calibration of tfg sensor for heat flux measurements and...

Olivier Collet, Gery Fossaert

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

Academic year 2013-2014Faculty of Engineering and ArchitectureChairman: Prof. dr. ir. Jan VierendeelsDepartment of Flow, Heat and Combustion Mechanics

Master of Science in Electromechanical EngineeringMaster's dissertation submitted in order to obtain the academic degree of

Counsellor: Thomas De CuyperSupervisors: Prof. dr. ir. Sebastian Verhelst, Prof. dr. ir. Michel De Paepe

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

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

Calibration of TFG sensor for heat fluxmeasurements and validation on spark

ignitions engines

By


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 2013-2014

Summary

Due to the current issues of global warming and decreasing fossil energy resources, inter-

nal 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 intro-

duced 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 Trans-

port 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 fu-

els 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 measure-

ments as it offers different advantages compared to previously used sensors. The use of

iii

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

Calibration of the TFG sensor for heatmeasurements and validation on a SI engine


Supervisor(s): Sebastian Verhelst, Michel De Paepe, Stijn Broekaert and Thomas De Cuyper

Abstract—In the development of internal combustion engines, measure-ments of the heat transfer to the cylinder walls play an important role.These measurements are necessary to provide data for building a modelof the heat transfer, which can be used to further develop simulation toolsfor engine optimization. These measurements require an adequate sensor.This research will focus on the Thin Film Gauge (TFG) sensor. To use theTFG sensor, its thermal properties -namely the thermal coefficient and thethermal product- must be correctly calibrated. The Double Electric Dis-charge calibration set-up for the thermal product will be extensively dis-cussed. This paper ends with a comparison between heat transfer measure-ments in a CFR engine done with a non-calibrated TFG sensor, a calibratedTFG sensor and a HFM (Heat Flux Measurement) sensor.

Keywords—SI-engine, thin film gauge, heat flux, calibration, double elec-tric discharge

I. INTRODUCTION

ONE of the key factors in the research of internal combus-tion engines (ICE) is to fully understand the mechanisms

involving the heat transfer in the engine. The heat transfer fromthe combustion gases to the inner cylinder walls has large ef-fects in terms of efficiency, emissions and power output of anICE. Previous research [1] has shown that due to the differentflow conditions during the combustion the heat flux shows a lotof spatial variation. In order to enable a cheap and fast opti-mization of the engine parameters, a simulation model of thecombustion thermodynamics can be used. The development ofsuch a model demands accurate measurements inside the engine.Extensive research [2] has been performed on different kind ofsensors. This research showed that the Thin Film Gauge had themost potential for use in an ICE. They are sturdy and cheaperto manufacture. They have already been used with success inturbo machinery [3]. However, peak temperatures and pressuresare higher in ICE application, this must be taken into accountfor implementing the sensor in the combustion chamber. Also,differences in heat fluxes were observed between the TFG anda very accurate sensor. Therefore, further investigation on TFGsensors is necessary.

II. THIN FILM GAUGE

THE basic thin film gauge - a single layer TFG - consistsof 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 mostRTDs, the metal used is platinum. This is because platinumhas the most stable resistance-temperature relationship over thelargest temperature range, making it ideal for reliable measure-ments. The substrate is mostly a ceramic that has a low elec-trical and thermal conductivity. A low electrical conductivity isneeded to ensure there will be no short circuiting between thedifferent RTDs. The variation of material properties due to tem-

perature changes is why the substrate must have a low thermalconductivity. That way, when the sensor is exposed to a heatsource, only a small temperature rise will occur in the substrate.The material properties of the substrate are used in the calcula-tion of the heat flux and therefore need to remain as constant aspossible. MACOR R©, for instance, is a widely used ceramic inTFG sensors. It has good thermal and electrical properties andcan easily be machined. This makes it highly suited to be placedinside a bolt and to be mounted in a engine cylinder. The plat-inum film at the top is connected to the sensor wiring by goldleads and conductive resin.

Before the TFG can actually be used, there are two materialproperties that need to be calibrated. They are the thermal coef-ficient of the RTD and the thermal product of the substrate. Thecalibration of the thermal coefficient αR can be done by usingthe water bath calibration method. By measuring the resistanceof the RTD at different temperatures and by using the linear re-lationship between the temperature and the resistance, αR canbe calculated [1]. The thermal product is not calibrated as easy.That is why previously the thermal product of the bulk materialof the substrate was used in heat flux calculations. However, re-search has showed that the process of placing the thin film uponthe substrate changes the material properties of the substrate [4].It is also worth mentioning that no research has been done so faron the effect of sensor aging and wear on the thermal product.This shows that determining the right thermal product is im-portant. Over the years, two different methods have been usedto calibrate the thermal product: the water droplet method [5]and the hot air gun method [6]. Both methods are based on theone dimensional conduction equation which is solved by usinga step in heat flux or a step in fluid temperature [7]. Billiard [7]has shown that for short flow durations a step in fluid tempera-ture can be considered as a step in heat flux. However, by doingso, an error will be introduced. The water droplet and the hotair gun method are both setups that utilize a step in fluid tem-perature to solve the one dimensional conduction equation. Thehot air gun setup has already been used to calculate the TP whenstep in heat flux is applied. This introduces an error that shouldbe taken into account [6]. When using the water droplet setupto calculate the TP, two dimensional effects have been observedthat introduces errors [5]. Therefore, both methods have beenomitted for determining the TP. A third method exists, using astep in heat flux that is electrically generated.

III. DOUBLE ELECTRIC DISCHARGE

THERE is a third calibration method that can be used to de-termine the thermal product of the substrate: the double

electric discharge method (DED). The difference between this

v

method and the two previous ones, is that the solution of theone dimensional analysis is attained when a step in heat flux isapplied. Therefore, the transient heat flux can be written as afunction of the surface temperature as long as the semi-infiniteprinciple is valid. The heat flux is electrically simulated by thedischarge of a current through the thin film. This dischargecauses ohmic heating of the thin film, therefore, increasing thethin film temperature and its resistance. When a step in heat fluxis considered, the temperature will be proportional with the thesquare root of time as can be seen in figure 1. By controllingthe heat flux and monitoring the surface temperature, the TP canbe achieved. The thin film is placed in a Wheatstone bridge.Once the bridge has been balanced, a voltage pulse is sent to thebridge which causes ohmic heat of the thin film. This voltagepulse functions as the step function. Since the heat flux is gen-erated electrically, only the electrical power or the heat acrossthe thin film will be known. The surface area of the thin filmis necessary to determine the heat flux which is very difficult toobtain accurately. Therefore, the calibration is performed twicein different media to eliminate the knowledge of the thin filmsurface area. The thermal product can then be written as func-tion of the thermal product of the chosen fluid which glycerinand the slopes of the regression of the recorded out of balancevoltage according to equation (1):

√ρck =

√ρckglyc

(∆V/√t)air

(∆V/√t)glyc

− 1(1)

Fig. 1. Out of balance voltage and corresponding regression

Figure 1 represents the recorded out of balance voltages of thecalibrations in air and glycerin together with their regressions.The correlation coefficient of these regressions are higher than99 %. Therefore, the slopes of the regressed data perform a goodrepresentation of the actual ones.

IV. RESULTS

THE following results are taken from measurements done ona single layer TFG with a MACOR R© substrate as can be

seen in figure 2. In this specific case a voltage pulse of 8 and9 V has been applied to the bridge and pulse time duration of5 and 10 ms has been considered. The voltage pulse level isproportional with the magnitude of the heat flux while the pulsetime duration is related to the time that the heat flux is applied,thus influencing the thin film final temperature.

Fig. 2. TP vs Time variation

Voltage variation results does not represent a specific trendsince the TPs at 8 and 9 V differ from each other for differenttime durations. Time duration variation results in a slight in-crease of TP. However, measurements taken at 9 V do not differa lot from each other. Higher pulse levels resulted in lower in-accuracy. The lowest inaccuracy of 4.5 % has been obtainedwhere from the largest part is due to the inaccuracy of the TP ofthe fluid (4 %).

V. CONCLUSIONS

THE measurements discussed in this paper have led to anumber of conclusions, which will now be summarized.

• A step in heat flux can be perfectly generated with the DEDcalibration.• Higher bridge voltages resulted in the best regression withlowest relative error of 4.5%.• The variation of the amplitude of the voltage pulse does notaffect the thermal product of the substrate much. The mean val-ues and error levels are approximately the same for differentvoltage levels.• Variation of the bridge time duration has also not shown anysignificant changes in the thermal product.• In order to lower the inaccuracies, the accuracy of the thermalproperties of the fluid should be investigated.

REFERENCES

[1] T. De Cuyper and S. Broekaert, “Alcoholen als alternatieve brandstof voorvonkontstekingsmotoren: Experimentele studie naar het klopgedrag en dewarmteafgifte naar de cilinderwanden,” M.S. thesis, Universiteit Gent,2011-2012.

[2] M. Desoete and R. Vyvey, “Evaluatie van warmte uxsensoren voorvonkontstekingsmotoren aan de hand van metingen op kalibratieproefs-tanden en een cfr-motor,” M.S. thesis, Universiteit Gent, 2010-2011.

[3] Schultz. D.L and Jones T.V., “Heat-transfer measurements in short-durationhypersonic facilities,” AGARDograph, 1973.

[4] Lu K. Kinnear K., “design, calibration and testing of transient thin film heattransfer gauges,” Journal of Turbomachinery, 2008.

[5] R. Buttsworth, “Assessment of effective thermal product of suface junc-tion thermocouples on millisecond and microsecon time scales,” Elsevierexperimental thermal and fluid science, 2001.

[6] E. Piccini, S.M. Guo, and Jones T.V., “The development of a nex direct-heat-flux gauge for heat-transfer facilities,” Measurement Science and Tech-nology, 2000.

[7] N. Billiard, F. Illiopoulou, and R. Ferrera, “Data reduction and ther-mal product determination for single and multi-layered substrates thin-filmgauges,” Turbomachinery and Propulsion Department, 2002.

vi

Contents

Acknowledgement ii

Summary iii

Extended abstract v

Nomeclatuur x

1 Introduction 1

1.1 Heat transfer measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Heat flux sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Eroding ribbon sensor . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Heat Flux Microsensor . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.3 TFG sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Thin Film Gauge Sensor 8

2.1 Construction of the TFG . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 RTD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Sensitivity of the RTD . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 RTD callibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.3 Ohmic heating and RTD burnout . . . . . . . . . . . . . . . . . . . . 14

2.3 TFG concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 One dimensional analysis . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Film thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3 Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3.4 Thermal product of the TFG substrate . . . . . . . . . . . . . . . . 19

2.4 Calibration setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.1 Heat gun setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

vii

Contents viii

2.4.2 Water droplet setup and shock tube experiment . . . . . . . . . . . . 22

2.4.3 Double electric discharge calibration . . . . . . . . . . . . . . . . . . 26

3 Double Electric Discharge calibration 27

3.1 DED setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 Theoretical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.1 Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.3.2 Regression accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Calibration results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.1 Voltage variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.2 Time duration variation . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4.3 Different RTD’s on same substrate . . . . . . . . . . . . . . . . . . . 41

3.4.4 Results of the single layer calibration . . . . . . . . . . . . . . . . . . 41

3.5 Double layer TFG calibration . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4 Engine measurements 46

4.1 CFR setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2 TFG sensor setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3 Validation of TFG sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.4 CFR Heat flux measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.4.1 EGR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.4.2 Inlet temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Conclusions and future insights 71

A Calculations Fourier method 73

A.1 2T Fourier method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

A.2 1T Fourier method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B Calculations impulse response FIR-method 75

B.1 TFG Single Layer through surface temperature . . . . . . . . . . . . . . . . 76

B.2 TFG Double Layer through surface temperature . . . . . . . . . . . . . . . 78

B.3 TFG through surface temperature and depth thermocouple temperature . . 79

B.4 Steady state component of heat flux . . . . . . . . . . . . . . . . . . . . . . 80

C Error analysis 82

C.1 Measured quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

viii

Contents ix

C.1.1 Ambient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C.1.2 Engine speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C.1.3 Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

C.1.4 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

C.1.5 Flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

C.2 Calculated quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

C.2.1 Mass in cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

C.2.2 Air/fuel ratio and air factor . . . . . . . . . . . . . . . . . . . . . . . 86

C.2.3 Specific gas constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

C.2.4 Gas temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

C.2.5 Error analysis calibration TFGs . . . . . . . . . . . . . . . . . . . . . 87

C.2.6 surface temperature, flux and convection coefficients . . . . . . . . . 88

C.2.7 Convection coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 90

C.3 Error analysis on the DED setup . . . . . . . . . . . . . . . . . . . . . . . . 91

D Double Electric Discharge calibration appendix 93

D.1 DED setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

D.2 DED calibration process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

D.3 DED data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

D.4 Linearity error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

E MATLAB code 104

Bibliography 115

ix

Nomenclature

Abbreviations

AFR Air to Fuel RatioGUEST Ghent University Engine Simulation ToolIC Internal CombustionICE Internal Combustion EngineATDC After Top Dead CenterBTDC Before Top Dead CenterCFR Cooperative Fuel ResearchCR Compression RatioDAQ Data AcquisitionDED Double Electric DischargeECU Engine Control UnitEGR Exhaust Gas RecirculationFIR Finite Impulse ResponseHFM Heat Flux Micro sensorRTS Resistance temperature sensingHRR Heat Release RateIT Ignition TimingLTI Linear Time InvariantMAP Manifold Absolute PressureNSR Noise to Signal RationPID Proportional Integrating DifferentialPVD Physical Vapor DepositionRPM revolutions per minuteRTD Resistance Temperature DetectorSI Spark IgnitionTFG Thin Film GaugeTP Thermal Product

x

Greek symbols

α thermal diffusivity [m2

s ]θ crank angle []λ air factor [-]

ρ density [ kgm3 ]

ω natural frequency [ rads ]

Subscripts

avg averageaw adiabatic wallc cyclecyl cylinderliq liquids surfacess steady statetrans transientw wall

xi

Roman symbols

A surface [m2]B bore of combustion chamber [m]b slope of regression [V/

√s]

C covariance coefficient [-]

c specific heat capacity [ JkgK ]

F non-uniform film heating factor [-]f frequency [Hz]

h convection coefficient [ Wm2K

]I current [A]

k thermal conductivity [ WmK ]

M Metric [mm]m mass [kg]N number [-]n revolutions [rev]P Power [W ]p pressure [pa]Q heat [J ]

q heat flux [ Wm2 ]

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

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 CO2.

On another scale, there is also the emission of NOx 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

CO2-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

Chapter 1. Introduction 2

change issue.

1.1 Heat transfer measurements

To innovate and improve current technologies, a good understanding of the engine opera-

tions 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 en-

gine 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 pro-

cesses (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 perfor-

mance 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 NOx is strongly dependent

2


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].

1.2.1 Eroding ribbon sensor

The first sensor that will be discussed is an eroding ribbon K-type thermocouple manu-

factured by Nanmac. It has Alumel and Chromel lamellae which are surrounded by an

3


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


1.2.2 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 differ-

ence 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 thermis-

tor 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. Never-

theless, 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


1.2.3 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


will be discussed in full in this master’s thesis). The main advantage of the (double-

layer) 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

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, espe-

cially 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 sub-

strates 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

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


(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 com-

bustion 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 elec-

trical 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


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 αR. 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


R = R0[1 + α1(T − T0) + α2(T − T0)2 + ...] (2.1)

Where R0 is the resistance at temperature T0 and α1, α2 are thermal coefficients. For sen-

sor 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 = R0[1 + αR(T − T0)] ⇐⇒ ∆R = αRR0∆T (2.2)

Here αR 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 (I0) is supplied to the RTD which

enables us to monitor a voltage variation corresponding to the temperature variation:

∆V = ∆RI0 ⇐⇒ (V − V0) = (R−R0)I0 (2.3)

The 0 -subscript indicates that those values were taken at ambient temperatures. The

constant current I0 is set to a desired value with an amplifier.

2.2.1 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= αRV0 (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


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 αR will increase the sensitivity of the RTD. The

thickness of the film and the way it is applied on the substrate will influence αR. 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.

2.2.2 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 αR 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 2.4.

13


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.

2.2.3 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


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.

2.3.1 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


∂2T (x, t)

∂x2= α

∂T (x, t)

∂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 qs penetrates the thin fim with thickness ε 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 temper-

ature 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−

x2

4αt −√

π

αt

x

2erfc

(x√4αt

)(2.7)

16


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]

2.3.2 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


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.

2.3.3 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


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, Ts 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

Ts(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. In that case, the assumption that the properties remain

constant is acceptable.

2.3.4 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 2.3.3. 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


Twall(t)− T0 =2qwall√

π

√t√ρck

(2.9)

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− t0, where t0 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 t0. The time t0 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]:

Twall(t)− Twall(t = 0)

Tgas − Twall(t = 0)= 1− eβ2

erfc(β) (2.10)

with β:

β =h√t√

ρck(2.11)

Figure 2.9 compares the solution obtained through the use of the constant heat flux tech-

nique and the one obtained through the use of constant temperature. The upper graph

shows the wall surface temperature Twall for both techniques and the lower graph repre-

sents the heat flux to the wall qwall. 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 qwall 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


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]

2.4.1 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 2.10.

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


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 Ts

and the adiabatic wall temperature of the gas Taw:

q = h(Taw − Ts) (2.12)

In order to generate a constant heat flux, the driving temperature (Taw-Ts) 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 Ts 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 Taw), 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.

2.4.2 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


The water drop setup is illustrated in figure 2.11. 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 Tw contacts the heated sensor at temperature Ts,

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 − TsTw − Ts

=TPwater

TPwater + TPsensor(2.13)

Equation 2.13 strictly only applies to the hypothetical case of one-dimensional droplet im-

pact with no rebound, and one-dimensional heat conduction with constant (temperature-

independent) thermal properties in both droplet and thermocouple. If the necessary tem-

peratures are recorded and the TPwater is known, the TPs 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 func-

tion. 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 2.12. However,

the principal difference between different runs is only in transient behavior. Buttsworth

23


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


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]:

T − TsTair − Ts

=TPair

TPair + TPsensor(2.14)

This can be reduced to:

T − TsTair − Ts

≈ TPairTPsensor

(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


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.

2.4.3 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 = RI2 =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 Denos [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

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 2.4.3. 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 R0). 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 2.2.3. The components of the bridge are shown in figure 3.2. The

27

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: R0 represents the TFG’s RTD. The bridge is balanced

using a potentiometer represented by R1

(a) Potentiometer used to cali-

brate 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 Vout and the voltage

supplied to the bridge by Vin. 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


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


3.2 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

TRTD(t)

2√t

(3.1)

This equation can be rewritten to contain the resistance change of the RTD:

q =√π√ρck

∆R

αRR0

1

2√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 V0 can be expressed in function

of the intput voltage of the bridge VB:

V0 =R1R4− R2

R3

(1 + R1R4

)(1 + R2R3

)VB (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:

V0 =VB4

[∆R

R+ ∆R2

](3.4)

30


The relationship between the out of balance voltage VB 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 2.49875mV 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 0.00125mV 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

2I30R

20RpotαR

∆V√t

(3.5)

With A is the film area,∑R the sum of all four resistors in the bridge, Rpot is the

resistance value of the potentiometer and I0 and R0 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:

It is necessary to know the surface area of the thin film which may not be straight-

forward to determine.

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.

The non-uniformities in the thin film may cause some errors

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


√ρckliqR0αR

=2FxRI2

√πA(

∆R√t

)2

(3.6)

√ρck

R0αR=

2F (1− x)RI2

√πA(

∆R√t

)2

(3.7)

√ρck

R0αR=

2FRI2

√πA(

∆R√t

)2

(3.8)

Where TPliq 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

(3.9)

This can also be expressed in function of the out of balance voltage:

√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√ρcksubstrate (3.11)

The TFG is subjected to a electric discharge twice, hence the name Double Electric Dis-

charge method.

3.3 Data processing

3.3.1 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


∆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


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


Figure 3.7: The out of balance voltage plotted together with the regression, in air and in glycerin

3.3.2 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 =PnoisePsignal

(3.13)

Where Pnoise and Psignal 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 corre-

sponding 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 ma-

trices 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


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.

3.4.1 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 0.2400 and 0.2650 J/cm2/K/s1/2, 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


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) NSRair NSRglycerin

4 0.047 0.064

5 0.036 0.063

6 0.11 0.069

8 0.0010 0.00090

9 0.00068 0.00021

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


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) rair rglycerin

4 0.869 0.859

5 0.894 0.807

6 0.755 0.782

8 0.994 0.995

9 0.999 0.998

Table 3.2: Mean correlation coefficient of the regressions

To confirm the trend of an improved accuracy at higher voltages, a second series of mea-

surements 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 measure-

ments 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, in-

dicating 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


Figure 3.9: TP calculated at different voltages with a constant time duration of 10ms.

3.4.2 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 0.2450 and

0.2650 J/cm2/K/s1/2, just as the overlap in the voltage-variation-measurements.

39


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 217.44 197.41

9 V 5 ms 232.88 206.79

8 V 10 ms 220.17 203.31

9 V 10 ms 236.41 215.38

Table 3.3: RTD temperatures

40


3.4.3 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

0.1700 to 0.1975 J/cm2/K/s1/2. 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 1.

3.4.4 Results of the single layer calibration

The following could be concluded from the calibration results:

41


The regression procedure has proven to be accurate, attaining correlation coefficients

over 0.99.

Low bridge supply voltages (under 4V) have a too large NSR, lowering the accuracy

of the regression.

RTD temperatures should be taken into account to avoid sensor burn-out.

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.

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.

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.

Comparing the value of the TP of a used MACOR® single layer substrate (0.2500J/

cm2 /K/ s1/2) to a new sample (0.1850J/cm2/K/s1/2), 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.

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


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:

TxTs≤ 1%↔ x ≥ L and L = 3.16

√αt (3.16)

Here Tx is the temperature at a certain x, Ts 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 2.3.1

.

The calibration of the second layer of the double layer sensor is done by using the hot

air gun setup [25], as discussed in 2.4.1. First, the heat gun is set to appropriate set-

ting. 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(Tgas − Ts) (3.17)

Tgas 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 thermo-

couple 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


Twall(t) =2qwall√π√ρck2

√t+ qwall

L

k1

[1− ρck1

ρck2

](3.18)

Where Twall(t) is the temperature recorded at the thin film surface, qwall is the heat flux

calculated by equation 3.17.√ρck1 and

√ρck2 are the TPs of the first and second layer

respectively and the ratio L/k1 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 Tw 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/k1 [25]:

L

k1=

2√π

(t′1)0.5

1√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


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

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 break-

down. 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

Chapter 4. Engine measurements 47

Figure 4.1: CFR engine section [2]

47


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


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]

NI SCC

68

NI SCC

68DAQ NI PXI 1050

MoTeC M4ProECU

NI BNC2120

Heat Flux Microsensor

Vatell HFM 7- HFS

Heat Flux Microsensor

Vatell HFM 7- RTS

VersterkerKistler 4665


VersterkerVatell AMP-6

Krukhoek interpolatorCOM GmbH type 2614

Inlaattemperatuur

Type K-thermokoppel

Uitlaattemperatuur 2

Type K-thermokoppel

Uitlaattemperatuur 1

Type K-thermokoppel Luchtdebiet

Bronkhorst F-106BZ

Brandstofdebiet

Bronkhorst F-2010AC

CAM-encoder

Eroding Ribbon SensorType T-thermokoppel

Nanmac

TFG double layerOxford


Atmosfeersensor

Atal

CAM

TRIG

Inlaatdruk

Kistler 4075A10

Uitlaatdruk

Kistler 4075A10

Cilinderdruk

Kistler 701A

TFG single layerOxford

Versterker

Olietemperatuur

Type K-thermokoppel

Koelwatertemperatuur

Type K-thermokoppel

Hardware-box

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


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 4.70. 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 47.0. 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


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


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


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


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 tempera-

tures. Also, severe knocking occurs when the ignition timing is further delayed. Therefore,

ignition is advanced compared to the reference measurement.

54


Operating point Fuel CR Air flow [kg/h] λ IT [°BTDC]

Reference (HFM) gasoline 9.12 7.00 0.88 0

Measurement (TFG) gasoline 9 7.00 0.84 5

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/cm2/K/s1/2 is the value supplied by the

manufacturer while the second one, 2500J/cm2/K/s1/2, 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


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


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 9.12 10.80 1.07 0

Measurement (TFG) gasoline 9 10.30 1.02 5


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 condi-

tions. Again the value from the bulk supplier (2050J/cm2/K/s1/2) and the calibrated

one (2500J/cm2/K/s1/2) 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


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


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

4.13. 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 mea-

surements 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 compres-

sion 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


4.4.1 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] Wi [J] COV [%]

1 9 90 7 0.44 1.08 0 17 324 15

2 9 90 7 0.44 1.00 7 17 288 19

3 9 90 6.9 0.44 1.07 1 17 322 9


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 4.16. 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


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


Figure 4.16: Gas temperature for variation on EGR

Amount EGR [%] Maximum temperature increase [°C]

0 23.2

1 21.7

7 16.7

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


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] Wi [J] COV [%]

1 9 90 6.5 0.48 0.91 7 17 298 12

2 9 90 6.5 0.44 1.00 7 17 288 19

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


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 4.20. 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


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 sur-

passes 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


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.

4.4.2 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] Wi [J] COV [%]

1 9 90 0.98 0 27 17 298 12

2 9 90 0.97 0 40 17 288 19

3 9 90 0.95 0 50 17 288 19

4 9 90 0.93 0 60 17 288 19

Table 4.7: Operating conditions with variation on inlet temperature

66


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 4.23. 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


slightly higher in those cases. This can also been seen in the HRR plot in figure 4.26. 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


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


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

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 per-

formed 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 differ-

ent 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

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

Appendix A

Calculations Fourier method

A.1 2T Fourier method

The 2T-Fourier method relies on the Fourier analysis of two measured temperature sig-

nals. These signals form the boundary conditions to solve the one dimensional conduction

equation (A.1):

∂T

∂t= α

∂2T

∂x2(A.1)

The Fourier analysis of these temperatures gives:

T1 = B1 +∞∑

n=1

Kn · cos(nωt) +Gn · sin(nωt) (A.2)

T2 = B2 (A.3)

with:

B1, B2, Kn, Gn: The coefficients of the Fourier decomposition, where temperature

T2 is assumed to be constant.

ω: The natural frequency,[rads

]

The analytical solution of equation A.1 with boundary conditions A.2 and A.3 is:

T = B1 −(B1 −B2) ·x

ldepth+

∞∑

n=1

e−F ·x [Kn · cos(nωt− F ·x) +Gn · sin(nωt− F ·x)] (A.4)

73

Appendix A. Calculations Fourier method 74

with:

ldepth: the distance between T1 and T2, [m]

F:√

nω2α ,

[radm

]

The heat flux can be determined by using Fourier’s conduction law: q = QA = −k dTdx |x=0

and equation (A.4). The heat flux can be written as:

q = k ·(B1 −B2)

X+ k ·

∞∑

n=1

F [(Kn +Gn) · cos(nωt) + (−Kn +Gn) · sin(nωt)] (A.5)

= k ·(B1 −B2)

X+ TP ·

∞∑

n=1

√nω

2[(Kn +Gn) · cos(nωt) + (−Kn +Gn) · sin(nωt)]

A.2 1T Fourier method

This method only relies on one surface temperature. The coefficient B2 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, B2 remains the

only unknown in equation (A.5). B2 can be determined according to:

B2 = B1 + ldepth ·

∞∑

n=1

F [(Kn +Gn) · cos(nωt0) + (−Kn +Gn) · sin(nωt0)] (A.6)

The factor ldepth is eliminated in equation A.5.

74

Appendix B

Calculations impulse response

FIR-method

To determine the impulse response h of the LTI-system, the set non-singular solutions q1[n]

and T1[n] need to be known. When these solutions are known, the following equation is

fulfilled:

q1[n] = h[n] ∗ T1[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) =qb(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 q1[n] and T1[n]. These set of functions are calculated according

to an one dimensional analytical method decribed by Oldfield [24].

75

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

∂2θ

∂x2(B.4)

with:

θ(x, t) = T (x, t)− Tss(x): The transient component of the temperature

Figure B.1: Model of the TFG single layer [24]

The boundary conditions are:

−k dθdx |x=0 = q

−k dθdx |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:

d2Θ(x, s)

dx2− s

αΘ(x, s) = 0 (B.6)

−k dΘ(x,s)

dx |x=0 = Lq−k dΘ(x,s)

dx |x=∞ = 0(B.7)

With:

L: The Laplace transform-operator

76


s: The Laplace-variable

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:

Θ(x, s) = A(s) exp

(−x√s

α

)(B.9)

Substituting into the first boundary condition gives:

Lq =√kρcp√sΘ(0, s) =

√kρcp√sLθs (B.10)

With:

θs(t) = T (t)− Tss: 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:

Lθs,step =1√

kρcps3/2(B.11)

In this case, a step function has been applied and is written as: Lqstep = 1/s in the

Laplace domain.

Going back to the time domain implies the inverse Laplace transform:

θs,step =2√

π√kρcp

√t (B.12)

The set functions to determine the impulse response h[n] is:

qstep(t) =

0 t < 0

1 t ≥ 0(B.13)

θs,step(t) =2√

π√kρcp

√t (B.14)

77


B.2 TFG Double Layer through surface temperature

This sensor is modeled according to the semi-infinite assumption where an insulating layer

lies in between (figure B.2).

Two layer substrate heat transfer gauges

[h,shift] = desT2q2limp1(fs,np,rrck1,rrck2,ak1,test)

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.

[h,shift] = desq2T2limp1(fs,np,rrck1,rrck2,ak1,test) Designs (des) a filter to convert heat transfer rate q to surface temperature T (q2T) for a two-layer substrate (2l) and gives impulse response (imp) h. Use T = fftfilt(h,q) to convert measured q to T.

The basis functions are those for a step in q1(t). In Laplace transformed form, the solution of the heat conduction equations for two layer substrate (Doorly and Oldfield,1987) gives

1

11

1111

2exp1

2exp111

saA

saA

sqskc

sT ,

where 222111

222111

kckc

kckcA and the thermal diffusivity

1

11 c

k .

For a step in q1(t) = u(t), s

sq1

1 , and so

1

123

1111

2exp1

2exp11

saA

saA

skc

sT .

Expanding the denominator as a power series, and taking the inverse Laplace transform,

Semi- infinite layer

T1

222 kc

q1 Thin-film gauge

111 kcInsulating layer

x = 0

x = a

Figure 2 Two layer heat transfer gauge

6

Figure B.2: Model of the TFG double layer [24]

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 are:

−k1dθ1dx |x=0 = q

−k1dθ1dx |x=a = −k2

dθ2dx |x=a

−k2dθ2dx |x=∞ = 0

θ1(a, t) = θ2(a, t)

(B.15)

In the Laplace domain:

Lq =√k1ρ1c1

√s

[1−A exp(−2a

√sα1

)]

[1 +A exp(−2a

√sα1

)]Lθs (B.16)

With:

A=√ρ1c1k1−

√ρ2c2k2√

ρ1c1k1+√ρ2c2k2

α1= k1ρ1c1

: the thermal diffusivity of the first layer

As with the TFG single layer a step in heat flux is applied at the surface of the sensor.

Equation (B.16) becomes:

Lθs,step =1√

k1ρ1c1s−

32

[1 +A exp(−2a

√sα1

)]

[1−A exp(−2a

√sα1

)] (B.17)

78


After decomposition into a power series and taking the inverse Laplace transformation,

the obtained set of functions for the TFG double layer are:

qstep(t) =

0 t < 0

1 t ≥ 0(B.18)

θs,step(t) =2√

k1ρ1c1

[√t

π+∞∑

n=1

2An

(√t

πexp

(−k

2s

4t

)− ks

2erfc

(ks

2√t

))](B.19)

With:

ks=2an√α1

a: The thickness of the first layer

erfc the complimentary error -function: erfc(z) = 1− erf(z) = 2√π

∞∫ze−t

2dt

B.3 TFG through surface temperature and depth thermo-

couple 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 T1−T22 and −T1−T2

2 . Besides

that, a common mode sensor with T1+T22 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


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 hd[n] and hc[n] when a

step in heat flux is applied (qd en qc) 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:

q1 = qd + qc = hd ∗T1 − T2

2+hc ∗

T1 + T2

2=hd + hc

2∗T1 +

hc − hd2

∗T2 = h1 ∗T1 +h2 ∗T2

(B.20)

Therefore:

h1 = hd+hc2

h2 = hc−hd2

(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


qss =Q

A= k

Twall − Tdepthldepth

=Tsurf − Tdepth

ak1(B.23)

where the DC - component of the surface temperature measured by the RTD functions

as the wall temperature ( Twall ). Together with the temperature measured by the ther-

mocouple 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

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 AEX and the relative error as REX .

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 AEX Unit

Tamb 0, 4 C

pamb 130 Pa

RV 2,5 %

C.1.2 Engine speed

The engine speed is measured with a crank angle interpolator type 2614 of the manufac-

turer 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

Appendix C. Error analysis 83

Table C.2: Absolute error on the measured engine speed

Variable X AEX 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 AEX REX [%] Unit

Kistler 4075A10 0, 03 - bar

Kistler 701A - 1 bar

Kistler 4665 - 0, 1 −Kistler 5064 - 0, 1 −PXI-6143 2, 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


pinlet 0, 03 - bar

poutlet 0, 03 - bar

pcylinder - 1 bar

C.1.4 Temperatures

The inlet, the two outlet temperatures, the oil temperature and the cool water tempera-

ture 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


Table C.5: Absolute errors on the acquired temperatures

Variable X AEX Unit

Ttype 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 AEX Unit

Qlair 0, 2 Nm3/h

Qmethane 0, 036 Nm3/h

Qhydrogen 0, 047 Nm3/h

mass flow rate of liquid fuels is calculated as

mliquid =∆m

∆t(C.1)

The absolute error on the mass flow rate is therefore,

AEmliquid =

√(AE∆m

∆m

)2

+

(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


∆m 1 - g

∆t 1 - s

mmethanol - 2 kgs

84


C.2 Calculated quantities

To obtain the error on a calculated value, an error analysis must be performed. This

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:

AEf =

√(∂f

∂aAEa

)2

+

(∂f

∂bAEb

)2

+

(∂f

∂cAEc

)2

(C.3)

If no analytical expression is available of a function f , the derivatives in the above equation

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:

REf =AEff

(C.4)

In the next sections, a representative value of the relative error on methane based measure-

ments, will be given. Details of the operating condition are listed in table reftab:vgl-q-wp.

Wi [J ] Fuel ignition timing [CA BTDC] Throttle position [] λ CR

290 Methane 24 79 1, 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.

mmixture = mair +mfuel +mrest (C.5)

Here,

mair =2mair

60 N(C.6)

mfuel =2mfuel

60 N(C.7)

mrest =pcylVcyl

RrestToutlet(C.8)

85


mrest is evaluated when the exhaust valve closes.The relative error of these separate com-

ponents are:

REmair =√RE2

N +RE2mair

(C.9)

REmfuel =√RE2

N +RE2mfuel

(C.10)

REmrest =√RE2

pcyl+RE2

Texhaust+RE2

Rrest(C.11)

The relative error of the total mass in the cylinder is

REmmixture =√RE2

mair +RE2mfuel

+RE2mrest (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

afr =mair

mfuel(C.13)

The relative error can be calculated as:

REafr =√RE2

mair +RE2mfuel

(C.14)

The air factor λ is calculated as

λ =afr

afrstochiometric(C.15)

The error on the ratio can be calculated as

REλ =√RE2

afr +RE2afrstochiometric

(C.16)

Since afrstochiometric is fixed for a certain fuel, the relative error on λ will be the same as

the relative error on afr:

REλ = REafr (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 Rinlet of the sucked gas mixture is calculated

as:

Rinlet =afr

(afr + 1)Rair +

1

(afr + 1)Rfuel (C.18)

86


If the error on the specific heat constant of air an fuel is neglected, the error can be

determined accordingly

AERinlet =

√(Rair −Rfuel)2AEafr (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,

AERmixture = AERinlet (C.20)

This results in a relative error of 7, 6% for the specific gas constant of the mixture.

C.2.4 Gas temperature

The gas temperature of the mixture can be calculated by the equation of state:

Tgas =pcylVcyl

Rmixturemmixture(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:

RETgas =√RE2

pcyl+RE2

Rmixture+RE2

mmixture (C.22)

This calculation leads to a relative error of 8, 3% on the gas temperature.

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:

AEa = AER

√N

∆(C.24)

AEb = AER

√∑(Tj)2

∆(C.25)

N is the amount of data points and ∆ en AER are calculated as:

∆ = N∑

x2 −(∑

x)2

(C.26)

87


AER =

√1

N − 2

∑(Rj − b− a Tj)2 (C.27)

The value of α0 can be calculated as:

α0 =a

b+ a T0(C.28)

The absolute error of α0 is then given as:

AEα0 =

√b2(AEa)2 + a2(AEb)2 + a4(AET0)2

(b+ a T0)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

Tw = TTFGS =VTFGS

GTFGS α0 V0+ Tatm (C.30)

The absolute error becomes:

AETw =√(

AEVTFGSVTFGS

)2

+

(AEGTFGSGTFGS

)2

+

(AEα0

α0

)2

+

(AEV0

V0

)2

+

(AETamb

GTFGSα0V0

VTFGS

)2

VTFGSGTFGS α0 V0

(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:

qtrans = fftfilt(h, Tw) (C.32)

The flux is dependent of the impulse response h of the 1T FIR-method and the surface

temperature Tw of the sensor. There is no literal function available that relates these

variables with the resulting flux. A sensitivity analysis will be used to determine the

absolute error, which can be written as:

AEqtrans =

√(∂qtrans∂Tw

AETw

)2

+

(∂qtrans∂h

AEh

)2

(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:

AEqtrans =

√(∂qtrans∂Tw

AETw

)2

+

(∂qtrans∂TP

AETP

)2

(C.34)

88


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 Torig and the

value for the thermal prodcut TPorig of 2050J/m2.K.s1/2.

2. On the resulting flux were some recognizable points (eg. peak flux) chosen. The flux

qorig is noted in these points.

3. The variable, temperature is varied 0, 1%, 0, 01% en 0, 001% resulting in Tvar. The

resulting flux qvar is noted again for the previous chosen points.

4. For every variation of the variable, the ratio can be calculatedqorig−qvarTorig−Tvar . Note that

this is an approximation (C.34).

For ∂qtrans∂Topp

we obtain a temperature dependent trace:

∂qtrans∂Topp

∼= 7, 2174e−0,112 Topp (C.35)

Transient heat flux - Fourier method The transient part of the heat flux is given

in equation (A.5):

qtrans = TP ·

∞∑

n=1

√nω

2[(Kn +Gn) · cos(nωt) + (−Kn +Gn) · 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∂Tw

bekomen we:

∂qtrans∂Tw

= 0, 62 (C.36)

For ∂qtrans∂TP we obtain:

Steady state component flux the steady state part of the flux can be calculated as:

qss =Tw − Tdepth

ak1(C.37)

The absolute error is:

AEqss =

√(AETwak1

)2

+

(AETdepthak1

)2

+

((−Tw + Tdepth)AEak1

ak21

)2

(C.38)

89


Total flux The total flux, which is the sum of the transient and the steady state part,

is given by:

qtot = qtrans + qss (C.39)

The absolute error is:

AEqtot =√AE2

qtrans +AE2qss (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 REX [%] AEX Unit

V0 - 10.10−3 V

GTFGS 1 - -

VTFGS - 2, 5.10−3 V

Tdepth - 0, 5 C

TP 4, 2 - J

m2.K.s12

ak1 10 - m2.KW

qtotFIR 1, 2 - Wcm2

qtotFOUR 8, 8 - Wcm2

C.2.7 Convection coefficient

For every sensor, the convection coefficient can be calculated as:

h =q

Tg − Tw(C.41)

The error on the temperature difference ∆T between gas and wall can be written as:

AE∆T =√AE2

Tg+AE2

Tw(C.42)

The error can be calculated as:

REh =√RE2

q +RE2∆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 REX [%] Unit

hTFGFIR 12, 83 Wm2K

hTFGFOUR 20, 29 Wm2K

90


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:

AEf =

√(δs

δaAEa

)2

+

(δs

δbAEb

)2

+

(δs

δcAEc

)2

(C.44)

The relative error can be calculated as the ratio of the absolute error to the function itself:

REf =AEff

(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:

V0 =VB4

[∆R

R+ ∆R2

](C.46)

Where V0 represents the out of balance voltage, VB the bridge supply voltage which is

generated by the data acquisition which has an absolute error of 2µV. R1,R2,R3 and R4

are the resistors of the bridge. R2 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:

√ρck =

√ρckglyc

(bair)

(bglyc)− 1

(C.48)

Where bair and bglyc are the slopes of the linearized out of balance voltage when regression

is performed. The error on these slopes can be written as:

91


AEb =

√√√√1

N−2

∑Ni=1(Tj − aVj − b)2

∑Ni=1 x

2 − (∑Ni=1 x)2

N

(C.49)

The absolute error on the TP can be written as:

AEf =

√(δTP

δbairAEair

)2

+

(δTP

δbglycAEbglyc

)2

+

(δTP

δTPglycAETPglyc

)2

(C.50)

AEf =

√√√√(−TPglycbglycbair − bglyc

AEbair

)2

+

(TPglycbairbair − bglyc

AEbglyc

)2

+

(1

bairbglyc− 1

AETPglyc

)2

(C.51)

Each successful regression will have a correlation coefficient that is 99% or higher. There-

fore, 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

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

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


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 100 000 Hz. The amount of samples can be set as desired, when the program is run

95


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


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


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


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


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


time should be monitored at the out of balance voltage display. Click right mouse button

and store the data to clipboard. Then open an empty text file and paste the data in it.

This text file will then be used for data processing which is explained in the next section.

Repeat the same procedure for storing the RTD voltage and shunt voltage.

When this procedure is performed, repeat the same steps with the sensor immersed in

glycerin. The thermal product can then be determined.

D.3 DED data processing

In order to achieve the calibrated value of the thermal product, the recorded data must

be processed to achieve the actual thermal product. The routine is explained in the m-file

itself. The structure of the file will be explained here as well.

The first part of the algorithm reads the three recorded signals which are the voltage

across the shunt in series with the RTD, the voltage across the RTD and the out of

balance voltage for measurements taken in air and glycerin. With this data, the power

across the RTD can be calculated.

Once the data is read, the data that used for regression needs to be determined. This

determination relies on the power function that has been calculated in the previous step.

The power function is proportional with the heat flux and therefore, this function will also

be a step function. However, the power function still represents a transient part that does

not follow the step function well. Therefore, an algorithm to determine the data points

that follow the step function well, will be conducted to achieve a reliable set of data points

to perform the regression. First, the end point of the step function will be located since

the step function is constant there. This is performed with a while loop that runs from

the end of the data points until a value higher than the noise is achieved. This value will

be the end point of the step function. Next, the point of origin of the step function needs

to be determined, this point lies a certain amount of steps earlier. This amount of steps

can be calculated when the pulse time duration and sample rate are known. In this case, a

step of 5 ms time duration sampled at 100 000 Hz requires 500 steps. Then the amount of

regression points needs to be determined, this can be performed by a loop that determines

the point that the step function varies 2 % from its end point, determined earlier. The

interval between this point and end point will then be used for regression. However, this

loop struggles with noise, therefore, the amount of regression points has been chosen hard

coded in order to achieve a reliable set of regression points.

101


After that the regression points are determined, the regression process on the out of balance

voltage can begin. First, the useful data must be derived before actual regression can be

performed. When the DAQ is triggered, it sends a pulse of certain time duration and data

is recorded at the same moment. The amount of samples that is read can be adjusted with

”Signal Express”. In this case, the amount of samples has been chosen twice as high than

pulse time duration. Every time a new set of samples are taken, the trigger has some delay

resulting in another start of rise time for each recorded voltage. Therefore, an algorithm

must be defined that takes the useful data out of this. This is done by taken the part

of the out of balance voltage that is defined from the origin and end point as discussed

in previous paragraph. When the step function originates the out of balance voltage will

start to rise, therefore, these points are taken for defining the subset of the out of balance

voltage that will be used for regression. Before regression can be performed the this subset

of out of balance voltage needs to be shifted to the origin. The out of balance voltage

must originate from zero in order to perform a regression.

Once, the out of balance voltage is shifted to the origin, the regression can be performed.

An non linear model is used where the only unknown is the slope which is required. This

slope will be calculated with a least squares method. The slopes of the measurements

taken in air and glycerin will be used to determine the thermal product.

D.4 Linearity error

It has been mentioned that the bridge implies a linearity error when the bridge consists

of a single varying element. The out of balance voltage will not be proportional with the

change of resistance due to this error. However, for small resistance variations the error

will be small. When the resistors of the bridge are chosen equal at ambient conditions,

the linearity error will be 0.5 % per % variation of thin film resistance.

There is a solution to this problem. Figure D.11 represents a Wheatstone bridge with

an OP amp configuration that might be applied in order to avoid the non linearity of

the bridge. Here, the out of balance voltage functions as the input of the operational

amplifier. The OP amp produces a forced null, by adding the a voltage in series with

the variable arm. This voltage is equal in magnitude and opposite in polarity to the

incremental voltage across the varying element and is linear with ∆R. The output of the

OP amp can then be connected to the DAQ. This active bridge has a gain of two over the

standard single-element varying bridge, and the output is linear, even for large values of

∆R. The amplifier used in this circuit requires dual supplies because its output must go

102


negative. Note that the resistances are chosen equal when no change in the single-varying

element is monitored. Therefore, each resistance should be an accurate potentiometer

that needs to be set to appropriate value when a calibration is performed since the thin

film resistance varies with the temperature. Also, each thin film has another resistance at

ambient conditions which makes the potentiometers necessary.

Figure D.11: The optimized DED setup

Another benefit of this setup is that the change in resistance can be calculated easily since

the out of balance voltage is proportional to the change in resistance. The error on the

voltage pulse can also be omitted by applying the radiometric principle. It can be seen

that the output of the bridge or OP amp is proportional with the bridge supply voltage.

By dividing the output, by hard or software, with the bridge supply voltage, the error or

drift on voltage will be omitted, so reducing the error.

103

Appendix E

MATLAB code

104

% DED processing tool% Created by Gery Fossaert & Olivier Collet% This tool reads recorded out of balance voltages wherefrom a regression% is perfomed in order to acquire the thermal product

% First, the recorded data must be read

% Data from air measurementsR_shunt = 1.45; %shunt resistanceV_I1 = dlmread('shunt_8V_5ms_air2.prn'); %voltage across shuntV1 = dlmread('RTD_8V_5ms_air2.prn'); %voltage across RTDOB1 = dlmread('8V_5ms_air2.prn'); %out of balance voltageI1 = V_I1(:,2)/R_shunt; %calculation of actual currentR1 = V1(:,2)./I1; %calculation of RTD resistanceI_square1 = I1.^2;Q1 = R1.*I_square1; %calculate power across RTD

% Data from glycerin measurementsV_I2 = dlmread('shunt_8V_5ms_glyc1.prn'); %voltage across shuntV2 = dlmread('RTD_8V_5ms_glyc1.prn'); %voltage across RTDOB2 = dlmread('8V_5ms_glyc1.prn'); %out of balance voltageI2 = V_I2(:,2)/R_shunt; %calculation of actual currentR2 = V2(:,2)./I2; %calculation of RTD resistanceI_square2 = I2.^2;Q2 = R2.*I_square2; %calculate power across RTD

% The first step is to acquire the indeces where the heat flux is constant% this is done by the following while loops that determines the% indices where end_i1 is the index where the heat flux is constant at the% end of the step. Then start_i1 is the index where the heat flux lies in% a high confidence interval. With these indices, actual regression data is% determined

i1 = length(V1);while( Q1(i1) < 0.08) %determination of end point step power function,

i1 = i1 - 1; %the threshold of the condition is hard coded sinceend %it varies for different voltage rangesend_i1 = i1-1 ;

zero1 = end_i1-498; %origin of square root of time defined as zero1

% j1 = end_i1-1;% while( Q1(j1) > 0.99*Q1(end_i1) && Q((j1) < 1.01*Q1(end_i1))% j1 = j1 -1;% j1 = end_i1 - 1;%% end% determination of the instant when step function start to vary

start_i1 = end_i1-400; %the instant where the power is constant, hard coded

%In order to perform regression, the resistance and voltage trace needs%to be shifted to the origin. First, the subset of useful data is taken,%this is when the out of balance voltage starts to rise. Then a new time%array is created that corresponds with the shifted traces

delta_x1 = end_i1 - zero1; %defining the subset of dataR11 = R1(zero1:end_i1); %subset of resistanceR11 = R11 - R11(1); %subset originates from zero now

1

OB11 = OB1(zero1:end_i1,2); %subset of out of balance voltageOB11 = OB11 - OB11(1); %subset originates from zero nowx1 = [0:0.00001:(delta_x1*0.00001)]'; %defining new time array

%startv_reg1 and endv_reg1 are the shifted values from where the heat%power step function is constant. It is between these values that the%regression is performed.

startv_reg1 = start_i1 - zero1;endv_reg1 = end_i1 - zero1;

% The non linear regression is performed where the heat power is% considered constant on the resistance trace and on the out of balanc% voltage

modelfun1 = @(b,s) b(1).*sqrt(s); %defining non linear modelbeta01 = 0.1; %initial guess

[beta1,ER1,J1,CovB1,MS1E] = nlinfit(x1(startv_reg1:endv_reg1),...R11(startv_reg1:endv_reg1),modelfun1,beta01);

modelfunv1 = @(bv,sv) bv(1).*sqrt(sv); %defining non linear modelbetav01 = 0.1; %initial guess

[betav1,ERv1,Jv1,CovBv1,MSv1E] = nlinfit(x1(startv_reg1:endv_reg1)..., OB11(startv_reg1:endv_reg1),modelfunv1,betav01);

y1 = beta1*sqrt(x1); %regression on resistancev1 = betav1*sqrt(x1); %regression on out of balance voltage

%The same process is performed for glycerin

i2 = length(V2);while( Q2(i2) < 0.06)

i2 = i2 - 1;endend_i2 = i2-1;zero2 = end_i2 - 498;

%j2 = end_i2 - 1;% while( Q2(j2) > 0.98*Q2(end_i2))% j2 = j2 -1;% end

start_i2 = end_i2-400;

delta_x2 = end_i2 - zero2;R22 = R2(zero2:end_i2);R22 = R22 - R22(1);OB22 = OB2(zero2:end_i2,2);OB22 = OB22 - OB22(1);x2 = [0:0.00001:(delta_x2*0.00001)]';

startv_reg2 = start_i2 - zero2;endv_reg2 = end_i2 - zero2;

modelfun2 = @(b2,s2) b2(1).*sqrt(s2);beta02 = 0.1;[beta2,ER2,J2,CovB2,MS2E] = nlinfit(x2(startv_reg2:endv_reg2),...

R22(startv_reg2:endv_reg2),modelfun2,beta02);

2

modelfunv2 = @(bv2,sv2) bv2(1).*sqrt(sv2);betav02 = 0.1;[betav2,ERv2,Jv2,CovBv2,MSv2E] = nlinfit(x2(startv_reg2:endv_reg2),...

OB22(startv_reg2:endv_reg2),modelfunv2,betav02);

y2 = beta2*sqrt(x2);v2 = betav2*sqrt(x2);

% determintation of the temperatures:alpha_r = 0.0015;T0 = 23;R0 = 58;T1 = T0 + (R1-R0)/(alpha_r*R0);T2 = T0 + (R2-R0)/(alpha_r*R0);T11 = T1(zero1:end_i1);T22 = T2(zero2:end_i2);

%signal to noise ratio%calculation of signal powerpow_ER1 = (sum(abs(ERv1).^2))/length(ERv1);pow_ER2 = (sum(abs(ERv2).^2))/length(ERv2);pow_v1 = (sum(abs(v1).^2))/length(v1);pow_v2 = (sum(abs(v2).^2))/length(v2);NSR_air = pow_ER1/pow_v1;NSR_glyc = pow_ER2/pow_v2;

%plot RTD resistancefigure(6)subplot(2,1,1)plot(V1(zero1:end_i1,1),R1(zero1:end_i1));title('RTD resistance in air')xlabel('Time (s)')ylabel('Resistance (Ohm)')subplot(2,1,2);plot(V2(zero2:end_i2,1),R2(zero2:end_i2));title('RTD resistance in glycerin')xlabel('Time (s)')ylabel('Current (R)')

%plot RTD powerfigure(7)subplot(2,1,1)plot(V1(1:zero1,1),Q1(1:zero1),V1(zero1:start_i1,1),...Q1(zero1:start_i1),V1(start_i1:end_i1),Q1(start_i1:end_i1),...V1((end_i1):(length(V1))),Q1((end_i1):(length(V1))));title('RTD power in air')xlabel('Time (s)')ylabel('Power(W)')legend('start points','origin points','regression points','end points')subplot(2,1,2);plot(V2(1:zero2,1),Q2(1:zero2),V2(zero2:start_i2,1),Q2(zero2:start_i2),...V2(start_i2:end_i2),Q2(start_i2:end_i2),V2((end_i2):(length(V2))),...Q2((end_i2):(length(V2))));title('RTD power in glycerin')xlabel('Time (s)')ylabel('Power (W)')legend('start points','origin points','regression points','end points')

%plots of the curves and the regressionfigure(8)subplot(2,1,1);plot(x1(1:(startv_reg1-1)),R11(1:(startv_reg1-1)),...

3

'g',x1(startv_reg1:endv_reg1),R11(startv_reg1:endv_reg1),...'r',x1,y1,'b');title('Regression of resistance in air')xlabel('Time (s)')ylabel('Resistance (Ohm)')legend('data points','regression points','regression')subplot(2,1,2);plot(x2(1:(startv_reg2-1)),R22(1:(startv_reg2-1)),...

'g',x2(startv_reg2:endv_reg2),R22(startv_reg2:endv_reg2),...'r',x2,y2,'b');

title('Regression of resistance in glycerin')xlabel('Time (s)')ylabel('Resistance (Ohm)')legend('data points','regression points','regression')

%plots of out of balance voltage with regressionfigure(9)subplot(2,1,1);plot(x1(1:(startv_reg1-1)),OB11(1:(startv_reg1-1)),'g',...

x1(startv_reg1:endv_reg1),OB11(startv_reg1:endv_reg1),'r',x1,v1,'b');title('Out of balance voltage in air')xlabel('Time (s)')ylabel('Out of balance voltage (V)')legend('data points','regression points','regression')subplot(2,1,2);plot(x2(1:(startv_reg2-1)),OB22(1:(startv_reg2-1)),'g',...

x2(startv_reg2:endv_reg2),OB22(startv_reg2:endv_reg2),'r',x2,v2,'b');title('Out of balance voltage in glycerin')xlabel('Time (s)')ylabel('Out of balance voltage (V)')legend('data points','regression points','regression')

% Out of balance voltagesfigure(10)subplot(2,1,1);plot(OB1(1:zero1,1),OB1(1:zero1,2),OB1(zero1:start_i1,1),...

OB1(zero1:start_i1,2),OB1(start_i1:end_i1,1),OB1(start_i1:end_i1,2),...OB1(end_i1:(length(OB1)),1),OB1(end_i1:(length(OB1)),2))

title('Out of balance voltage in air')xlabel('Time (s)')ylabel('Out of balance voltage (V)')legend('data points','origin points','regression points','end points')subplot(2,1,2);plot(OB2(1:zero2,1),OB2(1:zero2,2),OB1(zero2:start_i2,1),...

OB2(zero2:start_i2,2),OB2(start_i2:end_i2,1),OB2(start_i2:end_i2,2),...OB2(end_i2:(length(OB2)),1),OB2(end_i2:(length(OB2)),2))

title('Out of balance voltage in glycerin')xlabel('Time (s)')ylabel('Out of balance voltage (V)')legend('data points','origin points','regression points','end points')

%regressionfigure(11)subplot(2,1,1);plot(x1(1:(startv_reg1-1)),OB11(1:(startv_reg1-1)),...

'g',x1(startv_reg1:endv_reg1),OB11(startv_reg1:endv_reg1),...'r',x1,v1,'b');

title('Out of balance voltage in air')xlabel('Time (s)')ylabel('Out of balance voltage (V)')legend('data points','regression points','regression')subplot(2,1,2);plot(x1(1:(startv_reg1-1)),R11(1:(startv_reg1-1)),...

'g',x1(startv_reg1:endv_reg1),R11(startv_reg1:endv_reg1),...'r',x1,y1,'b');

4

title('Regression of resistance in air')xlabel('Time (s)')ylabel('Resistance (Ohm)')legend('data points','regression points','regression')

%Temperaturefigure(14)plot(x1,T11,x2,T22);xlabel('Time (s)')ylabel('Temperature (C)')legend('air', 'glycerin')

% the thermal product with constant TP of glycerin

PtP1 = max(v1(2:length(v1))-OB11(2:length(v1)))...-min(v1(2:length(v1))-OB11(2:length(v1))); %peak to peak air

PtP2 = max(v2(2:length(v2))-OB22(2:length(v2)))...-min(v2(2:length(v2))-OB22(2:length(v2))); %peak to peak glycerin

sv1 = sqrt(sum((v1-OB11).^2)/(length(OB11)-1)); %standard variation V1sv2 = sqrt(sum((v2-OB22).^2)/(length(OB22)-1)); %standard variation V2sr1 = sqrt(sum((y1-R11).^2)/(length(R11)-1)); %standard variation R1sr2 = sqrt(sum((y2-R22).^2)/(length(R22)-1)); %standard variation R2

rck_gly = 0.0925; %TP taken from AGARD documentrck_sub_R = rck_gly/((beta1/beta2)-1); %TP from resistance tracerck_sub_OB = rck_gly/((betav1/betav2)-1); %TP from out of balance voltag

%error on slopes of regressionxlin1 = x1.^(1/2);xlin2 = x2.^(1/2);[b1, bint1] = polyfit(xlin1(startv_reg1:endv_reg1),...

OB11(startv_reg1:endv_reg1),1);[b2, bint2] = polyfit(xlin2(startv_reg2:endv_reg2),...

OB22(startv_reg2:endv_reg2),1);figure(3)plot(xlin1,OB11,xlin1,(b1(1)*xlin1+b1(2)))figure(4)plot(xlin2,OB22,xlin2,(b2(1)*xlin2+b2(2)))AE_b_air = sqrt(sum((OB11-b1(1)*xlin1-b1(2)).^2)/...

(length(OB11)-2))/sqrt(sum(xlin1.^2)-(sum(xlin1).^2/length(OB11)));AE_b_glyc = sqrt(sum((OB22-b2(1)*xlin2-b2(2)).^2)/...

(length(OB22)-2))/sqrt(sum(xlin2.^2)-(sum(xlin2).^2/length(OB22)));

AE_glyc = 0.0925*0.04; %glycerin has an relative error of 4%

AE_TP = sqrt((-(rck_gly*b2(1))/(b1(1)-b2(1))^2*AE_b_air)^2+...((rck_gly*b1(1))/(b1(1)-b2(1))^2*AE_b_glyc)^2+(1/((b1(1)/b2(1))-1)...*AE_glyc)^2);

RE_TP = AE_TP/rck_sub_OB;

5

Published with MATLAB® 7.9

10

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