)

With n being the power of the polynomials varying between 4 and 14 depending on the typeof thermocouple. Since not all thermocouples have their terminus connection kept at 0C thesepolynomials can be used to obtain the temperature of the thermocouple junction. This is done bythe following algorithm [6]:

1. Measuring the voltage across the terminus connection.

2. Measuring the temperature at the terminus connection with an external device.

3. Converting the measured temperature in point 2 into an equivalent voltage using the poly-nomials.

4. Adding the measured voltage in point 1 and the equivalent voltage in point 3 into a totalvoltage.

5. Converting the total voltage in point 4 to the corresponding temperature using the polyno-mials.

23

4.2 Thermopiles

Since the thermoelectric voltage produced by thermocouples are rather low, thermocouples arenot good at measuring small temperature dierences. To overcome this issue one can connect anumber of thermocouple in series with their thermocouple junctions and terminus connections atthe same temperatures, see Fig. 4.3.

Figure 4.3: A simple thermopile conguration with six thermocouple connected in series. Thevoltage produced by the the thermopile is six times the voltage of the individual thermocouplevoltage.

Just connecting six thermocouples in series, as in Fig. 4.3, does not increase the thermoelectricvoltage much. Therefore a larger number of thermocouples need to be connected in series. Thiscan be hard to achieve with long metal wires, but is easier achieved through micro machining.In this way thermopiles can be made very small, which enable them to respond to temperaturedierences fast. This in turn make them suitable for non-contact temperature measurements, i.emeasuring the thermal radiation from a system. An example of a micro machined thermopile isseen in Fig. 4.4.

Figure 4.4: A schematic diagram of a thermopile detector structure. The thermocouple consti-tuting the thermopile are made of Bi-Te (orange) and Bi-Sb-Te (grey). The thermocouples areconnected in series by the interconnecting wires and the aluminium interlevel contacts. On top ofthe thermocouples is a layer of silicon nitride that exchange heat through thermal radiation withthe target. The temperature of the silicon substrate is measured with a thermistor (not shown inthe gure) in order to get the temperature of the terminus connections. [7]

An uncooled thermopile need to exchange relatively much radiation with the target in order to

24

perform well. So they usually operate in a broad spectral range, i.e receiving radiation from a largenumber of wavelengths. Working in a broad spectral range introduces some diculties since thegases also emit and absorb radiation. Though air seem transparent to humans it is opaque in somespectral ranges, see Fig. 4.5. If a detector would detect radiation in these spectral regions, someof the signal would come from the air which would result in an erroneous measurement. Some ofthe signal would also be absorbed by the air which also results in errors. Therefore sensors aredesigned to operate in spectral ranges where the atmosphere have large transmissivity. For sensorsoperating in air one of the following ranges are used:

Name Spectral range (µm)Middle Wavelength IR (MWIR) 3-5Long Wavelength IR (LWIR) 8-14Very Long Wavelength IR (VLWIR) 14-30

Figure 4.5: The transmissivity for air over a 300 m distance. The dark regions indicate that theair is opaque. A infra-red detector that operate at wavelengths where the air is opaque would giveerroneous measurements, since part of the signal then originate from the air. [6]

As has been discussed in section 2.3, the relation between thermal radiation and temperatureis described by the Stefan-Boltzmann law (Eq. 2.7) and Planck's law (Eq. 2.8). For thermopiledetectors the Stefan-Boltzmann law is most commonly used to describe the interaction betweenthe detector and the target. The reason for this is because thermopile detectors operate in a largespectral range. According to reference [8] PerkinElmer thermopile detectors are calibrated usingthe formula:

∆V = K(εtargetT 4−δtarget − T 4−δ

detector) (4.5)

Where Ttarget is the target temperature, εtarget is the emissivity of the target, Tdetector is thetemperature of the backside of the detector, K and δ are the detector parameters that is specicfor the detector and tells how it responds to a heat ux. The reason for the smaller exponent ofEq. 4.5 compared to the Stefan-Boltzmann law is because not the whole electromagnetic spectrais seen by the detector. From Eq. 4.5 one see that the thermopile sensor is calibrated to respondto the heat ux between the target and the thermopile.

The two parameters K and δ are usually temperature dependent (both of Ttarget and Tdetector)which limits the temperature range of the thermopile detector. To achieve more accurate measure-ments in a wide Ttarget-range the detector is cooled, in order to reduce the Tdetector dependenceon the accuracy.

25

4.3 Sensors similar to thermocouples

There are a lot of sensors functioning in a way similar to thermocouples, i.e changing its behaviourwith changing temperature. They can be used either as contact measurement sensors or as infra-red sensors. The two most usual physical phenomena used in temperature sensors that has anelectrical output signal, apart from the thermoelectric eect, are the pyroelectric eect and thetemperature dependence of the electrical resistance.

4.3.1 Resistance thermometer & bolometer

The electrical conductance for a metal or a semiconductor is described by the equation:

σ =ne2τem∗e

+pe2τhm∗h

(4.6)

where n is the electron density, p the hole density, e the electron charge, τ the mean timebetween collisions, and m∗ the eective mass. The subscripts e and h stands for electron and holerespectively.

From Eq. 4.6 one can identify two parameters that vary strongly with temperature, namelythe mean time between collisions and the charge carrier density. With increasing temperaturethe atoms in the material vibrate more about there equilibrium positions, i.e the phonon densityincreases. With increasing phonon density the probability of electron-phonon scattering increases,i.e τ decreases. But as the temperature increases more charge carriers are excited to the conduc-tion band and can contribute to an electrical current. Put shortly, with increasing temperaturethe charge carrier density increases but the mean time between collisions decreases. For semicon-ductors the charge carrier density is more prominent than τ in equation 4.6, and the opposite formetals. But for larger temperatures τ gets more prominent even in the case of semiconductors.Since resistivity is the inverse of conductivity (R = 1/σ) the resistance decreases with increasingtemperature for semiconductors (at low temperatures) and increases for metals. Both metals andsemiconductors can be used to measure the temperature if their resistance has a stable dependenceon temperature.

The temperature dependence can either be used in contact thermometers or in thermal radia-tion sensors. Resistance temperature detector (RTD) is the name of contact thermometers madeof pure metals, usually platinum. RTDs work in wide temperature ranges with high accuracy butthey need to be relatively big. The relatively large size of the RTD makes them less sensitive forsmall temperature changes and gives them a longer response time than the thermistors.

While RTDs are made of pure metals, thermistors can be made of dierent materials. Usuallythey are made of ceramics or polymers. Their temperature dependence of the resistance is not asstable as the RTDs in wide temperature ranges, but is more sensitive to small temperature changesin small temperature ranges. This property enables thermistors to be made smaller than RTDs,and thereby more suitable to use in radiation sensors.

Radiation sensors using thermistors are called bolometers and was invented in 1880 by SamuelPierpont Langley. His bolometer consisted of two thin wires of platinum covered with soot. Thewires formed two arms of a Wheatstone bridge, where one arm was exposed to the radiation andthe other shielded. Since Langley's bolometer these sensors have been developed a lot and platinumhas been substituted by dierent thermistor materials. The size of the bolometers have changedduring the years and are now micro-machined, just as thermopiles. A structure example of a microbolometer can be viewed in Fig. 4.6.

4.3.2 Pyroelectric sensors

Another physical phenomena that relates electricity and temperature is the pyroelectric eect.A pyroelectric material generates a temporary electrical potential when the temperature of the

26

Figure 4.6: A schematic sketch of the structure of a micro bolometer. The reason for the λ/4spacing is to form a resonant optical cavity to optimize the absorption of photons of wavelengthλ. [9]

material changes. This potential is used in radiation sensors, where the radiation changes thetemperature of the sensor. The created potential disappears after the dielectric relaxation time.So in order for a pyroelectric sensor to work as the radiation must be chopped. This is donemechanically, usually with rotating blades that periodically interrupts the incoming radiation.This way the sensor periodically changes its temperature which results in a periodically potentialoutput. The periodical potential can be related to the targets temperature since the heat owbetween the sensor and the target is proportional to T 4−δ

target − T 4−δsensor as in Eq. 4.5.

4.4 Thermal IR sensor

In this section some general properties of a thermal detector used for radiation measurement willbe discussed. As mentioned bolometers, thermoelectric- and pyroelectric sensors all work in asimilar way. They absorb thermal radiation which results in a temperature change of the sensorwhich in hand results in an electrical output signal. In reference [10] Rogalski presents a generaltheory for these sensors. He begins with a general picture for such a sensor, Fig. 4.7.

Figure 4.7: A general image of a thermal radiation sensor. The thermal sensor receives radiationwhich changes is temperature from the heat sinks temperature T by an amount of ∆T . The sensorhas a thermal capacity Cth and is connected to the heat sink via the thermal conductance Gth.[10]

The temperature change, ∆T of the sensor in Fig. 4.7 when exposed to a periodic radiant uxq′′ with frequency ω can be expressed as:

∆T =αq′′

G2th + ω2C2

th

(4.7)

27

with α being the absorptivity of the sensor. From Eq. 4.7 it is clear that the temperaturechange can be maximized through one of the following procedures:

• Maximize the absorptivity, α.

• Minimize the thermal capacity, Cth.

• Minimize the the thermal coupling to the surrounding, Gth.

An example of design made to maximize the absorptivity is seen in Fig. 4.6 where a reectivelayer is inserted behind the absorbing layer. The reective layer reects the radiation transmittedby the absorbing layer back to the absorbing layer. A solution to minimize the thermal capacityis simply to make the sensor as small as possible. To minimize the thermal coupling to the sur-rounding it is advantageous for the sensor to operate in a vacuum environment or at least at a lowpressure. It is also favourable for the connections between the sensor and the heat sink to be madeas small as possible.

Since the temperature change is proportional to the electrical output, it is an advantage for itto be big. Another property that is important for these sensors is the thermal response time τth,i.e how fast the sensor can adjust to temperature changes. This property can be expressed as:

τth =CthGth

= GthRth (4.8)

where Rth is the thermal resistance. Now in order to minimize τth, Cth should be minimized andGth should be made big. Making Gth big contradicts the last point in the list of how to maximize∆T . Depending on the situation Gth is either made big or small. For a fast moving target, or fora target that changes it temperature quickly, a small Gth is desirable. For thermal sensors τth isusually in the ms range.

Another gure of merit for sensors is the specic detectivity, D∗, which is the normalized signalto noise ratio. Rogalski discuss three dierent noise sources for a thermal sensor, namely:

• Johnson noise, due to thermal agitation of the charge carriers in an electrical conductor.

• Thermal uctuation noise, due to temperature uctuations in the sensor.

• Background uctuation noise, due to variations in the background radiation.

Dierent sensors are limited by dierent noises, but a well designed sensor is either limited bythe thermal or background uctuations. The detectivity for such a sensor can be expressed as:

D∗ =(

α2A

4kBT 2sensorGth

)1/2

(4.9)

If the heat transfer is dominated by heat transfer through radiation, then Gth is the rstderivative of the Stefan-Boltzmann equation with respect to temperature. Eq. 4.9 can then bewritten as:

D∗ =

(α

8kBσ(T 5sensor + T 5

background)

)1/2

(4.10)

where σ is the Stefan-Boltzmann constant, kB the Boltzmann constant, and α the absorptivity.In the equation it is seen that a sensor that is limited by the thermal and background uctuationsis optimized if the temperatures Tsensor and Tbackground is kept as low as possible.

For a sensor as the one discussed above the detectivity with a background temperature ofTbackground = 300K is 1.98 × 1010 cmHz1/2W−1. This detectivity is the ultimate limitation ofa thermal sensor and for most sensors other noise sources limit the performance decreasing thedetectivity. Typical values of the detectivity for real thermal sensors are on the order of 108 −109 cmHz1/2W−1 [10]. In most commercial product specications the detectivity is not listed.

28

Instead the minimum resolvable temperature dierence (MRTD) is given at a certain temperature.The MRTD can be dened as the minimum temperature dierence between a target and thebackground which still enables the target to be detected. The relation between MRTD and D∗

are discussed by Lopez-Alonso in reference [11]. No details on this relation will be discussed butrather just state how they are related:

MRTD ∝ 1∫∞0D∗dλ

(4.11)

Where the parameters relating the two are sensor specic parameters.

4.5 Photonic IR sensors

Unlike thermal IR sensors, photonic IR sensors generate an electrical signal directly from the in-coming radiation. The radiation excites electron-hole pairs in the photon sensor. As the chargecarrier density increases so does the conductivity. Monitoring the current in a photon sensorwill give information of how much radiation that is falling on the sensor. There are basicallytwo dierent ways of making use of the increased charge carrier density, namely by photodiodesor photoconductors. In photodiodes the photovoltaic eect is used in which an internal voltage,caused by a p-n junction, forces the charge carriers to move in a circuit. In photoconductors anexternal voltage forces the charge carriers to move in a circuit.

There are a lot of dierent materials that can be used as photon sensors so the spectral rangesthat they operate in can be engineered. The maximum wavelength of the sensor can be engineeredby controlling the bandgap Eg, since no electron-hole pair can be created if λmax ≥ hc

Eg. The

minimum wavelength can be achieved by using some material in front of the sensor with a largerband gap, Eg = hc

λmin.

An example of how the geometry of a photonic sensor can look like is seen in Fig. 4.8.

Figure 4.8: A general image of a photonic IR sensor. [10]

In the gure above all the basic components of a photon sensor are shown. Radiation from thetarget hits the concentrator and is deected towards absorber where the photons excite electron-hole pairs. The photons that are not absorbed are reected by the reector and hopefully absorbedon the way out.

The current responsivity, R, depends on the quantum eciency, η, and the photoelectric gain, g.The quantum eciency is usually dened as the number of electron-hole pairs created per incidentphoton. It tells how well the sensor interacts with the incident radiation. The photoelectric gain isthe number of electron-hole pairs that contribute to the current per created pair. Not all electron-hole pair contribute to the current since some recombine before reaching the contacts. The spectralcurrent responsivity can be expressed as:

29

Rλ =λη

hcqg (4.12)

Where q is the electron charge.Now there are, as in the case of thermal sensors, dierent sources of noise. If one assume that thecurrent induced by the noise has the same gain as the photoelectric one, the noise current due togeneration and recombination processes is given by [10]:

I2noise = 2(G+R)Aet∆fq2g2 (4.13)

where G is the generation rate, R is the recombination rate, ∆f the frequency band, Ae theelectrical area, and t the thickness of the absorber. The detectivity of a photonic sensor can bedened as [10]:

D∗ =Rλ(A0∆f)1/2

Inoise(4.14)

Now combining Eq. 4.12-4.14 one obtain the relation [10]:

D∗ =λ

hc

(A0

Ae

)1/2

η[2(G+R)t]−1/2 (4.15)

For a given wavelength the sensor's detectivity is optimized by maximizing η[2(G + R)t]−1/2.This is achieved by designing a sensor that has a high quantum eciency as well as a thin absorber.The generation and recombination processes is strongly dependent on the temperature of thesensor. Therefore the sensors usually are cooled to cryogenic temperatures so that the noise due totemperature uctuations is reduced. The optimal situation is when the optical generation, due tobackground radiation, is higher than the thermal generation. This is achieved when the followinginequality holds [10]:

ηq′′backgroundτ

t> nthermal (4.16)

where q′′background is the photon ux density due to background radiation, τ the carrier lifetime,and nthermal the density of charge carriers excited due to thermal excitations. If this relation holdsthe sensor is only limited by the background radiation which is always present, i.e one has an idealphotonic sensor. These sensors are called background limited infrared photodetector (BLIP). Thedetectivity of a BLIP photovoltaic sensor is given by [10]:

D∗BLIP =λ

hc

(η

2q′′background

)1/2

(4.17)

The BLIP detectivity for a photoconducting sensor is√

2 lower than for photovoltaic. Thisis due to the recombination process in a photoconducting sensor which is uncorrelated to thegeneration process, giving a contribution to the noise. Detectivities for a number of commercialsensors are shown in Fig. 4.9. It is clear that the photonic sensors are superior to the thermalsensors. Photonic sensors are also superior to the thermal sensors when is comes to response time,since they do not need to be heated in order give a response.

4.6 Techniques using IR sensors

The mentioned IR sensors electrical signal, S(T ), depend on the targets radiation as (Planck'slaw):

S(T ) ∝ c1∫ λ2

λ1

ε(λ, T )λ5[exp

(c2λT

)− 1]dλ (4.18)

where c1 is a constant that includes the constants of Planck's law as well as sensor constantsand c2 = hc0

kB. From Eq. 4.18 one see that the signal strongly depends on the emissivity of the

target. If the emissivity of the target is unknown the temperature measured by the IR sensor

30

Figure 4.9: Spectraldetectivities of com-mercially availablephotonic sensors. Allsensors have an updatefrequency of 1000 Hzexcept for the ther-mopile, thermocouple,Golay cell, and thepyroelectric detectorwhich have an updatefrequency of 10 Hz.Theoretical curves forthe detectivity of BLIP(ideal) sensors forphotovoltaic, photocon-ductive, and thermalsensors are also plotted.[10]

will not be the true temperature of the target. More on how the emissivity aects the measuredtemperature is discussed in section 5.6.1. There are however techniques that try to overcome thisdependence:

• Double-band pyrometers.

• Gold cup pyrometer.

These techniques will be described in more detail below.

Double-band pyrometer

The idea behind double-band (also called ratio- and two colour-) pyrometers is to use two photonicIR sensors measuring at dierent bands (spectral ranges). The ratio of these signal is then used toobtain an emissivity independent temperature measurement. When describing the signal for sucha sensor it is advantageous to use Wien's law. Wien's law is similar to and a good approximationto Planck's law when λT hc0

kB[12]. The signal of the sensor, S(T )i, is then described as [12]:

S(T )i =c1ε(λi, T )

λ5i exp

(c2λiT

) (4.19)

where i denotes the sensor letter, c1 and c2 the constants seen in Eq. 2.8. Dening the ratiobetween signal from sensor a and b as:

Γ =S(T )aS(T )b

=ε(λa, T )ε(λb, T )

(λbλa

)5

exp[c2T

(1λb− 1λa

)](4.20)

The ratio temperature can be obtained by rearranging Eq. 4.20:

TR = c2

(1λb− 1λa

)1

ln(Γ) + ln( ε(λb,T )ε(λa,T ) ) + ln(λ

5a

λ5b)

(4.21)

Now if the target is a grey body, i.e ε(λa, T ) = ε(λb, T ), Eq. 4.21 return the true temperature.A relation between the ratio temperature and the true temperature can be obtained by puttingtwo ratios (Eq. 4.20) equal to each other [13]:

exp[c2TR

(1λb− 1λa

)]=ε(λa, T )ε(λb, T )

exp[c2T

(1λb− 1λa

)](4.22)

31

where the left hand side of the equation correspond to the ratio temperature assumptionε(λa, T ) = ε(λb, T ). Rearranging in Eq. 4.22 one get that TR depends on the true temperature, Tand true emissivity ratio, ε(λb, T )/ε(λa, T ), as:

TR =(

ln(ε(λb, T )/ε(λa, T ))c2(λ−1

b − λ−1a )

+1T

)−1

(4.23)

From Eq. 4.23 one see again that TR = T if the emissivities are equal. TR also comes closeto T as λa and λb are largely separated. But separating λa and λb makes it more uncertain thatthe emissivities are equal. This is a simplied picture of the double-band pyrometer since thereare additional parameters aecting the signal, such as sensor parameters, but show the biggestobstacles and advantages of the technique.

One disadvantage of this technique is that relatively short wavelengths are used, in order forWien's law to be a good approximation to Planck's law (λT hc0

kB). Targets with low tempera-

ture, T < 300C, do not emit much radiation at these wavelengths. The small amount of radiationcoming from a cold target disappears in the thermal noise of the photonic sensors. So in order touse this technique to measure targets with low emissivity the sensors must be cooled to low tem-peratures. This makes these devices bigger, heavier, and more expensive. During the course of thisproject a search for double-band pyrometers that can measure temperatures around T ≈ 100Cwas made, but none was found. In order to get a double band pyrometer that measures suchtemperatures one probably has to order a custom made device further increasing the price.

There are also similar techniques utilizing more than two wavelength bands. These techniquest the dierent signals to dierent mathematical emissivity models, such as power functions (ε(λ) =aλb) and exponential functions (ε(λ) = exp(a + bλ)) [14]. Dierent models are used for dierentmaterials. These emissivity approximations work better for materials that are not grey. But to usethese models the target surface radiation properties must be known so that the best mathematicalmodel approximating the emissivity is used. These pyrometers also use photonic sensor with anarrow spectral range which makes them less suitable to use for low temperatures T < 300C.While searching for commercial products using this technique no products were found since theyare still very much under development.

Gold-cup pyrometer

This technique uses a gold-plated hemisphere that is placed very close to, ideally in contact, withthe target. Other coatings than gold can be used as long as they have a high reectivity. Insidethe hemisphere a quartz window is present through which an IR sensor can collect the radiation.The idea is that this hemisphere forms a blackbody cavity with the target surface. Since the goldis highly polished the hemisphere has a very high reectivity (ideally ρ = 1) which increase theeective emissivity of the target. This is done since almost all emitted radiation from the targetis reected back. So the background radiation falling onto the target is its own emitted radiation.Ideally this enhances the eective emissivity of the target to unity. But since it is impossible toconstruct a perfect reector, in practice the eective emissivity is smaller. A schematic of a gold-cup pyrometer can be viewed in Fig.4.10.

These types of pyrometers can use photonic as well as thermal IR detectors. Their electronicresponse, S(T ), to the radiation can be said to depend on the targets temperature as:

S(T ) ∝ εeff∫ λ2

λ1

1λ5[exp( c2λT )− 1]

dλ (4.24)

with εeff being the eective emissivity created by the target-gold-cup interaction, and [λ1, λ2]being the spectral range of the sensor. εeff is approximately given by [15]:

εeff =ε

1− ρ(1− ε)= 1− (1− ρ)(1− ε)

1− ρ(1− ε)(4.25)

32

Figure 4.10: Schematic of a gold-cup pyrome-ter. [15]

Where ε is the emissivity of the target, and ρ being the reectivity of the gold hemisphere.From Eq. 4.25 it is seen that the eective emissivity approaches unity as the reectivity of thehemisphere goes to unity. It is also seen that εeff depend on the emissivity of the target. To showthese dependences the eective emissivity was plotted versus the reectivity of the hemisphere forve xed emissivities of the target, see Fig. 4.11.

Figure 4.11: Plotof εeff versusρ for ve xedemissivities.

From Fig. 4.11 it is clear that large errors is obtained if the gold cup pyrometer does not havea reectivity equal to one. Since the environment surrounding the Yankee cylinder is all but aclean environment (steam and paper dust) it is questionable if a gold cup could be kept as cleanas required. The fact that the gold-cup must be kept very close to the surface also introduces adiculty since the Yankee cylinder rotates with high velocities. If the gold-cup would come incontact with the Yankee cylinder it could be damaged. The damage could be in form of smallcracks in the gold hemisphere which would reduce the reectivity.

There are many commercial products using this technique, where Heitronics LT13EB is oneexample of such a product.

33

5 Experimental

In order to investigate dierent temperature measurement methods three dierent devices weretested and the results was analysed. The devices that were tested were:

• The Thermophone, a contact measurement device.

• Raytek RAYNGER MX4, a pyrometer.

• FLIR P640, a thermographic camera.

All measurements were made on the pilot machine of Metso Paper in Karlstad. The machinehad dierent operational parameters during dierent measurements. So the true Yankee dryertemperature was not the same in all measurements. Some of the pilot machine's operationalparameters will be listed in the result for each measurement. In the following sections it will bediscussed how the measurements were performed.

5.1 Thermophone measurements

The Thermophone is the device that Metso Paper use at present to measure the temperature ofthe Yankee dryer. It measures the temperature with a thermocouple, discussed in section 4.1. Thethermoelectric junction is attached to a brass piece that is kept in close proximity to the Yankeedryer. This brass piece is kept inside a teon cup that shields the brass piece from the surroundingair streams. More on how the Thermophone is constructed is discussed in section 5.4.

The measurements were performed by rst attaching the thermophone to a ∼1.5 m long pole.While standing beside and under the Yankee dryer the pole was held in such way so that the teoncup of the Thermophone, was pressed uniformly against the Yankee dryer. Pressed uniformlymeans that the teon cup was pressed against the Yankee dryer so that little, or ideally no, aircomes in between the teon cup and the Yankee dryer. The Thermophone was held in contact withthe Yankee dryer for about 5-20 min. Between two consecutive measurements the Thermophonewas rested for about 10 min so that it would reach room temperature again. This was made inorder to investigate inuence of the teon cup temperature on the measured temperature. Thethermocouple signal was stored, along with the time, on a memory card (MMC) by a YSM3. TheYSM3 is a device constructed by Metso Paper used to display and store the temperatures measuredby the Thermophone. The stored values was imported to Microsoft Excel where they were madeinto graphs.

Figure 5.1: How the Thermophone was heldagainst the Yankee dryer during the measure-ments. The Thermophone was attached to a∼1.5 m long pole which was held so that theThermophone was in contact with the Yankeedryer.

Figure 5.2: Showing one good (left) and onebad (right) way of holding the teon cupagainst the Yankee dryer. If the teon cup isheld in a bad way cold air (∼ 50C) can owinto the teon cup and disturb the measure-ment. Ideally no cold air ow into the teoncup, but as can be seen in the results this wasnot always the case.

34

In order to compare these graphs to something, measurements were made on a non movingiron block with a surface curvature similar to the Yankee dryer surface. The iron block was heatedon a single stove plate and had a temperature of about ∼ 100C. The measured temperature wasstored on a MMC memory card along with the time. These values was also imported to MicrosoftExcel and made into graphs. Since no complicated air stream is present inside the teon cup heatis almost only transferred between the surface and the brass piece. Comparing the graphs frommeasurements made on the non-moving iron block to measurements made on the pilot machinecan get a hint of how the movement of the air streams inside the teon cup inuence the measuredtemperature.

5.2 Pyrometer measurements

The pyrometer measurements was performed with a Raytek RAYNGER MX4 (specications insection 5.5) while standing directly below the Yankee dryer, see Fig. 5.3. The distance betweenthe Yankee dryer and the pyrometer was approximately 30 cm. Dierent distances were tried butthese measurements gave the same result.

Figure 5.3: The pyrometer measurementsetup. The pyrometer was held directly be-low the Yankee dryer during operation. Itcollects radiation from a relatively small areacompared to the thermographic camera. Thearea it collects radiation from is circular witha diameter of ∼2 cm.

Since the emissivity of the surface was unknown and varying the emissivity used by the pyrom-eter (assumed emissivity) was set to εm = 1.0. If the assumed emissivity had been varied betweendierent spots and dierent occasions then the values would have been hard to compare.

While doing the measurements the surface was photographed with a digital camera. This wasdone in order to show the relation between the measured temperature and the surface nish. Themeasured temperatures was displayed on the pyrometer and written down on a piece of paper. Thevalues were associated with an area on the cylinder having a certain surface nish. The values waslater coupled with the photographs.

To get some sort of reference temperatures, simultaneous measurements were made with theThermophone. Even if the Thermophone do not show an exact value, these values can show thatthe temperature do not vary much over the surface. The values of the Thermophone was alsowritten down and coupled to the same areas as the pyrometer spots. During these measurementsthe RAYNGER MX4 was used as the display for the Thermophone. Since the Thermophone usea type K thermocouple that follows a standard no calibration was needed.

5.3 Thermographic camera measurements

In order to easier get a picture of how the thermal radiation from the surface varies, thermo-graphic pictures was taken. The camera used was a FLIR P640 which was borrowed from KarlstadUniversity. Lars Pettersson and Stefan Frodeson from Karlstad University helped to take thethermographic pictures. The aim of these pictures was to show:

• How the radiation varied on the Yankee cylinder.

• That the radiation varied less over the paper on the Yankee cylinder.

• What the temperature evolution of the Thermophone looked like.

35

Unfortunately no good thermographic pictures could be taken of the paper on the Yankee dryer.The reason for this was that no clear shots could be obtained since there were machine parts inthe way. The setup of how the thermographic pictures was taken can be viewed in Fig. 5.4.

Figure 5.4: The setup of how the thermographic pictures was taken. Pictures was taken from thetending side (TS) as well as from the drive side (DS). As the image shows the position of the camerawas below and beside the Yankee dryer. In numbers it was approximately 1.5 m below and 0.5 mbeside the Yankee dryer. By adjusting the lenses of the camera, the area from which radiation wascollected could be altered. All images were acquired with with the assumed emissivity εm = 0.99.

The pictures were taken in a similar way while a temperature measurement was made with theThermophone. The thermographic camera then zoomed in on the Thermophone and a numberof pictures were taken. The objective of these pictures was to show that the Thermophone getswarmer with time. After the measurements with the Thermophone was made, a picture inside theteon cup was taken in order to see the temperature distribution there.

After all pictures were taken with the thermographic camera, the pictures were imported toa computer and processed with a software from FLIR. One feature in this software is to creategraphs of how the temperature varies along a selected line. A couple of such line graphs were madein order to see more clearly how the temperature varied along the Yankee dryer.Another feature in the software is that one can get the maximum temperature of a selected area.This was made on the pictures of the Thermophone in order to get its maximum temperature. Yetanother feature allowed one to get the mean temperature of a selected area. This was made on apicture of a aluminium foil in order to get the background radiation.

5.4 Thermophone specications

As mentioned earlier in the report, Metso Paper already have a method for measuring the temper-ature of Yankee dryer surface, the Thermophone. The Thermophone consists of a thermocoupleinside a cup made of teon. The thermocouple is mounted on a circular thin brass piece that isheld in place by four metal wires, two of them being the wires of the thermocouple. The brasspiece should be kept as close to the Yankee dryer surface as possible without touching it. If thebrass piece comes in contact with the Yankee dryer it will get heated by frictional heating and anincorrect temperature will be measured. A sketch of the geometry of the Thermophone can beviewed in Fig. 5.5 below.

The purpose of the Teon cup is to protect the thermocouple from the surrounding air streamscaused by the motion of the Yankee dryer. These streams would otherwise cool the thermocoupleresulting in a incorrect temperature measurement. The reason for the choice of teon as materialis because of its low coecient of friction and its low thermal conductivity. With a material hav-ing a higher coecient of friction and thermal conductivity the cup would quickly get heated byfrictional heating which would disturb the measurement.

36

Figure 5.5: A sketch of the Thermophone geometry. The wires holding the brass piece in place aremissing in this picture. The geometry is cylindrically symmetric about the z-axis.

The brass piece and the teon cup are attached to a plate of stainless steel which holds all ofthe components of the Thermophone in place. On the stainless steel plate a footing is mounted onwhich a pole can be attached in order to easier perform the measurements. The footing and thestainless steel plate is shown in the pictures in Fig. 5.6.

The metal wires that holds the brass piece in place are attached to a circular piece of bre-glass. The reason for this is because breglass is a poor electrical conductor. If the wires hadbeen attached to a more conducting material the thermocouple output voltage would have beendisturbed, resulting in less accurate temperature measurement. The breglass piece is glued ontothe steel plate with an electrical isolating glue.

Even if the Thermophone looks like a simple temperature measurement device it is hard toanalyse the heat transfer involving the thermocouple. The fact that the Yankee dryer rotates fastduring the measurements promotes:

• Complicated air streams both outside and inside the teon cup.

• Frictional heating of the teon cup.

The frictional heating along with the air streams makes it hard to determine which heat transferthat contributes most to the thermocouple temperature. The surrounding air has an approximatetemperature of T = 50C and thereby cools the teon cup from the outside, since the Yankeedryer has a temperature around T = 100C. Even if the coecient of friction between the Yankeedryer and the teon cup is small (µ ≈ 0.1) frictional heating is unavoidable. The rate at which thefriction heats the teon cup can be estimated by:

q = F∆s∆t

= Fv = µNv = 0.1× 20× 30 = 60W (5.1)

with µ = 0.1 being the coecient of friction, N = 20N being the force at which the teoncup is pressed against the Yankee dryer, and v = 30m/s being the velocity of the Yankee dryer.The rate at which the friction heats the teon correspond to having a light bulb of 60 W heatingit. This is a very simple estimation but it shows that even for a small µ frictional heating is present.

The brass piece exchanges heat through convection both from the bottom (facing the Yankeedryer) and top side. The heat transfer on the bottom side can be approximated with a Couetteow which will be discussed more in detail in section 5.4.1. The top side exchanges heat throughconvection caused by the complicated air streams inside the teon cup. It is believed that the

37

Figure 5.6: Photos of the Thermo-phone. The upper photo shows howthe Thermophone looks like whenbeing used. Notice that the brasspiece is painted black. This wayit is obvious if the brass piece hasmade contact with the Yankee dryerduring measurement. The middlephoto shows the aluminium footingat which a pole can be attached tosimplify measurements. The lowerphoto shows the Thermophone whenthe teon cup has been removed. Ifone looks carefully one sees the ther-mocouple reection in the stainlesssteel plate.

temperature of the teon walls plays a prominent role in this heat transfer which will be discussedmore later. Heat is also conducted by the metal wires which keeps the brass piece in place whichfurther complicates the analysis of the heat transfer.

The output voltage of the thermocouple was received by a YSM3. The YSM3 was manufac-tured by Metso Paper as a display and storing device for the Thermophone. It basically consistsof a thermistor, an amplier, and a processor. The amplier receives the voltage output fromthe thermocouple and a voltage from the thermistor. These two input signals is then processedaccording to the list in the last part of subsection 4.1. After the processing the amplier sendsan output voltage to the processor that converts the analogue voltage signal to a digital one andconverts it into a temperature value. This temperature value is sent to a display and to a memorycard (MMC) where it is stored along with the time. The sampling rate of the YSM3 is 10 Hz, i.e10 temperature values per second.

5.4.1 Couette ow in Thermophone

A Couette ow is a ow between two parallel planes, where one plane is xed (brass piece) and theother one moves with a constant velocity parallel to the plane (Yankee cylinder). Since the owcan be seen as parallel, i.e the uid has only velocities in one direction, it has an exact solution.The discussion below follows the discussion of Couette ow in [3]. In Fig. 5.7 the geometry of theCouette ow is explained.

38

Figure 5.7: The parameters of the Couette ow. The velocities in the x− and y−direction is calledu and v respectively. The distance between the plates is h. The velocity of the Yankee dryer iscalled U .

The quantity of interest in the Couette ow, for the purpose of this report, is the heat ux atthe brass piece q′′y (h). In order to obtain this heat ux one rst has to get the velocity prole u(y).This is obtained by solving a momentum equation for a two dimensional ow:

ρ(u∂u

∂x+ v

∂u

∂y) = −∂p

∂x+

∂

∂xµ[2

∂u

∂x− 2

3(∂u

∂x+∂u

∂y)]+

∂

∂y[µ(

∂u

∂y+∂y

∂x)] +X (5.2)

where ρ is the density of the uid, µ the viscosity, p is the uids pressure, and X is a forceproportional to a uid elements volume. Eq. 5.2 looks hard to solve, but under the assumptionthat the ow is parallel a number of simplications can be made. To read more about thesesimplications the reader is referred to Chapter 6.4 in reference [3]. After these simplications Eq.5.2 reads:

∂2u

∂y2= 0 (5.3)

This equation looks more manageable and with the boundary conditions u(0) = U and u(h) = 0the solution is:

u(y) = −Uhy + U (5.4)

Now the objective is to obtain an expression for the heat ux q′′y (y). Another step on the wayis to solve the energy equation below:

ρcp(u∂T

∂x+ v

∂T

∂y) =

∂

∂x(k∂T

∂x) +

∂

∂y(k∂T

∂y) + µΦ + q (5.5)

Where µΦ is given by the expression:

µΦ = µ(∂u∂y

+∂v

∂x)2 + 2[(

∂u

∂x)2 + (

∂v

∂y)2]− 2

3(∂u

∂x+∂v

∂y)2 (5.6)

Just as in Eq. 5.2 a lot of simplications can be made in Eq. 5.5. From the assumption thatthe ow is parallel v = ∂T

∂x = ∂u∂x = ∂v

∂x = 0. Since no heat is generated in the area of interest one

can put q = 0. If one also assumes that ∂k∂x = 0 then Eq. 5.5 can be written as:

k∂2T

∂y2+ µ(

∂u

∂y)2 = 0 (5.7)

The partial derivative ∂u∂y is obtained from Eq. 5.4. So Eq. 5.7 can be written as:

39

k∂2T

∂y2= −µ(

U

h)2 (5.8)

Integrating Eq. 5.8 and using the boundary conditions T (y = 0) = TY and (Ty = 0) = Tth oneget the following expression for the temperature distribution in the y−direction:

T (y) =µU2

2k(y

h− y2

h2) + (Tth − TY )

y

h+ TY (5.9)

Using this temperature distribution in Fourier's law one obtain an expression for the heat uxin the y−direction:

q′′y (y) = −k∂T∂y

=µU2

2(2yh2− 1h

) + (TY − Tth)k

h(5.10)

It is this Couette heat ux that should be the dominating ux when the temperature of thebrass piece is determined. But as mentioned there is also a more complicated convection heat uxat the top side of the brass piece which also contributes to the heat ux to and from the brasspiece. If only the Couette ow was present then the Thermophone would give a good temperaturemeasurement, but with this other convection the measurement get disturbed.

The heating of the brass piece with contribution only from the Couette ow was simulated.This was done in order to get a picture of how the Thermophone would respond to the Yankeecylinder temperature without the disturbance from the complex convection. In the model the brasspiece was isolated at all surfaces except at the surface facing the Yankee dryer. The thickness of thebrass piece was neglected since it is only 0.1 mm thick and brass is a good thermal conductor. TheCouette ow was assumed to be fully developed over the whole brass piece and the properties of airwas assumed to be constant (independent of T and p). With these assumptions the temperaturechange, ∆T , of the brass piece under the time interval ∆t can be written as:

∆Tth =q′′y (h)A∆tcpm

(5.11)

where A is the area aected by the Couette ow, cp is the specic heat capacity, and m themass of the brass piece. Inserting the expression for q′′y (y) (Eq. 5.10) into Eq. 5.11 one get thefollowing expression:

∆Tth = [µU2

2h+ (TY − Tth)

k

h]A∆tcpm

(5.12)

This equation was implemented in the software MATLAB where the response of the brasspiece was simulated. The Yankee temperature was then assumed to be constant and equal toTY = 100C. The change in temperature of the brass piece for a small time step ∆t was expressedas:

∆Tth(t) = [µU2

2h+ (TY − Tth(t))

k

h]A∆tcpm

(5.13)

For every time step the brass piece temperature was updated through:

Tth(t) = Tth(t− dt) + ∆T (t) (5.14)

The brass piece temperature Tth(t) was then plotted vs. the time.

5.5 RAYNGER MX4 specications

The RAYNGER MX4 is a handheld pyrometer manufactured by Raytek. It measure the thermalradiation of a target and converts this into a temperature. This device was borrowed from theKarlstad University. A picture of this device can be seen below.

In order for a pyrometer to return a correct measured temperature the true emissivity of thetarget must be used. RAYNGER MX4 can use assumed emissivity in the interval ε ∈ [0.1, 1.0].

40

Figure 5.8: Showing how the brass piece at initial temperature T = 35C respond to a Yankeecylinder temperature of T = 100C. The heat transfer between the brass piece and the Yankeedryer is made through Couette ow. The brass piece is thermally isolated from the environmentexcept for the Couette ow.

Figure 5.9: A pic-ture of the RAYN-GER MX4. [16]

More on how the assumed emissivity aects the measured temperature will be discussed in section5.6.1.

This pyrometer is equipped with a laser sight that enables the user to measure the areas ofinterest more easily. It is a common misunderstanding that the laser sight is involved with thetemperature measurement. But the RAYNGER MX4 has a spectral range of λ ∈ [8, 14]µm and thewavelength of the laser is λ ≈ 0.6µm, so the laser does not inuence the temperature measurement.Since the RAYNGER MX4 uses a thermopile, see section 4.2, as sensor it needs to collect muchradiation (large spectral range) in order to respond accurately to the target's temperature. Thereason for this specic spectral range is that the transmissivity of air is large in this region, seeFig. 4.5.

RAYNGER MX4 can operate in the temperature range T ∈ [0, 50]C and detect temperaturesin the range T ∈ [−30, 900]C. These restriction are not violated when measuring the temperatureon the Yankee dryer, although the operation temperature gets close to T = 50C.

The minimum resolvable temperature dierence (MRTD) of this pyrometer is 0.1C up to900C, and the accuracy ±1% or ±1C whichever is greater. The accuracy value was measuredfor an operating temperature of T = 23C. Its response time is 250 ms giving the MX4 an up-date frequency of 4 Hz. So while measuring on the Yankee dryer a point on the surface moves30× 0.25 = 7.5m while collecting radiation. So the measured temperature is a mean value of the

41

points on the surface passing the sensor under 0.25 s.

As an accessory a thermocouple of type K can be connected to the MX4 that displays the tem-perature of the thermocouple. Using a thermocouple is a way of getting a reference temperatureof the target. This can give a good reference temperature if one has a good thermocouple and anon-moving target. The target of interest, in this work, is however rotating with a speed of ∼30m/s which makes it hard to measure the temperature with a contact temperature measurementmethod. The Thermophone was however used to get some reference temperatures. Even if thesereference temperatures does not give an exact absolute temperature they can show how the tem-perature varies over the surface.

The data in this section was taken from reference [16].

5.6 FLIR P640 specications

The instrument used to take the thermographic pictures was a FLIR P640. It was borrowed fromthe faculty of technology and science at Karlstad University. It is similar to the RAYTEK MX4in that it measures the thermal radiation and converts it into a temperature. A picture of thiscamera can be seen below.

Figure 5.10: A picture of the thermo-graphic camera FLIR P640. [17]

While RAYNGER MX4 only has one sensor FLIR P640 has an array of sensors in order tobuild up a thermographic picture. This array is called a focal plane array (FPA). There are twotypes of FPAs: scanning and starring FPAs. In the scanning FPA usually a single row of sensorsare scanned by a mechanical scanner. Each sensor has an electrical contact that goes from theFPA to the outside and each sensor are read individually. For a starring array the scanning isdone electronically by readout integrated circuits (ROIC). The array is 2D and the ROIC selectsone sensor at a time and read its electrical signal. Since the ROIC handles the scanning there isno need for a mechanical scanner and the devices using a starring FPA can be made smaller andfaster [10].

The P640 uses a 640x480 pixels staring array with uncooled microbolometers as sensors, seesection 4.3.1. The sensors operate in the spectral region λ ∈ [7.5, 13]µm which is the same atmo-spheric window as the MX4 but with a narrower range.

In addition to the FPA the P640 is equipped with a 3.2 Mpixel digital camera that can takedigital pictures or record digital video. This camera was used to take digital pictures from thesame positions as the thermographic pictures. Comparing these two images can give useful infor-mation about the origin of the measured temperature. If one measures a low temperature thiscan be due to that the assumed emissivity, used by the camera, is higher than the true emissivity.More on how the assumed emissivity aects the measured temperature is discussed in section 5.6.1.Comparing the thermographic picture to the digital picture can sometimes reveal that the trueemissivity is in fact lower than the assumed one. The assumed emissivity can be varied in theinterval ε ∈ [0.01, 1.0].

42

This camera can operate in a temperature range of T ∈ [−15, 50]C and detect temperaturesin the interval T ∈ [−40, 500]C. So measuring the temperature of the Yankee dryer will not be aproblem as long as the camera is not kept too close to it. The MRTD of the P640 is 0.055C at30C and the update frequency of the detectors is 50-60 Hz. Since the Yankee surface moves witha velocity of about 30 m/s a point on the surface moves 0.6 m while the thermographic picture istaken. So the images taken becomes a mean value of the points passing the camera under 0.02 s,and not an instant image as in the ideal case.

All pictures taken by the P640 are stored on a removable SD memory card. This card can beread by a computer and imported to the FLIR reporter software. This software has a lot of featureenabling the data to be presented in a number of ways.

5.6.1 Measurement error due to incorrect emissivity

As has been mentioned, one big source of error in temperature measurements with a pyrometeris the emissivity of the surface. This section will give an estimation of this source of error, thediscussion closely follows the discussion in reference [18].

The voltage output signal of the detector, S(T ), is proportional to Planck's law and can bewritten as:

S(T ) =∫ λ2

λ1

k(λ)ε(λ)λ5[exp( c2λT )− 1]

dλ (5.15)

Where k is a union of constants of the instrument and Planck's law, [λ1, λ2] is the spectral rangeof the instrument, and c2 = hc0

k = 1.439×104 µmK. Since all materials have dierent dependenciesof ε(λ) and this discussion regards an arbitrary material the material is assumed to be a grey body,i.e ε(λ) = ε. Another assumption is that the detector properties is independent of the wavelength,i.e k(λ) = k. From these assumptions Eq. 5.15 can be rewritten as:

S(T ) = kε

∫ λ2

λ1

dλ

λ5[exp( c2λT )− 1]= kεF12(T ) (5.16)

This equation can be used to yield an expression for the temperature error caused by anuncertainty of emissivity. An assumed emissivity, εm, results in a measured temperature Tm. Thesignal that yields Tm is the same signal, S(T ), that would yield the correct temperature T if thecorrect emissivity, ε, was assumed. This statement can be written as the equality:

εF12(T ) = S(T ) = εmF12(Tm) (5.17)

Now introducing the fractional errors in emissivity and temperature:

δε =εm − εε

(5.18)

δT =Tm − TT

(5.19)

Subtracting the term εF12(Tm) from both sides in Eq. 5.17 yields:

εmF12(Tm)− εF12(Tm) = εF12(T )− εF12(Tm) (5.20)

This can be rearranged to:

εm − εε

=F12(T )− F12(Tm)

F12(Tm)(5.21)

Using the relations in Eq. 5.18 and 5.19 Eq. 5.21 can be written as:

δε =F12(T )− F12[(δT + 1)T ]

F12[(δT + 1)T ](5.22)

43

The equation above is rather dicult to evaluate by hand since it contains the integral seen inEq. 5.16. Therefore Eq. 5.22 was put in the numerical computing environment MATLAB whichhas a built in function, quad, for evaluating integrals. This function approximates the integral byusing recursive adaptive Simpson quadrature. The code that was put in MATLAB can be seenin Appendix A. The code produced a graph that shows how the fractional errors δε and δT arerelated. This graph can be viewed in Fig. 5.11.

Figure 5.11: Showing how the fractional errors δε and δT are related. This graph was generatedwith a spectral range of λ ∈ [7.5, 13] µm and a true temperature of T = 100 C.

One can use the graphs obtained from the discussion above to estimate the true emissivityof the surface if the true temperature is known and vice versa. To give an example one canmeasure a surface simultaneously with a pyrometer and a thermocouple. The temperature that thethermocouple show can be assumed to be the true temperature. Let's assume that this temperatureis Tth = T = 100C. Now assume that the pyrometer measures a temperature of Tp = Tm = 91Cwhen using εm = 1.0 as emissivity. This gives a a fractional temperature error of about δT = 10%.From the graph in Fig. 5.11 this corresponds to a fractional emissivity error of about δε = 53%.Using the denition of δε (Eq. 5.18) the true emissivity of the surface can be estimated to beε = εm

1.53 = 1.01.53 ≈ 0.65.

44

6 Results

6.1 Thermophone

In Fig. 6.1-6.3 the graphs are the results of measurements made on the pilot machine. In Fig. 6.4the graphs are the results of measurements made on a iron block heated by a stove plate.

When performing the measurements for graph 1.1 the machine had a speed of 1200 m/minand the vapour had an overpressure of 7 bar. While performing the other measurements somemachine parameters changed. These changes are explained in each gure. The reason for splittingthe results into three gures is because they were saved on three dierent memory cards.

The time between the measurements varied but they were approximately separated by 5-10 min,so that the teon cup could reach room temperature. Since most of the graphs show a logarithmicbehaviour, logarithmic ts to the graphs was inserted in the gures. The logarithmic t functionsagree well with the graphs that was acquired under a shorter period of time, less than ∼ 6 min. Thepart of the graphs that deviates the most from the logarithmic ts are the growth after greater than∼ 6 min where the logarithmic ts grow faster than the graphs. Even if the graphs do not growas fast as logarithmic functions most graphs still show an increasing temperature even after 15 min.

In the graphs the temperature axis start at T = 35C which approximately is the temperatureof the brass piece just before coming in contact with the Yankee dryer. The time axis nish att = 16 min. This was made so that all graphs would have the same axis, but as a result somegraphs are cut before they end.

Figure 6.1: While acquiring graph 1.1 and 1.2 the machine parameters did not change. Themachine speed was 1200 m/min and the vapour had an overpressure of 7 bar. The two graphs arevery similar and their logarithmic ts agree well with them. Even though the graphs look good thebehaviour is not ideal for a temperature measurement technique since the temperature is increasingeven after 15 minutes. This makes it hard for the person that performs the measurement since onedoes not know when to stop.

45

Figure 6.2: While acquiring graph 2.1-2.4 the machine speed was 1200 m/min and the steamoverpressure 7 bar. Before graph 2.4 was acquired the hood temperature was raised which seemsto have increased the Yankee cylinder temperature. The operators of the machine made no changeson the machine between graph 2.1-2.3. One reason for the big dierence between graph 2.1 andgraphs 2.2 and 2.3 can be that regulators changed some machine parameter. It can also be due toa change of the Thermophone behaviour. Between measurements the position of the brass piecewas adjusted which can have an inuence on the measured temperature.

Figure 6.3: While acquiring graph 3.1-3.4 the steam overpressure was constantly 7 bar. Afterabout 9 min in graph 3.3 the machine speed was raised from 1200 m/min to 1400 m/min, resultingin a colder Yankee cylinder. This speed was kept while acquiring graph 3.4. Having this change inmind, the graphs look quite similar.

46

Figure 6.4: These graphs was obtained when performing measurements with the Thermophone ona iron block heated by a stove plate. Since the stove plate did not have a constant temperature themaximum value of each graph varies. Between two consecutive measurements the Thermophonewas rested for about 10 min so that it reached room temperature. The important result in thegraphs are not the absolute temperature but the response time. All graphs show similar behavioursince they go quickly (10-30 s) from their initial temperature to the Yankee block temperature.Comparing these responses to the responses of the Yankee cylinder temperature in Fig. 6.1-6.3 they are quicker in obtaining an equilibrium temperature. In the graphs in Fig.6.1-6.3 theThermophone rst after about 3-5 min begin stabilise at an equilibrium temperature. The largedierence in response time indicate that the air streams have a large inuence on the measuredtemperature.

47

6.2 Pyrometer

As was said in the section Experimental a number of measurements was made with the pyrometerRAYNGER MX4 manufactured by Raytek. Along with these measurements digital photos weretaken in order to show the surface nish. In all measurements the assumed emissivity was set toεm = 1.0. All measurements showed similar results, namely that the temperature measured by thepyrometer varied a lot along the surface. These variations can be explained by the varying surfacenish. As a rule of thumb the surface looked more metallic and reective when low temperatureswas measured and more dull and less reective when higher temperatures was measured. More onhow the surface nish aect the measured temperature is discussed below.

Below in Fig. 6.5 digital photos of dierent regions on the Yankee cylinder surface is shownalong with how the measured temperature varied in these regions. The top three photos are takenat the tending side edge of the Yankee cylinder while the bottom three show the center of theYankee cylinder. The two photos to the left show a newly sandpapered surface, i.e a clean surfacewithout any coating or paper residues on it. It is clear that these photos show a highly reectivemetallic surface, with the exception of the tending side edge where the surface looks darker andless reective.

The two middle photos show the surface when a coating layer have been sprayed on. Coatingdo not cover the whole surface leaving the edges uncovered. It is clear that the coating makes thesurface more dull and less reective.

The two photos to the right shows the surface after the paper have been pressed onto theYankee cylinder and the doctors begun to scrape it. Since the scraping is not uniform it results ina stripy nish where some stripes are dull and little reective while others are highly reective.

Figure 6.5: Showing two regions; the tending side (top photos) and the center (bottom photos) ofthe Yankee cylinder with dierent things covering the surface. The temperatures shown are thetemperatures measured by the pyrometer in these regions. It should be noted that the overpressureof the steam was raised from 1 bar to 3 bar and the machine speed increased from 300 m/min to900 m/min just before the coating was sprayed onto the surface. The surface nish varies the mostnear the edge and it is also in this region the temperature varies the most.

48

Clean surface

Before the coating was sprayed on the steam inside the Yankee dryer had an overpressure of about1 bar and rotated with a velocity of 300 m/min. When measuring this surface with the Thermo-phone temperatures in the range T ∈ [103, 106]C was obtained, i.e quite uniform temperaturedistribution. The dierent temperatures was distributed randomly, i.e no region was hotter thanthe other. From these measurements one can conclude that the Yankee dryer had the same temper-ature along the cylinder, but one cannot say exactly what temperature because of the uncertaintyof the Thermophone.

When measuring the same surface with the pyrometer temperatures in the range T ∈ [58, 78]Cwas obtained. The highest temperatures were measured at the edges, both at the tending side andthe driver side. This can be explained by that ε is higher in those regions. From Fig. 6.5 itis clear that the end of the cylinder has another nish (a darker colour) than the rest of thecylinder, which support the diering ε theory. As the nish becomes more metallic and less darkthe measured temperature decreases indicating a varying ε. Areas with similar surface nish hadthe same temperatures.

Coated surface

Just before the coating was sprayed on the surface the overpressure in the Yankee dryer was in-creased to 3 bar and the machine speed was increased to 900 m/min. In the areas where coatingwas sprayed on the surface, the surface nish clearly changed, see Fig. 6.5. No measurement wasmade with the Thermophone since the paper was pressed onto the Yankee cylinder briey afterthe coating. Instead only pyrometer measurements were made. Since no paper was on the cylinderit can be assumed that the Yankee dryer had an almost constant temperature, as in the case ofthe clean surface.

The pyrometer measurements showed temperatures in the range T ∈ [85, 120]C. This timehowever the highest temperatures were not measured in the darker regions but in the coatedregion. There, the coating formed a uniform dull layer a uniform temperature of T = 120C wasmeasured. At the edges of the cylinder the temperature varied because of the varying nish, butwere clearly lower than the coated region.

Scraped surface

The overpressure was kept at 3 bar and the machine speed was kept at 900 m/min. When perform-ing measurements with the pyrometer, temperatures in the range T ∈ [65, 120]C were obtained.In the region where the paper was scraped o the temperature varied a lot. In this region tem-peratures in the range T ∈ [65, 95] were measured and the dips and peaks in temperature wasrandomly distributed. This indicate a strongly varying ε in the regions where the paper had beenscraped o. The highest temperatures was measured just after the paper edge, i.e where therestill was a uniform coating layer. The farer away from the paper edge one measured the lowerthe temperature got. This is explained by that the coating thickness got thinner with increasingdistance from the paper edge.

It is usually this type of stripy surface that is the surface nish of Yankee dryers in real papermachines. Since a stripy surface most likely leads to varying emissivity, temperature measurementswith a pyrometer will result in measurement errors, according to Fig. 5.11.

49

6.3 Thermographic camera

In this section a number of thermographic pictures will be presented and discussed. They wereacquired with an assumed emissivity of ε = 0.99. If the targets, shown in the pictures, do nothave an emissivity of ε = 0.99 the measured temperature is not the true temperature of the target.The aim of these pictures is not to show how the temperature varies along the Yankee surface,but to show how the temperature measured through thermal radiation depend on the surface nish.

In order to get a picture of the surrounding radiation, a piece of aluminium foil was heldup in front of the Yankee dryer and a thermographic image was taken of the foil, see Fig. 6.6.Since aluminium foil is highly reective a thermographic image of it gives information about thesurrounding radiation. In the software, that comes with the thermographic camera, an area onthe foil was selected. The picture shows this area and also the average temperature in this area,Taverage = 30.5C which can be assumed to be the surrounding radiation.

Figure 6.6: A thermographic picture of aluminium foil. It was taken in order to determine thebackground radiation.

The pictures in Fig. 6.7 was taken from the tending side. The graph in the lower part of theimage shows how the temperature varies along the green line shown in the top left picture. Thecenter part of the graph show a rather constant temperature, around Tm = 100± 5C. This is theregion where the paper was dried by the Yankee cylinder, which is why this region is cooler thanthe ends of the cylinder. At the ends the measured temperature rst goes up to about Tm = 160C,then drop to about Tm = 110C, and nally goes up again to about Tm = 130C. From theorythe Yankee cylinder should get colder at the ends since the cooling eect from the airow getsmore pronounced here. But the fact that the measured temperature goes up again at the ends isprobably due to variations of the emissivity. If one looks at the digital photo of the Yankee dryerone can draw parallels between the appearance of the surface and the thermographic image. Thisalso indicates a varying emissivity.

The pictures in Fig. 6.8 was taken from the driver side and shows the far end of the cylinder(TS). From this gure it is even more obvious that the emissivity varies. To highlight the similaritiesof the two pictures two stripes have been marked purple and turquoise respectively. The peaksin the graph corresponding to these stripes have also been marked. Because the emissivity variesthe measured temperatures gives a false picture of the real temperature of the Yankee dryer. Thefractional errors of the emissivity, δε, can be related to the fractional error in temperature, δT byusing graphs as the one in Fig. 5.11.

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Figure 6.7: A thermographic picture of the Yankee cylinder taken from the tending side along witha digital photo taken from the same position. The graph show how the temperature varies alongthe green line in the thermographic picture.

The pictures in Fig. 6.9 was taken from the driver side and shows the near end of the cylinder(DS). As in Fig. 6.8 it is obvious that the emissivity varies. What makes it even more clear inthis picture are the greater dierences in emissivity. The highest measured temperature is aboutTm = 160C while the lowest is about Tm = 80C. Assuming that Tm = 160C correspond to thetrue temperature the largest fractional temperature error in this picture is about δT = −18.5%.By using a graph, similar to Fig. 5.11, this corresponds to a fractional emissivity error of aboutδε = 120%, which means that the emissivity of the surface varies in the interval ε ∈ [0.45, 0.99].But these calculations does not take the reected radiation into account, why the emissivity isprobably smaller than ε = 0.45. The surface almost look like a mirror in the digital photo. So itis possible that the emissivity in these regions are as low as ε = 0.10 since polished iron has anemissivity in the interval ε ∈ [0.06, 0.2] [6].

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Figure 6.8: A thermographic picture along with a digital photo of the Yankee cylinder taken fromthe driver side. The two stripes highlighted with turquoise and purple show the relation betweenthe temperature measured by a thermographic camera and the surface nish. The graph show howthe temperature varies along the green line in the thermographic picture.

The pictures in Fig. 6.10 show the same picture as in Fig. 6.8 but with other line graphs. Theseline graphs show another obstacle, when measuring the temperature by measuring the thermalradiation, that is the reected radiation. In the graphs when going from left to right there is abig and sudden drop in the measured temperature, ∼ 10− 20C. This drop is most pronounced inthe lowest graph where the measured temperature is the lowest indicating a low emissivity. A lowemissivity corresponds to a high reectivity in general. So even if the true emissivity of the surfaceis known large errors in the measured temperature can be obtained if the reected radiation varies.At the right end of the graph there is an increase in temperature also due to reected radiation.This increase is however not as obvious and sudden as the one in the left end. The variation of theradiation is due to the cleaning doctor (left side) and the coating shower (right side). These twoparts have a higher temperature than the ambient temperature and therefore emits more thermalradiation. These parts were measured in a subsequent measurement with the MX4 (εm = 0.99)which indicated that both the coating shower and the cleaning doctor had a measured temperatureof about Tm = 60C. This is higher than the measured surrounding temperature, that was acquiredin Fig. 6.6, indicating an enhanced radiation from these sources.

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Figure 6.9: A thermographic picture along with a digital photo of the Yankee cylinder takenfrom the driver side. The graph show how the temperature varies along the green line in thethermographic picture. The pictures show the driver side end of the Yankee cylinder. The bigtemperature dierences in the thermographic picture are due to a varying emissivity which is seenin the digital photo as varying surface nish.

The pictures in Fig. 6.11 show the temperature development of the thermophone while beingin contact with the Yankee dryer. The pictures were taken in order to investigate the frictionalheating of the thermophone. The time that is displayed in each picture is the number of secondsthe thermophone has been in contact with the Yankee dryer. The temperature is the maximumtemperature that was measured near the head of the thermophone. These temperatures was ac-quired in a similar fashion as the surrounding temperature in Fig. 6.6, with the dierence that themaximum temperature was read instead of the mean temperature. The maximum temperaturedoes not change much with time but it is clear that the thermophone gets hotter with time. Themaximum measured temperature Tm ≈ 110C is higher than the maximum measured temperatureof the Yankee dryer Tm ≈ 95C. This can either be due to that the thermophone has a highertemperature or that teon has a higher emissivity than the Yankee dryer.

Teon has an emissivity in the interval ε ∈ [0.85, 0.92] [6] which is probably close to the emissiv-ity of the Yankee since it is covered with a well developed coating layer, though not homogeneous.The coating layer consists of dierent chemicals and rests of paper bre. Paper has an emissivityin the interval ε ∈ [0.90, 0.98] [6]. So teon and the Yankee cylinder should have about the sameemissivity, at least where the measured temperature of the Yankee cylinder is high. This indicatesthat the teon of the Thermophone has a higher temperature than the Yankee cylinder. Since thepictures was taken with ε = 0.99 the true temperature of the teon cup is probably higher thanTm ≈ 110C.

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Figure 6.10: A thermographic picture along with a digital photo of the Yankee cylinder takenfrom the driver side. The graphs show how the temperature varies along the green lines in thethermographic picture. The thermographic picture along with the graphs clearly show a reectionfrom the cleaning doctor to the left in the picture, since it increases the measured temperaturedramatically.

Another thing indicating the teon cup having a higher temperature than the Yankee cylinderis the temperature measured by the Thermophone. The maximum temperature measured by theThermophone, while simultaneously the thermographic pictures of it was taken, is Tm,Thermophone =99C. This is at least 10C smaller than the temperature of the teon cup. More on the relationbetween the temperature measured by the Thermophone and the temperature of the teon cup isseen in Fig. 6.13.

The pictures in Fig. 6.12 are thermographic pictures of the Thermophone just after it hasbeen removed from the Yankee dryer. One interesting thing, though not surprising, is that theinner wall of the teon cup is hotter than the outer wall. Since the inner wall is close to thebrass piece and the thermocouple its temperature probably aects the temperature measured bythe Thermophone. Since the inner wall have a higher temperature than the outer wall, that inturn has a higher temperature than the Yankee, there is a risk that the Thermophone measures atemperature higher than the Yankee dryer's.

The graphs in Fig. 6.13 show the maximum temperature, shown in Fig. 6.11, on the outerwall of the Thermophone together with the temperature measured by the Thermophone, as afunction of time. The maximum temperature of the outer wall only has 9 values. So the relationbetween the two temperatures is hard to determine. A more careful investigation that measuresthe temperature of the inner wall while the Thermophone is in contact with the Yankee dryerwould give a more clear picture of how the frictional heating aects the measured temperature.This is however outside the scope of this paper. The maximum measured temperature by theThermophone is Tm,Thermophone = 99C and by looking at the graph it should have increasedfurther. The maximum measured temperature by the thermographic camera (inside the paperwidth) was Tm,tg < 95C. This results in a measured temperature dierence of ∆Tm = Tm,tp −Tm,tg ≈ 4C which can be either due to frictional heating of the Thermophone or the use of a toosmall emissivity in the thermographic camera.

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Figure 6.11: Thermographic pictures of the Thermophone while it measures the temperature ofthe Yankee cylinder. The temperatures written in the pictures are the maximum temperature ofthe Thermophone in the images. The time written in the pictures is the time the Thermophonehave been in contact with the Yankee cylinder.

Figure 6.12: Thermographic pictures of the Thermophone just after it had been removed from theYankee cylinder. The pictures show that the inner teon walls have a higher temperature than theouter walls.

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Figure 6.13: The graphs show the temperature measured by the Thermophone (green) and themaximum temperature of the teon cup measured by the thermographic camera (orange) as afunction of time. Also a logarithmic t of the temperature measured by the Thermophone isviewed. This logarithmic t highlight the increase of the measured temperature even after 6minutes of measurement.

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7 Discussion & Conclusions

Thermophone

From the temperature measurements made on the Yankee dryer it is clear that none of the threedevices tested gives a reliable measurement. The Thermophone experiences a rising temperatureeven after ∼10 min which makes it hard to know when to stop measuring. This rising tempera-ture is probably due to the frictional heating of the teon cup. The theory that the teon cup isfrictionally heated is supported by the thermographic pictures taken of the Thermophone duringmeasurement. These picture show that the outside of the teon cup achieves temperatures approx-imate 10C above the temperature of the Yankee dryer. A thermographic picture of the inside ofthe Thermophone briey after measurement show that the inner walls have a higher temperaturethan the outer walls. This is not a surprise since the outer walls are cooled by the air streamscaused by the rotation of the Yankee dryer. This implies that the inner walls are at least 10Chotter than the Yankee dryer surface.

It is thought that the temperature of the inner walls contribute, through the air streams inthe teon cup, to the temperature of the brass piece. This is supported when comparing Fig. 5.8,6.4, and 6.1-6.3 to each other. The response time of the calculated value for a Couette ow isonly t < 5s (Fig. 5.8) where the brass piece is assumed to be isolated, i.e only exchanging heatwith the Couette ow. In the measurements with the Thermophone of a Yankee block on a stoveplate the response time is t < 20s. In this case no forced convection is present but only naturalconvection making the heat ow between the brass piece and Yankee surface more dominant. InFig. 6.1-6.3 the response time are in some cases t > 5min. The reason for the long response timecan be the heat transfer through the forced convection of the air streams inside the teon cup.Since the thermoelectric junction is placed on the face of the brass piece not facing the Yankeedryer its temperature should be even more sensitive to the forced convection.

When the inner walls of the teon cup are colder than the Yankee dryer the forced convectionprobably cools the thermoelectric junction. As they get hotter than the Yankee dryer the forcedconvection begins to heat the thermoelectric junction instead. How large inuence the temperatureof the walls have on the temperature of the thermoelectric junction is hard to determine because ofthe complex air streams. An attempt was made to simulate the heat transfer inside the teon cup.The simulations were performed in the FEM software COMSOL Multiphysics but the solution didnot converge due to the air streams. Since a lot of the input parameters in the model had to beassumed no further attempt was made to simulate the heat transfer.

As the distance between the brass piece and the Yankee surface increases the contribution fromthe inner walls should increase. This introduces a diculty when trying to repeat measurementswith the Thermophone. If the distance between the brass piece and the Yankee surface is variedbetween measurements the Thermophone would behave dierent. Another diculty in repeatingmeasurements is to determine how hard the Thermophone is to be pressed against the Yankeedryer surface. The harder it is pressed the more frictional heating will be present.

A suggestion for future work on the Thermophone is to investigate the inuence of the tempera-ture on the inner walls on the measured temperature. This can be done by attaching thermocouplesto the inner walls and measure the temperature on these walls simultaneously as the Yankee dryertemperature. Comparing how these temperatures develop over time could give useful information,and ultimately a direct relation that could be used to determine the true temperature of the Yankeedryer surface.

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IR sensors

Both the MX4 and the P640 measurements show the diculties in measuring the temperaturewith IR sensors. The most obvious diculty is the emissivity dependence of the measured tem-perature. Since a normal Yankee dryer surface does not have a uniform surface nish, becauseof the uneven scraping of the doctors, the emissivity of the surface varies. Using a graph similarto that in Fig. 5.11, and assuming that one of the temperatures measured with the pyrome-ter/thermographic camera is correct inside the paper width, one gets that the emissivity of thesurface varies in the interval ε ∈ [0.65, 1.0]. The graph used does however not take the reectedradiation in consideration so the true emissivity is probably lower than 0.65. Having a surfacewith an emissivity varying in such a large interval which also rotates with a speed of 1800 m/minmakes it hard to measure with an IR sensor, which results in large errors as indicated in the results.

Another diculty when performing measurements with an IR sensor is the reected radiation.This is most obvious in Fig. 6.10, where reected radiation from the coating shower and thecleaning doctor is visible in the thermographic picture. Not having this in mind can cause largeerrors in the measured temperature. In Fig. 6.10 the reected radiation from the cleaning doctorraises the measured temperature with ∼ 20C. For a surface with an uniform reectivity this canbe solved by using a constant background radiation, by for example having a cooled cone, similarto the gold cup, between the Yankee surface and the sensor. If the cone can be kept at a constanttemperature the background radiation will be constant. But for a surface with a varying reectivitythis constant background radiation will give dierent contributions to the measured temperature.In order to minimize this error further the cone could be cooled to low temperatures compared tothe Yankee surface, which would give negligible background radiation. Even without such a conethe inuence of the reected radiation can be made smaller by pointing the sensor in the samedirection as the hot radiation, see Fig. 7.1

Figure 7.1: Two ways of making the contribution from the background radiation smaller. A hotsource is present to the left in the image which radiation (black arrows) would disturb the temper-ature measurement of the target (red arrows). In the left image a cone of constant temperature isused which blocks out the radiation from the hot source and keeps the background radiation con-stant. This method is advantageous if there are hot sources radiating from many dierent angles.In the image to the right the sensor is tilted in the same direction as the hot source. This wayno radiation from the hot source will be reected into the sensor. This method is advantageous ifthere are few and easily identied hot sources.

The emissivity dependence of the measured temperature can be xed in two ways; making theemissivity of the surface constant or using a emissivity independent measuring method. The emis-sivity could be made constant by spraying the surface with a coating just before measuring. Butintroducing yet another chemical in the process could disturb the process and aect the quality ofthe paper. So this method was not investigated further.

The second way of getting around the emissivity dependence is to use a emissivity indepen-dent measurement method. Two such methods are suggested in section 4.6. The double bandpyrometer requires a grey surface in order to be emissivity independent. Since there are a numberof dierent materials constituting the Yankee dryer surface (polished iron, coating chemicals, andpaper residues) it is not certain that all these materials display grey body behaviour. Anotherdisadvantage with the double band pyrometer is the need for small spectral ranges of the sensors,

58

requiring photonic sensors and cooling of the sensors. These requirements make the double-bandpyrometers more expensive and increase their size. For future work it could be a good idea to testa double-band pyrometer and investigate how well it excludes the emissivity dependence.

The gold cup method is also said to be emissivity independent but it requires the gold hemi-sphere to be an almost perfect mirror (ρ = 1) and for it to be in contact with the target. Therequirement of a perfect mirror can be hard to achieve while measuring the Yankee dryer temper-ature. In this environment steam is present which could condense on the gold and reducing thereectivity. There are also paper dust in the air which also could reduce the reectivity if hittingthe gold. The need for keeping the gold cup close to the surface could endanger the gold nishbecause of the high speed of the Yankee dryer. Since this method was never tested it is a suggestionfor future work.

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References

[1] Boudreau, J. Improvement of the tissue manufacturing process. PhD thesis, Karlstad Univer-sity, (2009).

[2] Eckert, E. R. G. and Drake, R. M. Analysis Of Heat And Mass Transfer. CRC Press, (1986).

[3] Incropera, F. P. and DeWitt, D. P. Fundamentals of heat and mass transfer (4th edition).John Wiley & sons, (1996).

[4] webpage on the work of T. J. Seebeck, A. Available at: http://chem.ch.huji.ac.il/

history/seebeck.html 2009-05-30.

[5] Meijer, G. C. M. and van Herwaarden, A. W. Thermal Sensors. Institute of Physics Publishing,(1994).

[6] Childs, P. R. N. Practical temperature measurement. Butterworth-Heinemann, (2001).

[7] Fote, M. and Gaalema, S. Proceedings of SPIE 4369, 350354 (2001).

[8] Schilz, J. PerkinElmer Optoelectronics GmbH (2000).

[9] Niklaus, F. et al. SPIE conference Infrared Technology and Applications XXXIII (2007).

[10] Rogalski, A. Progr. Quant. Electron. 27, 59210 (2003).

[11] Driggers, R. G. et al. Encyclopedia of Optical Engineering, Vol. 2. CRC PRESS, (2003).

[12] Michalski, L., Eckersdorf, K., and McGhee, J. Temperature Measurement, 2nd Edition. JohnWiley and Sons Ltd, (2001).

[13] Muller, B. and Renz, U. Rev. Sci. Instrum. 72(8), 33663374 (2001).

[14] Madura, H., Kastek, M., and Piatkowski, T. Infr. Phys. & Tech. 51, 18 (2007).

[15] Saunders, P. Radiation Thermometry: Fundamentals and Applications in the PetrochemicalIndustry. SPIE, (2007).

[16] specications of RAYNGER MX4, T. Available at: http://www.watlow.co.uk/literature/specsheets/files/sensors/ricmx0401.pdf 2009-05-30.

[17] specications of FLIR P640, T. Available at: http://www.flirthermography.com/media/

P640%20Datasheet_I102908PL.pdf 2009-05-30.

[18] Corwin, R. R. and Rodenburgh II, A. Appl. Opt. 33(10), 19501957 (1994).

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A MATLAB code

%% planck.m by:Henrik Jackman

global Tt c2 Tm

l1=7.5; %smallest wavelength [mu m]

l2=13; %largest wavelength [mu m]

E=1; %emissivity

K=273.15; %degrees K @ 0 degree C

Tt=K+100;

Tmax=Tt+100;

Tmin=Tt-100;

T=K+100; %K

c2=1.4288e4; %mu m K

Ft=quad('planckt',l1,l2);

hold on

xlabel('\delta \epsilon (%)')

ylabel('\delta T (%)')

title('Plot showing the measured temperature error \delta T vs. the error...

.. in emissivity \delta \epsilon')

for Tm = Tmin: 1: Tmax

Fm=quad('planckm',l1,l2);

dE=100*(Ft-Fm)/Fm;

dT=100*(Tm-Tt)/Tt;

plot(dE,dT)

end

%%end of planck.m

%% planchm.m by: Henrik Jackman

function s=planckm(x);

global Tm c2

s=zeros(size(x));

k=find(x~=0);

s(k)=x(k).^(-5)./(exp(c2./(x(k)*Tm))-1);

%%end of planckm.m

%% plancht.m by: Henrik Jackman

function s=planckt(x);

global Tt c2

s=zeros(size(x));

k=find(x~=0);

s(k)=x(k).^(-5)./(exp(c2./(x(k)*Tt))-1);

%%end of planckt.m

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