Faculty of Technology & Science Department of Physics and Electrical Engineering
Henrik Jackman
Surface temperature measurement on a Yankee cylinder during operation
Engineering Physics Master Thesis
Date/Term: 2009-06-10 Supervisors: Prof. Kjell Magnsson, Jonas Cederlöf, Hans Ivarsson, Karl-Johan Tolfsson
Examiner: Prof. Lars Johansson Serial Number: X-XX XX XX
Karlstads universitet 651 88 Karlstad Tfn 054-700 10 00 Fax 054-700 14 60 [email protected] www.kau.se Abstract The Yankee cylinder is used in most of Metso Paper's machines. It is used in the drying and creping process. Since the outcome of these processes largely aect the paper's nal quality it is important that the Yankee cylinder behaves in a controlled fashion. One important parameter aecting the behaviour of the Yankee cylinder is its surface temperature. The objective of this thesis was to search for and evaluate methods for measuring the surface temperature of a Yankee cylinder during operation. Metso Paper is looking for a method having an accuracy of ∆T = 1◦C, a response time of t < 10 ms, and being portable. Three dierent instruments were tested during the 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 in Karlstad during operation. The measurements revealed drawbacks for all three instruments. The biggest drawbacks of the Thermophone was its response time, t ≈ 5 min, and its dependence on the frictional heating of the te on cup. The frictional heating causes the measured temperature to increase even after 15 min making it hard to know when to stop the measurement. How much the frictional heating aects the measured temperature was di cult to analyse, making it a suggestion for future studies. The biggest drawback of the pyrometer and the thermographic camera is the measurement error due to emissivity errors. Since the Yankee cylinder have a varying surface nish the emissivity varies a lot along the surface introducing temperature errors as large as ∆T = 30◦C. Two methods that claim to be emissivity independent were investigated; double-band and gold cup pyrometers. Double-band pyrometers require the target to be a grey body and for it to have large temperatures, T > 300◦C, making this method unsuitable for measuring the surface temperature of the Yankee cylinder. Gold cup pyrometers require the gold hemisphere to have a re ectance of ρ = 1. Because of the environment surrounding the Yankee cylinder it would be di cult keeping the 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 me through this work. I would also like to thank my examiner Prof. Lars Johansson for giving me useful advices on how to improve this paper. Last but not least I would like to thank my supervisors at Metso Paper: Jonas Cederlöf, Hans Ivarsson, and Karl-Johan Tolfsson for answering all of my questions and making this project fun and challenging. Contents
1 Introduction 1 1.1 Background ...... 1 1.1.1 Metso Paper ...... 1 1.1.2 Yankee dryer ...... 3 1.2 Objective ...... 6
2 Heat transfer and temperature measurement 8 2.1 Conduction ...... 8 2.2 Convection ...... 9 2.3 Radiation ...... 10 2.3.1 Emissivity ...... 13 2.3.2 Absorptivity, re ectivity and transmissivity ...... 13 2.4 Temperature measurement ...... 15
3 The Yankee dryer 16 3.1 Inside the Yankee dryer ...... 16 3.2 Coating ...... 17 3.3 Nip load & Hood dryer ...... 19 3.4 Creping process ...... 19
4 Sensors 21 4.1 Thermocouples ...... 21 4.2 Thermopiles ...... 24 4.3 Sensors similar to thermocouples ...... 26 4.3.1 Resistance thermometer & bolometer ...... 26 4.3.2 Pyroelectric sensors ...... 26 4.4 Thermal IR sensor ...... 27 4.5 Photonic IR sensors ...... 29 4.6 Techniques using IR sensors ...... 30
5 Experimental 34 5.1 Thermophone measurements ...... 34 5.2 Pyrometer measurements ...... 35 5.3 Thermographic camera measurements ...... 35 5.4 Thermophone speci cations ...... 36 5.4.1 Couette ow in Thermophone ...... 38 5.5 RAYNGER MX4 speci cations ...... 40 5.6 FLIR P640 speci cations ...... 42 5.6.1 Measurement error due to incorrect emissivity ...... 43
6 Results 45 6.1 Thermophone ...... 45 6.2 Pyrometer ...... 48 6.3 Thermographic camera ...... 50
7 Discussion & Conclusions 57
A MATLAB code 61 List of Figures
1.1 Examples of tissue products ...... 1 1.2 Examples of tissue paper machines ...... 2 1.3 Dierent processes involving the Yankee dryer ...... 3 1.4 Steam inside the Yankee dryer ...... 4 1.5 Magni cation of the Yankee headers ...... 5 1.6 Crowning ...... 5 1.7 Resulting temperature distribution after FEM calculations ...... 6 1.8 Crowning curves from FEM calculations ...... 6 2.1 Thermal conductivity vs. temperature for three dierent phases...... 9 2.2 Pro les for the uid velocity and temperature in the boundary layer...... 10 2.3 Spectrum of electromagnetic radiation...... 11
2.4 Projection of dA1 normal to the direction of radation...... 12 2.5 The Planck distribution for a black body at dierent temperatures as well as the Wien displacement...... 12 2.6 Comparison between the emission of a black body and a real body...... 13 2.7 Radiation from and irradiation on a surface...... 14 2.8 An information system consisting of a sensor, a signal processor, and an actuator. . 15 3.1 How the steam condensate assemblies on the inside of the Yankee dryer...... 17 3.2 How the saturated steam temperature varies with pressure...... 17 3.3 Coating nozzles...... 18 3.4 Pictures of the Yankee surface with and without a coating layer...... 18 3.5 Hood dryer operation...... 19 3.6 The creping process...... 20 4.1 Seebeck's experiment...... 21 4.2 A simple thermocouple...... 21 4.3 A simple thermopile con guration ...... 24 4.4 A schematic diagram of a thermopile detector structure...... 24 4.5 The transmissivity for air over a 300 m distance...... 25 4.6 A schematic sketch of the structure of a micro bolometer...... 27 4.7 A general image of a thermal IR sensor ...... 27 4.8 A general image of a photonic IR sensor ...... 29 4.9 Spectral detectivities of commercially available photonic sensors...... 31 4.10 Schematic of a gold-cup pyrometer...... 33
4.11 Plot of εeff versus ρ for ve xed emissivities...... 33 5.1 How the Thermophone was held against the Yankee dryer during the measurements. 34 5.2 Bad and good way to hold the Thermophone...... 34 5.3 The pyrometer measurement setup...... 35 5.4 The setup of how the thermographic pictures was taken...... 36 5.5 A sketch of the Thermophone geometry...... 37 5.6 Photos of the Thermophone...... 38 5.7 The parameters of the Couette ow...... 39 5.8 The calculated response of the brass piece...... 41 5.9 RAYNGER MX4 ...... 41 5.10 FLIR P640 ...... 42 5.11 Showing how the fractional errors δε and δT are related...... 44 6.1 Thermophone graph 1 ...... 45 6.2 Thermophone graph 2 ...... 46 6.3 Thermophone graph 3 ...... 46 6.4 Thermophone graph single stove plate...... 47 6.5 Surface nish and measured temperatures...... 48 6.6 Thermographic image to determine the background radiation...... 50 6.7 Thermographic image 1...... 51 6.8 Thermographic image 2...... 52 6.9 Thermographic image 3...... 53 6.10 Thermographic image 4...... 54 6.11 Thermographic images on the Thermophone...... 55 6.12 Thermographic image on the Thermophone after measurement...... 55 6.13 Graph comparing the temperature measured by the Thermophone to the tempera- ture of the Thermophone viewed by the FLIR P640...... 56 7.1 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 measurement of a Yankee cylinder surface during operation. The work was performed at the department of Calculation at Metso Paper, Karlstad in 2009. It completes the author's studies for a M.Sc degree in 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 in Karlstad is specialised in designing and constructing tissue machines. Examples of tissue products include: napkins, handkerchiefs, industrial wipers, kitchen towels, and bathroom paper. Some of the 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. Each machine 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. It should be noted that the names of the techniques are Metso Paper's own. Examples of machines using 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 ve steps in the production line:
• A slurry of pulp, water, and chemicals is dispersed uniformly on a moving wire by an unit called 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 process Metso use two main designs: Crescent and C-wrap forming. In this process most of the water in the slurry is removed.
• In the next step the slurry is pressed onto a drying cylinder called the Yankee dryer by one or 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 techniques look quite dierent, but there are similarities. One component that is used in all machines above is a dryer cylinder called the Yankee dryer (marked red in the images). The Yankee dryer is used in nearly all of Metso Papers machines.
• The paper continues on the Yankee dryer, which, together with a drying hood, dries the paper 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 a creping doctor that scrapes the paper of the Yankee dryer. The paper then continues and is nally reeled onto big paper rolls.
2 Figure 1.3: The dierent processes involving the Yankee dryer. The paper is forced onto the Yankee dryer in the nip where the paper together with a felt is pressed between a suction press roll and the Yankee dryer. Since the Yankee dryer is covered with a coating that acts as a glue the paper sticks to the Yankee dryer. During the nip water is pressed out of the paper. The paper then continue on the Yankee dryer and enter the drying hood. In the drying hood water is evaporated from the paper partly because of the high Yankee dryer temperature and partly because of the hot air from the hood dryer. After the hood dryer the paper continue to the doctors. The rst doctor is the cut-o doctor and is used to cut o the paper and guiding it to a pulper. This doctor is only used while the next doctor, the creping doctor, is substituted due to maintenance. The creping doctor scrapes the paper o the Yankee cylinder and while doing this the paper is creped (explained in more 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 by a press roll. Secondly the water is evaporated from the paper partly because of the high Yankee dryer 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 these processes much of the paper's nal quality is determined. Therefore it is very important that the Yankee dryer behaves in a controlled fashion. An image of the dierent processes can be viewed in Fig. 1.3
3 The Yankee dryer is heated from the inside by overheated steam that keeps a pressure of 6-9 bar depending on what type of paper that is produced. Because the steam transfer some of its energy to the Yankee dryer and the paper the steam condensate on the inside of the Yankee cylinder. This condensate is removed by by a number of condensate headers that acts as straws and suck out the condensate out of the Yankee dryer. A more detailed picture of how the steam is introduced and removed 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.
4 Figure 1.5: Showing a cross-section of the Yankee dryer as well as a magni cation of a condensate header. The inside of the Yankee dryer is made of internal grooves which purpose is to collect the condensate. 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 order to get an evenly distributed pressure on the paper in the nip. Because of the high temperature and pressure inside the Yankee dryer it expands while in operation. The paper cools the Yankee dryer but close to the edges no paper is on the cylinder. Therefore the Yankee dryer is hotter close to the edges and the thermal expansion is larger in these regions. By knowing the operating temperatures and pressures it is possible to make up for this uneven thermal expansion by making the Yankee dryer thicker in the middle than close to the edges. In Fig. 1.6 three cases of crowning are 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 before the Yankee dryer is ground. Two dierent types of nite element method (FEM) simulations are 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 is considered which cannot be considered to be an axi-symmetric load. The inner pressure and centrifugal loads are rather straightforward to apply to the FEM model since they are constant while the machine is running. The temperature is however not constant since the paper cools the Yankee dryer and the hood dryer heats it. Instead of trying to input this cumbersome temperature variation, a revolution mean value is used in the 2D model. At the paper edge, where the paper ends, no cooling eect from the paper is present. Here a convection boundary condition is set depending on how fast the Yankee dryer is rotating. An example of the resulting temperature distribution at running conditions after a 2D FEM calculation can be viewed in Fig.1.7. After the two FEM (2D and 3D) calculations, a resulting total de ection curve of the Yankee dryer is achieved. An example of such a curve can be viewed in Fig. 1.8. This curve is then inverted and used as a template for the ground of the Yankee dryer.
5 Figure 1.7: Showing the resulting temperature distribution at running conditions after a 2D FEM calculation. In reality the transition in the sheet edge is probably not as sharp as the one pictured in the right image. More complex transitions have been tried, but the result does not deviate much from 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 achieved from 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 why the ends is ground more. The nip as well as the temperature load causes the ends of the Yankee dryer to expand more than the middle of it. Adding together the nip, temperature, rotation, and pressure curves one end up with the nal crown curve. This crown curve is inverted and used as a 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 the axial direction. The nip needs to be uniform in order to press away equal amounts of water along the paper. If the nip is non-uniform it can lead to dierences in moisture of the paper which can results in an unstable process. Metso Paper have a method to measure the surface temperature of the Yankee dryer which is called the Thermophone. This instrument consists of a thermocouple attached on a thin circular brass piece. This brass piece is kept inside a te on cup and held in place by four metal wires. The te on cup is used to protect the brass piece and thermocouple from the surrounding air. During measurements 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 the person who performs the measurement. This dependence is probably due to how the Thermophone is pressed against the Yankee cylinder and how close the brass piece comes to the Yankee dryer. Apart from these di culties it is a di cult task to analyse what temperature the Thermophone is showing, since it exchanges heat through conduction (metal wires), convection (air ow in te on cup) as well as radiation.
Because of the di culties regarding the Thermophone and the importance of knowing the temperature of the Yankee dryer, Metso Paper are looking for alternative methods. The objective of this thesis work was to look for and to investigate alternative temperature measurement methods.
7 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 mono atomic gas the heat is directly related to the average of the absolute velocity of all atoms. For other 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 the atoms and molecules about their equilibrium position.
Temperature is related to heat through the zeroth law of thermodynamics which states: "If two 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 each other heat will ow between them until they are in thermal equilibrium. When two bodies are in thermal equilibrium they have, by de nition, the same temperature. The exchange of heat is 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 system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the 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 added to the system, and δW being a small amount of work done by the system. This law is related to changes in temperatures through the speci c heat, Cp, which is a measure of the amount of energy needed to increase the temperature of a body. The speci c heat for a body at constant pressure is de ned as: ∂U ∂V ∂H Cp = + p = (2.2) ∂T ∂T ∂T p With ∂V being the partial derivative of the volume of the body with respect to the temperature, ∂T and H being the enthalpy de ned as H = U + pV . The speci c heat can also be de ned for a body at constant volume: ∂U Cv = (2.3) ∂T V In most cases when increases the temperature of a solid or liquid they expand which is why the speci c heat at constant pressure is usually used for these matters. For a gas kept at a constant volume the speci c heat at constant volume is more appropriate.
Rearranging Eq. 2.2 one see that if the temperature increases it results in an increase in internal energy 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 the gas is composed of, constantly and in a random fashion collide with each other. In these collisions energy and momentum are transferred between the particles. Particles with a higher free energy transfer some of their energy to particles with lower energy. The distance over which an individual particle can transfer its energy is equal to its mean free path, `. Assuming a temperature gradient in the -direction, dT , the particle heat transport is proportional to dT , while the heat transport of x dx ` dx the gas as a total is also proportional to the density, speci c heat, and the average particle velocity.
The picture of the conduction in liquids is similar if there are no free charge carriers (electrons or ions) which if present contribute to the conduction. Since liquids have a larger density than
8 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 is restricted 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 be seen 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 the conduction of heat in solids but a more thorough discussion about their nature is out of the scope for this paper. Apart from phonons, charge carriers also play a part in the conduction of heat in electrical conducting solids.
Heat transfer through conduction in one dimension is described by the equation:
∂T q00 = −k (2.5) ∂x Where q00 is the heat ux and k the thermal conductivity. The thermal conductivity varies between materials and is, as mentioned, dependent on the phase of the matter. A schematic picture of how the thermal conductivity varies with temperature for the dierent phases can be viewed 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 and molecules. The thing that dierentiate convection from conduction is the macroscopic uid motion associated with convection. The heat transfer through convection is made between a solid surface and 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 motion contribute to the heat transfer. The molecules still have a random motion in the aggregates. So convection can be seen as a superposition of the heat transfer due to the random motion and the bulk motion of the uid.
Convection can be described by looking at a boundary layer for the uid. When looking at a boundary layer one looks at a layer in which the heat transfer is active and disregard the rest of the uid motion. In the boundary layer two pro les can be identi ed: the velocity and the temperature
pro le 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 uid temperature T∞. Since the temperature and velocity goes asymptotically from their surface values to 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 pro les need not to be equal. The extent of the pro les are not constant along the surface since they develop and grow which further complicate the determination of their magnitude. In Fig. 2.2 the two pro les are shown.
Figure 2.2: Pro les for the uid velocity and temperature in the boundary layer. In this case the surface temperature Ts is higher than the uid temperature T∞ i.e Ts > T∞, which is the reason for the direction of q00. The velocity of the uid is zero near the surface, since the surface is not moving, and its temperature is Ts near the surface as indicated in the gure. The extent of the two pro les 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 uid is zero with respect to the surface. Further away from the surface the heat is transferred with the uid motion which is the origin of the boundary layer. Heat transfer from a surface by convection is described by the equation:
00 q = h(Ts − T∞) (2.6) With h being the convection heat transfer coe cient which depends on surface geometry, the na- ture of the uid motion, and the thermodynamical and transport properties of the uid. Since the boundary layer changes along the ow and the properties depend on parameters that changes along the ow an exact determination of h is in most cases impossible. Therefore approximate values of h are assumed when performing calculations.
The nature of the motion of the uid can either be forced or natural. Natural convection is when the motion of the uid is caused by temperature or pressure dierences in the uid. It is common knowledge that warm air rises because of the density reduction with temperature. This is an example of natural convection. An example of forced convection is a fan that forces the air to ow.
2.3 Radiation All matter that has a temperature higher than 0 K emit electromagnetic radiation. The source of this radiation is energy transitions in the atoms and molecules of the body. These transitions are maintained by the free energy of the body, i.e in close relation to the temperature. With higher free energy 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 not require any medium between the two bodies exchanging energy. This is however necessary for conduction and convection. Thermal radiation between two bodies are actually most e cient if there 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 the visible spectra. [3] the gas also emit and absorb radiation which must be taken into account when studying thermal radiation. The heat transfer between two bodies is accomplished through that the hotter surface emits 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 q00, due to thermal radiation, and the temperature of the emitting surface Ts on the basis of experimental results. In 1884 Ludwig Boltzmann derived the same relation from theoretical considerations using thermodynamics. This relation is called the Stefan−Boltzmann law and reads:
00 4 (2.7) q = σTs 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 following characteristics [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:
2 2hc0 (2.8) Iλ(λ, Ts) = 5 λ [exp(hc0/λkBTs) − 1] −34 8 With h = 6.6256 ∗ 10 Js being the Planck constant, c0 = 3 ∗ 10 m/s being the speed of −23 light, and kB = 1.805 ∗ 10 J/K the Boltzmann constant. The spectral intensity, Iλ(λ, Ts), is the radiated energy intensity for a blackbody at absolute temperature T per unit solid angle and per 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:
Z Z 2π Z π/2 Eλ(λ, Ts) = Iλ(λ, Ts) cos θdΩ = Iλ(λ, Ts) cos θ sin θdθdφ = πIλ(λ, Ts) (2.9) 0 0
11 The cos θ factor arises because one is only interested in the projection of the radiation from a dierential small surface dA1 normal to the direction of radiation. This term is easier understood from 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:
Z ∞ Z ∞ 2 2πhc0 4 (2.10) Eλ(λ, Ts)dλ = 5 dλ = σTs 0 0 λ [exp(hc0/λkBTs) − 1] Derivating Eq. 2.9 with respect to λ and putting the derivative equal to zero one get the wavelength at which Eλ(λ, Ts) peaks: d E (λ, T ) = 0 ⇒ λ T = C (2.11) dλ λ s max s 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 Wien displacement 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 Wien displacement. Only black bodies with a temperature over ∼800 K emit radiation in the visible spectra. Black bodies with lower temperatures emit radiation in the infrared spectra. [3]
12 2.3.1 Emissivity
Wien's displacement law, the Planck distribution, and the Stefan−Boltzmann law are only valid for perfect black bodies. In reality no material has the exact characteristics of a black body. When looking at emitting thermal radiation, all real bodies emit less (or equal) amount of radiation than a 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. Emissivity depends on the wavelength and the direction of the radiation, as well as on the temperature, i.e
ε = ελ,Ω(λ, θ, φ, T ). This makes the temperature dependence of the thermal radiation less trivial since the spectral directional emissivity of a real body is de ned as:
Iλ,real(λ, θ, φ, T ) ελ,Ω(λ, θ, φ, T ) ≡ (2.12) Iλ,black(λ, T )
The reason Iλ,black(λ, T ) do not depend on the space angles is simply because the black body is a diuse emitter. Depending on the situation there are alternative ways of de ning the emissivity. When looking at the total wavelength spectra, the total directional emissivity is de ned as:
Ireal(θ, φ, T ) εΩ(θ, φ, T ) ≡ (2.13) Iblack(T ) When looking at the total hemispherical radiation the spectral hemispherical emissivity is de ned as:
Eλ,real(λ, T ) ελ(λ, T ) ≡ (2.14) Eλ,black(λ, T ) The total hemispherical emissivity is de ned as:
R ∞ E (T ) ελ(λ, T )Eλ,black(T )dλ ε(T ) ≡ real = 0 (2.15) Eblack(T ) Eblack(T ) 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 the spectral distribution and (b) shows the directional distribution. [3]
2.3.2 Absorptivity, re ectivity and transmissivity Radiation leaving a surface is not only emitted radiation, but also transmitted and re ected, see Fig. 2.7. So in addition to emissivity, ε, real surfaces also have the properties absorptivity (α), re ectivity (ρ), and transmissivity (τ). By looking at the radiation from a surface one gets contributions from the surrounding. This makes it more di cult to relate the radiation from a surface to its temperature.
13 Figure 2.7: a) shows the origin of radiation leaving a surface. b) shows what happens at an irradiated surface. Where α is the absorptivity of the surface, τ the transmissivity, ρ the re ectivity, and ε the emissivity. In general α are not equal to ε, but they can be equal under speci c conditions.
The properties for an irradiated surface α, ρ, and τ depend on the wavelength, λ and one the solid angle, Ω. They are de ned as:
Iλ,i,abs.(λ, Ω) αλ,Ω(λ, Ω) ≡ (2.16) Iλ,i(λ, Ω)
Iλ,i,refl.(λ, Ω) ρλ,Ω(λ, Ω) ≡ (2.17) Iλ,i(λ, Ω)
Iλ,i,trans.(λ, Ω) τλ,Ω(λ, Ω) ≡ (2.18) Iλ,i(λ, Ω) They can also be de ned 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 in Fig. 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 at the same temperature as the surface. Or if 1. and 2. are true and if the surface is grey, i.e
αλ 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 means that for point 3 in the list above to be true ελ and αλ does not have to be independent of λ for all wavelengths, but only over the spectral range of the irradiation. This is the de nition of a grey
surface that says: "a surface is a grey surface if αλ and ελ are independent of λ over the spectral region 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 knowing ρ and τ one does not necessarily know ε.
14 2.4 Temperature measurement Measuring the temperature of a system involves a complex interaction between the sensor and the system. The sensor changes its behaviour with temperature or with a property related to the temperature. This change produces a signal that is processed by a signal processor and is from there 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 an actuator.
The physical signal in temperature measurement is usually related to the heat transfer between the sensor and the system changing the temperature of the sensor. In most thermal sensors heat is 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 properties and the mass of the system and the sensor, since the heat transfer goes two ways. If the factor cp,sensormsensor is comparable to cp,systemmsystem than there is risk that the temperature of the system changes. For a system's temperature not to be aected by the heat transfer with the sensor the equality cp,sensormsensor cp,systemmsystem must hold. This is achieved by using a small sensor with a small speci c heat. It is also an advantage that the thermal conductivity of the sensor is large so that it fast reaches thermal equilibrium. Some sensors measures the heat ux between the sensor and the target and can from there achieve the temperature of the target. But in order to achieve the temperature of the target a reference temperature must be known, i.e the temperature of the sensor. The reason for this is that heat ux is dependent on the temperature dierence 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, or in close proximity to the system of interest. Otherwise the heat transfer will be between the sensor and another system and the temperature felt by the sensor is not the one of interest. Sensors that exchange heat through radiation need not to be in close proximity to the target. But as the distance between the target and the sensor grows so does the sources of error. With increasing distance the atmosphere, i.e the medium between the target and the sensor, aects the radiation more as well as the background radiation. More of how dierent sensor works will be discussed in chapter 4.
15 3 The Yankee dryer
The objective of this project was to investigate methods for measuring the temperature of the Yankee dryer. In order to get a better picture of the system this section will be devoted to describing the Yankee and the environment around it. The Yankee dryer was explained shortly in section 1.1.2 so some references will be made to this section. Fig. 1.3 shows an overview of the dierent processes involving the Yankee cylinder. To follow the Yankee one revolution one can point 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 it can be useful to get a picture of the dimensions of the Yankee. As many of the machines that Metso Paper manufacture are custom made so are the Yankee dryers. Some of the Yankee dryer's constructional parameters are listed in table 1 below.
Parameter Min. value Max. value Length (mm) 3 380 6 500 Diameter (mm) 3 660 5 500 Mass (kg) 65 000 133 000 Machine speed (m/min) 200 2 000
Table 1: Some of the constructional parameters of the Yankee dryer. These values are taken from standard Yankee dryers. So for the custom made ones parameters can be outside the range of the tabulated values.
The Yankee dryer is made of cast iron that is highly polished on the shell surface so that the paper is dried on a smooth and uniform surface. To achieve this ne surface the Yankee dryer is worked upon in two steps. In the rst step the Yankee dryer is turned in a lathe so that almost the right 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 iron surface makes it sensitive to oxidation. In the following sections the dierent processes involving the 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 a rule of thumb the steam pressure varies between 6-9 bar depending on the process. Since the paper cools the cylinder from the outside thermal energy is transferred from the steam which causes the steam to condensate. Depending on the rotational speed the condensate is assembled dierently on the inside of the Yankee dryer. In Fig. 3.1 three dierent assemblies are shown. As the rotational speed seldom is lower than 600 m/min the condensate is in general assembled as a ring on the inside shell (the image to the right in Fig. 3.1).
Because condensate is covering the inside of the Yankee dryer the maximum temperature that can be achieved here is given by the saturated steam temperature at the appropriate pressure. A graph showing how the saturated steam temperature varies with pressure is shown in Fig. 3.2. As said above the pressure varies between 5-9 bar which corresponds to a maximum inside tempera- ture variation of ∼160-180◦C.
The steam is removed from the shell surface by headers, see Fig. 1.5. The headers consist of small metal pipes that acts as straws and suck up the condensate. The headers rotates along with the 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 given pressure this temperature corresponds to the maximum temperature on the inside of the Yankee dryer. the headers. The behaviour of the condensate layer aects the inner temperature of the Yankee dryer. A thicker condensate layer reduces the heat ux between the steam and the paper. This means that higher steam pressures must be used which demands more energy resulting in higher costs for the paper manufacturer. In order to maximize the heat transfer between the steam and the paper the inside walls are covered with grooves. The grooves are 25-32 mm deep, 12 mm wide and separated by 30 mm. The condensate assemblies inside these grooves which makes it easier for 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 the temperature pro le of the Yankee dryer. Since an uneven temperature pro le will cause an uneven thermal expansion, a malfunctionning header will cause a number of problems in the processes involving the Yankee dryer. A fast and dependable temperature measurement method would detect an uneven temperature pro le 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 aqueous solution. This solution contains of adhesives and release agents. Their task is to optimize the adhesion of the paper on the Yankee dryer, as well as protecting the cylinder from corrosion and the 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 Yankee dryer surface. A picture of this process is shown in Fig. 3.3. The chemicals are most commonly dierent polymers as adhesives and dierent oils as release agents [1]. Depending on the tissue grade 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 the boom 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's adhesive properties as well as its appearance. A clean Yankee dryer, without any coating or paper rests on it, is a polished cast iron surface, making it highly re ective. The coating makes the surface look white and dull. A thick coating layer seems opaque to the eye. A picture of how the coating 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 is introduced. a) and c) shows a clean Yankee before the coating was introduced. b) and d) shows the surface after the coating was introduced but before any paper was pressed on the Yankee dryer. It is obvious that the re ectance 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. Metso Paper produces machines that use a single nip as well as machines that use a double nip. The advantage of using a double nip is that more water can be pressed out of the paper before it is attached to the Yankee dryer. Having a higher dryness percentage before the Yankee dryer saves energy since less water has to be evaporated by the Yankee dryer. Depending on the dryness of the paper and the speed of the machine the paper cools the cylinder dierently.
The heat from the Yankee dryer is not su cient to dry the paper which is the reason for the use of a hood dryer. The hood dryer operates by blowing hot air jets through nozzles onto the paper. As is seen in Fig. 1.2 the hood dryer covers much of the Yankee dryer's surface, in order to blow as much hot air as possible on the paper. A picture of how the hood dryer operates is seen in Fig. 3.5.
Figure 3.5: Showing how the hood dryer operates (left image) and the dierent heat uxes in the paper while on the Yankee dryer (right image). The heat ux in the paper comprise conduction of heat from the Yankee dryer and forced convection of heat from the air jets. If much water is removed the Yankee dryer is heated by the air jets.
The temperature of the air blown from the hood dryer varies, depending on the process, and can be up to 700◦C. The impingement speed is also varied and can be up to 185 m/s. If too much of the water is removed the hood dryer warms up the Yankee dryer surface instead of drying the paper. Since the size of the nozzles can be varied, so can the jet streams. An uneven temperature distribution 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 manufacturing process.
3.4 Creping process The creping process is simply scraping the paper o the Yankee dryer with the doctor blades. In this process much of the papers nal quality is determined. When the paper reach the doctor blade 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 microfolds begins to grow. These piles of microfolds are called macrofolds, see Fig. 3.6. The structure of these 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 the doctor blade, see Fig. 3.6. Using a large impact angle, the crepes fall o the blade easier. This aects the macrofolds in such way that the number of microfolds per macrofold decreases with an increasing impact angle. A sheet with a large number of microfolds per macrofold has a high basis weight as well as high smoothness. This is a very simple picture of the creping process since it also depends on adhesion, geometry, and presence of a coating layer to name a few [1]. A more detailed discussion 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 creping with a small impact angle. With a larger impact angle the crepes fall of the blade easier which decrease the number of microfolds per macrofold.
In an ideal paper machine the doctor blade would only crepe o the paper leaving the Yankee cylinder and the coating layer unchanged. With the high speeds of these machines (up to 2000 m/min) this is a di cult 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 the paper while the creping doctor is being substituted. The next doctor is the creping doctor which crepes the paper and the last is the cleaning doctor. The cleaning doctor scrapes much of the paper residues as well as some coating. Without the cleaning doctor the surface would not be as smooth as required due to the paper residues. Since some of the coating is removed, new coating is constantly sprayed on the Yankee dryer.
As mentioned the crepe doctor is changed fairly often since it experiences big wear during operation which worsens its performance. Due to this wear the coating thickness varies with time since a fresh doctor scrapes of more coating and paper residues. It is not unusual that the doctors scrapes uneven in the cross machine direction leading to an unevenly coating layer. This aects the heat transfer and the appearance of the surface.
20 4 Sensors 4.1 Thermocouples In 1821 Thomas Johann Seebeck discovered the thermoelectric eect when he observed a magnetic needle move when being close to a circuit consisting of two metals, copper and bismuth. The circuit had two junctions, where the metals connected, which was held at dierent temperatures. Since the theory of the relation between electric and magnetic elds was still being investigated, Seebeck never recognized that an electric current was owing in the circuit. Instead Seebeck believed that the metals got directly magnetized by the temperature gradient and therefore called his discovery thermomagnetism. Later the discovery was renamed to the thermoelectric eect. An image of the experiment 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 these being a thermocouple. In its simplest form a thermocouple consists of two wires consisting of dierent materials that are connected to each other at one end. In the other end the two wires are connected 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 at one end and are connected to a voltmeter at the other end. Since the two end are at dierent temperatures 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 Fermi level, EF , in the two materials. This dependence is described by the Seebeck coe cient [5]: 1 dE α (T ) = F (4.1) s q dT Where q is the electron charge. Rearranging Eq. 4.1 the voltage dierence of a single wire in a temperature gradient that varies along the wire in the interval T ∈ [T1,T2] can be written as [6]:
Z T1 ∆V = ∆EF = q αs(T )dT (4.2) T2
21 Now combining two wires, as in Fig. 4.2, the measured voltage becomes:
Z T0 Z T0 Z T0 Z T0 ∆V = q αs,1(T )dT −q αs,2(T )dT = q αs,1(T )−αs,2(T )dT = q αs,12(T )dT (4.3) T1 T1 T1 T1
Where αs,1(T ) is the Seebeck coe cient of metal 1. It is clear from Eq. 4.3 that if the two wires consist of the same material, i.e αs,1 = αs,2, no voltage would be produced in the circuit. The magnitude of the voltage is on the order of µV/K, so one need to use a quite sensitive voltmeter. A table of absolute Seebeck coe cients of a number of metals can be viewed in Table 4.1, this table is taken from [5].
Metal 273 K 200 K Chrome (Cr) 18.8 17.3 Gold (Au) 1.79 1.94 Copper (Cu) 1.70 1.83 Silver (Ag) 1.38 1.51 Rhodium (Rh) 0.48 0.4 Lead -0.995 -1.047 Aluminium (Al) - -1.7 Platinum (Pt) -4.45 -5.28 Nickel (Ni) -18.0 -
Table 2: Absolute Seebeck coe cients, αs, for a number of metals. Notice that some metals have negative values of αs.
As is shown in Table 4.1 some metals have positive αs and some have negative. By convention the 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 temperature dierence. 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 charge carriers 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 same sign on αs. But an increased temperature also aects the mean free path and the scattering time of the charge carriers. If the mean free path increases much or if the scattering time decreases much with temperature the high energetic charge carriers gets trapped at the hot end. This leads to an accumulation of charge carriers at the hot end which, having only one charge carrier, would have 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 the voltage as electrons diusing from cold to hot.
In order to measure the temperature with a thermocouple either the thermoelectric junction temperature or the terminus connection must be known. This is because the produced voltage depends 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 external device. One way of keeping the temperature constant can be by keeping the terminus connection immersed in ice water which keeps the temperature constant at 0◦C. This makes the temperature measurement device rather di cult to use since one always need a bucket of ice water. A more common 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 of possible 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 Application Rare-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 other groups. Constantan negative E,J and T Suitable for measuring low tem- peratures since they have a high Seebeck coe cients 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. These tables relates the thermoelectric voltage to the temperature of the thermoelectric junction for a thermocouple with the terminus connection kept at 0◦C. The values in these tables were obtained from polynomial functions on the form.
n X i ∆V = ai(t90) (4.4) i With n being the power of the polynomials varying between 4 and 14 depending on the type of thermocouple. Since not all thermocouples have their terminus connection kept at 0◦C these polynomials can be used to obtain the temperature of the thermocouple junction. This is done by the 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 total voltage. 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 are not good at measuring small temperature dierences. To overcome this issue one can connect a number of thermocouple in series with their thermocouple junctions and terminus connections at the same temperatures, see Fig. 4.3.
Figure 4.3: A simple thermopile con guration with six thermocouple connected in series. The voltage produced by the the thermopile is six times the voltage of the individual thermocouple voltage.
Just connecting six thermocouples in series, as in Fig. 4.3, does not increase the thermoelectric voltage much. Therefore a larger number of thermocouples need to be connected in series. This can 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 temperature dierences fast. This in turn make them suitable for non-contact temperature measurements, i.e measuring the thermal radiation from a system. An example of a micro machined thermopile is seen 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 are connected in series by the interconnecting wires and the aluminium interlevel contacts. On top of the thermocouples is a layer of silicon nitride that exchange heat through thermal radiation with the target. The temperature of the silicon substrate is measured with a thermistor (not shown in the 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 large number of wavelengths. Working in a broad spectral range introduces some di culties since the gases also emit and absorb radiation. Though air seem transparent to humans it is opaque in some spectral ranges, see Fig. 4.5. If a detector would detect radiation in these spectral regions, some of the signal would come from the air which would result in an erroneous measurement. Some of the signal would also be absorbed by the air which also results in errors. Therefore sensors are designed to operate in spectral ranges where the atmosphere have large transmissivity. For sensors operating in air one of the following ranges are used:
Name Spectral range (µm) Middle Wavelength IR (MWIR) 3-5 Long Wavelength IR (LWIR) 8-14 Very Long Wavelength IR (VLWIR) 14-30
Figure 4.5: The transmissivity for air over a 300 m distance. The dark regions indicate that the air is opaque. A infra-red detector that operate at wavelengths where the air is opaque would give erroneous 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 temperature is described by the Stefan-Boltzmann law (Eq. 2.7) and Planck's law (Eq. 2.8). For thermopile detectors the Stefan-Boltzmann law is most commonly used to describe the interaction between the detector and the target. The reason for this is because thermopile detectors operate in a large spectral range. According to reference [8] PerkinElmer thermopile detectors are calibrated using the formula:
4−δ 4−δ (4.5) ∆V = K(εtargetTtarget − Tdetector)
Where Ttarget is the target temperature, εtarget is the emissivity of the target, Tdetector is the temperature of the backside of the detector, K and δ are the detector parameters that is speci c for the detector and tells how it responds to a heat ux. The reason for the smaller exponent of Eq. 4.5 compared to the Stefan-Boltzmann law is because not the whole electromagnetic spectra is seen by the detector. From Eq. 4.5 one see that the thermopile sensor is calibrated to respond to 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 dependence on 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 behaviour with 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 an electrical output signal, apart from the thermoelectric eect, are the pyroelectric eect and the temperature 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:
2 2 ne τe pe τh (4.6) σ = ∗ + ∗ me mh where n is the electron density, p the hole density, e the electron charge, τ the mean time between collisions, and m∗ the eective mass. The subscripts e and h stands for electron and hole respectively.
From Eq. 4.6 one can identify two parameters that vary strongly with temperature, namely the mean time between collisions and the charge carrier density. With increasing temperature the atoms in the material vibrate more about there equilibrium positions, i.e the phonon density increases. 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 temperature the 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 for metals. 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 increasing temperature for semiconductors (at low temperatures) and increases for metals. Both metals and semiconductors can be used to measure the temperature if their resistance has a stable dependence on 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 made of pure metals, usually platinum. RTDs work in wide temperature ranges with high accuracy but they need to be relatively big. The relatively large size of the RTD makes them less sensitive for small 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. Usually they are made of ceramics or polymers. Their temperature dependence of the resistance is not as stable as the RTDs in wide temperature ranges, but is more sensitive to small temperature changes in 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 Samuel Pierpont Langley. His bolometer consisted of two thin wires of platinum covered with soot. The wires formed two arms of a Wheatstone bridge, where one arm was exposed to the radiation and the other shielded. Since Langley's bolometer these sensors have been developed a lot and platinum has been substituted by dierent thermistor materials. The size of the bolometers have changed during the years and are now micro-machined, just as thermopiles. A structure example of a micro bolometer 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/4 spacing is to form a resonant optical cavity to optimize the absorption of photons of wavelength λ. [9] material changes. This potential is used in radiation sensors, where the radiation changes the temperature 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 done mechanically, usually with rotating blades that periodically interrupts the incoming radiation. This way the sensor periodically changes its temperature which results in a periodically potential output. The periodical potential can be related to the targets temperature since the heat ow between the sensor and the target is proportional to 4−δ 4−δ as in Eq. 4.5. Ttarget − Tsensor
4.4 Thermal IR sensor In this section some general properties of a thermal detector used for radiation measurement will be discussed. As mentioned bolometers, thermoelectric- and pyroelectric sensors all work in a similar way. They absorb thermal radiation which results in a temperature change of the sensor which in hand results in an electrical output signal. In reference [10] Rogalski presents a general theory 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 radiation which changes is temperature from the heat sinks temperature T by an amount of ∆T . The sensor has 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 ux q00 with frequency ω can be expressed as:
00 αq (4.7) ∆T = 2 2 2 Gth + ω Cth
27 with α being the absorptivity of the sensor. From Eq. 4.7 it is clear that the temperature change 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 re ective layer is inserted behind the absorbing layer. The re ective layer re ects the radiation transmitted by the absorbing layer back to the absorbing layer. A solution to minimize the thermal capacity is 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 low pressure. It is also favourable for the connections between the sensor and the heat sink to be made as small as possible.
Since the temperature change is proportional to the electrical output, it is an advantage for it
to 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:
Cth τth = = GthRth (4.8) Gth
where Rth is the thermal resistance. Now in order to minimize τth, Cth should be minimized and Gth 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 for a target that changes it temperature quickly, a small Gth is desirable. For thermal sensors τth is usually in the ms range.
Another gure of merit for sensors is the speci c detectivity, D∗, which is the normalized signal to 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 by the thermal or background uctuations. The detectivity for such a sensor can be expressed as:
2 1/2 ∗ α A (4.9) D = 2 4kBTsensorGth
If the heat transfer is dominated by heat transfer through radiation, then Gth is the rst derivative of the Stefan-Boltzmann equation with respect to temperature. Eq. 4.9 can then be written as:
!1/2 ∗ α (4.10) D = 5 5 8kBσ(Tsensor + Tbackground)
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 uctuations
is 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 of 10 1/2 −1 Tbackground = 300K is 1.98 × 10 cmHz W . This detectivity is the ultimate limitation of a thermal sensor and for most sensors other noise sources limit the performance decreasing the detectivity. Typical values of the detectivity for real thermal sensors are on the order of 108 − 109 cmHz1/2W−1 [10]. In most commercial product speci cations the detectivity is not listed.
28 Instead the minimum resolvable temperature dierence (MRTD) is given at a certain temperature. The MRTD can be de ned as the minimum temperature dierence between a target and the background 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 but rather just state how they are related:
1 MRTD ∝ (4.11) R ∞ ∗ 0 D dλ Where the parameters relating the two are sensor speci c 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 charge carrier density increases so does the conductivity. Monitoring the current in a photon sensor will give information of how much radiation that is falling on the sensor. There are basically two dierent ways of making use of the increased charge carrier density, namely by photodiodes or 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 an external 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 ranges that they operate in can be engineered. The maximum wavelength of the sensor can be engineered hc by controlling the bandgap Eg, since no electron-hole pair can be created if λmax ≥ . The Eg minimum wavelength can be achieved by using some material in front of the sensor with a larger hc band gap, Eg = . 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 the target hits the concentrator and is de ected towards absorber where the photons excite electron- hole pairs. The photons that are not absorbed are re ected by the re ector and hopefully absorbed on the way out.
The current responsivity, R, depends on the quantum e ciency, η, and the photoelectric gain, g. The quantum e ciency is usually de ned as the number of electron-hole pairs created per incident photon. It tells how well the sensor interacts with the incident radiation. The photoelectric gain is the 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 spectral current responsivity can be expressed as:
29 λη R = qg (4.12) λ hc Where q is the electron charge. Now there are, as in the case of thermal sensors, dierent sources of noise. If one assume that the current induced by the noise has the same gain as the photoelectric one, the noise current due to generation and recombination processes is given by [10]:
2 2 2 (4.13) Inoise = 2(G + R)Aet∆fq g
where G is the generation rate, R is the recombination rate, ∆f the frequency band, Ae the electrical area, and t the thickness of the absorber. The detectivity of a photonic sensor can be de ned as [10]:
R (A ∆f)1/2 D∗ = λ 0 (4.14) Inoise Now combining Eq. 4.12-4.14 one obtain the relation [10]:
λ A 1/2 D∗ = 0 η[2(G + R)t]−1/2 (4.15) hc Ae 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 e ciency as well as a thin absorber. The generation and recombination processes is strongly dependent on the temperature of the sensor. Therefore the sensors usually are cooled to cryogenic temperatures so that the noise due to temperature uctuations is reduced. The optimal situation is when the optical generation, due to background radiation, is higher than the thermal generation. This is achieved when the following inequality holds [10]:
ηq00 τ background > n (4.16) t thermal where 00 is the photon ux density due to background radiation, the carrier lifetime, qbackground τ and nthermal the density of charge carriers excited due to thermal excitations. If this relation holds the sensor is only limited by the background radiation which is always present, i.e one has an ideal photonic sensor. These sensors are called background limited infrared photodetector (BLIP). The detectivity of a BLIP photovoltaic sensor is given by [10]:
!1/2 ∗ λ η (4.17) DBLIP = 00 hc 2qbackground √ The BLIP detectivity for a photoconducting sensor is 2 lower than for photovoltaic. This is due to the recombination process in a photoconducting sensor which is uncorrelated to the generation process, giving a contribution to the noise. Detectivities for a number of commercial sensors are shown in Fig. 4.9. It is clear that the photonic sensors are superior to the thermal sensors. 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's law):
Z λ2 ε(λ, T ) S(T ) ∝ c1 dλ (4.18) 5 c2 λ1 λ exp λT − 1
where c1 is a constant that includes the constants of Planck's law as well as sensor constants and hc0 . From Eq. 4.18 one see that the signal strongly depends on the emissivity of the c2 = k target. If theB emissivity of the target is unknown the temperature measured by the IR sensor
30 Figure 4.9: Spectral detectivities of com- mercially available photonic sensors. All sensors have an update frequency of 1000 Hz except for the ther- mopile, thermocouple, Golay cell, and the pyroelectric detector which have an update frequency of 10 Hz. Theoretical curves for the detectivity of BLIP (ideal) sensors for photovoltaic, photocon- ductive, and thermal sensors are also plotted. [10] will not be the true temperature of the target. More on how the emissivity aects the measured temperature is discussed in section 5.6.1. There are however techniques that try to overcome this dependence:
• 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 photonic IR sensors measuring at dierent bands (spectral ranges). The ratio of these signal is then used to obtain an emissivity independent temperature measurement. When describing the signal for such a sensor it is advantageous to use Wien's law. Wien's law is similar to and a good approximation hc0 to Planck's law when λT [12]. The signal of the sensor, S(T )i, is then described as [12]: kB
c1ε(λi,T ) (4.19) S(T )i = λ5 exp c2 i λiT
where i denotes the sensor letter, c1 and c2 the constants seen in Eq. 2.8. De ning the ratio between signal from sensor a and b as:
S(T ) ε(λ ,T ) λ 5 c 1 1 Γ = a = a b exp 2 − (4.20) S(T )b ε(λb,T ) λa T λb λa The ratio temperature can be obtained by rearranging Eq. 4.20: 1 1 1 (4.21) TR = c2 − 5 λ λ ε(λb,T ) λa b a ln(Γ) + ln( ) + ln( 5 ) ε(λa,T ) λb
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 putting two ratios (Eq. 4.20) equal to each other [13]:
c 1 1 ε(λ ,T ) c 1 1 exp 2 − = a exp 2 − (4.22) TR λb λa ε(λb,T ) T λb λa
31 where the left hand side of the equation correspond to the ratio temperature assumption
ε(λa,T ) = ε(λb,T ). Rearranging in Eq. 4.22 one get that TR depends on the true temperature, T and true emissivity ratio, ε(λb,T )/ε(λa,T ), as: −1 ln(ε(λb,T )/ε(λa,T )) 1 (4.23) TR = −1 −1 + c2(λb − λa ) T
From Eq. 4.23 one see again that TR = T if the emissivities are equal. TR also comes close to T as λa and λb are largely separated. But separating λa and λb makes it more uncertain that the emissivities are equal. This is a simpli ed picture of the double-band pyrometer since there are additional parameters aecting the signal, such as sensor parameters, but show the biggest obstacles and advantages of the technique.
One disadvantage of this technique is that relatively short wavelengths are used, in order for Wien's law to be a good approximation to Planck's law (λT hc0 ). Targets with low tempera- kB ture, T < 300◦C, do not emit much radiation at these wavelengths. The small amount of radiation coming from a cold target disappears in the thermal noise of the photonic sensors. So in order to use 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 this project a search for double-band pyrometers that can measure temperatures around T ≈ 100◦C was made, but none was found. In order to get a double band pyrometer that measures such temperatures 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 techniques t 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 dierent materials. These emissivity approximations work better for materials that are not grey. But to use these models the target surface radiation properties must be known so that the best mathematical model approximating the emissivity is used. These pyrometers also use photonic sensor with a narrow spectral range which makes them less suitable to use for low temperatures T < 300◦C. While searching for commercial products using this technique no products were found since they are still very much under development.
Gold-cup pyrometer This technique uses a gold-plated hemisphere that is placed very close to, ideally in contact, with the target. Other coatings than gold can be used as long as they have a high re ectivity. Inside the 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 gold is highly polished the hemisphere has a very high re ectivity (ideally ρ = 1) which increase the eective emissivity of the target. This is done since almost all emitted radiation from the target is re ected 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 to construct a perfect re ector, 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 electronic response, S(T ), to the radiation can be said to depend on the targets temperature as:
Z λ2 1 S(T ) ∝ εeff dλ (4.24) λ5[exp( c2 ) − 1] λ1 λT
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]: ε (1 − ρ)(1 − ε) ε = = 1 − (4.25) eff 1 − ρ(1 − ε) 1 − ρ(1 − ε)
32 Figure 4.10: Schematic of a gold-cup pyrome- ter. [15]
Where ε is the emissivity of the target, and ρ being the re ectivity of the gold hemisphere. From Eq. 4.25 it is seen that the eective emissivity approaches unity as the re ectivity of the hemisphere goes to unity. It is also seen that εeff depend on the emissivity of the target. To show these dependences the eective emissivity was plotted versus the re ectivity of the hemisphere for ve xed emissivities of the target, see Fig. 4.11.
Figure 4.11: Plot
of εeff versus ρ for ve xed emissivities.
From Fig. 4.11 it is clear that large errors is obtained if the gold cup pyrometer does not have a re ectivity equal to one. Since the environment surrounding the Yankee cylinder is all but a clean environment (steam and paper dust) it is questionable if a gold cup could be kept as clean as required. The fact that the gold-cup must be kept very close to the surface also introduces a di culty since the Yankee cylinder rotates with high velocities. If the gold-cup would come in contact with the Yankee cylinder it could be damaged. The damage could be in form of small cracks in the gold hemisphere which would reduce the re ectivity.
There are many commercial products using this technique, where Heitronics LT13EB is one example of such a product.
33 5 Experimental
In order to investigate dierent temperature measurement methods three dierent devices were tested 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 machine had dierent operational parameters during dierent measurements. So the true Yankee dryer temperature was not the same in all measurements. Some of the pilot machine's operational parameters will be listed in the result for each measurement. In the following sections it will be discussed how the measurements were performed.
5.1 Thermophone measurements The Thermophone is the device that Metso Paper use at present to measure the temperature of the Yankee dryer. It measures the temperature with a thermocouple, discussed in section 4.1. The thermoelectric junction is attached to a brass piece that is kept in close proximity to the Yankee dryer. This brass piece is kept inside a te on cup that shields the brass piece from the surrounding air 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 te on cup of the Thermophone, was pressed uniformly against the Yankee dryer. Pressed uniformly means that the te on cup was pressed against the Yankee dryer so that little, or ideally no, air comes in between the te on cup and the Yankee dryer. The Thermophone was held in contact with the Yankee dryer for about 5-20 min. Between two consecutive measurements the Thermophone was rested for about 10 min so that it would reach room temperature again. This was made in order to investigate in uence of the te on cup temperature on the measured temperature. The thermocouple signal was stored, along with the time, on a memory card (MMC) by a YSM3. The YSM3 is a device constructed by Metso Paper used to display and store the temperatures measured by the Thermophone. The stored values was imported to Microsoft Excel where they were made into graphs.
Figure 5.1: How the Thermophone was held against the Yankee dryer during the measure- ments. The Thermophone was attached to a ∼1.5 m long pole which was held so that the Thermophone was in contact with the Yankee dryer.
Figure 5.2: Showing one good (left) and one bad (right) way of holding the te on cup against the Yankee dryer. If the te on cup is held in a bad way cold air (∼ 50◦C) can ow into the te on cup and disturb the measure- ment. Ideally no cold air ow into the te on cup, but as can be seen in the results this was not always the case.
34 In order to compare these graphs to something, measurements were made on a non moving iron block with a surface curvature similar to the Yankee dryer surface. The iron block was heated on a single stove plate and had a temperature of about ∼ 100◦C. The measured temperature was stored on a MMC memory card along with the time. These values was also imported to Microsoft Excel and made into graphs. Since no complicated air stream is present inside the te on cup heat is almost only transferred between the surface and the brass piece. Comparing the graphs from measurements made on the non-moving iron block to measurements made on the pilot machine can get a hint of how the movement of the air streams inside the te on cup in uence the measured temperature.
5.2 Pyrometer measurements The pyrometer measurements was performed with a Raytek RAYNGER MX4 (speci cations in section 5.5) while standing directly below the Yankee dryer, see Fig. 5.3. The distance between the Yankee dryer and the pyrometer was approximately 30 cm. Dierent distances were tried but these measurements gave the same result.
Figure 5.3: The pyrometer measurement setup. The pyrometer was held directly be- low the Yankee dryer during operation. It collects radiation from a relatively small area compared to the thermographic camera. The area it collects radiation from is circular with a 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 between dierent 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 was done in order to show the relation between the measured temperature and the surface nish. The measured temperatures was displayed on the pyrometer and written down on a piece of paper. The values were associated with an area on the cylinder having a certain surface nish. The values was later coupled with the photographs.
To get some sort of reference temperatures, simultaneous measurements were made with the Thermophone. Even if the Thermophone do not show an exact value, these values can show that the temperature do not vary much over the surface. The values of the Thermophone was also written down and coupled to the same areas as the pyrometer spots. During these measurements the RAYNGER MX4 was used as the display for the Thermophone. Since the Thermophone use a 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 Karlstad University. Lars Pettersson and Stefan Frodeson from Karlstad University helped to take the thermographic 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 in the 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 the tending side (TS) as well as from the drive side (DS). As the image shows the position of the camera was below and beside the Yankee dryer. In numbers it was approximately 1.5 m below and 0.5 m beside the Yankee dryer. By adjusting the lenses of the camera, the area from which radiation was collected 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 the Thermophone. The thermographic camera then zoomed in on the Thermophone and a number of pictures were taken. The objective of these pictures was to show that the Thermophone gets warmer with time. After the measurements with the Thermophone was made, a picture inside the te on cup was taken in order to see the temperature distribution there.
After all pictures were taken with the thermographic camera, the pictures were imported to a computer and processed with a software from FLIR. One feature in this software is to create graphs of how the temperature varies along a selected line. A couple of such line graphs were made in 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. Yet another feature allowed one to get the mean temperature of a selected area. This was made on a picture of a aluminium foil in order to get the background radiation.
5.4 Thermophone speci cations 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 thermocouple inside a cup made of te on. The thermocouple is mounted on a circular thin brass piece that is held in place by four metal wires, two of them being the wires of the thermocouple. The brass piece should be kept as close to the Yankee dryer surface as possible without touching it. If the brass piece comes in contact with the Yankee dryer it will get heated by frictional heating and an incorrect temperature will be measured. A sketch of the geometry of the Thermophone can be viewed in Fig. 5.5 below. The purpose of the Te on cup is to protect the thermocouple from the surrounding air streams caused by the motion of the Yankee dryer. These streams would otherwise cool the thermocouple resulting in a incorrect temperature measurement. The reason for the choice of te on as material is because of its low coe cient of friction and its low thermal conductivity. With a material hav- ing a higher coe cient of friction and thermal conductivity the cup would quickly get heated by frictional heating which would disturb the measurement.
36 Figure 5.5: A sketch of the Thermophone geometry. The wires holding the brass piece in place are missing in this picture. The geometry is cylindrically symmetric about the z-axis.
The brass piece and the te on cup are attached to a plate of stainless steel which holds all of the components of the Thermophone in place. On the stainless steel plate a footing is mounted on which a pole can be attached in order to easier perform the measurements. The footing and the stainless 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 had been attached to a more conducting material the thermocouple output voltage would have been disturbed, resulting in less accurate temperature measurement. The breglass piece is glued onto the steel plate with an electrical isolating glue.
Even if the Thermophone looks like a simple temperature measurement device it is hard to analyse the heat transfer involving the thermocouple. The fact that the Yankee dryer rotates fast during the measurements promotes:
• Complicated air streams both outside and inside the te on cup. • Frictional heating of the te on cup. The frictional heating along with the air streams makes it hard to determine which heat transfer that contributes most to the thermocouple temperature. The surrounding air has an approximate temperature of T = 50◦C and thereby cools the te on cup from the outside, since the Yankee dryer has a temperature around T = 100◦C. Even if the coe cient of friction between the Yankee dryer and the te on cup is small (µ ≈ 0.1) frictional heating is unavoidable. The rate at which the friction heats the te on cup can be estimated by:
∆s q = F = F v = µNv = 0.1 × 20 × 30 = 60W (5.1) ∆t with µ = 0.1 being the coe cient of friction, N = 20N being the force at which the te on cup 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 te on correspond to having a light bulb of 60 W heating it. 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 Yankee dryer) and top side. The heat transfer on the bottom side can be approximated with a Couette ow which will be discussed more in detail in section 5.4.1. The top side exchanges heat through convection caused by the complicated air streams inside the te on cup. It is believed that the
37 Figure 5.6: Photos of the Thermo- phone. The upper photo shows how the Thermophone looks like when being used. Notice that the brass piece is painted black. This way it is obvious if the brass piece has made contact with the Yankee dryer during measurement. The middle photo shows the aluminium footing at which a pole can be attached to simplify measurements. The lower photo shows the Thermophone when the te on cup has been removed. If one looks carefully one sees the ther- mocouple re ection in the stainless steel plate. temperature of the te on walls plays a prominent role in this heat transfer which will be discussed more later. Heat is also conducted by the metal wires which keeps the brass piece in place which further 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 consists of a thermistor, an ampli er, and a processor. The ampli er receives the voltage output from the thermocouple and a voltage from the thermistor. These two input signals is then processed according to the list in the last part of subsection 4.1. After the processing the ampli er sends an output voltage to the processor that converts the analogue voltage signal to a digital one and converts it into a temperature value. This temperature value is sent to a display and to a memory card (MMC) where it is stored along with the time. The sampling rate of the YSM3 is 10 Hz, i.e 10 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 the other one moves with a constant velocity parallel to the plane (Yankee cylinder). Since the ow can 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 the Couette ow is explained.
38 Figure 5.7: The parameters of the Couette ow. The velocities in the x− and y−direction is called u and v respectively. The distance between the plates is h. The velocity of the Yankee dryer is called U.
The quantity of interest in the Couette ow, for the purpose of this report, is the heat ux at the brass piece 00 . In order to obtain this heat ux one rst has to get the velocity pro le . qy (h) u(y) This is obtained by solving a momentum equation for a two dimensional ow:
∂u ∂u ∂p ∂ ∂u 2 ∂u ∂u ∂ ∂u ∂y ρ(u + v ) = − + {µ[2 − ( + )]} + [µ( + )] + X (5.2) ∂x ∂y ∂x ∂x ∂x 3 ∂x ∂y ∂y ∂y ∂x where ρ is the density of the uid, µ the viscosity, p is the uids pressure, and X is a force proportional to a uid elements volume. Eq. 5.2 looks hard to solve, but under the assumption that the ow is parallel a number of simpli cations can be made. To read more about these simpli cations the reader is referred to Chapter 6.4 in reference [3]. After these simpli cations Eq. 5.2 reads:
∂2u = 0 (5.3) ∂y2 This equation looks more manageable and with the boundary conditions u(0) = U and u(h) = 0 the solution is:
U u(y) = − y + U (5.4) h Now the objective is to obtain an expression for the heat ux 00 . Another step on the way qy (y) is to solve the energy equation below:
∂T ∂T ∂ ∂T ∂ ∂T ρc (u + v ) = (k ) + (k ) + µΦ +q ˙ (5.5) p ∂x ∂y ∂x ∂x ∂y ∂y Where µΦ is given by the expression: ∂u ∂v ∂u ∂v 2 ∂u ∂v µΦ = µ{( + )2 + 2[( )2 + ( )2] − ( + )2} (5.6) ∂y ∂x ∂x ∂y 3 ∂x ∂y Just as in Eq. 5.2 a lot of simpli cations can be made in Eq. 5.5. From the assumption that the ow is parallel ∂T ∂u ∂v . Since no heat is generated in the area of interest one v = ∂x = ∂x = ∂x = 0 can put . If one also assumes that ∂k then Eq. 5.5 can be written as: q˙ = 0 ∂x = 0 ∂2T ∂u k + µ( )2 = 0 (5.7) ∂y2 ∂y The partial derivative ∂u is obtained from Eq. 5.4. So Eq. 5.7 can be written as: ∂y
39 ∂2T U k = −µ( )2 (5.8) ∂y2 h
Integrating Eq. 5.8 and using the boundary conditions T (y = 0) = TY and (T y = 0) = Tth one get the following expression for the temperature distribution in the y−direction:
µU 2 y y2 y T (y) = ( − ) + (T − T ) + T (5.9) 2k h h2 th Y h Y Using this temperature distribution in Fourier's law one obtain an expression for the heat ux in the y−direction:
∂T µU 2 2y 1 k q00(y) = −k = ( − ) + (T − T ) (5.10) y ∂y 2 h2 h Y th h It is this Couette heat ux that should be the dominating ux when the temperature of the brass piece is determined. But as mentioned there is also a more complicated convection heat ux at the top side of the brass piece which also contributes to the heat ux to and from the brass piece. If only the Couette ow was present then the Thermophone would give a good temperature measurement, 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 Yankee cylinder temperature without the disturbance from the complex convection. In the model the brass piece was isolated at all surfaces except at the surface facing the Yankee dryer. The thickness of the brass piece was neglected since it is only 0.1 mm thick and brass is a good thermal conductor. The Couette ow was assumed to be fully developed over the whole brass piece and the properties of air was assumed to be constant (independent of T and p). With these assumptions the temperature change, ∆T , of the brass piece under the time interval ∆t can be written as:
00 qy (h)A∆t ∆Tth = (5.11) cpm
where A is the area aected by the Couette ow, cp is the speci c heat capacity, and m the mass of the brass piece. Inserting the expression for 00 (Eq. 5.10) into Eq. 5.11 one get the qy (y) following expression:
µU 2 k A∆t ∆Tth = [ + (TY − Tth) ] (5.12) 2h h cpm This equation was implemented in the software MATLAB where the response of the brass piece was simulated. The Yankee temperature was then assumed to be constant and equal to ◦ TY = 100 C. The change in temperature of the brass piece for a small time step ∆t was expressed as:
µU 2 k A∆t ∆Tth(t) = [ + (TY − Tth(t)) ] (5.13) 2h h cpm 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 speci cations The RAYNGER MX4 is a handheld pyrometer manufactured by Raytek. It measure the thermal radiation of a target and converts this into a temperature. This device was borrowed from the Karlstad 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 the target 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 = 35◦C respond to a Yankee cylinder temperature of T = 100◦C. The heat transfer between the brass piece and the Yankee dryer is made through Couette ow. The brass piece is thermally isolated from the environment except 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 section 5.6.1.
This pyrometer is equipped with a laser sight that enables the user to measure the areas of interest more easily. It is a common misunderstanding that the laser sight is involved with the temperature measurement. But the RAYNGER MX4 has a spectral range of λ ∈ [8, 14]µm and the wavelength of the laser is λ ≈ 0.6µm, so the laser does not in uence the temperature measurement. Since the RAYNGER MX4 uses a thermopile, see section 4.2, as sensor it needs to collect much radiation (large spectral range) in order to respond accurately to the target's temperature. The reason for this speci c spectral range is that the transmissivity of air is large in this region, see Fig. 4.5.
RAYNGER MX4 can operate in the temperature range T ∈ [0, 50]◦C and detect temperatures in the range T ∈ [−30, 900]◦C. These restriction are not violated when measuring the temperature on the Yankee dryer, although the operation temperature gets close to T = 50◦C.
The minimum resolvable temperature dierence (MRTD) of this pyrometer is 0.1◦C up to 900◦C, and the accuracy ±1% or ±1◦C whichever is greater. The accuracy value was measured for an operating temperature of T = 23◦C. 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 moves 30 × 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 temperature of the target. This can give a good reference temperature if one has a good thermocouple and a non-moving target. The target of interest, in this work, is however rotating with a speed of ∼30 m/s which makes it hard to measure the temperature with a contact temperature measurement method. The Thermophone was however used to get some reference temperatures. Even if these reference 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 speci cations The instrument used to take the thermographic pictures was a FLIR P640. It was borrowed from the faculty of technology and science at Karlstad University. It is similar to the RAYTEK MX4 in that it measures the thermal radiation and converts it into a temperature. A picture of this camera 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 to build up a thermographic picture. This array is called a focal plane array (FPA). There are two types of FPAs: scanning and starring FPAs. In the scanning FPA usually a single row of sensors are scanned by a mechanical scanner. Each sensor has an electrical contact that goes from the FPA to the outside and each sensor are read individually. For a starring array the scanning is done electronically by readout integrated circuits (ROIC). The array is 2D and the ROIC selects one sensor at a time and read its electrical signal. Since the ROIC handles the scanning there is no need for a mechanical scanner and the devices using a starring FPA can be made smaller and faster [10].
The P640 uses a 640x480 pixels staring array with uncooled microbolometers as sensors, see section 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 take digital pictures or record digital video. This camera was used to take digital pictures from the same 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 this can 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 true emissivity is in fact lower than the assumed one. The assumed emissivity can be varied in the interval ε ∈ [0.01, 1.0].
42 This camera can operate in a temperature range of T ∈ [−15, 50]◦C and detect temperatures in the interval T ∈ [−40, 500]◦C. So measuring the temperature of the Yankee dryer will not be a problem as long as the camera is not kept too close to it. The MRTD of the P640 is 0.055◦C at 30◦C and the update frequency of the detectors is 50-60 Hz. Since the Yankee surface moves with a velocity of about 30 m/s a point on the surface moves 0.6 m while the thermographic picture is taken. 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 be read by a computer and imported to the FLIR reporter software. This software has a lot of feature enabling 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 pyrometer is the emissivity of the surface. This section will give an estimation of this source of error, the discussion closely follows the discussion in reference [18].
The voltage output signal of the detector, S(T ), is proportional to Planck's law and can be written as:
Z λ2 k(λ)ε(λ) S(T ) = dλ (5.15) λ5[exp( c2 ) − 1] λ1 λT
Where k is a union of constants of the instrument and Planck's law, [λ1, λ2] is the spectral range of the instrument, and hc0 4 mK. Since all materials have dierent dependencies c2 = k = 1.439×10 µ of 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:
Z λ2 dλ S(T ) = kε = kεF12(T ) (5.16) λ5[exp( c2 ) − 1] λ1 λT This equation can be used to yield an expression for the temperature error caused by an
uncertainty of emissivity. An assumed emissivity, εm, results in a measured temperature Tm. The signal that yields Tm is the same signal, S(T ), that would yield the correct temperature T if the correct 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:
ε − ε δε = m (5.18) ε T − T δT = m (5.19) T
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:
ε − ε F (T ) − F (T ) m = 12 12 m (5.21) ε F12(Tm) Using the relations in Eq. 5.18 and 5.19 Eq. 5.21 can be written as:
F (T ) − F [(δT + 1)T ] δε = 12 12 (5.22) F12[(δT + 1)T ]
43 The equation above is rather di cult to evaluate by hand since it contains the integral seen in Eq. 5.16. Therefore Eq. 5.22 was put in the numerical computing environment MATLAB which has a built in function, quad, for evaluating integrals. This function approximates the integral by using recursive adaptive Simpson quadrature. The code that was put in MATLAB can be seen in Appendix A. The code produced a graph that shows how the fractional errors δε and δT are related. 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 generated with 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 emissivity of the surface if the true temperature is known and vice versa. To give an example one can measure a surface simultaneously with a pyrometer and a thermocouple. The temperature that the thermocouple show can be assumed to be the true temperature. Let's assume that this temperature ◦ ◦ is Tth = T = 100 C. Now assume that the pyrometer measures a temperature of Tp = Tm = 91 C when 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 de nition of δε (Eq. 5.18) the true emissivity of the surface can be estimated to be εm 1.0 . ε = 1.53 = 1.53 ≈ 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. 6.4 the 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/min and the vapour had an overpressure of 7 bar. While performing the other measurements some machine parameters changed. These changes are explained in each gure. The reason for splitting the 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 te on cup could reach room temperature. Since most of the graphs show a logarithmic behaviour, logarithmic ts to the graphs was inserted in the gures. The logarithmic t functions agree well with the graphs that was acquired under a shorter period of time, less than ∼ 6 min. The part 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 grow as fast as logarithmic functions most graphs still show an increasing temperature even after 15 min.
In the graphs the temperature axis start at T = 35◦C which approximately is the temperature of the brass piece just before coming in contact with the Yankee dryer. The time axis nish at t = 16 min. This was made so that all graphs would have the same axis, but as a result some graphs are cut before they end.
Figure 6.1: While acquiring graph 1.1 and 1.2 the machine parameters did not change. The machine speed was 1200 m/min and the vapour had an overpressure of 7 bar. The two graphs are very similar and their logarithmic ts agree well with them. Even though the graphs look good the behaviour is not ideal for a temperature measurement technique since the temperature is increasing even after 15 minutes. This makes it hard for the person that performs the measurement since one does 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 steam overpressure 7 bar. Before graph 2.4 was acquired the hood temperature was raised which seems to have increased the Yankee cylinder temperature. The operators of the machine made no changes on the machine between graph 2.1-2.3. One reason for the big dierence between graph 2.1 and graphs 2.2 and 2.3 can be that regulators changed some machine parameter. It can also be due to a change of the Thermophone behaviour. Between measurements the position of the brass piece was adjusted which can have an in uence on the measured temperature.
Figure 6.3: While acquiring graph 3.1-3.4 the steam overpressure was constantly 7 bar. After about 9 min in graph 3.3 the machine speed was raised from 1200 m/min to 1400 m/min, resulting in a colder Yankee cylinder. This speed was kept while acquiring graph 3.4. Having this change in mind, the graphs look quite similar.
46 Figure 6.4: These graphs was obtained when performing measurements with the Thermophone on a iron block heated by a stove plate. Since the stove plate did not have a constant temperature the maximum value of each graph varies. Between two consecutive measurements the Thermophone was rested for about 10 min so that it reached room temperature. The important result in the graphs are not the absolute temperature but the response time. All graphs show similar behaviour since 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 the Thermophone rst after about 3-5 min begin stabilise at an equilibrium temperature. The large dierence in response time indicate that the air streams have a large in uence on the measured temperature.
47 6.2 Pyrometer As was said in the section Experimental a number of measurements was made with the pyrometer RAYNGER MX4 manufactured by Raytek. Along with these measurements digital photos were taken in order to show the surface nish. In all measurements the assumed emissivity was set to
εm = 1.0. All measurements showed similar results, namely that the temperature measured by the pyrometer varied a lot along the surface. These variations can be explained by the varying surface nish. As a rule of thumb the surface looked more metallic and re ective when low temperatures was measured and more dull and less re ective when higher temperatures was measured. More on how 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 shown along with how the measured temperature varied in these regions. The top three photos are taken at the tending side edge of the Yankee cylinder while the bottom three show the center of the Yankee cylinder. The two photos to the left show a newly sandpapered surface, i.e a clean surface without any coating or paper residues on it. It is clear that these photos show a highly re ective metallic surface, with the exception of the tending side edge where the surface looks darker and less re ective.
The two middle photos show the surface when a coating layer have been sprayed on. Coating do not cover the whole surface leaving the edges uncovered. It is clear that the coating makes the surface more dull and less re ective.
The two photos to the right shows the surface after the paper have been pressed onto the Yankee cylinder and the doctors begun to scrape it. Since the scraping is not uniform it results in a stripy nish where some stripes are dull and little re ective while others are highly re ective.
Figure 6.5: Showing two regions; the tending side (top photos) and the center (bottom photos) of the Yankee cylinder with dierent things covering the surface. The temperatures shown are the temperatures measured by the pyrometer in these regions. It should be noted that the overpressure of the steam was raised from 1 bar to 3 bar and the machine speed increased from 300 m/min to 900 m/min just before the coating was sprayed onto the surface. The surface nish varies the most near 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 about 1 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 temperature distribution. The dierent temperatures was distributed randomly, i.e no region was hotter than the 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 uncertainty of the Thermophone.
When measuring the same surface with the pyrometer temperatures in the range T ∈ [58, 78]◦C was obtained. The highest temperatures were measured at the edges, both at the tending side and the driver side. This can be explained by that ε is higher in those regions. From Fig. 6.5 it is clear that the end of the cylinder has another nish (a darker colour) than the rest of the cylinder, which support the diering ε theory. As the nish becomes more metallic and less dark the measured temperature decreases indicating a varying ε. Areas with similar surface nish had the 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 coating was sprayed on the surface, the surface nish clearly changed, see Fig. 6.5. No measurement was made with the Thermophone since the paper was pressed onto the Yankee cylinder brie y after the coating. Instead only pyrometer measurements were made. Since no paper was on the cylinder it can be assumed that the Yankee dryer had an almost constant temperature, as in the case of the clean surface.
The pyrometer measurements showed temperatures in the range T ∈ [85, 120]◦C. This time however the highest temperatures were not measured in the darker regions but in the coated region. There, the coating formed a uniform dull layer a uniform temperature of T = 120◦C was measured. At the edges of the cylinder the temperature varied because of the varying nish, but were 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 was randomly distributed. This indicate a strongly varying ε in the regions where the paper had been scraped o. The highest temperatures was measured just after the paper edge, i.e where there still was a uniform coating layer. The farer away from the paper edge one measured the lower the temperature got. This is explained by that the coating thickness got thinner with increasing distance from the paper edge.
It is usually this type of stripy surface that is the surface nish of Yankee dryers in real paper machines. Since a stripy surface most likely leads to varying emissivity, temperature measurements with 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 were acquired with an assumed emissivity of ε = 0.99. If the targets, shown in the pictures, do not have 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 held up in front of the Yankee dryer and a thermographic image was taken of the foil, see Fig. 6.6. Since aluminium foil is highly re ective a thermographic image of it gives information about the surrounding radiation. In the software, that comes with the thermographic camera, an area on the foil was selected. The picture shows this area and also the average temperature in this area, ◦ Taverage = 30.5 C 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 the background radiation.
The pictures in Fig. 6.7 was taken from the tending side. The graph in the lower part of the image shows how the temperature varies along the green line shown in the top left picture. The ◦ center part of the graph show a rather constant temperature, around Tm = 100 ± 5 C. This is the region where the paper was dried by the Yankee cylinder, which is why this region is cooler than ◦ the ends of the cylinder. At the ends the measured temperature rst goes up to about Tm = 160 C, ◦ ◦ then drop to about Tm = 110 C, and nally goes up again to about Tm = 130 C. From theory the Yankee cylinder should get colder at the ends since the cooling eect from the air ow gets more pronounced here. But the fact that the measured temperature goes up again at the ends is probably due to variations of the emissivity. If one looks at the digital photo of the Yankee dryer one can draw parallels between the appearance of the surface and the thermographic image. This also 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 similarities of the two pictures two stripes have been marked purple and turquoise respectively. The peaks in the graph corresponding to these stripes have also been marked. Because the emissivity varies the measured temperatures gives a false picture of the real temperature of the Yankee dryer. The fractional errors of the emissivity, δε, can be related to the fractional error in temperature, δT by using graphs as the one in Fig. 5.11.
50 Figure 6.7: A thermographic picture of the Yankee cylinder taken from the tending side along with a digital photo taken from the same position. The graph show how the temperature varies along the 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 in this picture are the greater dierences in emissivity. The highest measured temperature is about ◦ ◦ ◦ Tm = 160 C while the lowest is about Tm = 80 C. Assuming that Tm = 160 C correspond to the true 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 about δε = 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 re ected radiation into account, why the emissivity is probably smaller than ε = 0.45. The surface almost look like a mirror in the digital photo. So it is possible that the emissivity in these regions are as low as ε = 0.10 since polished iron has an emissivity in the interval ε ∈ [0.06, 0.2] [6].
51 Figure 6.8: A thermographic picture along with a digital photo of the Yankee cylinder taken from the driver side. The two stripes highlighted with turquoise and purple show the relation between the temperature measured by a thermographic camera and the surface nish. The graph show how the 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. These line graphs show another obstacle, when measuring the temperature by measuring the thermal radiation, that is the re ected radiation. In the graphs when going from left to right there is a big and sudden drop in the measured temperature, ∼ 10 − 20◦C. This drop is most pronounced in the lowest graph where the measured temperature is the lowest indicating a low emissivity. A low emissivity corresponds to a high re ectivity in general. So even if the true emissivity of the surface is known large errors in the measured temperature can be obtained if the re ected radiation varies. At the right end of the graph there is an increase in temperature also due to re ected radiation. This increase is however not as obvious and sudden as the one in the left end. The variation of the radiation is due to the cleaning doctor (left side) and the coating shower (right side). These two parts have a higher temperature than the ambient temperature and therefore emits more thermal radiation. 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 temperature ◦ of about Tm = 60 C. This is higher than the measured surrounding temperature, that was acquired in Fig. 6.6, indicating an enhanced radiation from these sources.
52 Figure 6.9: A thermographic picture along with a digital photo of the Yankee cylinder taken from the driver side. The graph show how the temperature varies along the green line in the thermographic picture. The pictures show the driver side end of the Yankee cylinder. The big temperature dierences in the thermographic picture are due to a varying emissivity which is seen in the digital photo as varying surface nish.
The pictures in Fig. 6.11 show the temperature development of the thermophone while being in contact with the Yankee dryer. The pictures were taken in order to investigate the frictional heating of the thermophone. The time that is displayed in each picture is the number of seconds the thermophone has been in contact with the Yankee dryer. The temperature is the maximum temperature 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 the maximum temperature was read instead of the mean temperature. The maximum temperature does not change much with time but it is clear that the thermophone gets hotter with time. The ◦ maximum measured temperature Tm ≈ 110 C is higher than the maximum measured temperature ◦ of the Yankee dryer Tm ≈ 95 C. This can either be due to that the thermophone has a higher temperature or that te on has a higher emissivity than the Yankee dryer.
Te on 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 emissivity in the interval ε ∈ [0.90, 0.98] [6]. So te on and the Yankee cylinder should have about the same emissivity, at least where the measured temperature of the Yankee cylinder is high. This indicates that the te on of the Thermophone has a higher temperature than the Yankee cylinder. Since the pictures was taken with ε = 0.99 the true temperature of the te on cup is probably higher than ◦ Tm ≈ 110 C.
53 Figure 6.10: A thermographic picture along with a digital photo of the Yankee cylinder taken from the driver side. The graphs show how the temperature varies along the green lines in the thermographic picture. The thermographic picture along with the graphs clearly show a re ection from the cleaning doctor to the left in the picture, since it increases the measured temperature dramatically.
Another thing indicating the te on cup having a higher temperature than the Yankee cylinder is the temperature measured by the Thermophone. The maximum temperature measured by the
Thermophone, while simultaneously the thermographic pictures of it was taken, is Tm,T hermophone = 99◦C. This is at least 10◦C smaller than the temperature of the te on cup. More on the relation between the temperature measured by the Thermophone and the temperature of the te on cup is seen in Fig. 6.13. The pictures in Fig. 6.12 are thermographic pictures of the Thermophone just after it has been removed from the Yankee dryer. One interesting thing, though not surprising, is that the inner wall of the te on cup is hotter than the outer wall. Since the inner wall is close to the brass piece and the thermocouple its temperature probably aects the temperature measured by the Thermophone. Since the inner wall have a higher temperature than the outer wall, that in turn has a higher temperature than the Yankee, there is a risk that the Thermophone measures a temperature higher than the Yankee dryer's.
The graphs in Fig. 6.13 show the maximum temperature, shown in Fig. 6.11, on the outer wall of the Thermophone together with the temperature measured by the Thermophone, as a function of time. The maximum temperature of the outer wall only has 9 values. So the relation between the two temperatures is hard to determine. A more careful investigation that measures the temperature of the inner wall while the Thermophone is in contact with the Yankee dryer would 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 the ◦ Thermophone is Tm,T hermophone = 99 C and by looking at the graph it should have increased further. The maximum measured temperature by the thermographic camera (inside the paper ◦ width) was Tm,tg < 95 C. This results in a measured temperature dierence of ∆Tm = Tm,tp − ◦ Tm,tg ≈ 4 C which can be either due to frictional heating of the Thermophone or the use of a too small emissivity in the thermographic camera.
54 Figure 6.11: Thermographic pictures of the Thermophone while it measures the temperature of the Yankee cylinder. The temperatures written in the pictures are the maximum temperature of the Thermophone in the images. The time written in the pictures is the time the Thermophone have been in contact with the Yankee cylinder.
Figure 6.12: Thermographic pictures of the Thermophone just after it had been removed from the Yankee cylinder. The pictures show that the inner te on walls have a higher temperature than the outer walls.
55 Figure 6.13: The graphs show the temperature measured by the Thermophone (green) and the maximum temperature of the te on cup measured by the thermographic camera (orange) as a function of time. Also a logarithmic t of the temperature measured by the Thermophone is viewed. This logarithmic t highlight the increase of the measured temperature even after 6 minutes of measurement.
56 7 Discussion & Conclusions
Thermophone From the temperature measurements made on the Yankee dryer it is clear that none of the three devices tested gives a reliable measurement. The Thermophone experiences a rising temperature even 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 te on cup. The theory that the te on cup is frictionally heated is supported by the thermographic pictures taken of the Thermophone during measurement. These picture show that the outside of the te on cup achieves temperatures approx- imate 10◦C above the temperature of the Yankee dryer. A thermographic picture of the inside of the Thermophone brie y after measurement show that the inner walls have a higher temperature than the outer walls. This is not a surprise since the outer walls are cooled by the air streams caused by the rotation of the Yankee dryer. This implies that the inner walls are at least 10◦C hotter than the Yankee dryer surface.
It is thought that the temperature of the inner walls contribute, through the air streams in the te on 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 is only t < 5s (Fig. 5.8) where the brass piece is assumed to be isolated, i.e only exchanging heat with the Couette ow. In the measurements with the Thermophone of a Yankee block on a stove plate the response time is t < 20s. In this case no forced convection is present but only natural convection making the heat ow between the brass piece and Yankee surface more dominant. In Fig. 6.1-6.3 the response time are in some cases t > 5min. The reason for the long response time can be the heat transfer through the forced convection of the air streams inside the te on cup. Since the thermoelectric junction is placed on the face of the brass piece not facing the Yankee dryer its temperature should be even more sensitive to the forced convection.
When the inner walls of the te on cup are colder than the Yankee dryer the forced convection probably cools the thermoelectric junction. As they get hotter than the Yankee dryer the forced convection begins to heat the thermoelectric junction instead. How large in uence the temperature of the walls have on the temperature of the thermoelectric junction is hard to determine because of the complex air streams. An attempt was made to simulate the heat transfer inside the te on cup. The simulations were performed in the FEM software COMSOL Multiphysics but the solution did not converge due to the air streams. Since a lot of the input parameters in the model had to be assumed no further attempt was made to simulate the heat transfer.
As the distance between the brass piece and the Yankee surface increases the contribution from the inner walls should increase. This introduces a di culty when trying to repeat measurements with the Thermophone. If the distance between the brass piece and the Yankee surface is varied between measurements the Thermophone would behave dierent. Another di culty in repeating measurements is to determine how hard the Thermophone is to be pressed against the Yankee dryer 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 in uence of the tempera- ture on the inner walls on the measured temperature. This can be done by attaching thermocouples to the inner walls and measure the temperature on these walls simultaneously as the Yankee dryer temperature. 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 Yankee dryer surface.
57 IR sensors Both the MX4 and the P640 measurements show the di culties in measuring the temperature with IR sensors. The most obvious di culty is the emissivity dependence of the measured tem- perature. Since a normal Yankee dryer surface does not have a uniform surface nish, because of the uneven scraping of the doctors, the emissivity of the surface varies. Using a graph similar to 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 the surface varies in the interval ε ∈ [0.65, 1.0]. The graph used does however not take the re ected radiation in consideration so the true emissivity is probably lower than 0.65. Having a surface with an emissivity varying in such a large interval which also rotates with a speed of 1800 m/min makes it hard to measure with an IR sensor, which results in large errors as indicated in the results.
Another di culty when performing measurements with an IR sensor is the re ected radiation. This is most obvious in Fig. 6.10, where re ected radiation from the coating shower and the cleaning doctor is visible in the thermographic picture. Not having this in mind can cause large errors in the measured temperature. In Fig. 6.10 the re ected radiation from the cleaning doctor raises the measured temperature with ∼ 20◦C. For a surface with an uniform re ectivity this can be solved by using a constant background radiation, by for example having a cooled cone, similar to the gold cup, between the Yankee surface and the sensor. If the cone can be kept at a constant temperature the background radiation will be constant. But for a surface with a varying re ectivity this 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 to the Yankee surface, which would give negligible background radiation. Even without such a cone the in uence of the re ected radiation can be made smaller by pointing the sensor in the same direction as the hot radiation, see Fig. 7.1
Figure 7.1: Two ways of making the contribution from the background radiation smaller. A hot source 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 is used 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 way no radiation from the hot source will be re ected into the sensor. This method is advantageous if there are few and easily identi ed hot sources.
The emissivity dependence of the measured temperature can be xed in two ways; making the emissivity 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. But introducing yet another chemical in the process could disturb the process and aect the quality of the 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 band pyrometer requires a grey surface in order to be emissivity independent. Since there are a number of dierent materials constituting the Yankee dryer surface (polished iron, coating chemicals, and paper residues) it is not certain that all these materials display grey body behaviour. Another disadvantage 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-band pyrometers more expensive and increase their size. For future work it could be a good idea to test a 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. The requirement 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 the re ectivity. There are also paper dust in the air which also could reduce the re ectivity if hitting the gold. The need for keeping the gold cup close to the surface could endanger the gold nish because of the high speed of the Yankee dryer. Since this method was never tested it is a suggestion for future work.
59 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. John Wiley 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 Petrochemical Industry. SPIE, (2007). [16] speci cations of RAYNGER MX4, T. Available at: http://www.watlow.co.uk/literature/ specsheets/files/sensors/ricmx0401.pdf 2009-05-30. [17] speci cations 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).
60 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
61