Quantification of Fourth Generation Kapton Heat Flux Gauge Calibration Performance

A THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Matthew Paul Hodak B.S. Graduate Program in Mechanical Engineering

The Ohio State University 2010

Master’s Examination Committee:

Dr. Charles W. Haldeman, Advisor

Dr. Michael G. Dunn

Matthew Paul Hodak

2010

ABSTRACT

Double sided Kapton heat flux gauges which are used routinely by the Ohio State University Gas Turbine Laboratory are driven by two main calibrations, the sensors temperature as a function of resistance and the material properties of Kapton. The material properties separate into those that govern the steady-state response of the gauge and those that influence the transient response. The steady-state response, as it forms the key to data processing, will be the topic of this investigation and is based on the thermal conductivity divided by the thickness (k/d). Calibration accuracies for the heat flux gauge sensors reached levels on the order of +-.05 °C and were well within the target accuracy of +- 0.1 °C over a 100 °C calibration range. Time degradation of the gauges did occur and for these cases and a single point calibration method is introduced that maintains the accuracy to ±0.4 °C instead of the ± 3 °C that would have resulted from the resistance shift due to erosion. This method will allow for longer use of the gauges in the turbines. Various calibration methods for k/d were investigated and performed. Of the three methods presented, a hot air method provided the best results of a single value. For 1 mil Kapton k/d was calculated to be between 8520 - 8882, or a k = 0.2164 - 0.2256 W/mK (a 4% variation). Different gauge thicknesses were calibrated using a variety of methods resulting in similar values of thermal conductivity, although each method had different limitations on its accuracy.

ACKNOWLEDGMENTS

My family has been very supportive over the many years, and my collegiate career was no exception. They kept me going. I would like thank my advisor, Dr. Charles Haldeman. I have learned more from him than I can remember. I would also like to thank Dr. Michael Dunn for allowing me to work at the Ohio State Gas Turbine Laboratory. I am very appreciative to have had the opportunity to learn and grow as an engineering student at the OSU Gas Turbine Laboratory. My work would not have been possible without all the support staff, so I would like to recognize Dr. Randall Mathison, Jeff Barton, Ken Copley, Ken Fout, Dr. Igor Ilyin, Dr. Corso Padova and Cathy Mitchell. I would not have made it far without them. I was happy to have the opportunity to work with all the other graduate students of the GTL including Sam Kheniser, Mark Wishart, Mike Boehler, Matt Smith, Shanon Davis, and Mitch Parsons.

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VITA

1985...... Born, Toledo OH

2004...... Maumee Valley Country Day

2008...... B.S. Mechanical Engineering, Miami

University

2009-Present ...... Graduate Research Assistant, OSU Gas

Turbine Lab

FIELDS OF STUDY Major Field: Mechanical Engineering

TABLE OF CONTENTS

ABSTRACT ...... ii

Acknowledgments...... iii

VITA ...... iv

List of Figures ...... viii

List of Tables ...... xi

Nomenclature and Abbreviations ...... xii

Chapter 1 Introduction ...... 1

1.1 Measuring Heat Flux...... 2

1.2 Double Sided Kapton Heat Flux Gauges ...... 5

1.2.1 The Thin Film Sensors ...... 5

1.2.2 The Kapton Substrate ...... 8

1.2.3 k/d Calibration Techniques ...... 9

1.3 Objectives of this Work ...... 11

Chapter 2 Calibration of Sensors ...... 13

2.1 Experimental Setup ...... 13

2.1.1 Oil Bath ...... 15

2.1.2 Oven ...... 15

2.1.3 Comparison of Methods ...... 18

2.2 Linear vs. Quadratic Fits ...... 20

2.3 Shift in Ro ...... 23

2.3.1 1 Mil Stainless Steel Plate ...... 24

2.3.2 5 mil Copper Plate ...... 27

2.4 Correction of Shift ...... 30

2.4.1 1 mil Stainless Steel Plate ...... 32

2.4.2 5 mil Copper Plate ...... 34

Chapter 3 K/d Calibration Techniques ...... 38

3.1 Amp A/D Calibrations ...... 40

3.2 k/d Calibration Methods Considered ...... 43

3.3 Oil Bath ...... 44

3.3.1 Estimating Q ...... 44

3.3.2 Variation in k/d Oil Bath ...... 47

3.4 Kapton Heater ...... 49

3.4.1 Kapton Heater Difficulties ...... 49

3.4.2 Kapton Heater Initial Setup ...... 50

3.4.3 Kapton Heater Final Setup ...... 51

3.4.4 Kapton Heater Initial Results ...... 52

3.4.5 Estimating Heater Effeciency ...... 55

3.4.6 Variation in k/d Heater Test ...... 58

3.5 Hot Air Gun ...... 59

3.5.1 Hot Air Gun Viability ...... 60

3.5.2 Gauge Response ...... 62

Chapter 4 Hot Air gun Modifiaction - Feasibility Experiment ...... 64

4.1 Copper Test Plug...... 64

4.2 Final Design ...... 67

4.3 Initial Results ...... 69

4.4 Final Results...... 73

4.5 Recommendations for Future Implimentation ...... 75

Chapter 5 Conclusions ...... 77

Bibliography ...... 79

vii

LIST OF FIGURES

Figure 1: Semi-Infinite Heat Transfer Gauge (Oldfield [3]) ...... 2

Figure 2: Two Layer Heat Transfer Gauge (Oldfield [3]) ...... 3

Figure 3: Double sided heat flux gauge (Epstein et al. [5]) ...... 3

Figure 4: Gauge geometry as presented by Epstein et al. [5] ...... 6

Figure 5: First Gen (lower) and Second Gen (upper) HFGs, Linsley [11] ...... 7

Figure 6: Instrumented URETI Blade with Silver Leads...... 8

Figure 7: Gauge Variation before Any Runs ...... 11

Figure 8: Quasi Steady State Data Acquisition Setup ...... 14

Figure 9: Typical Cooling Curve Oven ...... 16

Figure 10: Resistance vs. Temperature ...... 17

Figure 11: Residual Error Oven and Oil Bath ...... 19

Figure 12: Residual Error Linear and Quadratic Fits...... 21

Figure 13: Residual Error due to Extrapolation Quadratic Fit ...... 22

Figure 14: Residual Error due to Extrapolation Linear Fit ...... 23

Figure 15: Percent Change First Order Terms 1 mil Gauges ...... 25

Figure 16: Percent Change Second Order Terms 1 mil Gauges ...... 25

Figure 17: Absolute Change in Ro 1 mil Gauges ...... 26

Figure 18: Percent Change First Order Terms 5 mil Gauges ...... 28

Figure 19: Percent Change Second Order Terms 5 mil Gauges ...... 28

viii

Figure 20: Absolute Change in Ro 5 mil Gauges ...... 29

Figure 21: Absolute Change in 5 mil Gauges all Runs ...... 30

Figure 22: Residual Error Calibration 13...... 32

Figure 23: Original Calibration Coefficients Residual Error ...... 33

Figure 24: Residual Error Predicted Coefficients ...... 33

Figure 25: Residual Error Calibration 14...... 35

Figure 26: Residual Error using Original Cal Coefficients ...... 35

Figure 27: Residual Error Predicted Cal Coefficients...... 36

Figure 28: Relative Error k/d as a function of Q uncertainty ...... 39

Figure 29: No Correction Factor Applied ...... 41

Figure 30: Resistor Cal Correction Factors Applied...... 42

Figure 31: Difference between Keithley and A/d System ...... 42

Figure 32: Estimated Heat Flux 2 Mil Copper Plate ...... 46

Figure 33: 2 mil Copper Plate Gauge Response ...... 47

Figure 34: Variation between Gauges Oil Bath ...... 48

Figure 35: Kapton Heater Assembly ...... 50

Figure 36: Final Kapton Heater Test Assembly ...... 52

Figure 37: 5 mil Gauge Response Kapton Heater ...... 53

Figure 38: Thermal Conductivity Nominal Q ...... 54

Figure 39: Increase in 6061 Al Temperature vs. Time ...... 56

Figure 40: Thermal Conductivity at 79% Heater Output...... 57

Figure 41: Heater Output Range ...... 58

Figure 42: Variation between Gauges Kapton Heater ...... 59

Figure 43: Jet Impingement Length Scales ...... 60

Figure 44: Local Heat Transfer Coefficient; d = 0.5mm; H/d = 2, 4; Re = 1000, 5000;

(Air Jet) (Glynn et al. [21]) ...... 61

Figure 45: Gauge Response Hot Air Gun ...... 62

Figure 46: Design Curve Copper Plug D = 0.5” ...... 65

Figure 47: Copper Test Plug Concept Design ...... 66

Figure 48: Concept Design Nozzle Extension ...... 66

Figure 49: Copper Test Plug ...... 67

Figure 50: Nozzle Extension ...... 67

Figure 51: Teflon Test Plug Stand ...... 68

Figure 52: Entire Hot Air Gun Rig ...... 69

Figure 53: Gauge Response Varying Distance from Nozzle ...... 70

Figure 54: 1" Distance from Nozzle Gauge Response ...... 71

Figure 55: Offset Difference between Initial and Recal ...... 72

Figure 56: Ambient Air Effect on HFG Plug...... 73

Figure 57: Final Run Data Hot Air Gun Method ...... 75

LIST OF TABLES

Table 1: Nominal Variation in k/d ...... 9

Table 2: Residual Error Ranges Flat Plate ...... 18

Table 3: Typical Heat Flux and Tdiff k/d Methods ...... 39

Table 4: Run Schedule Kapton Heater...... 53

Table 5: Lid Thicknesses ...... 74

NOMENCLATURE AND ABBREVIATIONS

∆k/d Uncertainty k/d ∆Q Uncertainty in Heat Flux ∆T Temperature Difference

∆Tdiff Uncertainty in Temperature Difference √ρcK Thermal effusively a1 First Order Calibration Coefficient a2 Second Order Calibration Coefficient Bi Biot Number c Specific Heat Cal calibration CFM Cubic Feet Per Minute d Thickness DAS Data Acquisition System dT/dt Differential of Temperature with GTL Gas Turbine Lab HFG Heat Flux Gauge K Kelvin k Thermal Conductivity k/d Thermal Conductance L Lower l Thickness m Meters Nu Nusselt Number OSU Ohio State University q Heat (Watts) xii

Q Heat Flux R Resistance Re Reynolds number RFT Resistance as a Function of Temperature Ro Physical Resistance of a Thin Film Sensor at 0 °C RTD Resistance Temperature Device T Temperature

Tdiff Temperature Difference (∆T) TFR Temperature as a Function of Resistance U Upper V Voltage W Watts ρ Density

xiii

CHAPTER 1

INTRODUCTION

Turbine inlet temperature is an important parameter that allows one to approximate the limitations and performance capabilities of a gas turbine. As the inlet temperature goes up, the output performance of the turbine increases. Increases in turbine inlet temperature tend to increase turbine blade temperature. Advances in materials and turbine cooling technology allow turbine inlet temperatures to increase without raising turbine blade temperature, however these advances in technologies usually come at a cost, and much time is spent quantifying the costs and benefits to decide if new technologies are really worthwhile. Often designers have only empirical relationships to guide their designs. Sometimes it is more advanced CFD codes, but often geometry and boundary conditions become so complex, that even the most advance codes cannot do proper predictions. Turbine blade temperature is one of the harder properties to predict in an engine, and thus it is often measured directly. However, measurements in real engines are very hard to obtain because of the high temperatures, so often measurements are made in rotating facilities operating at proper design conditions such as the Turbine Test Facility (TTF) at the Ohio State University. This facility belongs to a class of short-duration facilities where the experiments are performed at isothermal conditions (thus the blade temperatures do not change much) and so direct measurement of the heat-flux into the surface is used to help designers estimate the heat loads on the blades and thus the blade temperatures. Heat-flux is measured with heat flux gauges instrumented onto turbine hardware. The data acquired using heat flux gauges are used to not only characterize the heat flux, but also for code validation. The calibration of heat flux gauge sensors and thermal conductance (k/d) are the main topics of this work. In order to truly understand the variation in k/d between

sensors, it becomes important to understand the limitations and capabilities of the sensors, the test method, and data acquisition system. Each of these components dictates the interpretation of the heat flux gauge response and must be well characterized in order to calibrate the material property k/d.

1.1 Measuring Heat Flux Heat flux measurement techniques are as varied as the applications that require them. Depending on the application, different techniques are more suitable. Childs et al. presents a good overview of different heat flux measurement techniques, including thin film sensors [1]. Taler reviews the transient theory of thin film gauges, thick wall semi- infinite, and thin-skin calorimeters [2]. Oldfield gives a very good description of the types of gauges used in turbine rigs [3]. These tend to be grouped into three basic types of heat flux. First, semi-infinite heat transfer gauges, with a single resistor (sensor) instrumented on the rig. The use of the semi-infinite treatment requires the knowledge of √ρck of the underlying material. Figure 1 below depicts the semi-infinite gauge setup. The semi-infinite assumption pertains to the underlying material temperature during transient heat transfer. This approximation is valid when the back surface temperature has yet to be influenced by the change in surface conditions. Thus the semi-infinite assumption is also a function of time. A relatively thin material could still be treated as semi-infinite if the time of interest is sufficiently short. The property that governs this is the thermal diffusivity, and heat transfer situations are considered semi-infinite if the characteristic length is greater than the time it takes the thermal wave to propagate though the medium.

Figure 1: Semi-Infinite Heat Transfer Gauge (Oldfield [3])

Similarly the second type of gauge Oldfield mentions is the two layer heat flux gauge as depicted in Figure 2. The main difference being the extra insulating layer, of which the √ρck must also be known. The development and use of the two layer heat transfer gauges is documented by Piccini et al. [4].

Figure 2: Two Layer Heat Transfer Gauge (Oldfield [3])

The final gauge Oldfield mentions is the double sided thin film gauge, but the origins of this gauge are well documented by Epstein et al. [5]. Modeling, design, fabrication, calibration, and data reduction are all topics of discussion. Figure 3 below depicts the double sided heat flux gauge. The heat flux gauges described by Epstein et al. are the basis for the heat flux gauges now produced at the OSU GTL.

Figure 3: Double sided heat flux gauge (Epstein et al. [5])

Doorley et al. presents, theoretically, a transient method to measure heat transfer using multilayered gauges as well [6]. For steady state heat flux calculations using double sided heat flux gauges, Fourier’s law reduces to a simple 1-D heat conduction solution shown in equation (1.1), where Q is the heat flux, k/d is the thermal conductance of Kapton, Tu and Tl are the upper and lower temperatures.

(1.1)

∆T is inferred from the resistance measurements of the thin film sensors based on static temperature vs. resistance calibrations. k/d is the thermal conductance (thermal conductivity / substrate thickness) and is a material property of Kapton. There are many calibration techniques that have been employed to determine this property, and many will be addressed in this work. For high frequency transient heat transfer the thermal effusivity, √ρck, must be known. Equation (1.2) shows how transient heat flux is related to √ρck under the semi- infinite assumption. Where ∆Ts is the change in surface temperature of the Kapton and t is time.

(1.2)

Unsteady heat flux is much more complicated that the simple 1-D treatment referenced in the majority of this work. Numerical algorithms are used to reduce the heat flux data, and k/d, √ρck , temperature measurements, and time are all factored into the data reduction. However, the simplified treatment shown in equation 1.2 can provide a measure of the baseline accuracy in heat flux as a function of only k/d and temperature measurements and these will be the focus of this paper.

1.2 Double Sided Kapton Heat Flux Gauges Heat flux measurements have come a long way from early instrumentation as depicted by Vidal and Bogdan et al. [7] and [8]. Data acquisition systems, as with most electronic hardware, have become much more powerful and accessible than the hardware described by Oldfield et al. [9]. A very good overview of the history and development of thin film heat flux gauges can be found by Murphy [10]. An overview of the design process that goes into making the heat flux gauges at the OSU GTL is presented by Linsley [11]. Heat flux gauges instrumented onto the stator row of blades is presented by Iliopoulou et al. [12]. There are numerous accounts of double sided Kapton gauges used at the OSU GTL on a rotating rig including recently Haldeman et al. [13] . Flat plate experiments instrumented with gauges used at the OSU GTL are present by Murphy [10] and Zilles [14]. A more recent account of the Kapton gauges instrumented on a flat plate was portrayed by Kheniser [15].

1.2.1 The Thin Film Sensors The core of the Kapton heat flux gauges are nickel based films, which are applied to the Kapton through vapor deposition. These thin films resistance changes with temperature. The original mask as presented by Epstein et al. [5] had a serpentine pattern, resulting in a relatively large base resistance value Ro. Figure 4 below depicts the original sensor pattern.

Figure 4: Gauge geometry as presented by Epstein et al. [5]

Originally, the OSU GTL used this same geometry. Due to some difficulties presented by Linsley [11], including manufacturability and the bend in the serpentine pattern being susceptible to breaking, a second generation gauge was created with a different mask. The visible differences are depicted by Linsley below [11]. There have been a few more improvements since the second generation gauges which involve the removal of the feed-though holes.

Figure 5: First Gen (lower) and Second Gen (upper) HFGs, Linsley [11]

The general shape of the 4th generation gauges has not changed, however there have been improvements resulting in more reliable and durable gauges. These improvements include the removal of feed-thru holes for the leads, manufacturing changes to improve the copper nickel junction, and new copper lead lines to replace painted silver leads. Figure 6 shows the silver leads used to instrument gauges onto a URETI blade (generation 3).

Figure 6: Instrumented URETI Blade with Silver Leads

1.2.2 The Kapton Substrate Kapton is a unique material that offers great thermal and mechanical properties up to 360 °C. This material was originally selected by Epstein et al. [5] for double sided heat flux gauges and continues to be used by the OSU GTL. Type VN has been selected due to good dimensional stability. Other properties of Kapton have been collected and presented by Bouquet [16] and type VN specific properties can be found in the datasheet released by DuPont on their website [17]. The thermal conductivity of Kapton indicated by the data sheet on DuPont’s website is 0.12 W/mK. [17]. Dimensional tolerances were difficult to find, but were available at a distributors website reference [18]. For 1 mil Kapton, the dimensional tolerance was +- 15%. This tolerance trended downward as the nominal thickness increased. Through private communications with DuPont, it was found that the thermal conductivity is more accurately around 0.20-0.22 W/mK or 0.21 +-5%. It was also discovered that the dimensional tolerance for 1 mil Kapton, though quoted to be +- 15%, could be as low as +- 5% throughout one sheet [19]. Table 1 shows the maximum possible variation in k/d if K is taken to be the 0.2-0.22 W/mK and d varies due to the dimensional tolerance. The variation in thermal conductivity quoted by DuPont could

very well be explained by dimensional variation. If the tolerance is taken to be the minimum of +- 5%, the expected k/d for varying nominal thicknesses is shown in the last two columns of Table 1.

Table 1: Nominal Variation in k/d

K d Tolerance k/d Upper k/d Lower Min Tol k/d Upper k/d Upper (W/mK) d (mil) (+/- %) (W/K) (W/K) (+- %) (W/K) (W/K) 0.2-0.22 1 +- 15 10189.9 6846.9 +- 5 9117.3 7499 0.2-0.22 2 +-12.5 4949.4 3499.6 +- 5 4558.6 3749.5 0.2-0.22 5 +- 7 1862.7 1471.8 +- 5 1823.5 1499.8

Table 1 summarizes general information on three nominal thicknesses of Kapton. To date all Kapton gauges used the 1 mil thick Kapton substrate. There are some advantages, however, to using thicker Kapton for the cooled experiments currently being performed. First, for small heat flux signals, the ∆T signal scales with the nominal thickness. It is also apparent from DuPont that thicker substrate thicknesses are controlled to better dimensional tolerance % (resulting in better control of k/d).

1.2.3 k/d Calibration Techniques There have been many different techniques used to calibrate the material properties of Kapton. Originally, Epstein et al. used a laser in conjunction with a reference fluid dibutylphthalate. The reference fluid had a known √ρck, which could be used to find the √ρck of Kapton and avoid having to know the exact power output of the laser. A direct calibration of k/d would also require knowledge of the laser output. Epstein et al. avoided this again by relating k/d to the measured √ρck. Their published k/d value was 8086 W/k or a K of 0.205 W/mK assuming nominal 1 mil thickness [5]. Piccini et al. calibrated a similar double sided heat flux gauge that used Upilex (a material similar to Kapton) as the substrate [4]. The heat flux source was a heat gun of known area. A fast acting shutter opened after the heat gun had reached steady state to 9

allow the free jet of air onto the gauges. A thin skin copper calorimeter was used to measure Q from the heat gun. Because the copper has a low Biot number, a thermocouple can be place on the back side and record the temperature history of the copper. From this history, the heat flux can be inferred using equation (1.3). Where ρ is the density, c is the specific heat, l is the thickness of copper, and dT/dt is the differential change in temperature with respect to time.

(1.3)

It is difficult to make a direct comparison to the calibration methods employed to measure Kapton properties, however Piccini et al. estimated their uncertainty in √ρck to be about 4.2%. There have been multiple attempts at the OSU GTL to measure the thermal properties of Kapton. In 1999 Zilles employed a top gauge pulse technique. Effectively he applied 7.5 V to the top gauge and measured the response of the lower. Zilles quoted deviation of +-8% in the k/d value between gauges. He accounted much of this error to widely variable offsets, but also to the effective area of the top gauge and the assumption that the heat conduction is only 1-D [14]. In 2005 Murphy undertook the task of calibrating the k/d of Kapton at the OSU GTL. His final experimental setup included a thin etched foil Kapton heater manufactured by Minco. Heat was spread using aluminum foil and a thermal paste interface material. Using Pyrex heat flux gauges, of which the thermal properties are better known, Murphy estimated the heater output to be approximately 8-10% less than theoretical. Using this, he was able to get k/d calibration values within 5-15% of Zilles value. Much of the variation was attributed to difficulties using the thermal paste, contact resistance, and possible delaminating of the Kapton [10]. k/d of about 9154 W/k was calculated by Murphy, which is a k = 0.233 W/mK assuming a nominal value of 1 mil for d. This has remained the best estimate of K/D until now.

1.3 Objectives of this Work As stated in the introduction there are two sets of calibrations that are important for double sided heat flux gauges, the thin film sensor calibrations and the material property calibrations. The thin film sensors can be delicate, but have also been able to generate good temperature vs. resistance data. The difficulty comes when trying to calibrate the material properties of Kapton. As shown in the previous section, there are many different calibration techniques, each with advantages and disadvantages. Throughout the literature and from DuPont data sheets, there seems to be variations of at least +- 10%. Heat flux sensor variation before any runs can be seen in Figure 7. 1.5 K in absolute terms in not much variation, however for low heat flux signals where the temperature difference is of interest, this variation could be significant.

301

300

299

298

297

Temperature (K)Temperature 296

295

294

293 HR148U_T_LNHR39U_T_LNHR64L_T_LNHR89U_T_LN

Gauge

Figure 7: Gauge Variation before Any Runs

There were four main goals at the outset of this work. First was to quantify the accuracy and stability of the heat flux gauges. Second was to translate the accuracy of the calibrations to the A/D system used for high speed data acquisition. Third was to explore non destructive k/d calibration techniques and determine a baseline value. The final goal was to explore a method to calibrate k/d on a curved blade. The material property calibrations are highly dependent upon the accuracy of the upper and lower sensor. This resulted in an initial investigation into the behavior of the thin film sensors used for the heat flux gauge sensors. After this is documented, the various k/d calibration techniques explored will be presented. Three techniques will be explained, including the use of the oil bath, a thin film Kapton heater, and a hot air gun. For the hot air gun, an initial concept design was implemented with promising results, providing evidence that the use of hot air would be a feasible method to characterize k/d variation in the future.

CHAPTER 2

CALIBRATION OF SENSORS

These thin film sensors consist of Nickel film, where the resistance changes proportionally to a temperature change. Throughout the course of this work there were two main calibration techniques employed to characterize this relationship. The first was an oil bath using Dow Corning Xiameter 210 silicone oil bath fluid. The second method consisted of an evacuated pressure vessel inside an oven. Both had very low residual error, however due to some advantages of the oven setup, it is the recommended calibration technique. It was also determined that a single point calibration could recover lost accuracy of gauges that encountered a shift in resistance due to natural degradation with time. In this section the experimental setup that is common to both methods will be highlighted. From each experimental procedure, sample data depicts the expected accuracies based on the method employed and based on the data reduction. The thin film sensors variation over time due to exposure to thermal and mechanical stresses is shown, in conjunction with methods that account for these changes.

2.1 Experimental Setup The experimental setup is similar for both the oil bath and the oven configuration. Both methods record data using a 2001/7001 multimeter/switch system. The Keithley hardware connects to the computer though a General-Purpose Interface Bus card or GBIP interface. Labview is used to control the hardware and acquire the data. Once data is acquired, Labview is used to reduce the data, obtain both linear and quadratic fits for the resistance as a function of temperature (RFT) and the temperature as a function of resistance (TFR) equations. Once the regression fits are obtained, residuals are produced to determine the accuracy of the thin film sensors. Equation (2.1) depicts the quadratic 13

form of the TFR equation, while equation (2.2) depicts the quadratic form of the RFT equation.

(2.1)

(2.2)

The only difference between the linear and quadratic form is the second order term is dropped for the linear fit. Figure 8 depicts the quasi steady state data acquisition setup. All gauges were wired using 2-wires into a 37 pin D-sub connector and then converted to 4-wires to remove line resistance beyond that point. The 4-wire signal is processed by the Keithley 2001 multimeter, and then recorded as a resistance in Labview. A Keithley 7001 switch moves between channels every .05 sec to allow the 2001 multimeter to measure each individual sensor.

Resistance measured

Figure 8: Quasi Steady State Data Acquisition Setup

The main differences between the two methods are the surrounding fluid (oil and air/vacuum) and the method of cooling. In the oil bath, there is a slow convective cooling at the surface that causes slightly more noise in the HFG residuals, whereas when in a vacuum environment, radiation and minimal conduction are the only forms of heat transfer. Because the HFGs have such a high frequency response, the convective heat 14

transfer in the oil causes small but unwanted fluctuations that cannot be picked-up by the temperature standard which operates at a much lower frequency. If calibrations are performed in the oven without evacuating the pressure vessel, residual errors became worse than the oil bath.

2.1.1 Oil Bath Xiameter 210 silicone bath fluid offers good physical stability up to 288 °C, though most calibrations did not exceed 100 °C. This fluid is inert to most other substances. More fluid details can be found at reference [20]. The temperature standard used in the oil bath was an Azonix temperature probe. The accuracy of the Azonix is +- .01 °C. Resistance Temperature Devices (RTDs) were also place around the oil bath to ensure that the temperature gradient throughout the bath remained small. In order to nearly eliminate this gradient, an air motor stirred the oil. Heat was supplied to the oil inside a Blue M constant high temperature oil bath, which has had extra insulation applied to the outer casing to reduce heat transfer from the bath to the environment.

2.1.2 Oven The oven configuration consisted of a pressure vessel inside a Blue M Power-O- Matic 70 oven. In order to heat the instrumented plate, the pressure vessel was not evacuated until after the plate reached the desired temperature. RTDs were taped onto the plate with thermal paste to promote heat conduction and act as a temperature standard for the calibration. The RTDs were calibrated in the oil bath with residual errors on the order of .02 °C. It is theorized that because the RTDs have slightly more thermal inertia and slower response time, they are less susceptible to the convective current causing deviations from the Azonix temperature standard. Figure 9 shows a typical cooling curve for gauges calibrated in the oven. The oil bath produces similar curves.

Heating Phase Heat Turned Off

Cooling

Figure 9: Typical Cooling Curve Oven

The data during the heating phase is not used since the quasi-static assumption is not valid. Once heating is removed, the only source of heat transfer is radiation and the conduction through Teflon standoffs that hold the plate inside the test chamber. This results in slow cooling and is the portion of the data used for the calibration. Figure 10 shows the change in gauge resistance vs. temperature. The response looks quite linear, however, slight curvature is present and over large calibration ranges can cause significant error. This will be expended upon later.

190

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160

150 Resistance (ohm)

140

130 3U5 3L5 4U5 4L5 120 6L5 20 30 40 50 60 70 80 90 100 7U5 7L5

Temperature (C)

Figure 10: Resistance vs. Temperature

. Residual errors in the HFGs were on the same order as the oil bath; however the oil bath induced slight fluctuations in the heat flux data. It should be noted, a larger plate with HFGs along the axial plane of the pressure vessel was instrumented with RTDs showing a slight .75 °C peak gradient along the axial length of the plate. This error can be avoided by instrumenting RTDs along the length of the plate and calibrating the HFGs using a distance weighted average temperature to the nearest RTDs. Because the calibration chamber is evacuated, the main cooling source is radiation, and through better control of the surroundings it would be possible to make this cooling more uniform. This is problem only arises on large fixtures where a temperature standard is not instrumented in close proximity of the gauge. 17

2.1.3 Comparison of Methods Typical oil bath and oven calibrations can attain accuracies on the order of +- .05 °C. Depending on the gauge this could be slightly less or larger. Table 2 shows the number of gauges within certain residual error ranges for a flat plate calibrated with 30 pairs of gauges. The current plate calibration was run in the oven under a vacuum. Also depicted is the previous plate as a comparison. To date, the previous plate was representative of the expected residual errors. The current iteration of the flat plate gauges has well surpassed previous iteration.

Table 2: Residual Error Ranges Flat Plate

Number of Gauges Number of Gauges Residual Error Current Plate Previous Plate < +- .05 37 6 < +-0.1 17 27 < +- 0.5 1 9 < +- 1 1 1 Non - Working 2 8

For the current plate, the majority of the gauges were within +- 0.1 °C and produced nice sinusoidal residual plots for the quadratic fits. The two gauges that have larger residual errors are most likely due to a wiring issue or possibly a gauge that was close to failure. The two gauges that produced large errors were replaced, making a flat plate with all working gauges. This type of gauge retention rate was rare if possible using former gauge generations. For example, as depicted in Table 2, the last build using generation 3 gauges had 8/30 non-working gauges or just over a quarter. Higher residual errors will often be produced at the peak temperature due to the nature of least squares residual regression and the fact that the temperature change is more dynamic. Figure 11 depicts a typical residual error plot of the same HFG calibrated in the oil bath and oven over the 25 to 100 °C range. It is apparent that the oven

calibration produces a much narrower band and is closer to zero near the upper temperature limit.

0.06

0.04

0.02

Oven 0 Oil Bath 15 35 55 75 95

-0.02 Standard - Fit (C)

-0.04

-0.06 Temperature (C)

Figure 11: Residual Error Oven and Oil Bath

There are two other main issues with the oil bath calibration technique. First, oil would be very difficult to remove from cooling holes machined into air foils or the flat plate. The second issue involves cleaning the HFGs. The lower gauge is well protected by the Kapton; the upper gauge however, is susceptible to mechanical or physical contact. This type of contact will generally increase the base resistance Ro, but more importantly undermine the calibration just performed. With the stability of the new gauges, many of the advantages and disadvantages of the two methods were highlighted. With only the small temperature gradient issue to be resolved in the oven, this method can produce the same level of accuracy as the oil bath without the difficulty of cleaning oil off instrumented gauges.

2.2 Linear vs. Quadratic Fits Murphy [10] goes through uncertainty analysis between using linear and quadratic fits. He found that the quadratic fits resulted in larger uncertainty in calculated Nusselt number and Q for his application. He mentions that the uncertainty due to the quadratic calibrations is amplified due to non-linearity. One reason this may have been skewed towards linear fits is the temperature range over which he compared the calibrations. He used only a 20 °C temperature range. The magnitude of the residual errors is highly dependent on the calibration temperature range and when comparing over a small range the difference between linear and quadratic fits are not large. This difference becomes much more pronounced at higher temperature ranges. This idea will be addressed in chapter 5. The treatment here will focus more on absolute error. When calibrating k/d and implementing the steady state assumption, k/d is linearly dependent upon the ∆T. Increased uncertainty in ∆T will result in an increased uncertainty in k/d. The formulation for k/d can be found in equation (2.3).

(2.3)

To visualize the difference in residual error between linear and quadratic fits, Figure 12 shows the residual error for the same sensor. The oven quadratic and linear residuals are depicted along with the quadratic fit for that gauge run in the oil bath over the temperature range 25-100 °C. The linear fit has a peak error of just over 1 °C while the quadratic residual error is well below 0.1 °C for both quadratic fits.

Figure 12: Residual Error Linear and Quadratic Fits

Another advantage of a quadratic fit is observed when extrapolating beyond the calibrated range of the thin film sensor. Figure 13 below is a single calibration with a quadratic fit over two different ranges. The data in blue was fit over the range 25 – 100 °C. The other fit range is 25 – 60 °C. The error increases quickly and at about 80 °C the extrapolation error is 0.2 °C from the known standard as opposed to <0.05 °C as indicated by the arrow.

0.8

0.6

0.4 100C Quad Res

Residual Residual (C) 0.2 60C Quad Res

0 15 25 35 45 55 65 75 85 95 105 -0.2

Temperature (C)

Figure 13: Residual Error due to Extrapolation Quadratic Fit

Extrapolation error becomes more influential if linear fits are utilized. Over a wide temperature range linear fits do not capture the non-linear nature of the nickel response to temperature. This error is magnified when extrapolating beyond the data range used to determine the linear fit. Figure 14 depicts the same data as Figure 13 only using linear fits over the two data ranges. When extrapolating 20 °C beyond the fitted data range, the residual error is nearly 1.5 °C as opposed to ~0.2 ° C, again this is indicated by an arrow.

0 15 35 55 75 95 -1

-2 100C Lin Res 60C Lin Res Residual Residual (C) -3

-4

-5 Temperature (C)

Figure 14: Residual Error due to Extrapolation Linear Fit

It would be recommended that over a large temperature range, if the absolute temperature is to be known within less than 0.1 °C, quadratic fits should be used. However, as Murphy [10] points out, this is application specific. Murphy had a small temperature range over which he was collecting data. Over a small range, the quadratic nature of the nickel sensors is minimal. As shown in the appendix of Murphy’s thesis, linear fits resulted in less uncertainty for that application. If the temperature range is unknown before the calibration, it is best to calibrate over a large range because extrapolation can result in large errors. For the investigation presented here, quadratic fits were found to be more appropriate.

2.3 Shift in Ro One shortcoming of thin film sensors is durability. In order to minimize disruption of flow, approximate 1-D heat conduction, and be able to instrument many gauges onto a single turbine blade, the sensors must be small and thin. This small size makes the sensors delicate and susceptible to shift. A slight scratch or change in position after excitation can make the thin film sensors base resistance, Ro shift. Ro is the resistance corresponding to the sensors metal temperature at 0 °C. In order to 23

characterize this change the RFT equation was normalized to remove any influence of Ro on the first and second order terms. Equation (2.4) is the same as the RFT equation (2.2) only Ro has been divided out of the first and second order terms.

(2.4)

The next few sections use calibration coefficients of a select few test gauges acquired over multiple calibrations acquired over many months. In reviewing the curve fit coefficients for the calibration of the sensors, only the Ro value in the RFT equation showed some quantifiable pattern. There was seemingly no connection between calibrations in the TFR coefficients.

2.3.1 1 Mil Stainless Steel Plate The first set of test gauges were 1 mil thick Kapton gauges instrumented onto a stainless steel plate. Most calibrations were performed in the oil bath; however some as indicated, were performed in the oven. Before looking at the change in Ro, it is interesting to look at the first and second order terms. For reading the following figures, U corresponds to an upper gauge and L corresponds to a lower gauge. If there is a pair of gauges they will labeled with the same number. Figure 15 and Figure 16 show percent change in the normalized first and second order terms respectively. Most coefficients vary around zero percent change and stay essentially constant. A few calibration runs deviate from this trend. The two largest deviations occur in the oven; however during the first two runs the pressure vessel was not evacuated. The third oven calibration was run in a vacuum and is in line with the oil bath. The few other instances of a1 and a2 deviating occurred due to the orientation of the plate in the oil bath. These deviations are smaller than those caused by not evacuating the pressure vessel.

3.0000 Horizontal Plate 2.0000 4U 4L 1.0000 5U 5L 0.0000 6U 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 Percent 6L -1.0000 7U 7L -2.0000 Oven -3.0000 Calibration Run

Figure 15: Percent Change First Order Terms 1 mil Gauges

Oven 15.0000

4U 10.0000 4L 5U 5.0000 5L 6U

Percent 0.0000 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 6L 7U -5.0000 7L Horizontal -10.0000 Plate Calibration Run

Figure 16: Percent Change Second Order Terms 1 mil Gauges

It is important to note that the a1 and a2 coefficients are nearly stable if the same calibration procedure is followed and if there is a change in a1 it is offset by an opposite change in a2. The flip side of this is that one can measure small changes in calibration procedure with the sensors, which shows how sensitive they are. The absolute change in Ro is depicted in Figure 17.

1.5000 Post Dunk Test

1.0000 4U 4L Oven Cals 5U 0.5000 5L

Ro (Ω ) 6U

∆ 0.0000 6L 0.00 5.00 10.00 15.00 7U -0.5000 7L

-1.0000 Calibration Run

Figure 17: Absolute Change in Ro 1 mil Gauges

Over the series of calibrations performed, there was a slight shift in Ro. Runs 8 and 9 do not follow the pattern, but were the two calibrations in the non-evacuated pressure vessel. It was concluded that those calibrations resulted in large errors due to non-uniform cooling. There was also a large spike in the Ro of the lower gauges encountered during a k/d calibration technique. The oil bath was at a high temperature, ~100 °C, and the plate at ambient air temperature was dunked into the oil bath. This created a heat flux into the plate relative to the plate and oil temperatures. After this first trial, there was a large shift in the lower gauges and smaller shift in the upper gauges.

There are a few possible reasons the resistance may have shifted, but the focus of this work will pertain to the treatment of this shift. Similar problems could occur due to high pressure, hot air which is often encountered by gauges instrumented onto turbine hardware. It is interesting to note that after the first oil bath dunk test, the calibration shifts returned to the original drift pattern.

2.3.2 5 mil Copper Plate There were predominantly two other test plates utilized during this work. Both were flat 2X2” copper plates with 5 gauges instruments on each. One plate had 2 mil Kapton gauges, while the other plate had 5 mil Kapton gauges. The percent change from the first set of calibration coefficients in a1 and a2 are depicted in Figure 18 and Figure 19 respectively for the 5 mil plate. The a1 and a2 were a bit more dynamic, but they are essentially a mirror image. If the first order coefficient has a positive change, the second order term has a corresponding negative change. It should also be noted that calibrations 9-13 were in the oven under a vacuum. The fact that the first and second order terms are seemingly constant or change only relative to one another is an important aspect that will be addressed.

4.0000

3.0000

2.0000 3U5 1.0000 3L5

0.0000 4U5 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 4L5 -1.0000 Percent 6L5 -2.0000 7U5 7L5 -3.0000

-4.0000

-5.0000 Calibration Run

Figure 18: Percent Change First Order Terms 5 mil Gauges

35.0000 30.0000 25.0000 3U5 20.0000 3L5 15.0000 4U5 10.0000 4L5

Percent 5.0000 6L5 7U5 0.0000 7L5 -5.00000.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 -10.0000 -15.0000 Calibration Run

Figure 19: Percent Change Second Order Terms 5 mil Gauges

Figure 20 depicts the shift in Ro of the 5 mil gauges.

3.5000

3.0000

2.5000 3U5 3L5 2.0000 4U5

1.5000 4L5 Ro (Ω)

∆ 6L5 1.0000 7U5 0.5000 7L5

0.0000 0.00 5.00 10.00 15.00 -0.5000 Calibration Run

Figure 20: Absolute Change in Ro 5 mil Gauges

Again, it is predominantly the lower gauges that are affected by the cyclical heat up and cool down nature of a calibration as shown in Figure 20. Figure 21 depicts all of the calibrations on the 5 mil plate. Part of the shift in the upper gauges was encountered immediately after clamping a thin film heater setup onto the gauges. The lower gauge shift occurred during the induction of a constant heat flux, again mechanical and thermal stresses.

12.0000

10.0000

8.0000 3U5 3L5 6.0000 4U5

4L5 Ro (Ω)

∆ 4.0000 6L5 7U5 2.0000 7L5

0.0000 0.00 5.00 10.00 15.00 -2.0000 Calibration Run

Figure 21: Absolute Change in 5 mil Gauges all Runs

The main concepts to take away from the cyclical calibrations of heat flux gauges is that the lower gauges are more susceptible to a shift by some sort of thermal stress, while the upper sensors, not being protected by Kapton are also vulnerable to a shift due to mechanical stress. Most importantly is the fact that a1 and a2 are relatively constant and can be used to recovery much of the lost accuracy of the gauges. It should be noted, given the resistance range of these gauges, a 0.2 Ω shift in resistance roughly corresponds to a 0.5°C change in temperature.

2.4 Correction of Shift As previously mentioned, it was difficult to find a pattern in the TFR equation, but due to the physics of how nickel responds to temperature, the RFT equation could be used to recovery lost accuracy. The new Ro value of the sensor could be calculated by taking equation (2.4) and solving for Ro, resulting in equation (2.5). In the following case, a1’ and a2’ are the average normalized first and second order coefficients from cals

1-3, while R and T are the resistance and temperature recorded during a single point calibration.

(2.5)

Once Ro is found, a1’ and a2’ must be converted back to non-normalized values using the new Ro. Equation (2.4) can then be re-arranged into the quadratic equation form, equation (2.6).

(2.6)

Because there is no direct inversion for a second order equation, the quadratic equation must be solved using the quadratic formula equation (2.7). There are two solutions to the quadratic equation, in the case of the gauges the proper solution is a positive square root term.

(2.7)

This method could be continued to find new TFR cal coefficients. A pseudo data set could be created, then using temperature points over the calibration range and equation (2.7) the new one point cal data set could be curve fit for TFR coefficients. This may be a useful method for the current GTL setup, however the treatment here will primarily look at how the predictions in equation (2.7) compare to a full calibration.

2.4.1 1 mil Stainless Steel Plate From Figure 17 it is apparent that there is a large shift in resistance between calibrations 12 and 13. Figure 22 depicts the residual error for calibration 13 over the temperature range 25-100 °C. Being in the oil bath, the data is a bit noisy, however the residual error of all gauges is within +- 0.1 °C.

0.12 0.1 4U 0.08 4L 0.06 0.04 5U 0.02 5L 0 6U -0.02 20 40 60 80 100 6L -0.04

Residual (C) Error -0.06 7U -0.08 7L -0.1 Temperature (C)

Figure 22: Residual Error Calibration 13

Using the same data acquired during cal 13, then applying the original cal coefficients to the data gives the residual error shown in Figure 23. The upper gauges have not shifted quite as much, however there is a large shift in the lower gauges resulting in residual errors up to 3 °C.

2 1.5 4U 1 0.5 4L 0 5U -0.5 20 40 60 80 100 5L -1 6U -1.5 6L -2 7U -2.5 7L -3 -3.5

Figure 23: Original Calibration Coefficients Residual Error

It would be convenient to be able to calibrate the gauges whenever there seems to be a significant shift in a gauge. Due to the nature of where these gauges are instrumented that would not be practical. Figure 24 presents the residual error when Ro has been corrected using the single point cal. The residual error has dropped from the range 1.5 to -3 °C to 0.1 to -0.5 °C.

0.2 0.1 4U 4L 0 5U -0.1 20 40 60 80 100 5L -0.2 6U -0.3 6L -0.4 Residual Residual Error (C) 7U -0.5 7L -0.6 Temperature (C)

Figure 24: Residual Error Predicted Coefficients

There are a few ideas that should be noted from this single point cal. Every gauge is near zero error at 25 °C because that is where the single point cal data was acquired. If the data were acquired at the midpoint of the cal range, the residual error would cross 0 at that point. There is also a limit to how much accuracy this method will recovery. With a residual error of -0.5 °C in the prediction, there will not be much gain if the shift in Ro is < 0.2Ω. As a final note, Figure 24 is also a check on the validity that the higher order coefficients do not change, but can be taken as an average. The overall stability of the calibration varies with temperature, but up to about 80 deg c, all the sensor reside within a 0.1 to -0.3 deg C range, which means that this assumption of no change in the higher coefficients produces results within about at ±0.2 deg C range. This is very acceptable performance for a single point calibration.

2.4.2 5 mil Copper Plate In order to verify this method, the procedure used to correct the 1 mil gauges was performed on the 5 mil gauges instrumented onto the copper plate. Looking at Figure 21 there is a large shift in every gauge between calibrations 13 and 14. Calibration 14 was performed in the evacuated pressure vessel inside the oven. From Figure 25 it can be seen that the residual error is less noisy and apart from a few gauges at high temperature, < +- .05 °C.

0.15

3U5 0.1 3L5 0.05 4U5 4L5 0 6L5 20 40 60 80 100 7U5 Residual Residual Error (C) -0.05 7L5

-0.1 Temperature (C)

Figure 25: Residual Error Calibration 14

Again it would be advantageous to be able to re-calibrate to this level of accuracy, but for instrumented hardware it is not possible, since it is usually mounted in a turbine rig and there is no method to heat and control the temperature of the tunnel.

0 20 40 60 80 100 -5 3U5

-10 3L5 4U5 -15 4L5

-20 6L5

Residual Residual Error (C) 7U5 -25 7L5 -30 Temperature (C)

Figure 26: Residual Error using Original Cal Coefficients

Figure 26 illustrates the residual error using cal 14 data and predictions from the original calibration coefficients. The magnitude of this error is much larger than the 1 mil gauges, but is proportional to the magnitude of the shift in Ro. Using the normalized single point calibration procedure the resulting residual errors are shown in Figure 27.

0.7 0.6 3U5 0.5 0.4 3L5 0.3 4U5 0.2 4L5 0.1 6L5 0 7U5 Residual Residual Error (C) -0.1 20 40 60 80 100 7L5 -0.2 -0.3 Temperature (C)

Figure 27: Residual Error Predicted Cal Coefficients.

Again the residual error is lowest at the temperature the single point calibration data was acquired. For some of the lower gauges, the residual error reaches nearly .65 °C, however given the magnitude of the shift in Ro, this value is good. It is also promising to note that the gauges are still usable even with large magnitude shifts in Ro. Typical static gauge calibrations have an accuracy on the order of +- 0.1 °C. A small amount of drift will occur over the course of multiple calibrations, but this drift is negligible compared to possible drift due to mechanical or large thermal stresses encountered by instrumented gauges. Through the use of a single point calibration, accuracy recovery from a nearly 27 °C error back to .6 °C error has been shown. There are two main points to consider when performing a single point calibration. How well is the gauge temperature known? In the previous cases an RTD was instrumented on the plate close to the HFGs, and would be well within +- 0.1 °C. The second is the 36

magnitude of the drift. A 0.2 Ω shift in resistance corresponds roughly to 0.5 °C, if the shift in Ro is <0.2 Ω, the correction may be better near the single point calibration, but could be worse at the opposite end of the calibration range.

CHAPTER 3

K/D CALIBRATION TECHNIQUES

As mentioned in the introduction there have been many studies on the calibration of thin film heat flux gauges. In theory, the steady state calibration of k/d is simply a function of the Q imposed and the ∆T of the gauges. Measuring the temperature of the gauges is not a difficult problem, and as shown in chapter 2 can produce accuracies on the order of +- 0.1°C. The main difficulty comes when trying to know the source heat flux down to the necessary accuracy for calibration. As seen in Table 1, if the input Q is known to +- 5 %, it may be possible to confirm the validity of DuPont’s measurements, but it will not be possible to characterize any variation in d. For the simple 1-D treatment of heat conduction, error propagation of k/d simplifies to equation (3.1), where Q and Tdiff are the absolute heat flux and temperature difference respectively, and ∆Q and ∆Tdiff are the values to which you know the heat flux and temperature difference. For example, if Q is 30,000 W/m2, and you know this to within 10%, ∆Q would be 3,000 W/m2.

(3.1)

Table 3 summarizes typical heat flux values for the three methods that will be introduced. Tdiff is a function of the Q induced, and presented here are the nominal values that would be expected for 2 mil or 5 mil gauges. For instance, the heater method had heat fluxes on the order of ½ the hot air method, but because the Kapton heater method used 5 mil gauges, the expected Tdiff was larger.

Table 3: Typical Heat Flux and Tdiff k/d Methods

Oil Bath (2 mil) Heater (5 mil) Hot Air Gun (2 mil) Heat Flux 5000 15000 30000 Tdiff 1.1764 8.8235 7.0588 ∆Tdiff 0.2 0.2 0.2

∆Tdiff represents a current best practice level of accuracy for difference between the upper and lower sensor. Figure 28 show the expected relative error for each method. The initial value at zero is a function of how well the temperature difference is known. It is apparent, due to the low Q and subsequently low Tdiff that the oil bath had a large uncertainty. Even if there was no error in the measurement of Q, one would only be certain of the value with 18%.

0.7

0.6

0.5

0.4 Oil Bath Heater (5 mil) 0.3 Hot Air

Relative Error k/dRelative 0.2

0.1

0 0 500 1000 1500 2000 2500 3000 3500 ∆Q

Figure 28: Relative Error k/d as a function of Q uncertainty

Figure 28 also depicts another important fact. A larger Q allows for more uncertainty in the knowledge of the absolute value, but uncertainty in k/d does rise quickly as the uncertainty in Q increases. Each method of calibration helped characterize the true value of k/d. The oil bath method, as will be shown, revealed the expected variation between gauges, but due to difficulties in estimating Q, did not produce a solid average value of k/d. The variation between gauges was found to be consistent using the Kapton heater method and a better estimate of Q was produced. From the Kapton heater testing the average k/d value for 1 mil Kapton was about 8400 W/K or k = 0.2133 W/mK. This value confirmed the range of k provided by DuPont, however, the uncertainty in Q was about +- 5% and so this method could not be implemented to determine individual k/d values. Using the hot air gun was a final attempt to confirm the results of the prior two methods and get a handle on the individual gauge variation. A method was employed to independently verify Q. Through testing with the modified air gun method a k/d = 8520 or k = 0.2164 W/mK, was found.

3.1 Amp A/D Calibrations Before discussing the different methods of calibration, it is appropriate to mention the accuracy of the DAS system. All of the resistance calibrations could be recorded on the Keithley setup due to the slow quasi steady state nature. For the k/d calibrations it was important to be able to sample each gauge simultaneously with an appropriate sampling frequency. The DAS system consisted of 8 OSU pre-amplifiers (16 Channels) configured in 4-wire mode in conjunction with a Spectral Dynamics 8 channel A/D board. Much effort went into producing comparable levels of accuracy between the Keithley and A/D system. There are many points in the DAS system that can cause unwanted errors. Line resistance, the gain of the amps, the current of the amps, the offset of both the amps and the A/D system must all be accounted for. Wiring in four wire mode reduces some of these, such as line resistance, but the rest must be carefully accounted for. Figure 29 depicts the variation in 6 gauges without any correction to the A/D system. What isn’t

apparent, however, is that these values are not centered around the correct average temperature.

Figure 29: No Correction Factor Applied

A single resistor calibration of the amp will acquire better estimate of the amp gain and current leading to a better average value, but will not reduce the variation between gauges. Many calibration techniques were explored, focusing on different aspects of the A/D system; however the final method consisted of calibrating each channel with a set of resistors. Figure 30 shows the reduction in variation between gauges after applying the resistor calibration correction factors. It should also be noted the average value is around 20.5 °C as opposed to 20 °C.

Temperature vs. Time

22 21.5 4U 21 4L 20.5 5U 20

T (C) T 5L 19.5 6U 19 6L 18.5 18 0 10 20 30 40 50 60 70 80 Index

Figure 30: Resistor Cal Correction Factors Applied

In order to check the validity of the average temperature, data was taken on the A/D system and immediately following on the Keithley setup. Figure 31 depicts the difference between short duration sets of data acquired using the 1 mil stainless steel plate on both the Keithley and the A/D systems. Residual errors are on the order of < 0.1 °C. Through these calibrations it was believed that little if any accuracy would be lost due to A/D system limitations.

0.14

0.12 Del 4U 0.1 Del 4L 0.08 Del 5U

T (C) T 0.06 Del 5L Del 6U 0.04 Del 6L 0.02

0 0 10 20 30 40 50 60 Index

Figure 31: Difference between Keithley and A/D System

3.2 k/d Calibration Methods Considered As mentioned previously, there have been many attempts to measure k/d which often reduces to different techniques for creating a known, stable Q. Throughout the literature, lasers, thin film heaters, hot air, and an applied voltage to the upper gauge (top gauge pulse method) were favorites. The laser, and pulse measurements were considered but not pursued. An additional method of directly measuring the thickness was also examined, but was discarded as impractical for the current installation of sensors. There were a few problems with the laser method. The biggest problem was heat flux uncertainty. The laser would have a Gaussian distribution making it very difficult to estimate the heat flux into the gauge from the power output. If this heat flux could be estimated, power absorption was also a question. There is some data on Kapton absorption, and low wavelength visible to ultraviolet light seemed to have the best absorption as determined by datasheets, but was still associated with some uncertainty. Line generators were available; however the power output across the line could vary up to 15%. A 15% uncertainty in Q coupled with any uncertainty in the absorption of the Kapton would be well outside the level of accuracy sought for k/d. There were three main problems with the thickness measurement devices. First, very few can measure down to the tolerances that are specified by DuPont. 15% of 1 mil is a very small thickness and few devices could reach that level of accuracy. The devices that can measure within this tolerance are very expensive and are not designed or tested to measure Kapton glued onto metal. Lastly, the final goal of measuring k/d on the curved surface of a blade would not be possible for many of these devices. The top gauge pulse method could have been implemented, but the original implementation of this method had mixed results. Questions about 1-D errors and loading on the sensors led to the determination that it was best to continue with other ideas. There were three methods that were ultimately implemented throughout the course of this study, a hot oil dunk test, Kapton heater test, and the use of a hot air gun

similar to the method employed by Piccini et al. [4]. The following treatment describes the different methods and how each one was implemented.

3.3 Oil Bath The published value of k/d varies drastically between many of the studies and certainly between the published data on Kapton by DuPont. It was theorized that the same oil bath used to calibrate the resistors could be used to calibrate k/d. By increasing the oil to a high temperature and dunking gauges instrumented onto a small test plate (at ambient air temperature) into the hot oil, a ∆T between the plate and the gauges would be induced. The major difference between this method and many of the others is that the hot oil dunk test imposes a constant temperature boundary condition. This becomes an important fact that will be expanded upon later.

3.3.1 Estimating Q The most important part of any k/d calibration method is the knowledge of the heat flux imposed upon the gauges. When an object is placed into a liquid, the internal temperature can be assumed constant if the Biot number is < 0.1. The Biot number is a ratio of the external convection to the internal conduction of the metal and can be found in equation (3.2).

(3.2)

For the hot oil, it was estimated that the convective heat transfer coefficient h was about 200 W/m2k using recorded data. The test was performed on both the 1 mil 304 stainless steel and 2 mil copper plates. Thermal conductivities for 304 and copper are 16.2 and 398 W/mK. Due to the very large k for copper, Bi = .00024. Even the 304, due to the small length scale had a Bi = .03, meaning the internal temperature could be assumed constant. 44

To get an idea of the metal temperature, the lower gauges, which are only separated from the metal by a thin layer of M-bond 610 adhesive, were used to estimate the metal temperature. Equation (3.3) was used to estimate the heat flux into the plate.

(3.3)

M is the mass of the metal, c is the specific heat of the metal, ∆T was the temperature change over 0.1 second, ∆t was 0.1 seconds, and A was the surface area of the plate. This method assumes the heat flux to be constant over that short time duration. With the constant temperature boundary condition that is not the case, but the assumption that the heat flux is constant over the total area was the most detrimental to this method. Due to epoxy, lead wires, solder pads, and adhesive the heat flux seen by the gauges would be different from other areas of the plate. Averaging the heat flux over the entire surface area was not valid, but variation between gauges could be seen and is well within the possible variation of d. Figure 32 shows the estimated Q for the 2 mil copper plate. This figure depicts another shortcoming of the oil bath method, small Q signal. The heat flux is small and decays fairly rapidly.

10000 9000 8000 7000 6000 5000 Q

4000 Q(W/m^2) 3000 2000 1000 0 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Time (s)

Figure 32: Estimated Heat Flux 2 Mil Copper Plate

Related to the small Q signal, the ∆T of the gauges was also small. Figure 33 depicts the 2 mil gauge response sub sampled down to 10 Hz. The transient data was unusable and once the gauges reach steady state the ∆T is < 2 °C. With 1 mil gauges the usable ∆T is even lower.

16.00

14.00

12.00

10.00

8.00 ∆T1 T (C) T ∆T2 ∆ 6.00 ∆T4 4.00

2.00

0.00 0.00 5.00 10.00 15.00 20.00 Time (s)

Figure 33: 2 mil Copper Plate Gauge Response

3.3.2 Variation in k/d Oil Bath As previously mentioned, the k/d of both 1mil and 2mil gauges were calibrated in the oil bath. In order to make a comparison to the expected variation, the nominal thickness was divided out of the k/d and the data will be represented as a variation in thermal conductivity k. Though it is theorized that the true variant in k/d is the thickness of the Kapton, in order to compare between nominal thicknesses, the variation is expressed in terms of thermal conductivity. Figure 34 depicts the variation between gauges in the oil bath.

Figure 34: Variation between Gauges Oil Bath

Again, for the oil bath data it is not the variation between tests that is of interest, but the variation between gauges. For the oil bath test, Q was an estimate, and for previously stated reasons the Q estimate was not reliable. However, due to the proximity of the gauges to one another, the Q variation between gauges would be expected to be small. Looking at Figure 34, the variation between gauges seems to be consistent with the values expected from DuPont in Table 1. The unreliability of the Q estimate employed for the oil bath method led to the use of a small Kapton heater similar to the method employed by Murphy [10].

3.4 Kapton Heater The most recent k/d study conducted at the OSU GTL was done by Scott Murphy in 2005. There were some repeatability issues with his method, but due to some gauge improvements to date the Kapton heater heat flux source seemed plausible. The ultimate goal was to be able to press the small Kapton heater assembly onto instrumented gauges, but initial testing on flat plates revealed some shortcomings that could be addressed for the flat plate, but would be very difficult to avoid on instrumented hardware. Though there were some weaknesses to the heater technique, useful data was acquired and much was learned about the gauges.

3.4.1 Kapton Heater Difficulties The main problem encountered using the Kapton heater assembly was a shift in the upper gauge resistance. This is probably due to erosion on the gauges when they are touched mechanically and was the main failure mode during the Murphy calibration. In essence you could get one calibration on a gauge, but in general attaching the heater either changed the calibrations or ruined the gauge. When resistance changes during testing, it could be accounted for in post processing, but this would not be desirable for instrumented hardware. The second main problem was heater efficiency, a ratio of the Q recorded by the gauges to the nominal Q. The nominal heater output is governed by equation (3.4).

(3.4)

V is the applied voltage and R is the nominal resistance of the Kapton heater. The previous equation is the theoretical maximum heater wattage. The actual output of the heater will be less than the theoretical and any losses occurring before the heat flux signal is seen by the gauges must be accounted for to get an accurate measurement of k/d.

Murphy [10] used Pyrex gauges as a standard to measure the heater output and assumed through the same experimental setup that the heater output varied less than 2%. The current treatment employed a different method to measure the heater output.

3.4.2 Kapton Heater Initial Setup There were multiple iterations of the heater setup utilized to address problems that were encountered during testing, but only the final two will be discussed here. The ultimate goal was to create a calibration method which could be employed on instrumented gauges. Using that design parameter, initial testing tried to isolate the instrumented gauges to minimize losses. The different layers of the assembly are depicted in Figure 35.

Figure 35: Kapton Heater Assembly

Due to the serpentine pattern of Kapton heaters, the aluminum was used to equally distribute the heat flux signal. The thermal interface material was 3M 5591s silicone based thermal pad inserted to minimize thermal resistance due to air gaps. The full assembly was then clamped to a metal stand to ensure good contact pressure between the interface material and the gauges.

The ultimate goal of this setup was to reduce losses and simulate instrumented hardware. However, the plate temperature increased rapidly because the heat had no outlet. This increase in plate temperature resulted in larger losses before the heat flux signal reached the Kapton gauges and subsequently a smaller ΔT. There was no simple way of estimating the losses and it became apparent that the heater assembly needed re- evaluation.

3.4.3 Kapton Heater Final Setup The first difficulty addressed was driving the heat flux signal through the gauges. This was solved fairly easily by the application of thermal paste on the bottom of the copper plate, then clamping the full assembly to a large aluminum heat sink. Figure 36 depicts the final heater assembly. The only difference between the two test methods was the use of the thermal paste and the aluminum sink. The two changes resulted in much lower copper plate temperatures and higher ΔT’s for the gauges compared to previous runs at the same conditions.

Figure 36: Final Kapton Heater Test Assembly

3.4.4 Kapton Heater Initial Results Due to the layer of aluminum attached to the heater and the thermal interface material, the time each gauge took to reach steady state was much longer than the oil bath. Figure 37 shows the response of 5 mil gauges instrumented onto a copper plate. This particular run was at 28 V, which corresponds to a heat flux of about 14,350 W/m2.

Figure 37: 5 mil Gauge Response Kapton Heater

The Kapton heater method was employed on both the 2 mil and 5 mil copper plates. There were 2 fully functional gauges on the 2 mil plate and 3 on the 5 mil plate. Table 4 shows the run schedule carried out using the Kapton heater method. The voltage was varied to change the heat flux signal. The 2 mil gauges were run at 28.13 and 23.71 V, while the 5 mil gauges were run at 28.05, 23.71, and 14.08 V. The corresponding nominal heat flux is also listed in Table 4.

Table 4: Run Schedule Kapton Heater

Run Gauges Voltage (v) Estimated Heat Flux (W/m2) 1 2 mil 28.13 14432 2 2 mil 23.71 10252 3 5 mil 28.05 14352 4 5 mil 23.71 10254 5 5 mil 14.08 3615

Using the nominal heater wattage as determined by equation (3.4) and dividing by the cross sectional area of the interface material the estimated heat flux could be calculated. With Q, the measured ∆T of the gauges could be used to find k/d and subsequently k. The measured thermal conductivity is shown in Figure 38. The k values were higher than expected, but variation between the 2 mil and 5 mil gauges was very low. Another encouraging result of this testing was the low individual gauge variation between runs.

Figure 38: Thermal Conductivity Nominal Q

It was clear some method was needed to estimate the actual Q input to the gauges, however, the consistent gauge response was promising.

3.4.5 Estimating Heater Effeciency The addition of the aluminum thermal sink resulted in a higher ΔT of the gauges corresponding to an increase in heater efficiency; however there were still some losses (possibly up through the Teflon or to the air) before the signal reached the gauges. The actual output of the heater may be less the theoretical as well. Nonetheless, the only heat that is of interest is the heat that flows through the gauges into the plate. This point makes the addition of the aluminum thermal sink more useful than originally thought. The majority of the heat flux signal that goes through the gauges will flow into the aluminum, raising the internal temperature. The rise in internal temperature will be directly proportional to the heater wattage. It should be noted that this method does not estimate the total output of the heater, this method only estimates the heater wattage that is encountered by the gauges and subsequently flows into the aluminum sink, which should be the majority of the heat flux signal recorded by the gauges. Equation (3.5) was employed to estimate the wattage into the aluminum sink.

(3.5)

This technique was considered after the initial testing, so the experimental setup was repeated. An RTD was attached to the bottom of the 6061 Al sink. The Bi number of the sink was <<0.1 so it was the internal temperature was assumed to be constant. Figure 39 depicts the increase in Al temperature with time.

y = 0.0063492x + 20.9566093 R2 = 0.9995313 22.00 21.95 21.90 21.85 21.80 21.75 21.70 RTD3 21.65

Temperature (C) Temperature 21.60 Linear (RTD3) 21.55 100.0 110.0 120.0 130.0 140.0 150.0 160.0 Time (s)

Figure 39: Increase in 6061 Al Temperature vs. Time

The nominal voltage for this experiment was 23.69 V. Using the mass, specific heat, and temperature change, the heater efficiency was estimated to be 78.8% of the nominal heater wattage. Another run was attempted and estimated the efficiency to be 78.4%. This value, about 79%, represents the recorded minimum heater efficiency. It is likely there are some unaccounted losses that are not considered in only measuring the increase in aluminum temperature, and the actual heat wattage through the gauges would be higher. However, this measured efficiency was performed on the exact experimental setup. Other heater testing was performed, mounting the heater directly on the sink and minimizing losses as much as possible. This testing resulted in a maximum heater efficiency of 90%, but does not represent the experimental setup, only a maximum obtainable heat output. These tests essential bounded the heat flux within 79% – 90% of the nominal output, though it is thought to be closer to 79%. Figure 40 depicts the Kapton thermal conductivity assuming the heat flux seen by the gauges is 79% of the nominal.

Figure 40: Thermal Conductivity at 79% Heater Output

Similar to Figure 40, Figure 41 depicts the heater output range. The thermal conductivity of each gauge has been calculated twice, once at 79% and once and 90% hater output. If the maximum efficiency was encountered by the gauges, the average thermal conductivity would be just below the current value. However, it is likely that the thermal sink heater measurement is a closer approximation of the actual heat flux than the heater characterization tests.

90% Q

79% Q

Figure 41: Heater Output Range

3.4.6 Variation in k/d Heater Test Similar to the oil bath, there was some variation between gauges encountered during the Kapton heater test. Again this variation was consistent with the variation seen during the oil bath, and the expected variation from DuPont. Figure 42 depicts the variation seen between 5 mil gauges during the Kapton heater test.

Figure 42: Variation between Gauges Kapton Heater

3.5 Hot Air Gun Due to the uncertainty in the Kapton heater output, it was decided to pursue the hot air gun method, similar to the method employed by Piccini et al. [4]. Depicted in this section will be the initial testing and investigation used to see if this was a viable option for k/d calibration. The heat gun had a nominal diameter of 1”, a volumetric flow rate of 3.8 CFM, and an approximated air temperature of 200 °C. The estimated Re number was about 2600, in the laminar region.

3.5.1 Hot Air Gun Viability Many studies on jet impingement are cooling experiments used to measure Nu number or similarly the convective heat transfer coefficient hc distribution. Glynn et al. [21], O’Donovan et al. [22], and Juan et al. [23] are three such examples of jet impingement cooling for the purpose of electronic cooling. Kreith et al. [24], mentions an experimental study on jet impingement of water. Figure 43 is a simple diagram depicting the three main lengths that are useful when characterizing jet impingement.

Instrumented Surface

Jet Exit

Figure 43: Jet Impingement Length Scales

The aspect ratios of h/d and r/d are important factors in determining the surface distribution of the Nu number. The Reynolds number of the flow is also an important factor. In general, lower Re number flow will result in a more uniform Nu number distribution. The treatment by Kreith et al. [24] makes no mention of the aspect ratio h/d, however it is stated that the region of r < .8d Nu should be constant. Many of the other experimental studies depict a more uniform Nu distribution as r/d decreases and h/d increases. These two trends are understandable, as h/d increases the jet will diffuse and spread over a larger area. As r/d decreases, the area over which the Nu number is being assumed constant decreases. There are two major differences between many of the studies and the treatment here. First the nozzle exit diameter, ultimately 0.5”, is much larger than the .02” - .06” 60

exit diameter range of many of the studies. The second major difference is the Re number employed during the studies. Many studies use Re > 5,000 and upwards of 30,000 compared to the 2,000 – 3,000 range for this calibration method. This large difference may very well be related to the small nozzle exit diameter employed during the studies as Re is inversely proportional to the nozzle diameter. Figure 44 from Glynn et al. [21] depicts experimental results of the convective heat transfer coefficient distribution hc, for a nozzle exit diameter of 0.5 mm at varying Re and h/d aspect ratios.

Figure 44: Local Heat Transfer Coefficient; d = 0.5mm; H/d = 2, 4; Re = 1000, 5000; (Air Jet) (Glynn et al. [21])

As shown in Figure 44 and previously mentioned, as Re gets smaller and h/d increases the convective heat transfer coefficient is more uniformly distributed. This is important as hc is directly related to the heat flux. As long as the jet temperature and surface temperature stay relatively constant over the length of the experimental run, the heat flux will be constant over the surface given the selection of proper dimensions. It is also important to note that as hc becomes more uniform, it decreases, which will result in a smaller Q. All these factors become important when designing a feasible calibration rig.

3.5.2 Gauge Response Once it was understood that an essentially constant heat flux distribution could be induced by jet impingement, initial experiments were performed to see how the gauges responded to the hot air gun. The oil bath had a quick response, but also decayed very quickly. The Kapton heater had a good steady state signal, but took a long time to reach steady state. An ideal heat flux signal would be constant and reach steady state quickly. Figure 45 depicts the gauge response of the 5 mil gauges instrumented onto the flat copper plate.

Figure 45: Gauge Response Hot Air Gun

There are some promising qualities to the response seen by the gauges. First, steady state is reached in less than a second. Once steady state has been reached, ∆T is essentially constant, implying a constant heat flux. The signal is a bit noisy and trends downward at the end; however this was the nominal diameter outlet, held by hand with no control over the outlet temperature of the jet from the nozzle. Using the initial gauge response data, a heat flux estimate was calculated based off the lower gauge temperature and material properties of copper, similar to the method

employed in measuring the heater wattage for the Kapton heater method. This heat flux was seemingly a low estimate and resulted in low values of k. Because of the many uncontrolled factors of this initial experiment, it was believed that this method was a viable option, only it would be a necessary design criterion to instrument a gauge on a surface where the Q could be independently verified. This notion will be expanded upon in the next chapter.

CHAPTER 4

HOT AIR GUN MODIFIACTION - FEASIBILITY EXPERIMENT

Initial design and experiments for the hot air gun were mentioned in chapter 3. This chapter discusses the final design and results of the hot air gun method of calibration based off the initial findings presented in the previous chapter. Piccini et al. [4] used a thin copper calorimeter placed in the experimental rig in order to verify the Q output of the hot air gun. A similar method will be presented here, only a gauge will be instrumented onto the copper calibration fixture. This allows for the calibration of a gauge while independently verifying the heat flux. The design presented here is more accurately described as a feasibility experiment. The ultimate goal was to be able to induce a stable known heat flux onto an instrumented blade and characterize any variation among the gauges. The treatment here will introduce an intermediate hot air method and propose modifications for a more applicable method for instrumented gauges, with the goal of resolving individual gauge k/d which may change due to small changes in the thickness of the Kapton..

4.1 Copper Test Plug It was decided to design the copper plug that would ultimately be used to calibrate the Q output of the hot air gun first, because a gauge had to be instrumented onto the copper. The idea was to use a piece of OFE (oxygen free electrolytic) copper, which is at least 99.99% pure copper, and match the dimensions to the nozzle outlet. The copper alloy 101 has consistent material properties between multiple sources. Once the material had been selected, a minimum diameter of the slug was found using the gauge and lead dimensions as a primary constraint. The diameter selected was 0.5”. The length was then found using multiple design criteria, including a low Bi number and small % non copper thermal mass. The design curve is shown in Figure 46. 64

0.16 1.60 0.14 1.40 0.12 1.20 0.1 1.00 0.08 0.80 0.06 0.60

0.04 0.40 % Thermal Mass%

L, Bi #, Mass (Kg) Mass #, Bi L, 0.02 0.20L (V/SA) 0 0.00Bi 0 1 2 3 4 5 6 Mass (kg) h (in) Thermal Mass % Design Point

Figure 46: Design Curve Copper Plug D = 0.5”

Figure 45 depicts design curves for a diameter of 0.5” and height of varying length (L), the significant length scale in the calculation of the Bi number. It approaches a constant value for length greater than about 2” based off the 0.5” diameter. In order to use the assumption that the plug is at constant temperature, the Bi number had to be low, and in this case was not a concern. The second biggest design factor was the percent thermal mass or ratio of the mass of the (gauge + solder pads + adhesive) to the mass of the copper. This estimate shows that at about 1” height the % non copper thermal mass is 0.4%. After the final plug was instrumented, the thermal mass was about 1% due to a small amount of epoxy used for strain relief of the leads. Figure 47 depicts the copper plug concept design.

D = 0.5”

h = 1”

Figure 47: Copper Test Plug Concept Design

The next major part to design was the nozzle outlet. The nominal diameter was 1”, which was large and uncontrollable. In order to have a relatively uniform Q over the area of the plug, an outlet diameter of 0.5” was selected. Other modifications included extending the nozzle and the creation of an annular tube system. The main purpose of the annular tube was to preheat and insulate the inner tube in order to maintain a more consistent air temperature. The nozzle extension served a similar purpose. Once the nozzle reached a steady state temperature, the exit jet temperature should stay fairly constant. Exit holes were drilled in the end of the outer tube to allow ample outlet for the outer tube flow. Figure 48 is a drawing of the nozzle extension concept design.

Figure 48: Concept Design Nozzle Extension 66

It was important to reach a consistent nozzle exit temperature. Data was acquired using an RTD instrumented onto the end of the inner tube. The hot air gun took nearly 12 minutes to reach a nozzle exit temperature of ~ 162 °C. During each run the nozzle exit temperature was monitored to reach a value near this point before the DAS was triggered.

4.2 Final Design There were three main design concepts for the hot air gun method, the annular tube nozzle extension, the copper test plug, and the test plug stand used to insulate the copper plug from any unwanted heat transfer. Many of the design concepts were outlined in the previous section. Here the final design will be presented briefly. Figure 49 depicts the instrumented copper test plug with dimensions of D = 0.5”, h = 1”.

Figure 49: Copper Test Plug

In order to get a uniform Q over the area of the plug, the nozzle diameter was selected to match the diameter of the plug. The nozzle is shown in Figure 50.

Figure 50: Nozzle Extension 67

Once the test plug and nozzles’ were selected, a test stand was built to insulate the copper plug from unwanted heating, only exposing the instrumented face. Figure 51 depicts the Teflon stand.

Figure 51: Teflon Test Plug Stand

With the nozzle, plug, and stand all instrumented and assemble the entire rig could be put together. The full hot air gun rig can be seen in Figure 52.

Figure 52: Entire Hot Air Gun Rig

4.3 Initial Results Once the final experimental setup was established, the distance from the exit nozzle was still uncertain. A few initial runs were performed to establish the gauge response at varying distances from the nozzle exit. Figure 53 depicts the gauge response of a single 2 mil gauge instrumented onto the copper plug.

Figure 53: Gauge Response Varying Distance from Nozzle

The 3.95” and 2.85” distances were ruled out for the apparent reason that there was a large amount of noise associated with the heat flux signal. The 1.85” and 1” signal seemingly gave a similar response and the further distance from the exit would be more appropriate for the uniform heat flux distribution assumption. However, the calculated heat flux estimate is proportional to the slope of the lower gauge increase. This was found to be more consistent at the 1” nozzle distance making that distance preferable over the 1.85” distance. The 1” distance from nozzle gauge response is shown in Figure 54.

4 Tdiff (C) Tdiff 2

0 1"

-2 2 4 6 8 10 12

Time (s)

Figure 54: 1" Distance from Nozzle Gauge Response

With the distance from the nozzle selected, there was one more major unknown with the data. There was a large offset between the upper and lower gauges. The upper gauge was consistently higher than the lower. The first attempt at correcting the problem involved checking the amp calibrations. The two resistors were outside the range of the original amp cals. The difference in the offset after re-calibrating the amps can be seen in Figure 55. There seemed to be about a 0.4 °C error due to the being outside the range of the calibration, but there was still a lot of unexplained variation.

3.0000

2.5000

2.0000

Initial Offset 1.5000

T (C) T Amp Recal ∆ 1.0000

0.5000

0.0000 0 2 4 6 8 10 12 Run

Figure 55: Offset Difference between Initial and Recal

It is interesting to note in Figure 55 that runs 1, 3, and 9 where the beginning of a series of runs. This led to the theory that this offset was associated with the prior heating of the copper plug. Run 5 was also the beginning run in a series of tests leading to more mystery. These mysteries were solved by tracking the upper and lower gauge temperatures over a long period of time. From Figure 56, it is apparent that there is a thermal gradient between the upper and lower sensor caused by the copper plug being out of sync with the environment (U – L is plotted using the secondary y-axis). One might have thought that the copper plug would come to an ambient condition and track the change in the room temperature, but as shown in Figure 56, this does not seem to happen. The net effect is that there is always a small, but different additive heat-flux from the room into the copper plug that needed to be removed, which can be done by subtracting out this initial offset.

Figure 56: Ambient Air Effect on HFG Plug

4.4 Final Results As previous mentioned the primary reason for having a gauge instrumented on the copper test plug, was to obtain an independent measure of Q. This method was similar to the method employed for the Kapton heater estimate. The same equation (3.5) was used to estimate the hot air gun wattage into the copper. The cross sectional area of the plug face was then used to find the heat flux. The range of the heat flux estimate was 25,262 – 31,965 W/m2, meaning it would be difficult to translate this particular setup to

instrumented gauges with no other way of accurately measuring Q. With the Q estimate method standardized, the final runs were performed. Initial results were producing lower than expected estimates, k ~ 0.2 W/mK, so it was theorized that the contact area between the copper plug and the Teflon stand was the cause of unwanted heat loss. This led to the creation of multiple lids with different contact areas. The different lid thicknesses can be found in Table 5.

Table 5: Lid Thicknesses

Lid Mils Runs Thick 109 1-5 Mid Thick 88 6-10 Mid Thin 64 11-15 Thin 35 16-20

Figure 57 depicts the results of 20 independent runs. Each lid was run 5 times and then the average value was found. This average value represented the measured k at that contact area. Once an average was found for each thickness level, the four points were curve fit. Using this fit, an extrapolated value to zero Teflon copper contact was calculated. This extrapolation resulted in a k = 0.2164 or k/d = 8520 assuming a nominal 1 mil thickness. This reflects about a 7% decrease from the previous value.

Figure 57: Final Run Data Hot Air Gun Method

From Figure 57 there are 3 points (1, 14, and 16) that seem to be significant outliers. Though there is no assignable cause, other than possible experimental variation, the removal of these point results in a k = 0.2256 or k/d = 8882 for 1 mil Kapton.

4.5 Recommendations for Future Implimentation The intermediate modifications to the hot air gun method helped characterize how the gauges would respond to a more controlled air flow, and in general produced very clean good signals. However, there were some limitations, such as heat flux repeatability, which would make it difficult to translate this particular setup to an instrumented blade with no independent measure of Q. Without the copper plug to get an independent measure of Q, this method would have produced no results. Some of the promising qualities of the current method included a quick gauge response, larger Q than previous methods, and the fact that this method did not cause damage to the gauges. 75

If hot air were to be implemented in the future there would need to be some modifications to the current treatment. First, and most importantly, a stable repeatable Q would need to be produced. From the information gathered from DuPont and some of the k/d calibrations, if Q is not known to within +-5% there is no chance in characterizing any variation. To really get a handle on how this property behaves however, Q should be known within +- 1%. A method similar to the copper plug could be employed to independently verify Q, but again the experimental setup must have very limited affect on the measurement of Q. The aspect ratios h/d, r/d, and the Reynolds number are all important design criteria in creating a constant Q over the area of the gauge. A few less important aspects, but simple modifications include an improved nozzle alignment technique, faster heat up times, and a method to prevent gauge preheat.

CHAPTER 5

CONCLUSIONS

There are many factors that effect the heat flux measurement of thin film Kapton heat flux gauges, and presented was the effect of the thin film sensor accuracy and k/d. The method for calibrating thin film sensors has been presented and shown to produce residual errors on the order of +- 0.1 °C. Drift in the gauges resistance was encountered and a method to maintain levels of accuracy on the order of +- 0.4 °C was presented. After calibration, heat flux gauges are recorded using a high speed data acquisition system that records voltage. There are many values associated with the DAS that must be known in order to maintain the same level of accuracy achieved during the sensor calibrations. In order to obtain low offset errors between gauges, a resistor calibration technique was employed that yielded correction factors for the voltage recorded through each individual amp. However, this technique requires a change in the accounting system used in the main DAS software, and the question of how this technique should be implemented in larger systems with hundred of amplifiers is still in question and is currently being pursued. One major finding in this work is that the oven calibrations can produce calibrations of the same level of accuracy as the oil bath. That is a major step forward as oven calibrations are a much cleaner technique. However, to achieve this result, the gradients that existed in the larger test articles had to be accounted for. Fortunately these gradients were linear and this was easily done, but more complicated shapes (such as blades) may require a more complicated set-up to ensure that there are no gradients imposed by the oven system. There are several small changes that can be implemented on that set-up to improve these results. Variation in k/d was presented through Kapton heater tests, with low variation of the individual gauges between runs, and low variation between 2 and 5 mil instrumented

gauges. Due to heat flux uncertainty, the k/d value produced was only at best accurate to +- 5%. A hot air gun method was also presented, with a gauge instrumented onto a test plug in order to independently verify Q. Through multiple runs, a final range of 0.2164 - 0.2256 W/mK or k/d = 8520 - 8882 for 1 mil gauges was found. This represents a decrease of 3 - 7% from the current value, but is within the technical specifications as provided by DuPont and the wide range of the Kapton heater test. The hot air technique produced variations on the same order as the uncertainty in the heater system from loses, but it has become clear that the main driver for these small variations are a combinations of losses to the Teflon and changes in the ambient conditions. This implies that improved experimental techniques should allow these external conditions to be accounted for and improve the overall results. The key goal of measuring k/d on curved blades to check for variation in d has not been realized yet. While the hot air gun technique is promising, the overall size of the system is too large to be used with a blade, and the jet is not reproducible enough to assume a constant heat-flux level without independent measures. The empirical equations that describe the heat-flux as a function of jet properties do not seem to be accurate enough to be used as the main calibration source either, thus requiring an independent measure of heat-flux. However, even with these limitations, the knowledge of the overall behavior of the fourth generation heat-flux gauges has advanced greatly over the previous generation. The fact that a calibration system for k/d has been created which provides a reasonable estimate without damaging gauges is in itself a major step forward. The quantification of the overall performance of the temperature sensors and the change to a resistance based reduction has improved the temperature measurement capability and given natural degradation, provided a method for extending the usable life of gauges in a rig. This is a large improvement. The fact that typical temperature accuracies were increased an order of magnitude better than previous sensors, and for the lower heat-fluxes expected in typical cooling experiments, the increase in thickness doubles the signal strength, the signal to noise ratio has been improved by about a factor of 20 in these sensors.

BIBLIOGRAPHY

1. Childs, P.R.N., Greenwood, J.R., and Long, C.A., 1998, "Heat flux measurement techniques". Proceedings of the Institution of Mechanical Engineers, 213 (Part C): pp. 655-677

2. Taler, J., 1994, "Theory of transient experimental techniques for surface heat transfer". Int. Journal of Heat Mass Transfer, 39(17): pp. 3733-3748

3. Oldfield, M.L.G., 2008, "Impulse Response Processing of Transient Heat Transfer Gauge Signals". Journal of Turbomachinery, 130: pp. 1-9

4. Piccini, E., Guo, S.M., and Jones, T.V., 2000, "The development of a new direct- heat-flux gauge for heat-transfer facilities". Measure Science Technology, 11: pp. 342-349

5. Epstein, A.H., Guenette, G.R., Norton, R.J.G., and Yuzhang, C., 1985, "High Frequency Response Heat Flux Gauge". Review of Scientific Instruments, 75(4): pp. 639-649

6. Doorly, J.E. and Oldfield, M.L.G., 1986, "The Theory of Advanced Multilayer Thin Film Heat Transfer Gauges". Int. Journal of Heat Mass Transfer, 30(6): pp. 1159-1168

7. Vidal, R.J., "Model Instrumentation Techniques for Heat Transfer and Force Measurements in a Hypersonic Shock Tunnel".

8. Bogdan, L. and Garberoglio, J.E., 1967, "Transient Heat Transfer Measurements with Thin-Film Resistance Thermometers--Fabrication and Application Technology".

9. Oldfield, M.L.G., Jones, T.V., and Schultz, D.L., 1978, "On-Line Computer for Transient Turbine Cascade Instrumentation". IEEE Transaction on Aerospace and Electronic Systems, AES-14, No. 5: pp. 738-749 79

10. Murphy, J.S., "Control of the "Heat-Island" Effect on the Measurement of Pyrex Thin-Film Button Gauges Through Gauge Design", Department of Mechanical Engineering, Ohio State University, 2004, pp. 135.

11. Linsley, J.E., "Design and Manufacture of a New Double-Sided Kapton Heat Flux Gauge", Department of Aerospace Engineering, The Ohio State University, 2005, pp.

12. Iliopoulou, V., Dénos, R., Billiard, N., and Arts, T., 2004, "Time-Averaged and Time-Resolved Heat Flux Measurements on a Turbine Stator Blade Using Two-Layered Thin-Film Gauges". Transactions of the ASME, 126

13. Haldeman, C.W., Dunn, M.G., and Mathison, R.M., 2010, "Fully-Cooled Single Stage HP Transonic Turbine: Part II - Influence of Cooling Mass Flow Changes and Inlet Temperature Profiles on Blade and Shroud Heat-transfer".

14. Zilles, D., "The Effect of Non-Isothermal Wall Boundary Temperature on Convective Heat Flux over a Flat Plate", Department of Aerospace Engineering, The Ohio State University, 1999, pp.

15. Kheniser, I.E., "Film Cooling Experiments in a Medium Duration Blowdown Facility", Department of Mechanical Engineering, The Ohio State University, 2010, pp.

16. Bouquet, F.L., Engineering Properties of Kapton. 1990: Systems Company.

17. Dupont, "Dupont Kapton VN Polymide Film: Technical Data Sheet ". 2006 http://www2.dupont.com/Kapton/en_US/assets/downloads/pdf/VN_datasheet.pdf.

18. CSHyde, "Kapton Type VN". 2010 http://www.cshyde.com/Films/KaptonVN.htm.

19. Dupont, "Private Communication with Dupont North Americas (Mark Maclease)". 2010.

20. Corning, D., "Product Information Dow Corning 210H Fluid". 1997 http://www.latinquimicasrl.com.ar/pdf/Dow%20Corning%20210%20H%20Fluid. pdf. 80

21. Glynn, C., O’Donovan, T., and Murray, D.B. "Jet Impingement Cooling". in 9th UK National Heat Transfer Conference. 2005

22. O’Donovan, T.S. and Murray, D.B., 2007, "Jet impingement heat transfer – Part I: Mean and root-mean-square heat transfer and velocity distributions". Int. Journal of Heat and Mass Transfer, 50: pp. 3291–3301

23. Juan, T., Zhou, J., Jiang, L., and Yang, Y. "Experimental Research on Heat Transfer of Confined Air Jet Impingement with Tiny Size Round Nozzle In High Density Electronics Packaging Model". in High Density Microsystem Design and Packaging and Component Failure Analysis. 2005

24. Kreith, F. and Bohn, M.S., Principles of Heat Transfer. 6th ed. 2001: Brooks/Cole.