Calibration of TFG sensor for heat flux measurements and validation on spark ignition engines

Transcription

1 Calibration of TFG sensor for heat flux measurements and validation on spark ignition engines Olivier Collet, Gery Fossaert Supervisors: Prof. dr. ir. Sebastian Verhelst, Prof. dr. ir. Michel De Paepe Counsellor: Thomas De Cuyper Master's dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering Department of Flow, Heat and Combustion Mechanics Chairman: Prof. dr. ir. Jan Vierendeels Faculty of Engineering and Architecture Academic year

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3 Calibration of TFG sensor for heat flux measurements and validation on spark ignition engines Olivier Collet, Gery Fossaert Supervisors: Prof. dr. ir. Sebastian Verhelst, Prof. dr. ir. Michel De Paepe Counsellor: Thomas De Cuyper Master's dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering Department of Flow, Heat and Combustion Mechanics Chairman: Prof. dr. ir. Jan Vierendeels Faculty of Engineering and Architecture Academic year

4 The authors and promoters give the permission to use this thesis for consultation and to copy parts of it for personal use. Every other use is subject to the copyright laws, more specifically the source must be extensively specified when using from this thesis. Ghent, 2 juni 2012 The authors Olivier Collet Gery Fossaert

5 Acknowledgement This thesis is the final result of one year of hard work and full of challenges. The result of this thesis would never have been the same without the help of certain people. We would like to take a moment to thank them. First and foremost, we would like to thank our supervisors, Prof. dr. ir. S. Verhelst and Prof. dr. ir. M. De Paepe for their help and their much appreciated advice. We would especially like to thank them for given us the opportunity to participate in this interesting research. Special thanks go to our counselors, ir. S. Broekaert and ir. T. De Cuyper. They were always available to answer any question we may have and their support during the year was much appreciated. We do hope that our thesis will help them in their future research and we wish them the best of luck. We would also like to thank Prof. K. Chana of Oxford University for his help and useful insight. His visits were always very inspiring and instructive. Next, we would like to thank Mr. K. Chielens for his help concerning the CFR setup and his all round good mood in the laboratory. At the same time, we thank Mr. P. De Pue for sharing his technical advice to help us with the electronic aspect of our work. We wish to thank our fellow students for the good times around the setups and in the class room and specially during these past years. Last but certainly not least, we wish to thank our parents, for their love, support and for giving us the opportunity to get an education and prepare us for the future. We thank our sisters, brothers,family and friends for all the good times we had together. Finally, we want to thank each other for the wonderful year we had together. It was a great experience that we will cherish for life. Olivier Collet and Gery Fossaert ii

6 Calibration of TFG sensor for heat flux measurements and validation on spark ignitions engines By Olivier Collet and Gery Fossaert Supervisors: Prof. dr. ir. Sebastian Verhelst, Prof. dr. ir. Michel De Paepe Counsellor: ir. Thomas De Cuyper Master s dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering Departement of Flow, Heat and Combustion Mechanics Chairman: Prof. dr. ir. Jan Vierendeels Faculty of Engineering and Architecture Ghent University Academic year Summary Due to the current issues of global warming and decreasing fossil energy resources, internal combustion engines still are a hot topic for research and development. Fuels, such as methanol and ethanol, are being researched because they could offer an alternative to the fossil fuels that are still primarily used today. Multiple techniques have also been introduced over the years, such as charging, exhaust gas recirculation and others, to improve engine efficiency, fuel consumption and limit the emissions of noxious gasses. However, further research is still needed to optimize the use of internal combustion engines. This optimization requires the use of engine simulations. Within the research group Transport Technology of the Department of Flow, Heat and Combustion Mechanics at Ghent University, a simulation tool is being developed to research the effects of alternative fuels and engine enhancements on engine performances. This requires a good knowledge of multiple processes taking place in the engine, one of which is the heat transfer to the cylinder walls. Intensive measuring is done to comprehend this process. The researchers at Ghent University wish to use a Thin Film Gauge sensor to perform heat flux measurements as it offers different advantages compared to previously used sensors. The use of iii

7 iv this sensor requires an adequate calibration. This thesis offers an insight on the function of the sensor and an overview of the different existing calibration techniques and setups. Next, the Double Electric Discharge calibration technique and its setup are discussed in depth. Lastly, heat flux measurements obtained with the calibrated TFG are compared to results obtained with other sensors to validate the calibration process. Some suggestions are made to further ameliorate the calibration setup. Keywords heat flux measurements, Thin Film Gauge sensor,double Electric Discharge, spark-ignition engine, iv

8 Calibration of the TFG sensor for heat measurements and validation on a SI engine Olivier Collet and Gery Fossaert Supervisor(s): Sebastian Verhelst, Michel De Paepe, Stijn Broekaert and Thomas De Cuyper Abstract In the development of internal combustion engines, measurements of the heat transfer to the cylinder walls play an important role. These measurements are necessary to provide data for building a model of the heat transfer, which can be used to further develop simulation tools for engine optimization. These measurements require an adequate sensor. This research will focus on the Thin Film Gauge (TFG) sensor. To use the TFG sensor, its thermal properties -namely the thermal coefficient and the thermal product- must be correctly calibrated. The Double Electric Discharge calibration set-up for the thermal product will be extensively discussed. This paper ends with a comparison between heat transfer measurements in a CFR engine done with a non-calibrated TFG sensor, a calibrated TFG sensor and a HFM (Heat Flux Measurement) sensor. Keywords SI-engine, thin film gauge, heat flux, calibration, double electric discharge I. INTRODUCTION ONE of the key factors in the research of internal combustion engines (ICE) is to fully understand the mechanisms involving the heat transfer in the engine. The heat transfer from the combustion gases to the inner cylinder walls has large effects in terms of efficiency, emissions and power output of an ICE. Previous research [1] has shown that due to the different flow conditions during the combustion the heat flux shows a lot of spatial variation. In order to enable a cheap and fast optimization of the engine parameters, a simulation model of the combustion thermodynamics can be used. The development of such a model demands accurate measurements inside the engine. Extensive research [2] has been performed on different kind of sensors. This research showed that the Thin Film Gauge had the most potential for use in an ICE. They are sturdy and cheaper to manufacture. They have already been used with success in turbo machinery [3]. However, peak temperatures and pressures are higher in ICE application, this must be taken into account for implementing the sensor in the combustion chamber. Also, differences in heat fluxes were observed between the TFG and a very accurate sensor. Therefore, further investigation on TFG sensors is necessary. II. THIN FILM GAUGE THE basic thin film gauge - a single layer TFG - consists of two parts: a thin film of metal which is placed on a substrate. The film is a resistance temperature detector (RTD). Multiple RTDs are mounted on top of the substrate. As for most RTDs, the metal used is platinum. This is because platinum has the most stable resistance-temperature relationship over the largest temperature range, making it ideal for reliable measurements. The substrate is mostly a ceramic that has a low electrical and thermal conductivity. A low electrical conductivity is needed to ensure there will be no short circuiting between the different RTDs. The variation of material properties due to temperature changes is why the substrate must have a low thermal conductivity. That way, when the sensor is exposed to a heat source, only a small temperature rise will occur in the substrate. The material properties of the substrate are used in the calculation of the heat flux and therefore need to remain as constant as possible. MACOR R, for instance, is a widely used ceramic in TFG sensors. It has good thermal and electrical properties and can easily be machined. This makes it highly suited to be placed inside a bolt and to be mounted in a engine cylinder. The platinum film at the top is connected to the sensor wiring by gold leads and conductive resin. Before the TFG can actually be used, there are two material properties that need to be calibrated. They are the thermal coefficient of the RTD and the thermal product of the substrate. The calibration of the thermal coefficient α R can be done by using the water bath calibration method. By measuring the resistance of the RTD at different temperatures and by using the linear relationship between the temperature and the resistance, α R can be calculated [1]. The thermal product is not calibrated as easy. That is why previously the thermal product of the bulk material of the substrate was used in heat flux calculations. However, research has showed that the process of placing the thin film upon the substrate changes the material properties of the substrate [4]. It is also worth mentioning that no research has been done so far on the effect of sensor aging and wear on the thermal product. This shows that determining the right thermal product is important. Over the years, two different methods have been used to calibrate the thermal product: the water droplet method [5] and the hot air gun method [6]. Both methods are based on the one dimensional conduction equation which is solved by using a step in heat flux or a step in fluid temperature [7]. Billiard [7] has shown that for short flow durations a step in fluid temperature can be considered as a step in heat flux. However, by doing so, an error will be introduced. The water droplet and the hot air gun method are both setups that utilize a step in fluid temperature to solve the one dimensional conduction equation. The hot air gun setup has already been used to calculate the TP when step in heat flux is applied. This introduces an error that should be taken into account [6]. When using the water droplet setup to calculate the TP, two dimensional effects have been observed that introduces errors [5]. Therefore, both methods have been omitted for determining the TP. A third method exists, using a step in heat flux that is electrically generated. III. DOUBLE ELECTRIC DISCHARGE THERE is a third calibration method that can be used to determine the thermal product of the substrate: the double electric discharge method (DED). The difference between this v

9 method and the two previous ones, is that the solution of the one dimensional analysis is attained when a step in heat flux is applied. Therefore, the transient heat flux can be written as a function of the surface temperature as long as the semi-infinite principle is valid. The heat flux is electrically simulated by the discharge of a current through the thin film. This discharge causes ohmic heating of the thin film, therefore, increasing the thin film temperature and its resistance. When a step in heat flux is considered, the temperature will be proportional with the the square root of time as can be seen in figure 1. By controlling the heat flux and monitoring the surface temperature, the TP can be achieved. The thin film is placed in a Wheatstone bridge. Once the bridge has been balanced, a voltage pulse is sent to the bridge which causes ohmic heat of the thin film. This voltage pulse functions as the step function. Since the heat flux is generated electrically, only the electrical power or the heat across the thin film will be known. The surface area of the thin film is necessary to determine the heat flux which is very difficult to obtain accurately. Therefore, the calibration is performed twice in different media to eliminate the knowledge of the thin film surface area. The thermal product can then be written as function of the thermal product of the chosen fluid which glycerin and the slopes of the regression of the recorded out of balance voltage according to equation (1): ρck = ρckglyc ( V/ t) air ( V/ t) glyc 1 Fig. 1. Out of balance voltage and corresponding regression Figure 1 represents the recorded out of balance voltages of the calibrations in air and glycerin together with their regressions. The correlation coefficient of these regressions are higher than 99 %. Therefore, the slopes of the regressed data perform a good representation of the actual ones. IV. RESULTS THE following results are taken from measurements done on a single layer TFG with a MACOR R substrate as can be seen in figure 2. In this specific case a voltage pulse of 8 and 9 V has been applied to the bridge and pulse time duration of 5 and 10 ms has been considered. The voltage pulse level is proportional with the magnitude of the heat flux while the pulse time duration is related to the time that the heat flux is applied, thus influencing the thin film final temperature. (1) Fig. 2. TP vs Time variation Voltage variation results does not represent a specific trend since the TPs at 8 and 9 V differ from each other for different time durations. Time duration variation results in a slight increase of TP. However, measurements taken at 9 V do not differ a lot from each other. Higher pulse levels resulted in lower inaccuracy. The lowest inaccuracy of 4.5 % has been obtained where from the largest part is due to the inaccuracy of the TP of the fluid (4 %). V. CONCLUSIONS THE measurements discussed in this paper have led to a number of conclusions, which will now be summarized. A step in heat flux can be perfectly generated with the DED calibration. Higher bridge voltages resulted in the best regression with lowest relative error of 4.5%. The variation of the amplitude of the voltage pulse does not affect the thermal product of the substrate much. The mean values and error levels are approximately the same for different voltage levels. Variation of the bridge time duration has also not shown any significant changes in the thermal product. In order to lower the inaccuracies, the accuracy of the thermal properties of the fluid should be investigated. REFERENCES [1] T. De Cuyper and S. Broekaert, Alcoholen als alternatieve brandstof voor vonkontstekingsmotoren: Experimentele studie naar het klopgedrag en de warmteafgifte naar de cilinderwanden, M.S. thesis, Universiteit Gent, [2] M. Desoete and R. Vyvey, Evaluatie van warmte uxsensoren voor vonkontstekingsmotoren aan de hand van metingen op kalibratieproefstanden en een cfr-motor, M.S. thesis, Universiteit Gent, [3] Schultz. D.L and Jones T.V., Heat-transfer measurements in short-duration hypersonic facilities, AGARDograph, [4] Lu K. Kinnear K., design, calibration and testing of transient thin film heat transfer gauges, Journal of Turbomachinery, [5] R. Buttsworth, Assessment of effective thermal product of suface junction thermocouples on millisecond and microsecon time scales, Elsevier experimental thermal and fluid science, [6] E. Piccini, S.M. Guo, and Jones T.V., The development of a nex directheat-flux gauge for heat-transfer facilities, Measurement Science and Technology, [7] N. Billiard, F. Illiopoulou, and R. Ferrera, Data reduction and thermal product determination for single and multi-layered substrates thin-film gauges, Turbomachinery and Propulsion Department, vi

10 Contents Acknowledgement Summary Extended abstract Nomeclatuur ii iii v x 1 Introduction Heat transfer measurements Heat flux sensors Eroding ribbon sensor Heat Flux Microsensor TFG sensor Goals Thin Film Gauge Sensor Construction of the TFG RTD Sensitivity of the RTD RTD callibration Ohmic heating and RTD burnout TFG concepts One dimensional analysis Film thickness Signal processing Thermal product of the TFG substrate Calibration setups Heat gun setup vii

11 Contents viii Water droplet setup and shock tube experiment Double electric discharge calibration Double Electric Discharge calibration DED setup Theoretical approach Data processing Regression Regression accuracy Calibration results Voltage variation Time duration variation Different RTD s on same substrate Results of the single layer calibration Double layer TFG calibration Engine measurements CFR setup TFG sensor setup Validation of TFG sensor CFR Heat flux measurements EGR Inlet temperature Conclusions and future insights 71 A Calculations Fourier method 73 A.1 2T Fourier method A.2 1T Fourier method B Calculations impulse response FIR-method 75 B.1 TFG Single Layer through surface temperature B.2 TFG Double Layer through surface temperature B.3 TFG through surface temperature and depth thermocouple temperature.. 79 B.4 Steady state component of heat flux C Error analysis 82 C.1 Measured quantities viii

12 Contents ix C.1.1 Ambient conditions C.1.2 Engine speed C.1.3 Pressures C.1.4 Temperatures C.1.5 Flow rates C.2 Calculated quantities C.2.1 Mass in cylinder C.2.2 Air/fuel ratio and air factor C.2.3 Specific gas constant C.2.4 Gas temperature C.2.5 Error analysis calibration TFGs C.2.6 surface temperature, flux and convection coefficients C.2.7 Convection coefficient C.3 Error analysis on the DED setup D Double Electric Discharge calibration appendix 93 D.1 DED setup D.2 DED calibration process D.3 DED data processing D.4 Linearity error E MATLAB code 104 Bibliography 115 ix

13 Nomenclature Abbreviations AFR GUEST IC ICE ATDC BTDC CFR CR DAQ DED ECU EGR FIR HFM RTS HRR IT LTI MAP NSR PID PVD RPM RTD SI TFG TP Air to Fuel Ratio Ghent University Engine Simulation Tool Internal Combustion Internal Combustion Engine After Top Dead Center Before Top Dead Center Cooperative Fuel Research Compression Ratio Data Acquisition Double Electric Discharge Engine Control Unit Exhaust Gas Recirculation Finite Impulse Response Heat Flux Micro sensor Resistance temperature sensing Heat Release Rate Ignition Timing Linear Time Invariant Manifold Absolute Pressure Noise to Signal Ration Proportional Integrating Differential Physical Vapor Deposition revolutions per minute Resistance Temperature Detector Spark Ignition Thin Film Gauge Thermal Product x

14 Greek symbols α thermal diffusivity [ m2 s ] θ crank angle [ ] λ air factor [-] ρ density [ kg ] m 3 ω natural frequency [ rad s ] Subscripts avg aw c cyl liq s ss trans w average adiabatic wall cycle cylinder liquid surface steady state transient wall xi

15 Roman symbols A surface [m 2 ] B bore of combustion chamber [m] b slope of regression [V/ s] C covariance coefficient [-] c specific heat capacity J [ kgk ] F non-uniform film heating factor [-] f frequency [Hz] W h convection coefficient [ m 2 K ] I current [A] k thermal conductivity [ W mk ] M Metric [mm] m mass [kg] N number [-] n revolutions [rev] P Power [W ] p pressure [pa] Q heat [J] q heat flux [ W ] m 2 R resistance [Ω] r correlation coefficient [-] T temperature [K] t time [s] V voltage [V ] X fraction heat diffused into liquid [-] x penetration depth [m] xii

16 Chapter 1 Introduction Nowadays the world is confronted with different serious issues, two of which are global warming and the decreasing fossil energy resources. The transport of goods and people by means of combustion engines, contributes to the emission of the greenhouse gas CO 2. On another scale, there is also the emission of NO x and unburned hydrocarbons. Also, the decrease of the oil reserves has led to a rise in prices in recent years. These problems are the reason why there still is a continuous research for alternative fuels and new drive methods, for example, the development of electric engines and many hybrid drivetrains. These alternative drives however, still face too much flaws to be used on a large scale. Besides the limited driving range, the electric vehicle needs a large amount of rare metals for the construction of the battery and the motor. Furthermore, the recycling of the battery is not as straightforward as the recycling of a classic combustion engine because of the environmental concerns. For a long time hydrogen was viewed as the fuel of the future, but mass production of hydrogen fueled cars has not yet happened because of reduced driving range due to the low energy density of hydrogen. Because of the reasons stated above, there is still a place for the combustion engine in a near and distant greener future. Engines running on fuels produced from biomass can be CO 2 -neutral when those fuels are produced in a sustainable way. Besides new fuels offering new perspectives, new engine technologies are allowing us to further increase the engine efficiency. These technologies include charging to increase efficiency, improved lubrication to reduce losses and the use of high quality and lighter construction materials to reduce the mass and thereby the fuel consumption. Furthermore, the control of combustion and emissions has improved considerably. Taking into account the ease of recycling a classic combustion engine and the widespread use of those engines, it is clear that steadily replacing older engines by new improved bio-fuel engines can be an answer to the climate 1

17 Chapter 1. Introduction 2 change issue. 1.1 Heat transfer measurements To innovate and improve current technologies, a good understanding of the engine operations is necessary. This requires the use of engine simulations. Within the research group Transport Technology of the Department of Flow, Heat and Combustion Mechanics at Ghent University, a multi-zone thermodynamic model was constructed for the closed part of the engine cycle, the GUEST code (Ghent University Engine Simulation Tool). This simulation tool allows fast computation of the power and efficiency of SI-engines running on alternative fuels. To simulate the in-cylinder processes, an additional commercial engine simulation software (GT-Power) is used to calculate the gas dynamics during the IVC and EVO. These are then used as boundary conditions for the GUEST code. Figure 1.1 shows an overview of the engine simulation process. This figure shows the four main processes (heat transfers, flame propagation, mixture composition, turbulence) that need to be modeled in order to correctly calculate the efficiency, power and emissions of the engine. Figure 1.1: GUEST code [1] The heat transfer to the cylinder wall in an IC engine directly influences the engine performance and emissions. When the heat transfer becomes higher, the mean temperature and mean pressure in the combustion chamber will decrease. This leads to a lower efficiency and a lower power output. The production of emissions such as NO x is strongly dependent 2

18 Chapter 1. Introduction 3 on the temperature in the combustion chamber and thus dependent on the heat transfer. Furthermore, the heat transfer has an important influence on the occurrence of engine knock, due to the fact that knock is a phenomenon that is mainly thermally controlled [2]. The convection from the hot gases to the cylinder wall will be influenced by turbulence of the cylinder s charge, the combustion process and the piston motion. The turbulence appears due to the kinetic energy present in the intake flow. Additional to this turbulence, complex motions such as swirl and tumble are induced in the air-fuel mixture entering the cylinder [3]. Due to these motions and the interactions with the valve motion, the heat transfer undergoes unsteadiness and local changes. The combustion process will also influence the heat transfer, because it rapidly increases density, pressure and temperature in the cylinder. In SI-engines, the flame propagation front separates the cylinder charges into burned and unburned zones, thus creating a strong local change in heat transfer. Furthermore, the flame will interact with turbulent flows, adding to the complexity of the heat transfer. It is clear that the heat transfer depends on many different factors and cannot easily be modeled. Heat transfer measurements are needed to construct an accurate model of the heat transfer in a SI-engine. 1.2 Heat flux sensors To achieve reliable heat transfer data, it is import to have a sensor that can deliver accurate measurements. This accuracy imposes different important requirements. As a result of the fast changing boundary layer conditions of the mixture in the cylinder, the wall temperature will rapidly change. This results in a demand for a short response and rise time (70 µs [4]). Besides this, the sensor should keep the disturbance of the heat flux going through the cylinder wall to a minimum. To measure the heat transfer in places that are more difficult to access, the dimensions of the sensor should be kept small enough. Furthermore, sensors that are placed in a IC engine should be capable of resisting high temperatures and high pressures during a prolonged period of time. Different sensors have been investigated in recent years. In what is next, three different sensors will briefly be discussed. For more information about these sensors and their suitability to be used in IC engine heat transfer measurements we would like to refer to [5, 6, 7] Eroding ribbon sensor The first sensor that will be discussed is an eroding ribbon K-type thermocouple manufactured by Nanmac. It has Alumel and Chromel lamellae which are surrounded by an 3

19 Chapter 1. Introduction 4 aluminium alloy. The lamellae are separated by thin layers of mica. This is shown in figure 1.2. A micro junction between the two thermocouple elements is formed by grinding the surface with sand paper. In theory, this junction will be remade by the erosion of small particles in the combustion gases so the sensor should have a high durability. The finer the junctions, the smaller the thermal inertia is and the faster the sensor response will be. As discussed by Buttsworth [8], the thermal properties of this type of sensor are strongly dependent on the manner the junctions are made. When sand paper is used to form the junctions there will be a large uncertainty because there is no fixed pattern in how the junctions are formed. It is possible to avoid this by making the junctions with a scalpel but this is very time consuming. Figure 1.2: Eroding ribbon sensor [9] During a series of tests performed to compare the eroding ribbon sensor to other sensors, Demuynck [7] found that the eroding ribbon sensor was less durable than expected. Its junction was destroyed after almost every test in the research engine. Renewing the junction will have an influence on the signal processing as the material properties would change. Further testing revealed that the eroding ribbon did not have the same accuracy as other suitable sensors and behaved unpredictable. Finally, the rise time of the eroding ribbon was significantly higher than for any other sensor tested. 4

20 Chapter 1. Introduction Heat Flux Microsensor The next sensor that will be discussed is the Heat Flux Microsensor (HFM), type HFM-7 E/L manufactured by Vatell. This sensor has already been extensively used and discussed in previous works [4] [6]. The HFM sensor (shown in figure 1.3) actually consists out of two sensors, each delivering a signal. The first signal, the thermopile Heat Flux Sensor - signal (HFS), is delivered by a thermopile-sensor, which measures the temperature difference within the sensor. The temperature difference is measured over a very thin insulating layer, so several thermocouple pairs have to be put in series to obtain a measurable signal. This signal is proportional to the applied heat flux which therefore can easily be measured. However, the resulting voltage is temperature dependent, so a correction is needed. This correction can be done by taking a second signal into account, the Resistance Temperature Sensing element - signal (RTS). This signal is generated by a build-in thin film thermistor surrounding the thermopile. This RTS-signal is a temperature dependent voltage. Vatell has developed calibration procedures to correlate the sensor output directly with the imposed heat flux, making it easy to use [10]. Figure 1.3: HFM sensor [11] Wimmer et al. [12] compared the HFM sensor to several other sensors for research in internal combustion engines and concluded that it was the most accurate one. Due to the small thermal mass of the thermistor, the HFM is very well suited for measuring the instantaneous wall temperature. This makes the HFM a very promising sensor. Nevertheless, it has its limitations due to its large dimensions. This makes it impossible to use the HFM sensor in other IC engines than the CFR engine. 5

21 Chapter 1. Introduction TFG sensor The last sensor to be compared in [5] [6] [7] is the Thin Film Gauge (TFG) sensor, originally developed for heat flux measurements in gas turbines by the University of Oxford. Two different construction methods of these sensors exist as shown in figure 1.4. In the first method, the TFG is deposited directly onto a ceramic substrate, which needs to be inserted into the component of which the temperature is to be measured. The second method, consists of depositing the TFG on an insulating layer, which can be glued to all sorts of surfaces, including metals. The first type is called a single-layer sensor and the second type is called a double-layer sensor. The double-layer sensor is the only type of TFG sensor that could be used in any kind of IC engine, because there is not enough place to mount the ceramic insert needed for the single-layer sensor. Figure 1.5 shows an implementation of a single-layer TFG sensor. Figure 1.4: Left: single-layer TFG; right: double-layer TFG Figure 1.5: Single-layer TFG on a ceramic (MACOR ) substrate, mounted into a bolt Testing performed by Demuynck [7] showed that the TFG and HFM sensor have similar small rise times, which are needed to perform accurate measurements in IC engines as mentioned before. However, the author found that the TFG sensor was less accurate than the HFM sensor due to the uncertainty on the material properties of the sensor (these 6

22 Chapter 1. Introduction 7 will be discussed in full in this master s thesis). The main advantage of the (doublelayer) TFG-sensor compared to the HFM, is the possibility to install it in every type of combustion engine. 1.3 Goals As mentioned before, heat transfer measurements are necessary to build an accurate model of the heat transfer in an IC engine. Because of the factors influencing the heat transfer, it is expected that it will show some degree of spatial variation. To map this spatial variation, measurements need to be taken at multiple points in the cylinder. This is why the TFG sensor was chosen to be used in future research in IC engines [7] [2]. Different double-layer TFG s can be mounted around the cylinder wall providing simultaneous heat transfer measurements at different locations. However, before this sensor can be used, it is of the utmost importance that the uncertainty on the material properties are reduced to a minimum, in order to achieve as accurate measurements as possible. In a first instance, this master s thesis will attempt to calibrate the material properties of the TFG sensors as precisely as possible. Secondly, heat measurements will be taken with calibrated sensors and compared to measurements taken with a HFM sensor, which will serve as a benchmark. Succeeding in this task will open the way to further research into the heat transfer taking place in IC engines running on alternative fuels. 7

23 Chapter 2 Thin Film Gauge Sensor 2.1 Construction of the TFG A Thin Film Gauge sensor consists of a thin film, acting as an RTD, that is deposited on an insulating substrate. The most commonly used materials for RTDs are metals, especially platinum [13]. This is because platinum has the most stable resistance-temperature relationship over the largest temperature range. Platinum can also easily be shaped in film form and placed on top of the substrate in variable thicknesses. The insulating substrates are mostly ceramics. These ceramics must have a low thermal conductivity so that only small temperature rises would occur in the substrate when the sensor is exposed to a heat source. These small temperatures rises are desirable because thermal properties of the ceramics vary with the temperature. During the determination of the heat flux (see section 2.3.3) the material properties are considered constant, which explains why effective material property variations and consequently temperature variations should be kept to a minimum. As mentioned, the substrate must be an insulating material. In other words, the electrical conductivity of the substrate should be low. This is to avoid short circuiting between different RTDs. For the single-layer sensor, MACOR is a widely used ceramic. It has good thermal and electrical properties and can easily be machined, which allows it to be placed into a bolt. Furthermore, at 1000 C, MACOR shows no significant deformation. Figure 2.1 shows the layout of a single-layer TFG sensor. 8

24 Chapter 2. Thin Film Gauge Sensor 9 Figure 2.1: Single-layer TFG sensor [14] The platinum film, which act as the RTD element, is placed on top of the MACOR substrate. This RTD element is connected to the sensor wiring by gold leads and a conductive resin to ensure a proper electrical connection. The double-layer sensor consists of two successive layers instead of one. The first layer is an insulating substrate which is attached onto the second layer, which is a metal. Iliopoulou [15] discusses an example of a double-layer thin film gauge sensor (shown in figure 2.2). The thin films are mounted on top of flexible Upilex sheets, with thicknesses that go up to 50 micron. These sheets are bonded to the metal layer by using a glue. The thickness of the glue can reach 20 micron. The thermal properties of the glue and the Upilex are very similar, so from a thermal point of view, they are considered as one layer. Figure 2.2: Double-layer TFG sensor [6] 9

25 Chapter 2. Thin Film Gauge Sensor 10 (a) Single-layer TFG with MACOR substrate (b) Double-layer TFG with Upilex substrate Figure 2.3: TFG sensors used at Ghent University. They are mounted in a bolt for use in a CFR engine. In figure 2.3 an example can be seen of the single-layer (fig 2.3(a)) and double-layer (fig 2.3(b)) TFG sensors used at Ghent University. As can be seen, both types of sensors are mounted into a bolt. This is for practical reasons, as the research engine used contains room for mounting four M18 bolts. However, it is possible to glue a double-layer TFG directly onto the cylinder wall, which would fulfill the role of second layer of the sensor. This makes the double-layer sensor very attractive for engine heat flux measurements as multiple sensors can be installed without having to compromise the cylinder structurally by adding more pockets to place sensor-fitted-bolts. When the double-layer TFG is used under high temperatures and high pressures, conditions typically appearing in the combustion chamber during engine operations, the glue holding the two layers together can be destroyed. Also, the double-layer needs additional calibration of the material properties of the second layer. The single layer sensor only requires the calibration of one layer which allows a more simplified approach. On both sensors in figure 2.3 three platinum RTDs are visible. They are the thin grey lines between the gold connectors. Beneath the insulating substrate of each sensor, there is a K-type thermocouple. This thermocouple measures the temperature needed for calculating the heat flux (see section 2.3.3). The fabrication of a TFG is done in several steps. The procedure of constructing platinum RTDs on ceramic substrates includes surface preparation, material application and electrical lead connections. The order and accuracy of these steps must be followed strictly in order to reduce the temperature measurement errors to a minimum. 10

26 Chapter 2. Thin Film Gauge Sensor 11 In order to apply the film material, the substrate must be smooth and highly polished. The film can be painted [14] or sputtered [16] on the substrate. When the thin film is painted onto the substrate, it is baked in a oven to form a solid RTD. Sputtering is a physical vapor deposition (PVD) used for depositing materials onto a substrate, by ejecting atoms from these materials and condensing the ejected atoms onto a substrate in a high vacuum environment. Thicknesses of 0.1 to 1.0 microns can be applied. The thickness determines the resistance of the RTD and its thermal coefficient α R. Resistances decrease with increasing film thickness due to the fact that the area over which the current passes through increases. The thermal coefficient decreases with increasing film thickness. After the application of the painted film is done the whole substrate is cured in a furnace so that the RTD becomes solid. After the curing process is done, a second layer of thin film can be painted on top of the first one to vary its resistance. These resistances vary from 20 to 150 Ohm. Care must be taken when cooling of the sensor takes place. Rapid quenching is undesirable since this results in internal stresses of the thin film. These stresses appear to be the cause of instability in the electrical properties of the thin film. Painted thin films have several advantages over sputtered thin films. They have a good adhesion, films may be put down on complex curved substrates and a wide range of resistances may be obtained by varying the thickness of the RTD. However they suffer from irregularities in surface area, thickness and to a lesser extent in thermal coefficient. After the film has been applied, the electrical connections can be made. Usually gold is used to connect the thin film to the leads, because it has similar thermal properties as platinum. The liquid gold is painted on the outer surface of the ceramic substrate in thin strips on opposite sides of the film. After applying the gold the substrate is baked in the oven. The resistance of the leads must be sufficiently low so that it will not influence the measurements. The final step is to connect the gold strips to the electrical leads by using a conductive resin. 2.2 RTD A Resistance Temperature Detector (RTD) relies on the following principle: The RTD element is made from a pure material that has a predictable change of resistance as the temperature changes. This material is typically a metal such as platinum, nickel or copper. Increasing temperatures will cause higher vibration amplitudes of the atoms around their equilibrium in the metal grid, leading to reduced electron mobility. Reduced electron mobility is equivalent to an increase in electrical resistance. Generally, the resistance of the RTD can be written as 2.1: 11

27 Chapter 2. Thin Film Gauge Sensor 12 R = R 0 [1 + α 1 (T T 0 ) + α 2 (T T 0 ) ] (2.1) Where R 0 is the resistance at temperature T 0 and α 1, α 2 are thermal coefficients. For sensor applications, it is highly desirable that there is a linear relationship between resistance and temperature. The linear term has a larger contribution than the quadratic term for metals, which is the reason why they are preferred for sensor applications. Equation 2.1 may therefore be reduced to: R = R 0 [1 + α R (T T 0 )] R = α R R 0 T (2.2) Here α R represents the thermal coefficient of the resistance, which is a material property of the film material. The electrical resistivity determines how strongly a given material opposes the flow of electric current. The higher the electrical resistivity, the higher the resistance will be per length [17]. A higher resistivity leads to a higher resistance of the RTD, which leads to lesser self-heating of the film material when a constant voltage is applied to the RTD and results into a lower current flowing through the RTD when a constant power source is applied to it. The thin film thus functions as an RTD to monitor the wall surface temperature of the cylinder. In order to read out data, a constant current (I 0 ) is supplied to the RTD which enables us to monitor a voltage variation corresponding to the temperature variation: V = RI 0 (V V 0 ) = (R R 0 )I 0 (2.3) The 0 -subscript indicates that those values were taken at ambient temperatures. constant current I 0 is set to a desired value with an amplifier. The Sensitivity of the RTD An important property of a sensor is its sensitivity. The sensitivity of the TFG sensor is determined by the thin film. It can be expressed as the ratio of the voltage variation to the temperature variation. Combining 2.2 and 2.3 gives: V T = α RV 0 (2.4) Where T is the difference between the current temperature and the ambient temperature. The sensitivity is directly proportional the mean film voltage. Higher sensitivities can be obtained by operating the RTD at a higher mean film voltage, which can be achieved 12

28 Chapter 2. Thin Film Gauge Sensor 13 by raising the current supplied to the RTD. However, the current cannot be increased too much, otherwise the self-heating of the film will become too large and introduce a temperature offset. This effect limits the mean film voltage to a maximum. Equation 2.4 shows that the sensitivity is not only influenced by the mean film voltage but also by the thermal coefficient of resistance. A higher α R will increase the sensitivity of the RTD. The thickness of the film and the way it is applied on the substrate will influence α R. Schultz and Jones [18] investigated different materials to see which one would be best suited to achieve high sensitivities in TFG applications. This was done by calibrating the thermal coefficient of different film materials while keeping the same voltage over the RTD. They concluded that platinum thin films would have the highest sensitivity RTD callibration To achieve accurate temperature measurements, it is necessary that the thermal coefficient of resistance is determined as exact as possible. This calls for a calibration of the thin film element. A TFG sensor is usually provided with three or more RTDs. Even if each RTD is mounted on the substrate in the same way, the thickness of each film can still vary. Therefore each RTD should be calibrated. The determination of the thermal coefficient α R is done by a static calibration [2]. The test is performed by putting the TFG sensor in a PVC shell and then immersing it in a fluid bath filled with distilled water. The shells are necessary in order to avoid any electrical conduction between the water and the RTDs. Instead of water, another dielectric fluid is also an interesting alternative. The desired temperature of the fluid bath is achieved by a PID-controller which keeps the temperature at a constant value. A circulation pump is mounted in the fluid bath to achieve a homogeneous temperature. Every time a new temperature is set for the fluid, the temperature of the TFG will rise until it is in thermal equilibrium with the fluid. The exact temperature of the fluid is monitored by a PT-100 sensor, which is a highly accurate RTD sensor, that is mounted close to the TFG sensor and at an equal depth so that the errors are kept to a minimum. Every time a new temperature is set and thermal equilibrium is reached, the resistances of the RTDs are measured. These resistances increase almost linearly with respect to the temperature rise. Once a full set of data points is measured a linear regression is applied to determine the thermal coefficient and its error level. The entire setup is shown in figure

29 Chapter 2. Thin Film Gauge Sensor 14 Figure 2.4: Static calibration setup [2] Another disadvantage of using water, besides the possibility of electric conduction, is that local boiling can occur starting from 80 C, which limits the maximum temperature at which the calibration can be performed. Thermal oils could offer an alternative [18]. They can reach temperatures up to 280 C and are electrically insulating fluids. Therefore no PVC shells would be necessary anymore in the setup. These PVC shells can collapse if they are exposed to high temperature and foul the sensor when doing so Ohmic heating and RTD burnout As already mentioned, when a current flows through the thin film, it will be subjected to self-heating. This is due to the ohmic heating of the resistance. In 2.2.1, it was demonstrated that the sensitivity could be controlled by the voltage over the RTD (and hence the current flowing through it). If the current flowing through the RTD is too high, there will not only be an offset on the measurements due to the ohmic heating, but the sensor can burnout as well. However, the temperature offset will appear much sooner than a sensor burnout. It is important to operate the RTD at a current that is high enough to have sufficient sensitivity, but not too high so that an offset can be avoided. Before using or calibrating the TFG sensor, the operating limit must be determined by means of a ohmic heating test. 14

30 Chapter 2. Thin Film Gauge Sensor 15 The ohmic heating test consists of placing the RTD in a wheatstone bridge [13, 18]. The RTD will be one of the four resistors. The remaining three resistors must be as unaffected as possible by temperature changes. At the start of the test, the bridge must initially be balanced. When the supply voltage is raised, the current flowing through the sensor starts to increase. From a supply voltage level of 1V ohmic heating becomes apparent. From this point on, the measured temperature will show an offset. From 2V, the ohmic heating is not negligible anymore. Sensor burnout can be expected from voltages of 3V and more. The results of the ohmic heating test are shown in figure 2.5. In further use of the sensor, the maximum limit of the supply voltage will be set to 1V. Figure 2.5: Ohmic heating test results: The x-axis represents the supply voltage, the y-axis represents the out of balance voltage. 2.3 TFG concepts As explained in the previous sections, the thin film acts as an RTD and is used to measure the instantaneous wall temperature. This temperature is than used to calculate the heat flux going through the sensor. In this section, the concepts used to calculate this heat flux will be examined more closely One dimensional analysis The TFG is used to measure the surface temperature history. This is then used as a boundary condition for the one dimensional heat conduction equation: 15

31 Chapter 2. Thin Film Gauge Sensor 16 2 T (x, t) T (x, t) x 2 = α t (2.5) Where T (x,t) is the temperature of the substrate at a given depth x and time t and α is the thermal diffusivity of the material defined in terms of the thermal conductivity k, the density ρ and the specific heat c. α = k ρc (2.6) The solution of this one dimensional conduction equation is based on the semi-infinite principle. This principle implies that at a certain penetration depth of the substrate, the temperature of the substrate can be considered constant. Then equation 2.5 can be solved by using only the surface temperature history. To comply to this principle, the substrate must have a certain thickness. Figure 2.6 represents this model visually. In said figure, the heat flux q s penetrates the thin fim with thickness ɛ and T (x) represents the temperature at certain depth x. Figure 2.6: Semi-infinite principle [14] The minimal substrate thickness can be obtained by considering the ratio of the temperature at a certain depth x to the surface temperature. For a constant heat flux into the substrate surface this ratio is: ( ) T (x, t) T (0, t) = e x 2 π x x 4αt αt 2 erfc 4αt (2.7) 16

32 Chapter 2. Thin Film Gauge Sensor 17 Where α is the thermal diffusivity of the substrate, x the penetration depth and t the time. Kinnear and Lu stated that ideally, the temperature at the substrate base should be the same as ambient for all testing times. Therefore, at the end of a test, the ratio in 2.7 should be negligible [14, 19]. Ratio 2.7 is represented in figure 2.7. It is clear that for longer during exposures of the sensor to the constant heat flux, the penetration depth must be larger to achieve a negligible ratio. The same research showed that, for a MACOR substrate, a thickness of at least 3mm is required for a substrate base temperature to surface temperature ratio of less than 1% for a duration of 1 second. However, for reasons of mechanical strength, substrates always have a larger thickness. Therefore it is possible to conclude that the semi-infinite principle is well satisfied for short duration testing. Figure 2.7: Temperature ratio as a function of substrate penetration depth for different time durations [14] Film thickness The thin films deposited on the surface of the substrate have thicknesses on the order of a micron, but they still have an effect on the surface temperature history that cannot be neglected. These thin layers have a thermal capacitance that cannot be neglected without introducing a large error in the heat flux calculations in short flow durations (order of microseconds) [18]. In this case the thickness of the thin layer is neglected, 17

33 Chapter 2. Thin Film Gauge Sensor 18 larger thicknesses will lead to higher errors due to the fact that more time is needed to heat the film up to the temperature of the flow. However, the manufacturer has reasons to use a configuration thicker then necessary. In the manufacturing process, each successive layer of platinum has to be baked in the furnace. After being baked, internal thermal stresses occur in the thin film as already mentioned before. Thicker films cope better with these stresses. It is not known if there are flow duration shorter then a millisecond in combustion engines, so the error due to the thickness of the thin film is not yet determined Signal processing Different processing techniques can be used to transform the measured temperature in a heat trace. One type of technique consists of solving Fourier s law (eq. 2.5) analytically. Two boundary conditions are necessary to do this. The measured surface temperature is transformed into an analytical expression with a Fourrier analysis and used as a first boundary condition. There are two possibilities for the second boundary condition. The first option is to measure a second temperature in the cylinder wall at a known distance from the surface [20]. This is usually done by placing a K-type thermocouple underneath the TFG sensor. The second possibility is to assume zero heat flux at the instant that the gas temperature is equal to the wall temperature [21]. This requires a bulk gas temperature in the cylinder, which can be calculated out of pressure measurements with the equation of state of an ideal gas. In doing so, only one wall temperature is needed, which simplifies the sensor construction. However, since Lawton [22] and Nijeweme et al. [23] have reported non-zero heat fluxes at the instant of equal wall and gas temperature, there are some doubts about the accuracy. Both possibilities are fully elaborated in appendix A. To determine the transient part of the heat flux, a material property, the so called thermal product (TP = ρck, see section 2.3.4) is needed. An alternative to the Fourier method s is the Finite Impulse Response (FIR) method developed by Oldfield [24]. In this method, the TFG sensor is considered as a Linear Time Invariant (LTI) system. The input for this system is the surface temperature measured by the thin film and the output is the heat flux. This method assumes that the sensor is at a uniform temperature when the measurement is started (t=0). This is mostly not the case during measurements in an IC engine, because the measurement cannot be continued in between the selection of different operation modes. This is why only the transient part of the heat flux can be determined with the FIR method. The steady state component of the heat flux must be calculated separately. The main advantage of this method is that it requires less computation time because the impulse response needs to be calculated just 18

34 Chapter 2. Thin Film Gauge Sensor 19 once for every combination of sensor, sample frequency and number of data points. Once the impulse response is known, the output can be calculated using the Laplace transform. Just as for the Fourier method s, the TP needs to be determined to use the FIR method. For a more detailed use of the FIR method we would like to refer to appendix B. Both the Fourier and the FIR method lead to equation 2.8 for the transient heat flux, where q is the heat flux, T s is the surface temperature of the thin film, t is the time duration of the measurement and ρck is the thermal product of the substrate. ρ is the density, k the thermal conductivity and c the specific heat capacity of the substrate. q = π ρck T s(t) 2 t (2.8) During the heat flux calculations the material properties are considered constant. However, in reality, properties such as density, thermal conductivity and specific heat capacity are temperature dependent. This explains the demand that the substrate should only have small temperature changes. constant is acceptable. In that case, the assumption that the properties remain Thermal product of the TFG substrate In the previous section it became clear that the TP of the substrate needs to be known to conduct accurate measurements. Each substrate layer has it own TP. In previous engine measurements [2], the thermal properties of the bulk material of the substrate were used in the heat flux calculations. However, Kinnear and Lu [14] indicated that actual values of the thermal product differ from the ones supplied by the manufacturers of the bulk material. The reason is that the material properties of the substrate change during the manufacturing process, during which the film is baked onto the substrate. The platinum film interpenetrates the ceramic substrate, changing the material properties. Furthermore, no research has been done yet on the influence of aging and wear of the sensor on the material properties. Therefore it is important that the TP of the substrate is calibrated. 2.4 Calibration setups Over the years different calibration methods have been suggested. Each method is based on a solution of equation 2.5. In case of a single-layer TFG, the general solution can be obtained by using the Laplace transform as mentioned in There exists analytical solutions for the particular cases of a step function in heat flux and a step function in fluid temperature [25]. When a step function in heat flux is used, the analytical solution is: 19

35 Chapter 2. Thin Film Gauge Sensor 20 T wall (t) T 0 = 2q wall t (2.9) π ρck A typical wall surface temperature increase is shown in figure 2.8 for a single-layer MACOR TFG. The temperature profile is proportional to the square root of time. This means that the evolution can be linearized when plotted as a function of t t 0, where t 0 is the time at which the wall surface temperature starts to rise. By doing so, it becomes very convenient to determine the TP ρck when a known heat flux is applied or vice-versa. However the result of this linearization depends on the value of t 0. The time t 0 cannot always be determined with accuracy and generating a step function can be difficult. Figure 2.8: Wall surface temperature evolution for single-layered substrate MACOR TFG. [25] For the case of a step function in fluid temperature and a constant heat transfer coefficient h the solution is given by [26]: with β: T wall (t) T wall (t = 0) T gas T wall (t = 0) = 1 e β2 erfc(β) (2.10) β = h t ρck (2.11) Figure 2.9 compares the solution obtained through the use of the constant heat flux technique and the one obtained through the use of constant temperature. The upper graph shows the wall surface temperature T wall for both techniques and the lower graph represents the heat flux to the wall q wall. In this figure it is clear that the wall temperatures obtained by the use of both solutions are almost the same for short flow durations (50ms). Also, for flow duration on the order of milliseconds, the calculated heat flux q wall is similar for both techniques. Both techniques are expected to yield comparable results when used to calibrate the TP, as long as the time duration of the tests are sufficiently short. If we recall the semi-infinite principle 2.3.1, we know that flow durations will be short. 20

36 Chapter 2. Thin Film Gauge Sensor 21 Figure 2.9: Comparing the analytical solutions obtained through the use of a step function in heat flux and a step function in fluid temperature [25] Heat gun setup Piccini et al. [27] calibrated the TP by subjecting the TFG to a sudden heating with hot air. This method has since been used at Ghent University under the form of a Heat gun setup [2]. In their analysis, Piccini et al. treated the hot air jet as a step function in heat flux, while a step in fluid temperature is actually realized. The schematics of the setup are shown in figure Figure 2.10: Hot air gun calibration setup [27] The sensor and heat gun are separated by an insulating plate so that the heat gun s jet 21

37 Chapter 2. Thin Film Gauge Sensor 22 can reach steady state until the detachment mechanism is released which would expose the sensor to the heat source. The sensor and detachment frame are separated from each other in order to avoid vibrations to the sensor which would introduce errors. Piccini et al. suggested calibrating the heat flux generated by the hot air gun first by using a calorimeter sensor. The flow field under the jet is steady during the calibration test. The heat-transfer coefficient is primarily a function of the aerodynamic character of the flowfield alone and thus can be assumed to be a constant value during calibration. the local heat flux q is the product of the local heat-transfer and the difference between the surface temperature T s and the adiabatic wall temperature of the gas T aw : q = h(t aw T s ) (2.12) In order to generate a constant heat flux, the driving temperature (T aw -T s ) has to be constant. However, during the experiment the surface temperature increases and the temperature difference is reduced. This means that the heat transfer rate does not remain constant. To account for this discrepancy, a superposition technique is applied to the measured surface-temperature signal T s to correct to a constant heat flux experiment. The exact superposition technique is beyond the scope of this masters thesis, but can be found in [25, 27]. Piccini et al. estimated that the uncertainty on the measurements of the TP is 4.2%. This uncertainty could be contributed to the following sources: The error on the thermocouple measurements (needed for T aw ), the error in the calibration of the TFG s RTD, the error due to the data analysis and the error associated with the shutter opening time. The error on the generated heat flux was not considered. Even though the heat flux is calibrated with a calorimeter, the repeatability of this experiment has not been examined. Practical experience on the test rig at Ghent University showed that it was not easy to control the heat flux of the heat gun, which does not make this setup ideal for really precise calibration of the TP Water droplet setup and shock tube experiment Buttsworth [28] investigated the use of surface junction thermocouples for transient heat flux measurements. He noted that the accuracy of the sensor is dependent on the effective TP and this thermal product can be a function of the time scale of interest. He made use of two calibration setups to determine the TP: the water droplet calibration experiment to assess the TP for millisecond time scales and the shock tube experiment, to assess the TP for microsecond time scales. 22

38 Chapter 2. Thin Film Gauge Sensor 23 The water drop setup is illustrated in figure The sensor is mounted into a heated plate with a droplet catcher mounted just above it. In this setup, the sensor is heated and remains stationary. A drop of water at ambient temperature accelerates from rest under the action of gravity and impacts on the gauge surface. An insulating plate is mounted between the droplet and the sensor in order to avoid any heating of the droplet due to the heated plate surrounding the sensor. Figure 2.11: Water droplet setup [28] When the water droplet at temperature T w contacts the heated sensor at temperature T s, there is ideally a step function change in the temperature at water-sensor interface. The temperature at the surface of the sensor after contact with the water T, is given by [29]: T T s T w T s = T P water T P water + T P sensor (2.13) Equation 2.13 strictly only applies to the hypothetical case of one-dimensional droplet impact with no rebound, and one-dimensional heat conduction with constant (temperatureindependent) thermal properties in both droplet and thermocouple. If the necessary temperatures are recorded and the T P water is known, the T P s can be identified. The properties of water and the sensor actually vary with temperature, but the variations are relatively small and the experimentally observed surface temperature is approximately a step function. The sensor produces slightly different responses depending on the precise location of the droplet and the droplet catcher relative to the sensor as seen in figure However, the principal difference between different runs is only in transient behavior. Buttsworth 23

39 Chapter 2. Thin Film Gauge Sensor 24 concluded that there was no significant influence on the mean temperature level after 1ms. 5ms after impact two dimensional effects will have a significant influence on the heat transfer between the water droplet and the sensor and thus will limit the test duration. Figure 2.12: The water droplet setup yields slightly different responses due to misalignment [28] The estimated uncertainty of the thermal product of the sensor is approximately 3.9% with the strongest contribution from the uncertainty due to the value of the thermal product of water. The reason for this is that distilled water still can have some contaminants which influence its thermal product. To determine the sensor response on a microsecond timescale, the shock tube experiment is used [28]. It should be said that in IC engines, the millisecond time scale will be of greater importance than the microsecond time scale due to the fact that a low RPM engine is used. Figure 2.13 shows the shocktube setup. At the end of the shock tube, thermocouples are flush mounted so that the shock wave will cause a step in temperature when it passes. Prior to the shock tube test, ambient air from the environment fill both shock tube and driver section. The shock tube and driver section must be isolated from each other, which is done here with cellophane diaphragms. The driver section is filled with helium until the diaphragms ruptures. To measure the propagating shock wave along 24

40 Chapter 2. Thin Film Gauge Sensor 25 the shock too, measurements are made with surface junction thermocouples and pressure transducers. The shock speed must also be determined. When the shockwave reflects off the end wall of the shock tube, the air in contact with the end wall experiences a step in temperature. Here an idealized one-dimensional gas dynamic and a heat transfer processes with constant thermal properties are assumed. Therefore a similar technique as the water droplet calibration can be adopted. The gauges mounted in the end wall will measure a step function in fluid temperature according to [29]: This can be reduced to: T T s T air T s = T P air T P air + T P sensor (2.14) T T s T air T s T P air T P sensor (2.15) This is possible due to the fact that the TP of air is much smaller than the TP of the sensor. Providing that the sensor surface temperature is recorded during the shock reflection as well as the step function in air temperature and that the TP of air can be determined with sufficient precision, the TP of the sensor can be determined on microsecond scale. Figure 2.13: The shocktube setup, used to assess the sensor response on microsecond timescale [28] These two setups have however not yet been tested on TFG sensors. Since two dimensional 25

41 Chapter 2. Thin Film Gauge Sensor 26 effects limit the time duration of the test, not much variation in flow duration is attainable. Therefore, neither of the two setups have been implemented for this thesis Double electric discharge calibration Another way to generate a step function in heat flux is to use Joule heating. A step in current or in voltage will result in a step in heat according to: P = V I = RI 2 = R V 2 = q (2.16) Where P is the dissipated electrical power through the RTD of the TFG. By monitoring the change in resistance and using equation 2.2 to relate this change to the temperature variation, equation 2.8 can be used to calculate the TP. This setup is called Double Electric Discharge calibration. This method has already been used for gauges in turbo-machinery application by Schultz and Jones [18] and Dénos [30]. As this setup only consists of an electrical circuit, it is much easier to implement then previous discussed setups. A second advantage the electrical circuit offers, is that it can easily be used in combination with a DAQ for controlling the voltage levels and for further data processing. As it will be the main tool used in this thesis, we will dedicate the next chapter to the DED setup and its results. 26

42 Chapter 3 Double Electric Discharge calibration This chapter will go over the use of the Double Electric Discharge to calibrate the TP of a TFG used in IC engines. We will start by discussing the setup. This will highlight the reasons why the DED setup was chosen over the previously treated calibration setups. The following section will treat some theoretical aspects of the DED. Next, the data processing is looked at and finally the results of the calibration tests will be discussed. 3.1 DED setup The DED calibration method is based on the use of the analytical solution of Fourier s Law (2.5) in case of a constant heat flux, as mentioned in When applying a constant voltage to a resistive element, the electric power that is dissipated through heat in this element is constant (apart from the transient part when turning on the supply). In the DED, this resistive element is the RTD of the TFG sensor. The heat dissipated by the RTD goes through the substrate and thus acts as heat source. By monitoring the RTD temperature it is possible to reconstruct equation 2.8. Monitoring the temperature of the RTD is done by using the temperature-resistance relationship (eq. 2.2). To accurately measure the change in resistance, the RTD is placed in a wheatstone bridge [13]. Figure 3.1 shows the schematics of the wheatstone bridge that incorporates the TFG (represented by R 0 ). The bridge is originally balanced by a potentiometer (figure D.2). The remaining elements of the bridge are two resistors with the same resistance. These should be as unaffected by temperature changes as possible, just like the resistors used in the ohmic heating test The components of the bridge are shown in figure 3.2. The 27

43 Chapter 3. Double Electric Discharge calibration 28 bridge ensures that any noise present in both legs of the bridge is cancelled. Figure 3.1: Wheatstone bridge layout: R 0 represents the TFG s RTD. The bridge is balanced using a potentiometer represented by R 1 (a) Potentiometer used to calibrate the bridge (b) Temperature invariant resistors Figure 3.2: Main components of the wheatstone bridge besides the TFG. When the resistance of the RTD changes, the bridge will no longer be balanced. If we assume that the resistance of the potentiometer and the resistors remain unchanged, we can use the out of balance voltage of the bridge to calculate the change in resistance of the RTD. In figure 3.1 the out of balance voltage is represented by V out and the voltage supplied to the bridge by V in. It is important that the supply voltage can be controlled very precisely. This is why a data acquisition is used. A PXI-6251 by NI is used in this thesis. The PXI-6251 can deliver voltages ranging up to 10V. The input of the wheatstone bridge is connected to a analog output channel of the DAQ. The DAQ sends an initial voltage to the bridge. Once it has been balanced properly, a voltage pulse can 28

44 Chapter 3. Double Electric Discharge calibration 29 be superimposed to simulate a heat flux step. The amplitude and time duration can be regulated by the software used to control the DAQ. However the DAQ has its flaws: it can only generate currents up to 5mA, which limits the voltage that can be delivered if the load is too high. In the setup used for this thesis, the equivalent resistance of the bridge is 30Ω, thus limiting the supplied voltage to 150mV. This limitation can be avoided by placing a voltage follower between the DAQ and the bridge. The voltage follower consists of an op-amp in series with a transistor. These elements will deliver the necessary current to ensure that the voltage will not drop if the load becomes higher than the limit imposed by the DAQ. The DAQ is also used to measure the out of balance voltage. To calculate the power dissipated by the RTD and thus the heat generated, the voltage over the RTD and the current going must be measured as well. The DAQ however, cannot measure current directly. By placing a shunt resistor directly behind the TFG and measuring the voltage over it, the current going through the shunt resistor and thus also the RTD resistance can be determined. The complete DED setup is shown in figure 3.3. Figure 3.3: The DED setup: The bridge input and the out of balance voltage are connected to the DAQ through BNC cables. The advantage of the DED over the other setups is the fact that it can easily and precisely control and measure the heat. That is why this method is expected to be more accurate in determining the TP. 29

45 Chapter 3. Double Electric Discharge calibration Theoretical approach As discussed in the previous chapter, the analytical solution for Fourier s Law when a step in heat flux is applied, is given by the following equation 3.1: q = π ρck T RT D(t) 2 t This equation can be rewritten to contain the resistance change of the RTD: (3.1) q = π ρck R α R R t (3.2) The change in resistance can be related to the change in out of balance voltage. If the bridge in figure 3.4 is considered, the out of balance voltage V 0 can be expressed in function of the intput voltage of the bridge V B : V 0 = R 1 R 4 R 2 R 3 (1 + R 1 R 4 )(1 + R 2 R 3 ) V B (3.3) Figure 3.4 If the four resistors have the same value R and just one of the four resistors is variable equation 3.3 can be reduced to: V 0 = V B 4 [ R R + R 2 ] (3.4) 30

46 Chapter 3. Double Electric Discharge calibration 31 The relationship between the out of balance voltage V B and the resistance variation R is not linear. Consider the following example to illustrate the effect of the non-linearity. If R has a value of 100Ω and R of 0.1Ω, the output will be mV for a supply voltage of 10V. A linear relationship would have yielded an out of balance voltage of 2.5mV. Therefore an linearity error of mV occurs. The relative error due to the non-linearity is 0.05%. The linearity error depends on the magnitude of the resistance variation. In general, when the four resistors have the same resistance at the start, the linearity error will be 0.5% per % change of the variable resistor. By using equation 2.2 it can be shown that the parameter (ρck) 1/2 is given by [18]: 1 ρck = A π R V 2I0 3R2 0 R (3.5) potα R t With A is the film area, R the sum of all four resistors in the bridge, R pot is the resistance value of the potentiometer and I 0 and R 0 are the current through the RTD and the RTD resistance value before a pulse is applied. To simplify the equation V is the out of balance voltage taken while neglecting the linearity error. Using the DED setup with this procedure has some disadvantages however: ˆ It is necessary to know the surface area of the thin film which may not be straightforward to determine. ˆ Though the bridge is initially balanced under DC conditions, using a galvanometer as a variable resistance may not hold the bridge dynamically if there are inductive or capacitive elements. ˆ The non-uniformities in the thin film may cause some errors ˆ The initial current is necessary to determine the thermal product. The equation indicates the third power of the current is taken. So a variation of the constant current introduces an error in the thermal product. The errors introduced by the measurement of the film area may be avoided by a double calibration procedure. First a pulse is sent through the RTD while the sensor is held in air and the factor ( R/ t) air is deduced. Next, the measurement is repeated in a fluid whose thermal properties are well known and stable (such as glycerin). Maulard [31] performed an analysis using these two measurements to obtain an expression for the TP. 31

47 Chapter 3. Double Electric Discharge calibration 32 ρckliq R 0 α R = 2F xri2 ( ) πa R t ρck 2F (1 x)ri2 = R 0 α ( ) R πa R t ρck R 0 α R = 2F RI 2 ( ) πa R t (3.6) (3.7) (3.8) Where T P liq stands for the TP of the liquid, x is the fraction of the heat generated that is diffused in the liquid and F is the unknown factor which accounts for the non-uniform film heating. The indices 1 and 2 stand for the experiment carried out in air and a fluid respectively. Maulard determined that the TP of the substrate could be shown to be: ρck = ρckliq ( ) R t ( ) 1 R t 2 1 This can also be expressed in function of the out of balance voltage: (3.9) ρck = ρckliq ( ) V ( t ) 1 V t 2 1 (3.10) Thus the effect of non-uniform film thickness on a calibration in air and inaccuracies in the determination of the film surface A are eliminated. Maulard has demonstrated that the optimum ratio of the slopes to give the least error in TP is (1 + 2) and thus the liquid should in principle have thermal properties such that: ρckliq = 2 ρck substrate (3.11) The TFG is subjected to a electric discharge twice, hence the name Double Electric Discharge method. 3.3 Data processing Regression Before the calculation of the TP can take place, a regression is performed to fit the data to the adequate model. Section 2.4 showed that the temperature profile and subsequently the out of balance voltage is proportional to the square root of time. The regression will attempt to fit the data to a non-linear model, defined as: 32

48 Chapter 3. Double Electric Discharge calibration 33 V = b t (3.12) V is the measured out of balance voltage, t the time during which the voltage pulse is applied and b is the regression coefficient. The DAQ starts measuring the out of balance voltage from the instance that it is triggered to supply the voltage pulse. Inevitably, due to the inertia of the system, a time delay will be monitored before the out of balance voltage starts to rise due to the pulse. A typical data set is plotted in figure 3.5. The time delay is clearly noticeable. Also, indicated by the arrow, is an overshoot. This is due to the transient effects of supplying the bridge with the pulse and due to a slight, unavoidable unbalance of the bridge. Even when the bridge is balanced properly, a certain noise level will be present and thus causing an overshoot. To limit this, it is important to balance the bridge before every use. Figure 3.5 To achieve a good regression it is important that ideally the origin of the model should coincide with the data point at which the out of balance voltage starts to rise due to the applied voltage pulse. This is done by shifting the data set until this point is situated at t = 0. To do this, it is of course necessary to determine the exact point at which the voltage rise takes place. The transient effects and the overshoot taking place complicate this action. A difference between the origin of the model and the starting point of the voltage pulse will negatively affect the calculations of the TP. To avoid the lack of resolution, the starting point is determined based on the power dissipated by the RTD. Parallel to the out of balance voltage, the voltage and the 33

49 Chapter 3. Double Electric Discharge calibration 34 current of the RTD are measured and used to calculate the power. Because this power is approximately a square wave and so the rising edge can be used to mark the instant at which the voltage starts to rise. Figure 3.6 is a plot of the power dissipated by the RTD in air. Four regions can be distinguished. The first region (blue) represents the time delay between the start of the measurements and the rise in out of balance voltage. The second region (green) is formed due to the transient effects. The following region (red) contains all the points contained into a 2% error margin. In this region the dissipated power and thus heat flux is considered constant. It is the data in this region that will be fitted to the non-linear model. The transient part will not be taken into account in order to reduce the possible error. The region where the voltage pulse drops to zero again is shown in light blue. Figure 3.6 Now that the origin and the data fit for regression have been defined, the regression can be performed by using the MATLAB command nlinfit. The result of the regression is shown in figure 3.7. Data of the calibration in air and in glycerin are plotted together with their regression. Notice that the out of balance voltage reaches higher values in air than in glycerin. This is because heat is easier dissipated in glycerin than in air due to its higher thermal conductivity. Therefore, higher temperatures are reached in air which is expressed through a higher out of balance voltage. 34

50 Chapter 3. Double Electric Discharge calibration 35 Figure 3.7: The out of balance voltage plotted together with the regression, in air and in glycerin Regression accuracy In order to determine how well the regression is, two quality factors are introduced. First the noise to signal ratio is used. This ratio is defined as: NSR = P noise P signal (3.13) Where P noise and P signal are the power of the noise and signal respectively. The noise is defined as the residual, which is the difference between the actual data and regression fit. The signal represents the regression performed on the out of balance voltage data. The power can be calculated according to: P = 1 N N 1 n=0 x(n) 2 (3.14) x(n) represents the vector containing the data of the signal and the power in the corresponding power functions and N is their length. The NSR will be low if a signal has a low contribution of noise, therefore improving the quality of the regression. The second quality factor used is the correlation coefficient of the regression. This coefficient is given by: R(i, j) = C(i, j) C(i, i)c(j, j) (3.15) R(i,j) is a vector containing the correlation coefficients performed on the covariance matrices C(i, j), that contain the actual data i and the regression values j. A high correlation coefficient (order of 99%) represents a very accurate regression. 35

51 Chapter 3. Double Electric Discharge calibration 36 For the full MATLAB script and detailed information about the regression quality, we would like to refer to the corresponding appendices E. 3.4 Calibration results The final aspect of the DED setup that needs to be examined, is its dependance on the operating conditions of the calibration. Different voltage levels and time durations can be employed to perform the calibration. These were varied during different calibrations to observe their effect on the TP. Finally, a set of calibrations were performed on a MACOR block provided with multiple RTD s, each with a different resistance Voltage variation To investigate the influence of the voltage, the calibration of the TP was performed at different pulse voltages. The voltages used ranged up from 4V to 9V. Voltages lower than 4V cause almost no self-heating of the thin film. The monitored out of balance voltage is strongly affected by the noise, rendering the signal unusable. The upper limit was set to 9V for two reasons. Firstly, the DAQ can only supply a maximum voltage of 10V. Secondly, besides the voltage pulse, a DC signal is supplied to the bridge. Due to ohmic heating (see section 2.2.3), this DC signal cannot exceed 1V. A higher DC signal results in less overshoot, so the maximum of 1V is chosen to feed the bridge. Figure 3.8 shows the TP calculated from data obtained at different voltage levels. All the measurements were executed with a constant time duration of 5ms. The values for the TP were attained by taking the average of 3 calibration sets. The error flags represent the absolute error on the measurement (see appendix C.3). The error bars overlap in the zone where the TP reaches a value between and J/cm 2 /K/s 1/2, for all the voltages except for the measurement taken at 8V. There is actually almost no overlap between the 8V error bars and the error bars at the other voltages. A look at the 8V-data revealed that the measurements were compromised (probably due to an engine running in the background). Therefore, the measurements taken at 8V were not taken into account in further analysis of the results. 36

52 Chapter 3. Double Electric Discharge calibration 37 Figure 3.8: TP calculated at different voltages with a constant time duration of 5ms. The error level is the largest for the measurements taken at 6V. This error can be related to the NSR which is the highest for 6V (see table 3.1). The correlation coefficient given in table 3.2, indicates that the 6V data-set has the least accurate regression. Therefore, only measurements at 4V, 5V and 9V are used to form a conclusion about the influence of the voltage level. We notice that the error level decreases when the voltage increases. This could be explained due to the raising correlation coefficient with higher voltages as can be observed in table 3.2. A better correlation coefficient results in a smaller error on the slopes used to determine the TP. For the 9V measurements this error is so small that the relative error of the calculated TP is only 4,5%. This is a very good result if the relative error of the TP of glycerin, which is 4% [18], is taken into account. The relative error can be further brought down if the fluid properties of glycerin are known more accurately. Voltage (V) NSR air NSR glycerin Table 3.1: Mean NSR of measurements Table 3.1 contains the mean NSR of the measurements taken at different voltage levels. The noise levels seem to drop significantly when measurements are performed at a higher 37

53 Chapter 3. Double Electric Discharge calibration 38 pulse level. The noise levels at 8V or 9V are almost one hundred times lower than for measurements at 4V or 5V. As mentioned before, lower NSR implies a better regression, resulting in smaller error bars. In table 3.2 we can also see a positive effect at higher voltages for the correlation coefficients. Thus the regression quality improves with higher voltages. Measurements done at higher voltages deliver a more accurate TP. Voltage (V) r air r glycerin Table 3.2: Mean correlation coefficient of the regressions To confirm the trend of an improved accuracy at higher voltages, a second series of measurements were taken. This time the time duration was 10ms. The measurements are plotted in figure 3.9. This measurement confirmed the trend. The low-voltage measurements had a larger NSR and a lower correlation coefficient. Graphically, the error bars do almost not overlap at low voltages. On the contrary, At high voltages, a quasi perfect overlap could be noticed. The magnitude of the error bars does not vary a great deal, indicating that the variation for higher pulse levels is very similar. Also, the averaged values of TP lie very close to each other for the measurements taken at 8 and 9 V, indicating that voltage variation does not influence the TP that much. Therefore, voltage variation or power variation does not influence the values of the TP. 38

54 Chapter 3. Double Electric Discharge calibration 39 Figure 3.9: TP calculated at different voltages with a constant time duration of 10ms Time duration variation In this section, the effect of the time duration of the voltage pulse was investigated. The measurements were once taken with a time duration of 5ms and once with a time duration of 10ms (see figure 3.10). The voltage level was kept constant during both measurements. Two such sets were performed, one at 8V and one at 9V. These voltages were chosen in accordance with the previous section, where it was shown that these voltages had the highest accuracy. The magnitude of the error bars for measurements taken at 5ms and 10ms duration are very much alike. Furthermore there is a large overlap of the bars for the different time durations. There is also an important overlap of the bars for different voltage levels. However, the mean values of the TP vary more for the lower voltage than at the higher voltage level, which is consistent with the previous section. The region of the thermal product where the error bars overlap can be considered between and J/cm 2 /K/s 1/2, just as the overlap in the voltage-variation-measurements. 39

55 Chapter 3. Double Electric Discharge calibration 40 Figure 3.10: Measurements taken with different time durations. A variation in pulse time duration does not lead to a significant change in calculated TP. However, a longer time duration will affect the resistance increase due to ohmic heating of the RTD, hence increasing its temperature. The maximum temperatures reached by the RTD in air and glycerin are represented in table 3.3. Due to the higher thermal conductivity of glycerin, the maximum temperature recorded in glycerin is lower then the one recorded in air. The time duration will influence the maximum temperature in such a way that a higher time duration will yield a higher temperature. Still, the variation in resistance remains proportional to the square root of time, therefore the thermal product remains constant for different maximum reached temperatures. The temperature cannot be increased infinitely, otherwise burnout will occur. Therefore, pulse durations of 10 ms are considered as the upper limit to avoid sensor burnout. Measurement air C glycerin C 8 V 5 ms V 5 ms V 10 ms V 10 ms Table 3.3: RTD temperatures 40

56 Chapter 3. Double Electric Discharge calibration Different RTD s on same substrate In this section, a new block of MACOR substrate is calibrated with a pair of RTD s with a different ambient resistance. The applied voltage pulse is varied from 8V to 9V in order to maintain a low NSR. The time duration is set at 5ms. Figure 3.11 displays the TP of this substrate calculated with the data supplied by the two RTD s. Five measurement sets have been taken on each RTD at voltage levels of 8V and 9V while the TFG sensor was hold in air and glycerin. The mean values of the TP lie close together for both RTD s and both voltages. The error bars overlap in the region where the TP reaches values from to J/cm 2 /K/s 1/2. The correlation factor of every regression reached values of 0.99 or higher. Figure 3.11: TP calculated by two different RTD s on the same MACOR substrate So both RTD s deliver a similar value for the TP of the MACOR block. However, the difference between the mean values of RDT 1 is smaller then the difference between the values of RTD 2. The first RTD has a resistance of 40Ω and the second one a higher resistance of 46Ω. Kinnear and Lu [14] mentioned that a larger film thickness, which results in a lower film resistance, will have a better calibration repeatability due to the fact that thicker films cope better with internal stresses generated by the short current pulse. This could be the reason why the mean values of the TP lies closer to each other for RTD Results of the single layer calibration The following could be concluded from the calibration results: 41

57 Chapter 3. Double Electric Discharge calibration 42 ˆ The regression procedure has proven to be accurate, attaining correlation coefficients over ˆ Low bridge supply voltages (under 4V) have a too large NSR, lowering the accuracy of the regression. ˆ RTD temperatures should be taken into account to avoid sensor burn-out. ˆ The error on the TP seems to decrease with increasing voltage levels. The TP itself does not seem to be significantly affected by the voltage level. ˆ The time duration of the pulse does not seem to influence the TP. As long as the time duration is sufficiently small to satisfy the semi-infinite principle, it does not play a great importance. ˆ The pulse amplitude and time duration are directly related to the temperature that the thin film reaches. However, no considerable variation of the thermal product is reached at these temperatures which implies that the thermal product may be considered constant. ˆ Comparing the value of the TP of a used MACOR single layer substrate (0.2500J/ cm 2 /K/ s 1/2 ) to a new sample (0.1850J/cm 2 /K/s 1/2 ), lead us to believe that sensor aging and wear has an influence on the TP. However, no data sheet was found for the new sample, so a difference in material properties compared to the older sample cannot be excluded. ˆ While performing the DED calibration, maximum RTD temperatures reached values of about 240 C. The temperatures that the single layer sensor reaches during engine measurements is about 220 C which implies that an appropriate thermal product has been calibrated for this temperature range.[2] 3.5 Double layer TFG calibration Until now, only the calibration of the single layer TFG sensor has been discussed. However, as the double layer sensor will gain importance due to its wide range of applications, it is important to take a look at the calibration of the double layer sensor. Each substrate in the double layer TFG sensor has its own material properties and thus its own TP, which requires a calibration. The determination of the material properties is not enough to calculate the heat flux though. The thickness of the first layer has a crucial role 42

58 Chapter 3. Double Electric Discharge calibration 43 in the heat flux determination. When the TFG sensor is exposed to a known heat flux, the flux will go through the first layer and cause a temperature rise in the first layer. The temperature at the end of the first layer will be dependent of the thickness of this layer. So, three values need to be determined to calculate the heat flux: the TP of the two layers and the thickness of the first layer. The TP of the first layer can be determined with the DED calibration. To do this, the semi-infinite assumption must be valid. Consider the following equation: T x T s 1% x L and L = 3.16 αt (3.16) Here T x is the temperature at a certain x, T s is the surface temperature of the thin film and L is the substrate thickness. Equation 3.16 implies that the thickness must be 3.16 times the square root of the thermal diffusivity of the substrate multiplied with the time, in order that the temperature at the end of the substrate remains constant. If the thermal diffusivity remains constant, the time duration of the flow will determine the necessary thickness of the substrate. The time duration has already been discussed in section The calibration of the second layer of the double layer sensor is done by using the hot air gun setup [25], as discussed in First, the heat gun is set to appropriate setting. Then a well calibrated single layer TFG sensor is used to determine the heat flux. Additionally, the gas temperature is measured. With the heat flux, gas temperature and surface temperature known, the convection coefficient can be calculated: q = h(t gas T s ) (3.17) T gas is measured by a thermocouple. h is the convection coefficient. If the setting of the heat gun is left unchanged, then the field flow can be assumed constant, as well as the convection coefficient. The next step is to mount a double layer sensor in the heat gun setup without changing the setting of the hot air gun. The convection coefficient can then be considered unchanged. The heat flux can then be calculated with the gas temperature monitored by the thermocouple and by the surface temperature of the double layer sensor. Doorly and Oldfield [24] derived an analytical solution for Fourier s Law for double layer sensor when the sensor is submitted to a constant heat flux: 43

59 Chapter 3. Double Electric Discharge calibration 44 T wall (t) = [ ] 2q wall L t + qwall 1 ρck 1 π ρck2 k 1 ρck 2 (3.18) Where T wall (t) is the temperature recorded at the thin film surface, q wall is the heat flux calculated by equation ρck 1 and ρck 2 are the TPs of the first and second layer respectively and the ratio L/k 1 is the thermal thickness. At this stage, the TP of the second layer and the thermal thickness remain unknown. Figure 3.12 represents the temperature of the thin film T w as a function of the square root of time. Similar to the calibration of the single layer, the start of the temperature rise needs to occur at t = 0. The temperature of the thin fim rises more in the first part of the curve. This is due to insulating property of the substrate (Upilex ), which impairs the heat conduction through the substrate and therefore causes a larger increase in thin film temperature. Once the heat has penetrated the insulating substrate, the conduction takes place though the metal, which allows a better conduction, resulting in a reduced thin film temperature increase. Both slopes are displayed in the figure. Figure 3.12: Thin film temperature of a double layer sensor with substrate [15] The first slope is inversely proportional to the TP of the first layer, the second slope inversely proportional to the TP of the second layer. The time at which the two lines intersect allows the determination of the first layer thickness. The point at which the lines intersect (t 1 )0.5 is also called the switch point and characterizes the thickness of the top layer, the thermal thickness L/k 1 [25]: L k 1 = 2 1 (t π 1) 0.5 ρck1 1 ρck2 1 ( ρck2 ρck1 ) 2 (3.19) Equation 3.19 can be substituted in equation 3.18, which would make the TP of the second layer the only remaining unknown. Once the TP is found using the Thin film temperature trace, the thermal thickness can be determined. 44

60 Chapter 3. Double Electric Discharge calibration 45 The calibration of the double layer sensor contains several steps. Each step will introduce a certain error. First of all, the heat flux needs to be calibrated with a calibrated single layer sensor, which has an error of approximately 4%. Secondly, the thin film temperature time axis needs to be linearized to determine the switch point. In order to achieve a good linearization, the time when the surface temperature starts to rise needs to be determined accurately, otherwise errors will be introduced. Even if this is done with great care, this calibration technique will still hold substantial error. However, there may be another calibration technique possible that is based on this one. This calibration may be performed with the DED setup while the double layer sensor is hold in vacuum. First, the thermal product of the first layer can be calibrated with the DED calibration. Once the thermal product has been determined under the semi-infinite assumption, the surface area of the thin film can be calculated so that corresponding heat flux can be calculated when the power across the thin film is known. For the calibration of the second layer and thermal thickness, the sensor is still placed in the DED setup but now in a vacuum chamber. When a step in heat flux is generated, this heat flux conducts fully through the substrate since there is no fluid and heat loss to surroundings is negligible. The same theory as mentioned above can then be applied in order to determine the second layer s thermal product as well as the thermal thickness. Due to the fact that the heat flux is electrically simulated, the time when the surface temperature starts to rise is more accurate to determine since the time when the heat flux emerges is known very well. Therefore, applying the DED setup instead of the hot air gun may prove more useful to determine the material properties of the double layer sensor. 45

61 Chapter 4 Engine measurements 4.1 CFR setup For performing engine measurements, a CFR-engine (Cooperative Fuel Research) is used. This research engine is designed to withstand severe pressures in order to determine the knocking behavior of different kind of fuels. This makes it possible to perform engine measurements under severe knocking conditions without running the risk for engine breakdown. Due to the presence of holes in the cylinder head, it is possible to mount different sensors. The CFR-engine is a single cylinder four stroke engine which can run on liquid fuels such as gasoline, light alcohols as well as on gaseous fuels such as hydrogen and methane. The fuel is injected in the inlet manifold (port fuel injection) where the air-fuel mixture is ignited in the combustion chamber by the spark plug. The speed of the engine is kept constant by a synchronous motor at 600 RPM. The synchronous motor is first used to start the CFR-engine up until synchronisation is reached. When the combustion engine is fired, the synchronous motor functions as the load. The synchronous motor can also function as a motor which drives the CFR-engine. At this point, the CFR-engine functions as a compressor when no fuel is inserted. The ignition timing, injection timing and injection duration can be regulated with the programmable MoteC M4 Pro ECU. The load is manually varied with the throttle valve. The compression ratio can be varied by adjusting a lever. Figure 4.1 illustrates the section of the CFR engine block with the inlet (1), outlet (3), piston (4), worm (5), cooling tower (6), water jacket (6). 46

62 Chapter 4. Engine measurements 47 Figure 4.1: CFR engine section [2] 47

63 Chapter 4. Engine measurements 48 The cylinder head contains four orifices provided with M18 thread as can be seen in figure 4.3. The orifice on topside (P1) is used to mount the spark plug. The other three orifices are dispersed around the cylinder head (P2, P3 and P4) at the same height. These orifices allow sensors that are flush mounted with the cylinder wall. One of the orifices (P2) is inserted with a Kistler 701A piezo-electric pressure transducer in order to measure the cylinder pressure. The in and outlet pressures are measured with two Kistler 4075A10. The cylinder pressure is measured relatively and is calculated absolute by setting the cylinder pressure equal to the to the inlet pressure when the piston reaches bottom dead centre of the inlet stroke. Another orifice (P4) is provided with a TFG sensor for temperature measurements so that the heat flux can be calculated. Inlet, outlet, oil and cooling water temperatures are measured with K - type thermocouples. The air flow rate is measured with the Bronkhorst F-106BZ mass flow rate sensor which mounted on the suction. The delivered gaseous fuel flow rate is measured with the Bronkhorst F-201AC mass flow sensor and the liquid fuels mass flow rate is determined gravimetrically. The DAQ consists of the PXI developed by National Instruments. The DAQ is triggered by the signal generated by the crank angle encoder. The amount of samples that can be taken can go up to 0.1 sample/crank angle. The most important engine characteristics are listed in table 4.1. Figure 4.2: CFR engine sensor positions [2] 48

64 Chapter 4. Engine measurements 49 engine rev [rpm] 600 bore [mm] 83,06 conrod length [mm] 254 stroke [mm] 114,2 compression ratio [-] variable IVO [ ca] 10 IVC [ ca] 208 EVO [ ca] 501 EVC [ ca] 12 Table 4.1: properties CFR engine [2] MoTeC M4Pro ECU Uitlaattemperatuur 1 Type K-thermokoppel Uitlaattemperatuur 2 Type K-thermokoppel Inlaattemperatuur Type K-thermokoppel Olietemperatuur Type K-thermokoppel Koelwatertemperatuur Type K-thermokoppel Luchtdebiet Bronkhorst F-106BZ Brandstofdebiet Bronkhorst F-2010AC DAQ NI PXI 1050 NI SCC 68 NI SCC 68 Atmosfeersensor Atal Eroding Ribbon Sensor Type T-thermokoppel Nanmac Inlaatdruk Kistler 4075A10 Versterker Kistler 4665 TFG double layer Oxford Uitlaatdruk Kistler 4075A10 Versterker Kistler 4665 Versterker TFG single layer Oxford Cilinderdruk Kistler 701A Versterker Kistler 5064 NI BNC 2120 Hardware-box Heat Flux Microsensor Vatell HFM 7- HFS Heat Flux Microsensor Vatell HFM 7- RTS Versterker Vatell AMP-6 CAM TRIG Krukhoek interpolator COM GmbH type 2614 CAM-encoder Figure 4.3: CFR measurement setup [2] 4.2 TFG sensor setup The thin film sensor is mounted in a orifice of the CFR engine. The wires of the thin film are connected with the input of the HTA3 thin film signal conditioning amplifier. This amplifier is optimized for low noise with low source impedance and has a wide bandwidth 49

65 Chapter 4. Engine measurements 50 and low distortion. The amplifier is matched to low impedances which are typical 20 to 50 Ohm for thin film resistances. The amplifier consists of a low noise preamplifier which has a high frequency boost which counteracts the decreasing thin film gauge frequency response. This amplifier high frequency boost must be subsequently removed in the data processing tools to recover the thin film temperature signal. The HTA3 amplifier has three output channels which can be connected with the DAQ. The first channel is the DC output which has a gain of Therefore, the voltage at the output of the DC channel must be divided by 4.70 in order to obtain the temperatures. The frequency response is flat up to the cut-off frequency, therefore, it is not necessary to deboost. The second output channel is the AC output (low speed). It has a much lower cut off frequency than the DC output and the low frequency gain is approximately Note that the frequency response is flat until the cut-off frequency so that deboosting is not necessary again. The last output channel is the AC output (high speed). It has a low frequency response of 47.0 and has a high frequency boost which must be subsequently removed by digital processing. Note that the AC channels only monitor transient voltages while the DC channel monitors the steady state too. In this case, measurements do not represent high frequency spectrum. The engine runs at 600 RPM meaning that the engine runs at a frequency of 10 Hz, therefore, it can be seen that measurements are performed in the flat region of the frequency response which avoids deboosting. The amplifier delivers a constant current to the thin film which can be regulated from 0 to 20 ma. The current is set by measuring the mean film voltage across the thin film gauge. The thin film mean voltage is set to 250 mv in our case so that sensitivity of the sensor remains high and that ohmic heating of the thin film is avoided. For engine measurements, the DC and AC low output will be used to determine the temperatures of the thin film. Figure 4.4 represents the non processed DC and AC low signals during engine measurements. It can be seen that the AC low signal has a higher variation in voltage than the DC signal due to the higher gain. Also, the AC low signal only measures voltage variations while the DC channel monitors the DC component of the temperature. In order to determine the temperature of the AC low channel, the DC component of the DC channel will be added to AC low output. Figure 4.4 also shows a large amount of noise on the AC low channel. 50

66 Chapter 4. Engine measurements 51 Figure 4.4: Voltage of DC and AC low output channel Figure 4.5 displays the temperatures calculated from the voltages that have been displayed in figure 4.4. It can be seen that the noise on the AC low temperature is still present. Besides the noise, it can be seen that the temperatures for both channels are very similar to each other. Even the DC channel follows the variation in temperature very well. Therefore, the DC channel will be used for processing engine measurements. Figure 4.5: Temperature of DC and AC low output channel 4.3 Validation of TFG sensor In order to perform reliable engine measurements with the single layer sensor, the sensor calibration must be validated. This is done by evaluating the heat flux achieved with the new thermal product. The validation of the sensor will be performed on the CFR engine. 51

67 Chapter 4. Engine measurements 52 Extensive research has already been performed with this engine on a wide range of fuels such as methane, hydrogen, gasoline and methane. During this investigation, heat flux measurements were taken with three types of sensors, namely, the eroding ribbon, HFM and single layer sensor. The eroding ribbon was found too unreliable for further use in engine measurements. The single layer TFG sensor provided equally reliable values for the heat flux as the HFM. However, aging of the sensor had its effect on the measurements as well, causing lowered values of the heat flux. Therefore, the HFM sensor proves to be the most reliable of the three, so this sensor is used as reference for current investigation. To validate the recently calibrated sensor, a reference heat flux measurement taken with the HFM sensor will be used. New data, obtained with the TFG sensor will be compared with the one obtained by the HFM sensor to conclude if the calibration process positively affects the measurements done with the TFG sensor. Out of all the measurements taken, it is necessary to find the most representative heat flux trace over one engine cycle. Due to the fact that cyclic variations occur within a single set of heat flux measurements, certain criteria are introduced to achieve the most reliable heat flux representation. These criteria are displayed in figure 4.6. It displays the minimum, maximum, mean and best fitting cycle of a set of heat flux measurements. It can be seen that there is a difference in heat flux trace between minimum and maximum cycle due to cyclic variation in the combustion chamber. Therefore, the average of all the cycles will be taken, which is indicated as mean. The best fit cycle, indicated as best, is the cycle which has the highest correlation with the mean cycle. This cycle will be used to represent the heat flux trace over the entire engine cycle. Therefore, when engine measurements are discussed in this chapter, the best cycle will be basis for the discussion, except if mentioned otherwise. 52

68 Chapter 4. Engine measurements 53 Figure 4.6: Heat flux traces for determining best cycle A first set of measurements will be performed in fired conditions with gasoline as fuel. The reference measurement was taken at a compression ratio of 9. The throttle position has been kept constant and ignition was held on -4 and 0 BTDC, while λ, the air-fuel ratio, was varied. Figure 4.7 plots the observed heat flux traces for two values of λ obtained by the HFM sensor. The traces have been obtained while the sensor was fixed in location P3 in the CFR engine. The moment when ignition starts can be seen in figure 4.7, however, the ignition timing does not differ that much for both cases. The dominant effect on heat flux will be the variation in air-to-fuel equivalence ratio. Two heat flux traces were evaluated, one of a lean mixture and one of a rich mixture. The lean mixture trace shows a slow initial phase of combustion and has a longer duration than the rich mixture. A drop in heat flux is even noticeable since the expansion occurs at the moment when the lean mixture is ignited. The peak in heat flux occurs during the flame passage over the sensor position. The lean mixture has the lowest peak in heat flux, which starts to rise later due to the slower burning velocity. 53

69 Chapter 4. Engine measurements 54 Figure 4.7: Heat flux for variation on λ obtained by HFM sensor This measurement, taken with the HFM sensor, will be repeated with the single layer sensor. However, validation requires the exact same engine operating conditions. This is currently not possible anymore. First, only position P4 could be used to mount the sensor while reference measurements have been performed at location P3. Research [7] has already indicated that sensor allocation in the CFR engine has its influence on heat flux. It was shown that peak heat flux occurs at the moment that the flame passes over the sensor. For different sensor locations, this results in different heat flux traces. Therefore, directly relating the current measured heat flux traces to these at the previous conditions is not entirely correct. However, the total cycle heat loss should be the same since the total amount of heat that is lost must be the same, independent of the sensor location. Also, the CFR setup has been revised and an EGR and inline heater have been added. Therefore, throttle position cannot be considered anymore as reference, instead the air flow rate will now be used as reference. The measurements performed with the single layer sensor are taken at operating points close to the ones used during HFM measurements. In this case, a completely new single layer sensor is used. Therefore, heat fluxes calculated with the bulk material TP and calibrated TP will be compared. Table 4.2 summarizes the operating conditions. The ignition timing in the actual measurements is limited to avoid too high exhaust temperatures. Also, severe knocking occurs when the ignition timing is further delayed. Therefore, ignition is advanced compared to the reference measurement. 54

70 Chapter 4. Engine measurements 55 Operating point Fuel CR Air flow [kg/h] λ IT [ BTDC] Reference (HFM) gasoline Measurement (TFG) gasoline Table 4.2: Operating conditions reference 1 Figure 4.8 represents the mean and best cycle of the measurements performed with the single layer sensor. It can be seen that the averaged cycles is more representative for heat flux measurements since the best cycle has a large noise component. Besides the noise, it can be seen that the best cycle lies close to the averaged trace. Therefore, the averaged cycle will be used to eliminate the noise in this section. Figure 4.8: Heat flux for mean and best cycle Figure 4.9 displays the heat flux calculated from the single layer sensor with two values for the thermal product. The first value, 2050J/cm 2 /K/s 1/2 is the value supplied by the manufacturer while the second one, 2500J/cm 2 /K/s 1/2, is the calibrated one. These two heat flux traces are compared with the heat flux obtained by the HFM sensor. First, it can be seen that the traces obtained with the single layer sensor have the same trend. The reason for this is that the thermal product is considered constant and that the steady state heat flux is the same for both cases. This implies that a change in thermal product only influences the amplitude of the heat flux. The amplitude of the heat flux reaches the 55

71 Chapter 4. Engine measurements 56 highest values for the recently calibrated value because the transient part of the heat flux is proportional with the thermal product. The heat flux calculated with the calibrated thermal product reaches almost the same peak heat flux as for the HFM sensor. The time difference between these two peaks is due to the location of the sensor. The flame reaches P3 later than P4 because the spark plug, positioned in P1, is located closer to P4 than P3. This can clearly be seen in figure 4.9. However, the peak heat flux is higher for the HFM sensor than for the single layer sensor. Normally, the heat flux should be lower in case of the HFM sensor, due to the fact that the flame needs more time to reach the P3 resulting in a cooler flame which would exchange less heat with the cylinder walls. Besides the sensor position, the ignition timing is advanced and the fuel gas mixture is richer when the single layer sensor is used. This should lead to a larger heat flux. However, this is not the case: the compression ratio in the case of HFM sensor is a bit larger which leads to higher peak pressures and temperatures. These higher temperatures contribute to a larger heat flux. Figure 4.9: Heat flux for HFM and TFG sensor Figure 4.10 plots the heat release rate (HRR) for the obtained data from the HFM and TFG sensors. It can be seen that the HRR increases earlier for the TFG measurement than for the HFM. This is due to the fact that the fuel is ignited earlier during TFG measurements. Also, the peak HRR is reached faster and reaches a higher value for the TFG due to the higher burning velocity caused by the richer air-fuel mixture and the earlier ignition. Therefore, more heat is converted to work which implies that the heat loss to 56

72 Chapter 4. Engine measurements 57 cylinder walls is lower during the TFG measurements than during the HFM measurements. This does not say any imply which value of thermal product is correct in this case. Figure 4.10: Heat release rate for HFM and TFG sensor Another operating point will be set to further investigate the variation between HFM and TFG sensor. The operation point for reference and actual measurement are displayed in table 4.3. Operating point Fuel CR Air flow [kg/h] λ IT [ BTDC] Reference (HFM) gasoline Measurement (TFG) gasoline Table 4.3: Operating conditions reference 2 Figure 4.11 displays the heat flux as a function of crank angle for the HFM and TFG sensor when two thermal products are considered at the second set of operating conditions. Again the value from the bulk supplier (2050J/cm 2 /K/s 1/2 ) and the calibrated one (2500J/cm 2 /K/s 1/2 ) are used for the analysis. The same conclusions can be made as with the previous operation conditions. Peak heat flux is reached faster due to the sensor location. Compared with results found by Demuynck [7], peak heat fluxes for the TFG sensor are lower than for the HFM sensor. Figure 4.12 shows the heat release rate as a function of crank angle where it can be seen that the rise in HRR occurs sooner for the 57

73 Chapter 4. Engine measurements 58 TFG and it reaches a higher peak value. Figure 4.11: Heat flux for HFM and TFG sensor Figure 4.12: Heat release rate for HFM and TFG sensor From these measurements we can conclude that, to accurately compare the HFM sensor to the TFG sensor, they need to be operated at the exact same conditions. A small variation in operating conditions immediately leads to a change in HRR, therefore changing the 58

74 Chapter 4. Engine measurements 59 heat flux. However, the same trends are observed at the two operating conditions. The conditions for the HFM measurements featured a slightly higher CR, a leaner mixture and a more delayed ignition timing than the measurements obtained with the TFG sensor. The HRR indicated that burning velocity and peak HRR are lower for the HFM measurements. This might explain why heat fluxes are higher in these cases. The peak heat flux is reached faster for the TFG sensor. The peak itself is smaller than the one obtained by the HFM sensor, independent of the thermal product. However, the recently calibrated single layer sensor has an overlap of peak heat flux with the HFM sensor as can been seen in figure This was not validated in previous research. Figure 4.13: Error level on peak heat flux for HFM and TFG sensor 4.4 CFR Heat flux measurements The results in this chapter so far, showed that there is a clear improvement in the measurements that were processed with the most recent calibrated TP compared to those processed with the TP of the bulk material. The sensor could now be used to investigate the influence of different engine parameters. In recent years, parameters such as compression ratio, ignition timing, air-to-fuel ratio and throttle position have been examined at Ghent University [2, 7]. This was done for a variety of fuels on the CFR engine. Since then, the CFR engine has been modified, as mentioned before. In the following section, we will shortly investigate the effects of these modifications on the heat flux, thus demonstrating the practical use of a well-calibrated TFG sensor. 59

75 Chapter 4. Engine measurements EGR The first modification that will be investigated is the Exhaust Gas Recirculation. The EGR is provided with a control valve, which allows us to regulate the amount of EGR. Measurements will first be taken at different EGR levels while keeping the fuel flow rate constant. Next, the flow rate will be varied while keeping the amount of EGR the same. During these test, the coefficient of variation (COV) of the imep (indicated mean effective pressure) during 100 engine cycles will be monitored. COVs that are too high must be avoided, because they will not permit us to detect any trends. EGR variation The operating conditions are shown in table 4.4. By varying the EGR level, the λ will be influenced. It can be seen that the COV is rather high for all the operating points. Increasing the EGR level will increase the COV. The EGR has thus been limited to 7%. Operating point CR TP Air flow [kg/h] Fuel flow [kg/h] λ EGR [%] IT [ BTDC] W i [J] COV [%] Table 4.4: Operating conditions reference 2 Figure 4.14 displays the heat flux traces of all three operating conditions. Note that the traces represented in the figure are not the best cycle, like the previous investigation, but they are the mean cycle. This is done because due to the high COV. The highest peak flux is reached for the zero EGR level. This peak is also reached earlier in the case of zero EGR, implying that the combustion takes place at a faster rate. For 7% EGR, the burning velocity is noticeably lower, as is the heat flux peak. This is due to the increasing specific heat capacity C. A higher C will lower the temperature of attained by the mixture. The wall temperatures are plotted in figure 4.15 while the gas temperatures are plotted in figure It can be seen that increasing the EGR percentage results in lower wall temperate increase, therefore, lowering the transient heat flux, because the wall temperature functions as driving temperature for calculating the transient heat flux. The maximum wall temperature increases is given in table 4.5. The gas enters the engine at a higher temperature when EGR is introduced. This due the fact that EGR enters the inlet manifold at a temperature of 35 C while the ambient air enters there at a temperature of 25 C. This results in the largest inlet temperature for 7 % EGR. When combustion 60

76 Chapter 4. Engine measurements 61 starts, it can be seen that the smallest gas temperature increase occurs for an EGR level of 7% due to the large specific heat capacity C. However, the difference between 0% and 1% EGR is very small. In figure 4.16 we can even see that the temperature reaches a higher maximum for 1% than for 0% EGR. We attribute that to a trade off between an increased inlet temperature and a C that has not risen enough yet to lower the temperature. Figure 4.14: Heat flux for variation on EGR Figure 4.15: Wall temperature for variation on EGR 61

77 Chapter 4. Engine measurements 62 Figure 4.16: Gas temperature for variation on EGR Amount EGR [%] Maximum temperature increase [ C] Table 4.5: Wall temperature increase with EGR variation Figure 4.17 displays the heat release rate for the three operating conditions. The highest heat release rate is achieved when no EGR is introduced into the combustion chamber. Increasing the EGR level will result in a lower burning velocity and a lower amount of heat being released. A larger specific heat capacity of the mixture, which lowers the overall temperature (see figure 4.16, will lower the burning velocity. 62

78 Chapter 4. Engine measurements 63 Figure 4.17: Heat release rate for variation on EGR Fuel flow variation Now, the effect of changing the fuel flow rate will be examined. Two different flow rates will be compared while the other parameters are kept constant. Consequently, a change in air-to-flow ratio will be noticed. Table 4.6 represents the operating conditions of these measurements. Notice that the COV is higher for stochiometric mixtures then for a rich mixture. In the second experiment, two operating conditions are compared to each other. In this configuration, the fuel flow rate has been varied while maintaining a constant amount of EGR introduced into the combustion chamber. Consequently, a change in air to fuel ratio will be noticed. Table 4.6 displays the operating conditions for this set of measurements. Again, it can be seen that the COV is high for both cases. However, when the engine is run under stochiometric conditions with EGR, the COV is higher than for a rich mixture. This indicates that amount of EGR influences the fuel air interaction negatively. Operating point CR TP Air flow [kg/h] Fuel flow λ EGR [%] IT [ BTDC] W i [J] COV [%] Table 4.6: Operating conditions with constant EGR and variation on fuel flow rate Figure 4.18 displays the heat flux traces for the two different operating conditions. It can be seen that the richer mixture achieves a slightly larger peak heat flux. However this peak occurs at a later instant. At the moment when ignition is initiated, the heat flux increases more rapidly for the stochiometric mixture due to the fact that the initial specific 63

79 Chapter 4. Engine measurements 64 heat capacity is lower than the other mixture. However, at crank angle of 18 ATDC (the TDC is located at 360 ) the heat flux rises more rapidly for the rich mixture. Figure 4.19 represents the wall temperature as a function of crank angle. The wall temperature has a more significant increase for the stochiometric combustion at 10 ATDC while this occurs at 17 ATDC for the rich combustion. This explains the difference between the heat flux traces because the transient heat flux is proportional with the recorded wall temperature. However, it is difficult to see which mixture has the highest burning velocity. A closer look to the heat release rate will explain more about the burning velocity. The HHR is plotted as a function of the crank angle which as shown in figure It can be seen that the HRR traces for both operating conditions follow each other very well. Therefore, the burning velocities of both operating conditions can be considered the same. The richer mixture reaches the highest amount of HRR since more energy is added to the system. Figure 4.18: Heat release rate for variation on fuel flow rate 64

80 Chapter 4. Engine measurements 65 Figure 4.19: Wall temperature for variation on fuel flow rate Figure 4.20: Heat release rate for variation on fuel flow rate Figure 4.21 represents the gas temperature for both operating conditions. Initial after ignition, the temperature rises more rapidly for the stochiometric mixture due the smaller heat capacity. However, at 35 ATDC the temperature reached by the rich mixture surpasses the stochiometric mixture due to the larger amount of energy added to the system. Peak temperatures do not differ that much from each other and occur at the same instant. 65

81 Chapter 4. Engine measurements 66 Figure 4.21: Gas temperature for variation on fuel flow rate So, when a constant EGR level is applied, variations of air-to-fuel ratio will not noticeably influence the burning velocity or the heat flux Inlet temperature The second modification was the installation of an inlet heater. This makes it possible to change the inlet temperature. Varying the inlet temperature will change the density of the inlet air, thus changing the air-to-fuel ratio. The other parameters are again kept constant. The operating points are listed in table 4.7. Operating point CR TP λ EGR [%] Inlet temperature [ C] IT [ BTDC] W i [J] COV [%] Table 4.7: Operating conditions with variation on inlet temperature 66

82 Chapter 4. Engine measurements 67 Figure 4.22: pressure vs crank angle for variation on inlet temperature By increasing the inlet temperature, the mixture becomes richer, while the amount of fuel delivered to the system remains the same. The increasing inlet temperature, increases the gas temperature reached after compression as can be seen in figure Furthermore, the higher inlet temperatures causes higher combustion temperatures. This, increases the thermal efficiency and transfers more work to the piston which can be seen by the higher imep (see figure 4.22). Figure 4.23: Gas temperature for variation on inlet temperature Figure 4.24 displays the wall temperature monitored by the TFG sensor. The fuel gas mixture is ignited at 10 BTDC. The maximum reached temperatures occur for the different engine operating conditions at the same moment. This explains why the heat flux, plotted in figure 4.25, reaches its maximum value at almost the same instant for different settings. If we examine the figure more closely, we can see that the peak is advanced by a few crank angles when the inlet temperature is increased, which means that the burning velocity is 67

83 Chapter 4. Engine measurements 68 slightly higher in those cases. This can also been seen in the HRR plot in figure The trace with the highest HRR also displays the fastest drop in HRR, indicating it has the highest burning velocity. Figure 4.24: Wall temperature for different inlet temperature Figure 4.25: Heat flux for different inlet temperatures 68

84 Chapter 4. Engine measurements 69 Figure 4.26: Heat release rate for variation on inlet temperature The imep increases while the fuel flow rate remains constant, indicating a decreasing specific fuel consumption. The total heat flux to the cylinder walls increases when the inlet temperatures is increased while the total heat released, which is the sum of HRR in closed cycle, decreases. The cumulative heat release rate is shown in figure 4.27 where it can be seen that, at the moment that the exhaust valve opens, the cumulative heat release has reached its final value which is equal to the sum of HRR during closed cycle. Figure 4.27: Cumulative heat release rate for variation on inlet temperature It can be concluded, that increasing inlet temperatures contribute to higher peak pressures and temperatures, which in their turn contribute to a higher imep. Peak heat flux and 69

85 Chapter 4. Engine measurements 70 total heat flux also increase when the inlet temperatures are increased, while total heat release decreases. This is, however not a complete investigation of the EGR and inlet heater, but merely serves as an illustration that the single layer TFG sensor is ready to be used in more extensive research. 70

86 Chapter 5 Conclusions and future insights The main focus of this thesis was the development of a calibration procedure for the TFG sensor used at Ghent University. In order to do so, a calibration setup was developed to accurately determine the thermal product of the sensor substrate. This setup could directly be used to find the TP of a single layer sensor and was used in the process of determining the TPs of the double layer sensor. Once this has been done, the sensor can be used in further engine research. The Double Electric Discharge calibration setup is based upon solving Fourier s Law in case of a step function in heat flux. The main advantages of this setup compared to others is that the heat going through the sensor can directly be measured and controlled. The temperature and thus the resistance of the thin film can be monitored and controlled too. Once the setup was build, multiple calibrations at different operating conditions were performed to investigate the influence of the following parameters: Voltage pulse amplitude, Pulse time duration, the resistance of the RTD and the aging and wear of the sensor. The pulse amplitude did not influence the value of the TP, but a higher pulse amplitude did reduce the error on the TP. The time duration did not seem to influence the TP nor the error. The time duration should only be limited to ensure that the semi-infinite principle is still valid. Furthermore, two different RTDs mounted on the same substrate resulted in the same TP. A distinct difference between a new MACOR block and a used one was measured however. The DED calibration is expected to yield the same TP at different operating conditions. A higher voltage level is recommended to reduce the error on the measurements. Finally, care must be taken when repeatedly using a sensor as wear could have an influence. The lowest relative error achieved for the TP was 4.5%, which is comparable to other calibrations performed with different setups [14, 27, 28]. The largest contribution to this error comes from the uncertainty of the fluid properties of glycerin 71

87 Chapter 5. Conclusions and future insights 72 (an error of 4%). The correlation coefficients of the regression done on the data range from 99% to even higher values. After that the sensor was calibrated, it was placed in a test engine. Previous research showed that the results of the heat flux measurements performed with the TFG sensor deviated from the results obtained by using a very accurate HFM sensor [7]. This was due to the aging and wear of the sensor, which changed the thermal properties of the sensor. For this thesis, the TFG sensor was compared once more to the HFM sensor. The TFG measurements were performed with the TP provided by the manufacturer and once with the TP obtained after calibration. Comparing these two set of measurements to the measurements done with the HFM sensor, showed that the newly calibrated TFG sensor performs much better. The results are now very similar to those achieved with the very accurate HFM sensor. The single layer TFG sensor was then used to shortly investigate the effects of the new EGR and inlet heater mounted on the CFR engine, thus demonstrating that the single layer sensor is ready to be used in more extensive research to further develop the GUEST code. The DED setup can still be further developed. A first improvement that should be made, is to isolated the calibration from any noise as much as possible. This noise will influence the regression of the measurement greatly. Secondly, the linearity error introduced by using the current wheatstone bridge can be avoided. It can be corrected during the data processing, but this is a computationally intensive process. A second option is to use a wheatstone bridge that incorporates an extra OP-amp. A detailed discussion can be found in appendix D.4. Each resistor in the bridge is replaced by a potentiometer, that is set to the value of the RTD resistance at ambient conditions. This intensifies the calibration process and calls for balancing the bridge before every calibration. This setup would however avoid the linearity error. We can conclude that the work done during this thesis has improved the accuracy of the TFG sensor and set the basis for a further optimization of heat flux measurements at Ghent University. 72

88 Appendix A Calculations Fourier method A.1 2T Fourier method The 2T-Fourier method relies on the Fourier analysis of two measured temperature signals. These signals form the boundary conditions to solve the one dimensional conduction equation (A.1): T t = T α 2 x 2 (A.1) The Fourier analysis of these temperatures gives: T 1 = B 1 + K n cos(nωt) + G n sin(nωt) n=1 T 2 = B 2 (A.2) (A.3) with: ˆ ˆ B 1, B 2, K n, G n : The coefficients of the Fourier decomposition, where temperature T 2 is assumed to be constant. ω: The natural frequency, [ ] rad s The analytical solution of equation A.1 with boundary conditions A.2 and A.3 is: T = B 1 (B 1 B 2 ) x l depth + e F x [K n cos(nωt F x) + G n sin(nωt F x)] (A.4) n=1 73

89 Appendix A. Calculations Fourier method 74 with: ˆ ˆ l depth : the distance between T 1 and T 2, [m] F: nω 2α, [ ] rad m The heat flux can be determined by using Fourier s conduction law: q = Q A and equation (A.4). The heat flux can be written as: = k dt dx x=0 q = k = k (B 1 B 2 ) X (B 1 B 2 ) X + k + T P F [(K n + G n ) cos(nωt) + ( K n + G n ) sin(nωt)] n=1 n=1 A.2 1T Fourier method (A.5) nω 2 [(K n + G n ) cos(nωt) + ( K n + G n ) sin(nωt)] This method only relies on one surface temperature. The coefficient B 2 from equation (A.4) is then unknown. The gas temperature, determined pressure based, is then used to determine the instant where the heat flux equals to zero. It is then assumed that the gas temperature is equal to the wall temperature. When the heat flux is zero, B 2 remains the only unknown in equation (A.5). B 2 can be determined according to: B 2 = B 1 + l depth F [(K n + G n ) cos(nωt 0 ) + ( K n + G n ) sin(nωt 0 )] n=1 (A.6) The factor l depth is eliminated in equation A.5. 74

90 Appendix B Calculations impulse response FIR-method To determine the impulse response h of the LTI-system, the set non-singular solutions q 1 [n] and T 1 [n] need to be known. When these solutions are known, the following equation is fulfilled: q 1 [n] = h[n] T 1 [n] (B.1) To calculate the impulse response of this equation, the Z-transform is taken from equation (B.1). The convolution operation is therefore transformed into a multiplication: q(z) = H(z) T (z) H(z) = q(z) T (z) (B.2) By definition, the convolution of the impulse response with delta function δ[n] = 1, 0, 0,... results in the impulse response again. Therefore, H(z) = H(z) (z) = q b(z) T (z) (z) (B.3) With (z) the Z-transform of the discrete impulse δ[n]. By taking the inverse Z-transform of equation (B.3) h[n] can be determined. Every sensor that will be used to calculate the heat flux with this calculation method requires a set of functions q 1 [n] and T 1 [n]. These set of functions are calculated according to an one dimensional analytical method decribed by Oldfield [24]. 75

91 Appendix B. Calculations impulse response FIR-method 76 B.1 TFG Single Layer through surface temperature This sensor is modeled according to the semi-infinite assumption where the temperature at a certain depth is assumed constant (figure B.1). Starting from the following partial differential equation: θ t = α 2 θ x 2 (B.4) with: ˆ θ(x, t) = T (x, t) T ss (x): The transient component of the temperature Figure B.1: Model of the TFG single layer [24] The boundary conditions are: k dθ dx x=0 = q k dθ dx x= = 0 (B.5) To solve equation (B.4) with these boundary conditions, the Laplace transform is taken. This way, the partial differential equation is transformed into an ordinary differential equation: With: d 2 Θ(x, s) dx 2 s Θ(x, s) = 0 (B.6) α k dθ(x,s) dx x=0 = L{q} k dθ(x,s) dx x= = 0 (B.7) ˆ L: The Laplace transform-operator 76

92 Appendix B. Calculations impulse response FIR-method 77 ˆ s: The Laplace-variable ˆ Θ(x, s): The Laplace transform of θ(x, t) The general solution of the differential equation becomes: ( Θ(x, s) = A(s) exp x s α ) ( + B(s) exp x ) s α (B.8) After substituting equation (B.8) into the second boundary condition, we obtain B(s) = 0: ( ) s Θ(x, s) = A(s) exp x α Substituting into the first boundary condition gives: (B.9) L{q} = kρc p sθ(0, s) = kρcp sl{θs } (B.10) With: ˆ θ s (t) = T (t) T ss : The transient part of the temperature. When a step in heat flux is initialized on the surface on the instant when t = 0, equation (B.10) becomes: L{θ s,step } = 1 kρcp s 3/2 (B.11) In this case, a step function has been applied and is written as: L{q step } = 1/s in the Laplace domain. Going back to the time domain implies the inverse Laplace transform: θ s,step = 2 π kρcp t (B.12) The set functions to determine the impulse response h[n] is: 0 t < 0 q step (t) = 1 t 0 θ s,step (t) = 2 π kρcp t (B.13) (B.14) 77

93 Designs (des) a filter to convert surface temperature T to heat transfer rate q (T2q) for a two-layer substrate (2l) and gives impulse response (imp) h. Use q = fftfilt(h,t) to convert measured T to q. Appendix B. Calculations impulse response FIR-method 78 [h,shift] = desq2t2limp1(fs,np,rrck1,rrck2,ak1,test) B.2Designs TFG (des) Double a filter to convert Layerheat through transfer rate surface q to surface temperature T (q2t) for a two-layer substrate (2l) and gives impulse response (imp) h. This sensor is modeled according to the semi-infinite assumption where an insulating layer Use T = fftfilt(h,q) to convert measured q to T. lies in between (figure B.2). x = 0 x = a q 1 T 1 1 c 1 k 1 2 c 2 k 2 Thin-film gauge Insulating layer Semiinfinite layer Figure 2 Two layer heat transfer gauge Figure B.2: Model of the TFG double layer [24] The basis functions are those for a step in q 1 (t). In Laplace transformed form, the solution of the heat conduction equations for two layer substrate (Doorly and Oldfield,1987) gives The same manner of the TFG single layer is applied in this case. Equation (B.4) is now considered for the two layers. The boundary conditions s 1 A exp are: 2a T 1 s q 1 s, dθ 1 c k 1 k 1 s 1 1 dx x=0 = q 1 exp s A dθ 2a k 1 1 dx dθ x=a = k 2 2 dx x=a 1 dθ k 2 2 dx (B.15) x= = 0 1 c 1 k 1 2 c 2 k θ 2 1 (a, t) = θ 2 (a, t) k1 where A and the thermal diffusivity 1. 1 c 1 k 1 2 c 2 k c 2 1 In the Laplace domain: s [ ] 3 1 A exp 2a 1 1 For a step in q 1 (t) = u(t), q 1 s, and so 1 T 2 L{q} = 1 A exp( 2a s α 1 s 1 ) k 1 ρ 1 c s. s 1 s [ ]L{θ s } (B.16) 1 + A exp( 2a 1 c s 1 k 1 s α 1 ) 1 A exp 2a 1 With: Expanding the denominator as a power series, and taking the inverse Laplace transform, ˆ A= ρ1 c 1 k 1 ρ 2 c 2 k 2 ρ1 c 1 k 1 + ρ 2 c 2 k 2 ˆ α 1 = k 1 ρ 1 c 1 : the thermal diffusivity of the first layer 6 As with the TFG single layer a step in heat flux is applied at the surface of the sensor. Equation (B.16) becomes: L{θ s,step } = [ ] A exp( 2a s s 3 α 1 ) 2 [ ] (B.17) k1 ρ 1 c 1 1 A exp( 2a s α 1 ) 78

94 Appendix B. Calculations impulse response FIR-method 79 After decomposition into a power series and taking the inverse Laplace transformation, the obtained set of functions for the TFG double layer are: θ s,step (t) = [ 2 t k1 ρ 1 c 1 π + 0 t < 0 q step (t) = 1 t 0 ( ( t 2A n π exp k2 s 4t n=1 (B.18) ) k ( ) )] s 2 erfc ks 2 (B.19) t With: ˆ k s = 2an α1 ˆ a: The thickness of the first layer ˆ erfc the complimentary error-function: erfc(z) = 1 erf(z) = 2 π z e t2 dt B.3 TFG through surface temperature and depth thermocouple temperature It is also possible to calculate the heat flux when the surface and depth thermocouple temperatures are known. The benefit of this method for the TFG double layer is that only the thermal product of the first layer needs to be known. To determine the set non-singular functions, necessary to determine the impulse response, the sensor is assumed to be a superposition of two sensors (see figure B.3). The first one is a differential sensor with known upper and under temperature T 1 T 2 2 and T 1 T 2 2. Besides that, a common mode sensor with T 1+T 2 2 as upper and under temperature is implemented. These two sensors are modeled, based on the solution of the for the TFG double layer (see section B.2). Figure B.3: Model of the TFG double layer [24] For the differential sensor the middle applies (x = a/2) T = 0. This sensor lower layer conducts extremely well, therefore A = 1. For the common mode sensor the middle 79

95 Appendix B. Calculations impulse response FIR-method 80 applies (x = a/2) q = 0. This sensor has an perfectly insulating lower layer, therefore A = +1. These values for A are used to determine the impulse responses h d [n] and h c [n] when a step in heat flux is applied (q d en q c ) on the surface. Through equation (B.17) it can be seen that the thermal product of the second layer is unnecessary. The flux through the surface of the real sensor is equal to the sum of the partial fluxes through both partial sensors: q 1 = q d + q c = h d T 1 T h c T 1 + T 2 2 = h d + h c 2 T 1 + h c h d 2 T 2 = h 1 T 1 + h 2 T 2 (B.20) Therefore: h 1 = h d+h c 2 h 2 = hc h d 2 (B.21) (B.22) B.4 Steady state component of heat flux If the transient heat flux is calculated according to previous mentioned methods, the steady state component of the heat flux needs to be determined. So, this steady state component is always necessary when the transient heat flux is calculated by only using the surface temperature as boundary condition. The steady state heat flux can be determined by three methods. Average gas temperature First, the steady state component can be determined using the gas temperature. This method sets the heat flux equal to zero when the surface temperature of the wall, which is the thin film surface temperature, is equal to the gas temperature. Steady state component of wall temperature Second, the steady state heat flux can be determined by using Fourier s conduction law B.23. The steady state component can be written as: 80

96 Appendix B. Calculations impulse response FIR-method 81 q ss = Q A = k T wall T depth l depth = T surf T depth ak 1 (B.23) where the DC - component of the surface temperature measured by the RTD functions as the wall temperature ( T wall ). Together with the temperature measured by the thermocouple at certain depth (L), the temperature difference can be determined. The ratio of the thermal conductivity and depth of the thermocouple is needed, this inverse of this ratio is ak1 which is the thermal thickness. Averaged wall temperature The last method in order to determine the steady state heat flux is analogue as the method described above. However, instead of using the DC - component of the surface temperature in equation (previous), the mean wall temperature is used. 81

97 Appendix C Error analysis In this chapter, errors are calculated on the quantities that are used for calculations. The absolute error of variable X is indicated as AE X and the relative error as RE X. C.1 Measured quantities C.1.1 Ambient conditions The ambient conditions are measured with a sensor of manufacturer ATAL. The absolute errors on ambient temperature, ambient pressure and relative humidity are listed in table C.1 Table C.1: Absolute errors for ambient conditions ATAL sensor Variable X AE X Unit T amb 0, 4 C p amb 130 P a RV 2,5 % C.1.2 Engine speed The engine speed is measured with a crank angle interpolator type 2614 of the manufacturer COM GmbH. In table C.2, the absolute error on the engine speed is given. C.1.3 Pressures The in and outlet pressure are measured with the Kistler 4075A10 sensor. The signal is amplified with the Kistler 4665 amplifier. The cylinder pressure is measured with a Kistler 82

98 Appendix C. Error analysis 83 Table C.2: Absolute error on the measured engine speed Variable X AE X Unit N 6 rpm 701A pressure sensor. The signal is again amplified with the Kistler 5064 amplifier. The amplified pressure signals are read by the PXI-6143-module of National Instruments. The errors of this equipment are summarized in table C.3. The errors introduced by the Table C.3: Absolute en relative errors for measurement equipment Variable X AE X RE X [%] Unit Kistler 4075A10 0, 03 - bar Kistler 701A - 1 bar Kistler , 1 Kistler , 1 PXI , 5 - mv pressure signal amplifiers and the PXI-6143 are negligible in comparison with the error of the pressure sensor itself. The final errors on the pressure signals are listed in table C.4. Table C.4: Absolute en relative errors for measured pressure signals Variable X AE X RE X [%] Unit p inlet 0, 03 - bar p outlet 0, 03 - bar p cylinder - 1 bar C.1.4 Temperatures The inlet, the two outlet temperatures, the oil temperature and the cool water temperature are all measured with type K thermocouples and read with the PXI-6224-module of National Instruments. The error on these temperatures are listed in table C.5. 83

99 Appendix C. Error analysis 84 Table C.5: Absolute errors on the acquired temperatures Variable X AE X Unit T type K 5 C C.1.5 Flow rates The gaseous fuel flow rates are measured with a Bronkhorst F-2010AC mass flow rate sensor. The liquid fuel flow rate is determined gravimetric by measuring the consumed mass of fuel over a certain time period. The air flow rate is measured with the Bronkhorst F-106BZ flow rate sensor. In table C.6, the errors on the volumetric rates are given. The Table C.6: Absolute errors for volumetric flow rate of gaseous fuels Variable X AE X Unit Q lair 0, 2 Nm 3 /h Q methane 0, 036 Nm 3 /h Q hydrogen 0, 047 Nm 3 /h mass flow rate of liquid fuels is calculated as ṁ liquid = m t (C.1) The absolute error on the mass flow rate is therefore, AEṁliquid = (AE m ) 2 + m ( AE t t ) 2 m t (C.2) The errors on the measured time interal t and the measured fuel mass m are listed in table C.7. This calculation leads to a relative error on the fuel mass of maximum 2% when the mass fuel rate is monitored over an interval of 180 s. Table C.7: Absolute errors for the calculation of liquid fuel mass rate Variable X AE X RE X [%] Unit m 1 - g t 1 - s ṁ methanol - 2 kg s 84

100 Appendix C. Error analysis 85 C.2 Calculated quantities To obtain the error on a calculated value, an error analysis must be performed. analysis is based on the merit of Taylor. A function f, dependent on variables a, b en c, the absolute error can be obtained as: ( f ) 2 ( ) f 2 ( ) f 2 AE f = a AE a + b AE b + c AE c (C.3) If no analytical expression is available of a function f, the derivatives in the above equation This may be approximated by an experimental sensitivity analysis. C.2.6 will be dedicated to this analysis. The relative error is obtained by taking the ratio of the absolute error to its actual value: RE f = AE f f (C.4) In the next sections, a representative value of the relative error on methane based measurements, will be given. Details of the operating condition are listed in table reftab:vgl-q-wp. W i [J] Fuel ignition timing [ CA BTDC] Throttle position [ ] λ CR 290 Methane , 3 9 Table C.8: operating condition C.2.1 Mass in cylinder The total trapped mass in the cylinder is obtained by taking the sum of the charge that is sucked into the cylinder and the rest gases that are still present when the exhaust valve closes. m mixture = m air + m fuel + m rest (C.5) Here, m air = 2ṁ air 60 N m fuel = 2ṁ fuel 60 N p cylv cyl m rest = R rest T outlet (C.6) (C.7) (C.8) 85

101 Appendix C. Error analysis 86 m rest is evaluated when the exhaust valve closes.the relative error of these separate components are: RE mair = REN 2 + RE2 ṁ air RE mfuel = REN 2 + RE2 ṁ fuel RE mrest = REp 2 cyl + RET 2 exhaust + RER 2 rest (C.9) (C.10) (C.11) The relative error of the total mass in the cylinder is RE mmixture = RE 2 m air + RE 2 m fuel + RE 2 m rest (C.12) These calculations lead to an relative 3, 13% for the mixture mass in the engine. C.2.2 Air/fuel ratio and air factor The air/fuel ratio is given by The relative error can be calculated as: RE afr = afr = m air m fuel RE 2 m air + RE 2 m fuel (C.13) (C.14) The air factor λ is calculated as λ = afr afr stochiometric (C.15) The error on the ratio can be calculated as RE λ = RE 2 afr + RE2 afr stochiometric (C.16) Since afr stochiometric is fixed for a certain fuel, the relative error on λ will be the same as the relative error on afr: RE λ = RE afr (C.17) This calculation leads to an relative error of 0, 5% on the air/fuel ratio. C.2.3 Specific gas constant At fired operation, the specific gas constant R inlet of the sucked gas mixture is calculated as: R inlet = afr (afr + 1) R 1 air + (afr + 1) R fuel (C.18) 86

102 Appendix C. Error analysis 87 If the error on the specific heat constant of air an fuel is neglected, the error can be determined accordingly AE Rinlet = (R air R fuel ) 2 AE afr (C.19) Due to remaining rest gases, the value of the specific gas constant of the mixture will differ from the one of the fresh sucked mixture. The addition on the absolute error is negligible. Therefore, AE Rmixture = AE Rinlet This results in a relative error of 7, 6% for the specific gas constant of the mixture. (C.20) C.2.4 Gas temperature The gas temperature of the mixture can be calculated by the equation of state: T gas = p cyl V cyl R mixture m mixture (C.21) The error on the cylinder volume is negligible in comparison with the other errors. The relative error on the gas temperature is calculated as: RE Tgas = RE 2 p cyl + RE 2 R mixture + RE 2 m mixture This calculation leads to a relative error of 8, 3% on the gas temperature. (C.22) C.2.5 Error analysis calibration TFGs The calibration has been performed in the linear temperature resistance region, therefore the resistance can be written as a function of temperature: R = a T + b (C.23) The coefficients a and b are calculated according to a least squares method. The absolute error can be calculated on the coefficients according to: AE a = AE R N (C.24) AE b = AE R (Tj ) 2 N is the amount of data points and en AE R are calculated as: (C.25) = N x 2 ( x ) 2 (C.26) 87

103 Appendix C. Error analysis 88 AE R = The value of α 0 can be calculated as: 1 (Rj b a T j ) N 2 2 (C.27) α 0 = a b + a T 0 (C.28) The absolute error of α 0 is then given as: b AE α0 = 2 (AE a ) 2 + a 2 (AE b ) 2 + a 4 (AE T0 ) 2 (b + a T 0 ) 4 (C.29) C.2.6 surface temperature, flux and convection coefficients Surface temperature The surface temperature of the TFG single layer is calculated as T w = T T F GS = V T F GS G T F GS α 0 V 0 + T atm (C.30) The absolute error becomes: AE Tw = (AEVT F GS V T F GS ) 2 ( ) 2 AEGT + F GS + G T F GS ( ) 2 ( AEα0 AEV0 + α 0 V 0 ) 2 ( ) G T F GS α 0 V AE Tamb V T F GS V T F GS G T F GS α 0 V 0 (C.31) This calculation leads to relative error of 4, 6% on the surface temperature. Transient part of heat flux - 1T FIR-method The transient part of the heat flux is calculated with the 1T FIR-method. This translates itself in Matlab with the function fftfilt-commando: q trans = fftfilt(h, T w ) (C.32) The flux is dependent of the impulse response h of the 1T FIR-method and the surface temperature T w of the sensor. variables with the resulting flux. absolute error, which can be written as: AE qtrans = There is no literal function available that relates these A sensitivity analysis will be used to determine the ( qtrans T w AE Tw ) 2 ( ) 2 qtrans + h AE h (C.33) The impulse response h is only dependent on the thermal properties of the sensor. In case of the TFG single layer, this is the thermal product of MACOR. Then: AE qtrans = ( qtrans T w AE Tw 88 ) 2 ( ) 2 qtrans + T P AE T P (C.34)

104 Appendix C. Error analysis 89 Since, the partial derivatives in equation (C.34) cannot be determined explicitly, their values must be estimated on the basis of a measurement. The DED calibration was used for applying different heat flux levels. It was shown that these had no effect on the change of TP. Determination on the influence of temperature is explained in the next steps: 1. The flux is calculated on the basis of a measured temperature signal T orig and the value for the thermal prodcut T P orig of 2050J/m 2.K.s 1/2. 2. On the resulting flux were some recognizable points (eg. peak flux) chosen. The flux q orig is noted in these points. 3. The variable, temperature is varied 0, 1%, 0, 01% en 0, 001% resulting in T var. The resulting flux q var is noted again for the previous chosen points. 4. For every variation of the variable, the ratio can be calculated q orig q var T orig T var. Note that this is an approximation (C.34). For qtrans T opp we obtain a temperature dependent trace: Transient heat flux - Fourier method in equation (A.5): q trans = T P n=1 q trans T opp = 7, 2174e 0,112 T opp (C.35) The transient part of the heat flux is given nω 2 [(K n + G n ) cos(nωt) + ( K n + G n ) sin(nωt)] It is obvious that the partial derivatives are not easily determined of equation (C.34). Therefore, a sensitivity analysis must be performed. The transient part of the heat flux is only dependent on the temperature since the TP may be considered constant which has been proven with the DED calibration. Voor qtrans T w bekomen we: q trans T w = 0, 62 (C.36) For qtrans T P we obtain: Steady state component flux the steady state part of the flux can be calculated as: The absolute error is: (AETw ) 2 AE qss = + ak 1 q ss = T w T depth ak 1 ( AETdepth ak 1 (C.37) ) 2 ( ) ( Tw + T depth )AE 2 ak1 + (C.38) ak

105 Appendix C. Error analysis 90 Total flux is given by: The total flux, which is the sum of the transient and the steady state part, q tot = q trans + q ss (C.39) The absolute error is: AE qtot = AE 2 q trans + AE 2 q ss (C.40) In table C.9, the errors are listed for different calculation methods on the peak heat flux. Table C.9: Absolute en relative error for flux calculations TFG single layer Variable X RE X [%] AE X Unit V V G T F GS V T F GS - 2, V T depth - 0, 5 C J T P 4, 2 - m 2.K.s 1 2 m ak K W W q totf IR 1, 2 - cm 2 W q totf OUR 8, 8 - cm 2 C.2.7 Convection coefficient For every sensor, the convection coefficient can be calculated as: q h = T g T w (C.41) The error on the temperature difference T between gas and wall can be written as: AE T = AET 2 g + AET 2 w (C.42) The error can be calculated as: RE h = RE 2 q + RE 2 T (C.43) The relative errors are listed in table C.10 for different calculation methods. Table C.10: Relative errors for convection coefficients Variable X RE X [%] Unit h T F GF IR 12, 83 W m 2 K h T F GF OUR 20, 29 W m 2 K 90

106 Appendix C. Error analysis 91 C.3 Error analysis on the DED setup To calculate the error on the thermal product, a proper analysis should be made. Generally the absolute error of a function f that depends on the variables a,b and c can be calculated as: AE f = ( ) δs 2 ( ) δs 2 ( ) δs 2 δa AE a + δb AE b + δc AE c (C.44) The relative error can be calculated as the ratio of the absolute error to the function itself: RE f = AE f f (C.45) To determine the error on the TP, we need to determine the error on the out of balance voltage. This voltage is given by: V 0 = V B 4 [ R R + R 2 ] (C.46) Where V 0 represents the out of balance voltage, V B the bridge supply voltage which is generated by the data acquisition which has an absolute error of 2µV. R 1,R 2,R 3 and R 4 are the resistors of the bridge. R 2 is the thin film sensor and functions as the independent variable in this case. Two resistors have a fixed value and a third is the potentiometer necessary to balance the bridge. These three resistors have a relative error of 1%, so they do not influence the error analysis. Their error is the variation of the actual value, supplied by the data sheet. The bridge can be balanced accurately up to 100 µv. Therefore the absolute error of the out of balance voltage is 100 µv. The thermal product is calculated according to: ρck = ρckglyc ( ) V ( t ) air V t glyc 1 (C.47) And can be written as: ρckglyc ρck = (b air ) 1 (C.48) (b glyc) Where b air and b glyc are the slopes of the linearized out of balance voltage when regression is performed. The error on these slopes can be written as: 91

107 Appendix C. Error analysis 92 AE b = 1 N 2 The absolute error on the TP can be written as: N i=1 (T j av j b) 2 N i=1 x2 ( N i=1 x)2 N (C.49) AE f = (δt ) P 2 ( ) δt P 2 ( ) δt P 2 AE air + AE bglyc + AE T Pglyc (C.50) δb air δb glyc δt P glyc ( AE f = T P glycb glyc b air b glyc AE bair ) 2 ( ) ( T Pglyc b 2 air + AE bglyc + b air b glyc 1 b air b glyc 1 AE T P glyc ) 2 (C.51) Each successful regression will have a correlation coefficient that is 99% or higher. Therefore, the error on the slopes of the regression are very low. The relative error of glycerin is 4% [18]. The average relative error of the TP is 4.5%, which is comparable to values achieved with other setups [14, 27, 28]. 92

108 Appendix D Double Electric Discharge calibration appendix The Double Electric Discharge calibration is a tool for determining the thermal product of the single layer sensor. This calibration is performed in air and fluid, with known thermal properties, while a voltage pulse is sent to the RTD which causes ohmic heating. The RTD which is incorporated in a Wheatstone bridge will cause an out of balance voltage related to its changing resistance when ohmic heating occurs. A regression will be performed on the out of balance voltage because the slope of each regression is needed to calculate the thermal product. This text will explain the setup itself, the calibration process and the data processing to acquire the thermal product. D.1 DED setup The setup consists of a Wheatstone bridge where its input is connected to the DAQ, through an electronic circuit as can be seen in figure 1. This electronic circuit functions as a voltage follower. The voltage follower separates the DAQ from the load to protect the DAQ from high currents. Secondly, The DAQ can only deliver 5 ma which too low for the load which makes the voltage follower necessary. The follower supplies the voltage to bridge which is the same voltage set by the DAQ and sets the current as a function of the load. The voltage follower consists of the OP amp (AD741) and NPN transistor (2N1711). The NPN is necessary to deliver the high currents. More details about these components can be found in the datasheet. The Wheatstone bridge consists of 4 resistors as can be seen in figure 1. Rx is the RTD of the single layer sensor. R1 is the potentiometer which is the controllable resistance to balance the bridge and R2 and R3 are fixed resistances as can be seen in figure 2. Details of the resistors can be found in the datasheets. The DAQ 93

109 Appendix D. Double Electric Discharge calibration appendix 94 is the PXI-6251 which can deliver voltages from - 10 to 10 V. The DAQ has 8 analogue input channels and 2 analogue output channels. One of the analogue output channels is used to generate the signal that is sent to the bridge as can be seen in figure 3.3. Three analogue input channels are necessary to perform measurements. First, the out of balance voltage of the bridge will be recorded in order to acquire the data that is necessary for the digital signal processing as can be seen in figure D.1. Also, the voltage across the RTD is measured and a shunt resistor is placed in series with the RTD so that the resistance of the RTD is known. The voltage across the shunt resistor is measured since the DAQ only can acquire voltages. Details about the DAQ can be found in the datasheet. Figure D.1: The DED setup Figure D.2: The potentiometer Figure D.3: The fixed resistors 94

110 Appendix D. Double Electric Discharge calibration appendix 95 D.2 DED calibration process Once the setup is complete, the calibration process can begin. The calibration is performed with the program Labview Signal Express. This program is compatible with the DAQ and signals can be generated and acquired on command. First, the bridge needs to be balanced before sending a voltage pulse to it so that the out of balance voltage remains zero until the bridge sees the pulse. This process is always performed carefully and after each calibration, balancing of the bridge must be performed again. The initial voltage that is sent to the bridge may vary from 0 to 1 V in order to avoid ohmic heating of the RTD, this voltage range has been derived with the ohmic heating test. We start by clicking the Labiew Signal Express icon which can be seen in figure D.4. After that the program is opened, start an empty project to open the workspace. Figure D.4: Signal express icon First, we want to initialize the signals that we wish to generate and acquire. We need to acquire three signals, namely the out of balance voltage, the shunt voltage and the voltage across the RTD. The shunt voltage and the voltage across the RTD are necessary to calculate the RTD resistance. To do this, click on the icon Add Signals. Then click Add Step, Acquire Signals, Analog Input and finally Voltage. Then a screen will appear which can be seen in figure D.5, here the three input channels must be chosen, each analog input corresponds with a BNC plug from the DAQ panel. Once the channels are highlighted, press Ok. A screen appears were we can select the amount of samples and sample rate as can be seen in figure D.6. The sample rate should be chosen high enough since the voltage variations occur at small time intervals. Choose a sample rate higher than Hz. The amount of samples can be set as desired, when the program is run 95

111 Appendix D. Double Electric Discharge calibration appendix 96 continuously, this has no meaning. When the program is run once, this will determine the amount of samples. When this procedure is done, return to Data View, then add two more displays via Add Display and drag the three input signals to a separate display. Figure D.5: choose analog input channel 96

112 Appendix D. Double Electric Discharge calibration appendix 97 Figure D.6: choose amount of samples and sample rate Now that the inputs are defined, the outputs can be defined. First we need to calibrate the Wheatstone bridge. Therefore, a constant DC signal must be generated to balance the bridge. Two steps need to be done here, first we need to create the signal, then we need to generate this signal to a desired output channel. We start by clicking Add Step followed by Create Analog Signal, then a screen appears which can be seen in figure D.7. In the box Signal type the waveform needs to switched to DC signal. The amplitude can be modified in box Offset, here the amplitude may be set from 0 to 1 V as already explained, in this example 300 mv has been chosen. The other parameters may stay default. 97

113 Appendix D. Double Electric Discharge calibration appendix 98 Figure D.7: Signal express output signal window Then the output signal needs to be generated, this is done by clicking Add Step followed by Generate Signals, DAQmx Generate, Analog Output, Voltage. A similar screen appears as when signals are acquired, choose the appropriate output channel. Note that the appropriate PXI slot is connected with the BNC panel, otherwise, Signal Express will not be able to generate output signals. Every signal is now initialized, the final step is to run to program. This done by clicking on the arrow besides the Run icon as can be seen in figure D.8. Click on Run Continuously, otherwise, the program will run once which is the time corresponding with the amount of samples. In this case, we want to calibrate the bridge properly, therefore, the program needs to run the whole time. The out of balance voltage can be monitored in one of the displays. By varying the resistance of the potentiometer, the bridge can be balanced. The limits of the vertical axis can be set to proper value, close to zero. The resolution of this calibration can be set 100 µv, so that the bridge can be balanced carefully. 98

114 Appendix D. Double Electric Discharge calibration appendix 99 Figure D.8: run continuously Once the bridge is balanced, the program may be stopped by clicking Stop. Now the voltage pulse needs to be generated to perform the double discharge calibration. This can be simply done by clicking the Create Signal on the left tab. The screen of the DC signal appears again. The Signal type needs to be changed to Square Wave now as can be seen in figure D.9. It is very important to set every parameter to its correct value. First, the Frequency must be chosen, in this example, the value is set 100 Hz which corresponds to pulse duration of 5 ms during one period. The Phase is chosen to 180 so that the waveform starts from its low value. The pulse voltage level is set by adjusting two boxes namely Amplitude and Offset. For example, in this case we have chosen a pulse of 4 V, therefore the Amplitude is set to 2 V and Offset is set to 2.3 V. Note that the offset corresponds with 2 V offset to start from 0 V, however 2.3 V is necessary since the bridge is balanced to 300 mv and this functions as zero level. The final adjustment is Sample rate, this is the amount of samples that is desired to create the function. This is chosen to 67 ks/s so that one pulse is sent to the bridge instead of periodic signal. See to it that the pulse needs to drop to 300 mv, otherwise the output of the DAQ remains high. This could cause sensor burnout and must be avoided. The other parameters may be set to their default values. 99

115 Appendix D. Double Electric Discharge calibration appendix 100 Figure D.9: Signal express pulse waveform Once the signal is created, we can go back to the Data View. Then the program can be run. This is done by clicking on the arrow besides run as can be seen in figure D.10. See to it that the program is run once. If the program is continuously run, too much heat is generated in short time which can destroy the sensor. Figure D.10: run the program once When the calibration is performed, a function which is proportional with the square root 100