Politecnico di Milano
School of Industrial and Information Engineering
Master of Science in Mechanical Engineering
Design and Characterization of a Fast Response Temperature
Probe for Gas Turbine Test Rigs
Advisor: Prof. Paolo GAETANI
Supervisors: Prof. Sergio LAVAGNOLI & Bogdan CERNAT
Candidate:
Ringraziamenti
`
E mio dovere citare tutti coloro che hanno contribuito, in ambito accademico e non, alla stesura di questa Tesi.
Ringrazio il Professor Gaetani per i suoi preziosi insegnamenti, che hanno fatto nascere in me l’interesse per l’attivit`a di ricerca sperimentale in ambito turbomacchin-istico, e per la fiducia dimostrata nelle mie capacit`a affidandomi questo progetto.
Ringrazio anche il Professor Lavagnoli, per avermi accolto come studente al Von Karman Institute e per avermi spronato ogni settimana a dare il massimo. La ringrazio per aver pazientemente seguito ed indirizzato nel mio lavoro. La sua supervisione `e stata fondamentale.
Ringrazio tutti coloro che mi hanno aiutata a finalizzare questo progetto, in parti-colare Bogdan Cernat, per la disponibilit`a ed il sostegno morale oltre che nelle attivit`a di laboratorio, ed Andrea Attavino per avermi trasmesso le conoscenze necessarie allo svolgimento delle simulazioni numeriche.
Ringrazio anche il Professor Persico, perch`e ebbene si, `e grazie a lui e al suo corso del terzo anno che ho deciso che le turbomacchine sarebbero state le mie compagne di magistrale. Ad anni di distanza, ricordo ancora con piacere le sue lezioni, ed `e stato bello incontrarla di nuovo, con nuovi corsi, in quest’ultimo anno di studi. `E stato lei a creare questo mostro.
Ringrazio chi ha sempre creduto in me, a partire da mia sorella e dai miei genitori, che sono stati, fin dal primo giorno di universit`a, i miei tifosi piu grandi. Grazie per avermi permesso di studiare, per essere stati accanto a me in ogni difficolt`a, e per avermi tirato s`u quando mi buttavo gi`u. `E enorme il bene che provo per voi.
Un grazie speciale a chi mi ha amata e a chi mi ha donato il suo affetto, al mio ragazzo Aldo, che mi `e sempre stato vicino, seppur lontano: we are a good team!
Ringrazio tutti gli amici, meravigliosi, incontrati sui banchi universitari. Ringrazio Giorgia, Federica, Riccardo, Daniele, Sabino. Sono fortunata ad avervi nella mia vita. E ringrazio anche gli amici con cui ho condiviso i 7 mesi a Bruxelles: Manuela, Alessandro, Andrea, Miguel. Questa esperienza la porter`o per sempre con me, soprattutto grazie a voi.
Infine, ma non per importanza, ringrazio di cuore la mia mamma, per avermi inseg-nato la cosa piu importante: “non devi essere perfetta, devi essere felice”.
Abstract
The experimental investigation on the performance of modern gas turbines is of fun-damental importance for the quantification of the efficiency and the life-span of the components. Significant research efforts are presently devoted to the understanding of the unsteady flow structures generated in the high pressure turbine (HTP) stage in order to to quantify their contribution among the efficiency loss sources and to design innovative solutions for their containment.
In this thesis, we designed and assessed an innovative fast-response temperature probe equipped with an array of thin film sensors. The probe will be used in the short duration CT-3 facility at the Von Karman Institute for Fluid Dynamics for the char-acterization of novel rotor airfoil geometries with improved aerodynamic and thermal performance. The probe will be placed in a measurement plane located 50% of the axial chord downstream of the HPT rotor blade trailing edge. The goal of the application is a precise evaluation of the unsteady temperature field generated by the action of the blades, on a measurement grid extending over the entire span of the airfoil and covering the full spatial periodicity of the HPT stage, i.e. one complete vane pitch. The high frequency response (up to 100 KHz), the high spatial resolution of the sensor array (2.8 mm radial discretization step), the low intrusiveness and the ability of covering the measurement grid with the minimum number of tests are the main strengths of the probe, that make it outstanding in this research field.
The design process is explained in detail, focusing on the requirements that the probe needs to satisfy. The manufacturing procedure, entirely performed at the Institute, the assembly and the adopted materials are reported. Numerical simulations in OpenFOAM are exploited for the preliminary evaluation of the achievable measurement accuracy. Moreover, the data reduction routine is designed and implemented, allowing to solve the unsteady heat transfer problem by means of the finite volume method (FVM). Finally, a dedicated calibration setup is designed and realized and the probe is characterized in this controlled environment to precisely validate the numerically-predicted performance.
Sommario
La ricerca sperimentale in ambito turbomacchinistico ricopre un ruolo di fondamentale importanza per la validazione dei risultati numerici e per la valutazione diretta, medi-ante l’uso di sonde e sistemi di misura, dell’efficienza e della affidabilit`a dei componenti. In particolare, per quanto riguarda le turbine a gas, una grande parte della ricerca si concentra sull’indagine delle strutture vorticose che sono solite formarsi nel canale in-terpalare e nel passaggio fra pala e cassa. Tali strutture rappresentano una fonte di perdita di efficienza per la macchina, e risulta quindi necessario provvedere, con un design appropriato delle pale, al loro controllo e contenimento.
Questa tesi tratta la progettazione e la caratterizzazione di una nuova sonda di tem-peratura ad alta risposta in frequenza. La sonda `e equipaggiata un array di sensori di tipo thin film, e verr`a impiegata presso il Von Karman Institute For Fluid Dynamics all’interno di un’importante campagna sperimentale volta alla valutazione dell’efficienza di diversi design palari innovativi ad alta prestazione aerodinamica e resistenza termica. La sonda verr`a posta in un piano di misura posizionato al 50% della corda assiale a valle del bordo di uscita del rotore di alta pressione, montato sul banco prova per turbine dell’Istituto (CT-3). Lo scopo dell’analisi `e quello di quantificare con precisione il campo termico instazionario generato dall’azione dei profili sul fluido, considerando una griglia di misura che coprir`a interamente il canale interpalare da mozzo a cassa e per l’intera periodicit`a spaziale dello stadio, ovvero per un passo della schiera. La capacit`a di mis-urare segnali ad alta frequenza (fino a 100 KHz), l’elevata risoluzione spaziale dell’array di sensori (2.8 mm di step di discretizzazione radiale), la bassa intrusivit`a e la possibilit`a di coprire la griglia di misura con il minor numero di test possibili sono le caratteristiche che rendono la sonda innovativa e rilevante all’interno dell’ambito di ricerca sopra citato.
Il progetto `e spiegato dettagliatamente a partire dalla fase di design, con particolare attenzione ai requisiti da soddisfare. Successivamente, `e riportato il processo di pro-duzione della sonda, il suo assemblaggio e i materiali impiegati per la sua costruzione. Inoltre, abbiamo svolto uno studio numerico in OpenFOAM per la valutazione prelim-inare dell’errore di misura e dell’incertezza nella lettura della temperatura. Insieme a questo abbiamo proposto, sempre tramite l’utilizzo di OpenFOAM e del metodo a vo-lumi finiti, una routine per l’acquisizione dei dati. Per concludere, abbiamo testato la sonda in un setup sperimentale appositamente progettato per essa, per verificare con precisione le performance predette numericamente.
Contents
Acknowledgments I
Abstract III
Abstract V
List of figures IX
List of tables XIII
1 Introduction 1
1.1 Thin Film Probes Operating Principles . . . 3
1.2 Earliest Works . . . 9
1.3 Researches at the Von Karman Institute for Fluid Dynamics . . . 14
2 Probe Design 19 2.1 CT-3 Facility . . . 19
2.2 Aim of the Experimental Campaign and Design Requirements . . . 20
2.3 Gauge Components and Geometry . . . 22
2.4 Probe’s Head . . . 23
2.4.1 Probe’s Head Manufacturing . . . 26
2.5 Insulator and Stem . . . 28
2.6 Flow Field Around the Probe and Yaw Angle Sensitivity . . . 28
3 Thermal Simulations 35 3.1 The Finite Volume Method for Heat Conduction . . . 36
3.2 Steady State Validation . . . 38
3.3 Unsteady Validation . . . 41
3.4 Final Mesh Creation . . . 45
3.5 3D Simulations . . . 48
4 Data Reduction 57 4.1 2D and 1D Data Reduction With Uniform Initial Temperature . . . 60
CONTENTS
5 Experimental Characterization 69
5.1 GTP-A1 Preliminary Test and Annealing . . . 71
5.2 GTP-A1 Static Calibration . . . 76
5.3 Measurement Chain Calibration . . . 82
5.4 Investigation with Infrared Camera . . . 84
5.5 Hot Jet Experiment . . . 88
5.5.1 Pressure Transducer Calibration . . . 90
5.5.2 Thermocouple Calibration . . . 91 5.5.3 Test Settings . . . 92 5.5.4 Results . . . 95 6 Conclusions 105 Appendices 113 A Technical drawings 115
B GroovyBC for OpenFOAM 123
List of Figures
1.1 Metal capability and cooling technology trend [38] . . . 2
1.2 Early Macor (machinable ceramic) blade showing thin film gauges on surface and gold leads, from [33] . . . 5
1.3 Schematic of the 1D semi-infinite geometry for a single layers TF [30] . 6 1.4 Example of data interpolation and linear regression . . . 9
1.5 Typical analogue circuit used with thin film heat transfer gauges [26] . . 10
1.6 Total temperature probe designed by Buttsworth and Jones at Oxford University in 1997 [9] . . . 12
1.7 Schematic of the single prong probe designed by Buttsworth and Jones at Oxford University [7] . . . 12
1.8 Cylindrical probe with platinum thin films developed at Lewis Research Center, NASA [25] . . . 13
1.9 Photograph of the entropy probe developed at ETH: on the left the pres-sure probe is visible, as on the right side the thin films and the quartz rod are positioned [23] . . . 14
1.10 On the left: VKI CT-3 rotor blade equipped for heat flux measurements. On the right: inserts carrying 5 to 6 gauges, from [32] . . . 15
1.11 Turbine stage tested by Sieverding et Al: Thin film gauges used in stator and rotor (above) and measurement locations along the airfoil (below), from [27] . . . 15
1.12 Potograph of the probe designed by Carvalho [23] . . . 16
1.13 2D mesh of the turbine blade blade tested by Solano and Paniagua at the VKI [35] . . . 17
2.1 Technical scheme of the CT-3 facility with components indications and dimensions [27] . . . 20
2.2 Picture and exploded sketch of the first full-probe assembly GTP-A1 . . 22
2.3 Exploded and prospective sketch of the GTP-A . . . 24
2.4 Frontal drawing of the probe with detailed view of thin film sensors and nomenclature . . . 25
2.5 Picture of probe’s head under the microscope . . . 27
2.6 Flow regimes for cylinder in cross flow . . . 29
2.7 CFD study performed by Bassignana [4] . . . 30 2.8 Strouhal - Reynolds number dependency for flow around cylinders [20] . 31
LIST OF FIGURES
2.9 Error due to the vortex shedding interference with respect to the flow
angle of attack . . . 32
2.10 Variation of absolute flow angle at the measurement plane: blue maxi-mum variation, black mean variation and red minimaxi-mum variatoin [36] . . 33
2.11 Error in temperature measurement as function of the flow angle of attack and thin film length with respect to the probe’s diameter (L/D), from [4] 33 2.12 Nusselt number variation around the probe . . . 34
3.1 Temperature [K] imposed on the external surface for the steady state mesh validation . . . 39
3.2 Expected solutions for temperature and radial heat flux for the steady state mesh validation . . . 40
3.3 Mesh features for steady state Validation . . . 40
3.4 Weighting factor γ as function of Fo [14] . . . 43
3.5 Results of the unsteady validation for mesh N°3, F o = 800 . . . 45
3.6 Delay between numerical and analytical solution at high Fourier numbers. 46 3.7 Front view of the blocks for the creation of the final 3D mesh. Each color represents a single block. . . 46
3.8 View of the 3D model created in OpenFOAM. . . 47
3.9 Pacthes in 3D model: green = connection Macor-insulator; red = lateral surface; blue = thin films; yellow = heater. . . 47
3.10 2D model . . . 48
3.11 Temperature and heat transfer coefficient trends as function of time at probe’s stagnation point . . . 50
3.12 Initial temperature field for QH = 1200W/m2 . . . 51
3.13 Average temperature perceived by the 5th thin film during blow-down, for different heating powers QH . . . 52
3.14 Average convective heat flux perceived by the 5th thin film during blow-down, for different heating powers QH . . . 53
3.15 Detected adiabatic wall temperature through linear regression at different time step . . . 54
3.16 Detected adiabatic wall temperature for single test through linear regres-sion for t = 0.2 s to t = 0.4 s - 3D . . . 55
3.17 Detected adiabatic wall temperature for multiple tests through linear regression for t = 0.2 s to t = 0.4 s - 3D . . . 55
4.1 Heat Flux comparison - 2D vs 1D . . . 58
4.2 Temperature inside the probe - 2D step in heat flux . . . 58
4.3 Temperature at r = 3 mm for step in heat flux . . . 59
4.4 Heat flux from 1D data reduction compared with the 3D one . . . 61
4.5 Heat flux from 2D data reduction compared with the 3D one . . . 62
4.6 Comparison between 2D, 1D and corrected 1D models for data reduction 64 4.7 Starting temperature T0 before the blow-down for a section of the 3D model in correspondence of the 5th thin film, for QH = 1400W/m2 . . . 65
4.8 Temperature and HF evolution from probe’s power on to the end of the blowdown . . . 65
LIST OF FIGURES
4.9 Superposition principle for temperature evolution of Figure 4.8 . . . 66
5.1 Picture of the GTP-A prototype used for preliminary tests . . . 69
5.2 Results from the prototype heater characterization . . . 70
5.3 Picture of the GTP-A1 with thermocouples applied on the Macor surface 71 5.4 Results for the GTP-A1 heater characterization . . . 72
5.5 Setup for the annealing procedure with thin films off and indication of instruments accuracy . . . 73
5.6 Simplified schematic of the electronics of the thin film conditioning unit 74 5.7 Picture of control unit’s front and real panels . . . 74
5.8 Setup for the annealing procedure with thin films switched on and indi-cation of instruments accuracy . . . 75
5.9 Setup for the annealing procedure with thin films switched on: 1=PT-100, 2=calibration bath, 3=Fluke multimeter, 4=power supply, 5=inter-poser, 6=signal conditioning unit . . . 75
5.10 Voltage acquisition during the annealing - TF ON . . . 76
5.11 Ambient Temperature (24.8°C) Resistance Comparison before and after the last annealing procedure . . . 76
5.12 Thin film sensitivity expressed in Ω/K . . . 77
5.13 Intercept from least squares linear fit of calibration data . . . 78
5.14 Accuracy of the least square linear fit for static thin film calibration - R2 78 5.15 Thin film sensitivity as function of their nominal resistance Ω/C, from [17] 79 5.16 Tested inks and Macor specimen with the 6 thin films inserted in the calibration bath . . . 81
5.17 Variable resistance box . . . 82
5.18 IR camera setup . . . 84
5.19 Pictures of the GTP-A1 obtained with IR camera for increasing heater powers. . . 86
5.20 Temperature evolution along GTP-A1 head. . . 87
5.21 Temperature evolution along GTP-A2 head . . . 87
5.22 Maximum ∆T between sensors . . . 88
5.23 Test conduced on GTP-A1 with 20 mA for thin film and QH=0.42 W. Picture at 1 s, 30 s and 146 s after thin film turn on . . . 88
5.24 Setup for dynamic tests . . . 89
5.25 Dynamic tests setup pictures . . . 90
5.26 Validyne calibration law . . . 91
5.27 Signals for heater power of 165 mW, Mach = 0.3 . . . 96
5.28 Temperature and calculated HF, Mach = 0.2. Shutter opens at t = 2 s . 97 5.29 Temperature and calculated HF, Mach = 0.3. Shutter opens at t = 2 s . 97 5.30 2D data reduction of experimental wall temperature considering a single test (Mach 0.3, test N°1) . . . 98
5.31 2D data reduction of experimental wall temperature considering 12 tests (Mach 0.3) . . . 99
5.32 Total gas temperature TT variability between tests . . . 100
List of Tables
2.1 Minimum, maximum and average flow quantities in the measurement
plane behind the CT-3 rotor . . . 21
2.2 Macor reference thermophysical properties . . . 23
2.3 Thin films summary table . . . 25
2.4 Cross section of the probe’s head . . . 26
2.5 Probe’s head summary table . . . 26
2.6 Scheme of the heater . . . 26
2.7 Heater summary table . . . 26
2.8 Expected Reynolds numbers for the probe in CT-3 measurement plane . 29 2.9 Shedding frequencies for the probe in CT-3 facility . . . 31
3.1 Steady State Validation Summary . . . 41
3.2 Meshes parameters for the unsteady validation . . . 44
3.3 Transient Validation Summary . . . 45
3.4 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC calculated results - 3D model . . . 52
3.5 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC calculated with a single test - 3D model . . . 53
3.6 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC calculated with 4 tests - 3D model . . . 54
4.1 Initial thin film temperature from 3D simulations . . . 60
4.2 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC results - 1D uniform model . . . 61
4.3 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC results - 1D uniform model - all points regression . . . . 62
4.4 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC results - 2D uniform model . . . 63
4.5 Summary table for Adiabatic Wall Temperature Tw,ad and heat transfer coefficient HTC results - 2D uniform model - all points regression . . . . 63
4.6 Initial thin Film Temperature from 3D Simulations . . . 67
5.1 Prototype heater tests acquisitions . . . 70
5.2 GTP-A1 preliminary test summary table . . . 72
5.3 GTP-A1 annealing summary table . . . 74
LIST OF TABLES
5.5 Uncertainty analysis for GTP-A1 static calibration . . . 80
5.6 Sensitivity calculation for the new tested inks . . . 81
5.7 Resistance box characterization . . . 83
5.8 R-V coefficients . . . 83
5.9 Validyne linear regression coefficients: slope, intercept and R2 . . . 91
5.10 Nozzle thermocouple linear regression coefficients: slope, intercept and R2 91 5.11 Heater powers for each series of tests . . . 94
5.12 GENESIS settings for recorders: CH=channel, fs=sampling frequency, tS=acquisition time, trig.=trigger . . . 95
5.13 GENESIS settings for recorders: applied filters and trigger . . . 95
5.14 Post-process signal filtering with 3rd order Butterworth filter . . . 95
5.15 Jet thermodynamic quantities for each test series (S.I. units of measure-ments) . . . 96
5.16 Data reduction computational effort . . . 101
5.17 2D data reduction results for hot air jet experiments . . . 102
5.18 1D data reduction results for hot air jet experiments . . . 103
1.
Introduction
Gas turbines are a particular kind of internal combustion engines that exploit the Joule-Brayton thermodynamic cycle for converting the chemical energy of the fuel first into thermal energy for the gas and finally into mechanical energy for the utility. In turbo-machinery, the working fluid operates in continuum with a constant mass flow through the machine, passing by a series of cascades of blades called stages. Every stage is com-posed by a moving cascade, called rotor and a stationary cascade, called stator or vane: both contribute to the energy extraction process by applying a fluid dynamic action on the flow and provoking its gradual expansion through the machine. The application of gas turbines finds place in energy production as well as in propulsion, therefore the final utility for a gas turbine can be, for example, the shaft of an electrical generator or the propeller of an aeroengine. In particular, for what concerns propulsion and aero-engines, design of modern gas turbines is nowadays more and more addressed to an increase of the efficiency and of the lifespan of the machine, to reduce both the envi-ronmental impact of engines and their direct operating costs. The higher the efficiency, the longer the flight time of the aircraft and the least fuel has to be carried on board. In addition to that, the reliability of components represents a key factor for a robust and successful design, and being able of estimating life of components in an accurate way contributes in the reduction of maintenance costs and possible failures. In the last 70 years, efficiency of gas turbines has been increased mainly exploiting higher turbine entry temperatures (TET). This solution, on the other hand, opened the quest for the development of high temperature resistant materials and innovative cooling techniques. As a fact, the life-limiting component of a gas turbine is the high pressure (HP) stage, that is the one that the flow encounters as soon as it exits the burner. The HP stage is the one subjected to the highest thermal loads, and in addition to this, blades have to endure the gas pressure coming from the combustion chamber and the centrifugal forces arising from rotational movement. An example of failure that has to be faced in such harsh environment is the phenomenon of creep, that is the tendency of the metal to be permanently deformed when subjected to persistent mechanical stresses at high temperatures (close to the melting temperatures). Understanding the heat exchange between combustion gases and metal blades results necessary to extend the safe life of components and control the mechanism of damage.
In this research scenario, the experimental heat transfer and temperature data are essential for supporting the effort of turbomachinery designers and for the validation of CFD simulations, hence probe measurements still play a significant role in the test-ing and development of gas turbines. The targets of this work are manyfold. One of the goals of this thesis is the design of an innovative probe for unsteady temperature
Introduction
measurements, that we developed at the Von Karman Institute for Fluid Dynamics. The probe will be on duty at the Institute gas turbine test rig, the CT-3 facility, in the framework of an important experimental campaign for the characterization of a novel HPT test article by means of high-precision, high-bandwidth aerothermal mea-surements. The aim of this thesis is to pave the way for the experimental campaign that will fully investigate the thermodynamic condition of the flow field behind the stage.
According to [18], the global trend for the turbine entry temperature in the past decades has been of 10 K per year, as the material capability to withstand higher thermal loads with no damage has risen of 3 K per year up to temperatures close to 1600 °C. Figure 1.1, illustrates the contribution in rising the TET of different cooling techniques adopted in the history of gas turbines, such as the film cooling and the closed-loop cooling. On the other side, material science contributed to the cause providing solutions such as thermal barrier coatings (TBC) and ceramic matrix composites (CMC) to protect the metallic blades.
Figure 1.1: Metal capability and cooling technology trend [38]
It has to be noticed that the thermal loads of interest for this study are highly un-steady: those are created by the gas exiting from the combustion chamber, that is by nature extremely turbulent (turbulence is of fundamental importance for the enhance-ment of combustion) and by the work extraction created by the blade action on the flow. It can be intuited that the characteristic frequency of these events is somehow related to the rotational speed of the machine, or, in other words, to the blade passing frequency, that can reach 10 kHz in high speed turbomachines. Heat transfer measure-ments are traditionally inferred from temperature measuremeasure-ments since the heat driving force is always a temperature gradient. However, being able to capture fast temperature fluctuations in the HP stage is not only necessary for designing new cooling strategies, but also for gaining deeper insight of the fluid dynamic losses that limit the engine performance. The monitoring the flow total temperature, in fact, can highlight
1.1 Thin Film Probes Operating Principles
imentally the presence of possible sources of entropy i.e efficiency losses. These can be represented for example by unsteady flow non-uniformities at the outlet of the HP stage and rotor-related secondary flow structures (i.e. upper and lower passage vortex, tip leakage vortex).
Among many instruments for temperature measurements, thermocouples (TCs) are routinely and widely used as they provide accurate and relatively cheap measures. How-ever, their disadvantage stands in a poor frequency response that is approximately up to about 200 Hz, which limits their ability in measuring fast temperature fluctuations that are typical of gas turbines. Thin wire anemometers could be considered good can-didates as well: also in this case the low frequency response prevents their application in the field, along with their extreme fragility, that appears unsuitable for such aggres-sive environments. According to [25] the only method demonstrated to be capable of measuring high frequency temperature fluctuations, at frequencies higher than 50 kHz, is the one involving thin film (TF) temperature probes.
In this thesis, we contribute to the design and manufacturing of a thin film temper-ature probe.
In this Chapter, the working principle of thin film probes is explained and literature review on former probes, developed both at the Institute and in other research centers, is provided.
In Chapter 2 the probe is presented in detail, focusing on its novelty and design features.
Using numerical tools we preliminary assessed the performances of the probe, and the obtained results are given in Chapters 3 and 4.
Finally, we have empirically and extensively evaluated both performances and reli-ability of the probe in a set of controlled experiments under steady and unsteady flow conditions, and results are reported in Chapter 5.
1.1
Thin Film Probes Operating Principles
Thin film probes belong to the family of resistance temperature detectors (RTDs). Those instruments exploit the change of resistance of a sensing element (sensor) caused by a temperature variation. Using a measurement chain, this resistance variation can be easily transformed into a voltage variation and the latter can be acquired with a data acquisition system. In the case of thin film probes, the sensing element is a very thin layer of resistive material, usually platinum or nickel, plated onto a ceramic substrate. The platinum layer has a thickness in the range of 1 to 10 nanometers and a length of few millimeters, so that thanks to its reduced dimensions the thermal inertia of the sensor can be considered negligible and in every instant the sensor is found in thermal equilibrium with the substrate. That means that the sensor temperature corresponds instantaneously to the substrate surface temperature (or wall temperature) Tw, that is
the quantity of interest for the measurements. A direct consequence of the negligible thermal inertia of the sensor is the characteristic called high frequency response, that can be quantified looking at the transfer function of the probe: the amplitude spec-trum will present a flat or almost constant area up to a certain frequency, called cutoff
Introduction
frequency, after which the output signal of the sensor will start to decay in amplitude until becoming not readable. The higher the cutoff frequency, the higher will be the responsiveness of the sensor and therefore its ability of capturing rapid oscillations in the measured quantity. The cutoff frequency is proportional topα/d2 [30], where α is
the thermal diffusivity of the sensor and d is its thickness, and it is typically in the order of 100 kHz. Thus, thanks to their fast response, thin film gauges appear suitable for measurements in highly unsteady environments, such as those found in turbomachinery and short duration facilities.
Thin film gauges can be classified in two main families: the single layer gauges and the double layer gauges. The probe designed in this thesis belongs to the former.
In double layer gauges the sensing material is usually deposited onto a flexible polyamide sheet rather than directly onto the substrate. The polyamide is then ad-hesively bonded to the model, that can be metallic or ceramic and with complex geo-metrical features. This solution, in fact, was studied for the direct application of thin films on turbomachinery components, such as blades of portions of the casing, that have to resist consistent mechanical loads. In this way the use of fragile ceramic materials can be avoided. Despite the augmented robustness of the probes, however, the drawback for these gauges is the difficulty in their calibration and data processing, since the heat transfer into two different substrates should be considered. Moreover, the application of the polyamide layer on highly curved surfaces can result difficult and vulnerable during service.
Single layer probes, instead, make use of the sensing element directly applied on a ceramic insulating substrate. Even though the substrate can be shaped to reproduce entirely a turbine blade, the fragility of ceramic makes it more suitable for the construc-tion of the so called blade inserts or button gauges, that replace only a porconstruc-tion of the blade that remains mostly of metal. An example of entirely ceramic blade equipped with thin films is reported in Figure 1.2. Sensors were used for the study of the blade cooling system, whose channels are visible in the upper part of the blade.
Another possibility is that of positioning the sensors onto an appositely shaped support, usually cylindrical or hemispherical, to be placed in the measurement plane at the desired location. The governing equations of the functioning of single layer thin film gauges can be applied independently from the geometry of the substrate: those useful for the aim of this thesis are illustrated briefly in this Chapter. If necessary, a more comprehensive description of the fundamental theory and its assumptions can be found in [30].
Thin film probes are instrument for the indirect measure of gas temperature and convective heat transfer coefficient (HTC) h. Those quantities, in fact, do not represent the direct output of the probe, but are inferred from the wall temperature measurement Tw on the ceramic substrate. From the classical thermodynamic theory it is known
that the convective heat flux between a gas and a solid is directly proportional to the temperature difference between the gas and the solid and the HTC. Supposing an isentropic arrest of the flow at the probe’s wall, the convective heat flux at the probe’s surface can be written as in Equation 1.1
˙
qw00= h · (TT − Tw) (1.1)
1.1 Thin Film Probes Operating Principles
Figure 1.2: Early Macor (machinable ceramic) blade showing thin film gauges on surface and gold leads, from [33]
in which h is the HTC, Tw stands for the solid surface temperature (also referred to
as wall temperature) and TT the total temperature of the gas. The wall heat flux ˙qw00
can be found analyzing the heat conduction in the probe’s solid medium. In particular, two zones are considered: the first one is a metallic slab of thickness l, that is the thin film itself; the second one is the ceramic material. Both the metallic film and the substrate have a certain density ρ, a specific heat c and thermal conductivity k. A schematic of the problem can be found in Figure 1.3.
For the analytical solution of the problem two main assumptions are posed:
• Conduction is supposed to happen in one direction only, that is the one per-pendicular to the wall. This hypothesis decleares the monodimensionality of the problem.
• At a certain distance from the surface, the temperature in the substrate is not affected by any temperature change at the surface. This second hypothesis declares the semi-infinite medium for heat conduction.
Given that, the Fourier’s heat conduction law can be written for both the zones of the substrate, considering the x coordinate starting at the surface (x = 0) as in Equations (1.2), (1.3) ∂2T1 ∂x2 = 1 α1 ∂T1 ∂t (1.2) ∂2T2 ∂x2 = 1 α2 ∂T2 ∂t (1.3)
The thermophysical properties of the materials involved in the problem are consid-ered constant in time and space and are therefore grouped in the parameter α = k/ρc,
Introduction
Figure 1.3: Schematic of the 1D semi-infinite geometry for a single layers TF [30]
called material diffusivity. The Fourier’s differential equation can be analytically solved considering the surface subjected to a step of heat flux. Referring to Figure 1.3 the boundary condition for the problem are expressed:
˙ qw00(t) = −k1 ∂T1 ∂x at x = 0 (1.4) k1 ∂T1 ∂x = k2 ∂T2 ∂x, T1 = T2 at x = l (1.5) T2 = 0 at x = ∞ (1.6)
The general solution of the problem for this specific set of boundary conditions can be found with few mathematical passages involving the Laplace transform of the equation and of the boundary and initial conditions. If a further simplification of negligible film thickness (l=0) is done, the temperature evolution at the surface x = 0 caused by the step in heat flux can be found as in (1.7)
Tw= 1 √ π√ρck Z t 0 ˙ qw00(τ )dτ (t − τ ) (1.7)
Being the heat flux at the surface ˙qw00constant, it can be taken out from the integral
in equation 1.7, leading to a more simple expression for surface temperature as function of time t: Tw(t) = 2 ˙√qw00 π r t ρck (1.8) 6
1.1 Thin Film Probes Operating Principles
Finally, the complete analytical solution for temperature T (x, t) and heat flux ˙q”(x, t) is found, as in Equations 1.9 and 1.10.
T (x, t) = q˙w 00 √ ρck 2√t √ π exp −x 2 4αt − √x αerf c r x2 4αt (1.9) ˙ q00(x, t) = −k∂T ∂x = ˙qs· erf c r x2 4αt (1.10)
In practical situations, when the surface temperature Tw is know by acquisition
with the thin film, Equation 1.8 can be used to determine the wall heat flux responsible for the surface temperature variation, but only under the assumption of stationary constant heat flux. This situation is rarely encountered when operating with thin film probes, that are instruments specifically designed for unsteady conditions. The steady analysis is anyway valid and useful for the validation of numerical models, as explained in Chapter 3.
If different boundary conditions are considered, so that the analytical solution for the heat transfer problem is not available, the Fourier’s differential equation can still be solved and the wall heat flux can be found with a suitable data reduction technique, that can be numerical or analogical. Examples of data reduction techniques are explained in detail in the following Sections.
Once the surface heat flux and temperature are determined, only HTC and TT
remain as unknowns in Equation 1.1. In order to find them, at least two measurements at different wall temperatures have to be performed, assuming the HTC being constant for the two measurements. The problem is then translated in a system of two equations in two unknowns: ( ˙ q100= h(TT− Tw1) ˙ q200= h(TT− Tw2) (1.11a) (1.11b) and the gas total temperature is found as expressed in Equation 1.12.
TT= Tw1+ ˙ q100(Tw2− Tw1) ˙ q100− ˙q200 (1.12)
At this point, it is necessary to make a clarification for the definition of heat transfer coefficient and convective heat flux. The common definition of HTC in turbomachinery is based on the Newton’s law of cooling [5], and makes use of the total temperature upstream of the cascade as driving temperature, as expressed in Equation (1.13), in which ˙qw00 stands for the heat transfer rate per unit area [W/m2] and Tw for the wall
temperature of the object considered.
h = q˙w
00
(TT − Tw)
Introduction
In general terms, the HTC depends on the flow velocity around the body, on the body geometry and on thermal boundary layer conditions. For this reason, relating the HTC to the flow total temperature, considered as a constant far field stream temperature, can be misleading in situations where a strong variability of velocity and temperature appears. In those cases, local change of the driving temperature TT should be
consid-ered to avoid erroneous results, but on the other hand designers would like to rely on a robust invariant descriptor of the heat transfer process, so that the heat flux or surface temperature should not influence the HTC. As explained in [19], the definition of an invariant HTC also for situations involving flows with more than one fluid temperature helps in the comparison of archival data and the reuse of experimental correlations. In 1998 Prof. Moffat at Standford University [24] proposed the use of the adiabatic wall temperature Tw,ad instead of the mean total temperature of the flow in Equation (1.13).
In this way the HTC is only function of the geometry and flow field and no more related to the thermal conditions of the heat transfer surface. This kind of HTC is referred to as adiabatic heat transfer coefficient had. An exhaustive explanation on the physical
meaning of the adiabatic wall temperature can be found in [15], and is reported in this work in a summarized and hopefully intuitive manner.
The adiabatic wall temperature of a body can be defined as the temperature that forces the heat flux at the wall to be equal to zero, or, in other words, as the temperature of the body in a flow under adiabatic condition. In aerodynamics, it may also be referred to as recovery temperature and indicated with Tr. Every body immersed in a fluid in
motion acts as an obstacle, and forces the fluid to arrest and to turn around the body. Just as a velocity boundary layer develops when there is fluid flow over a surface, a thermal boundary layer must develop if the fluid free stream and surface temperatures differ. The thermal boundary layer is that region of the fluid in proximity of the body surface where temperature gradients in the fluid appear. If the flow deceleration is considered isentropic, no entropy is generated as the flow approaches the body, implying that at the surface of the body the flow temperature is equal to the free stream total temperature TT. However, when dealing with high speed flows, such a jet impinging
on the thin film probe, it is necessary to consider the action of viscous forces during the fluid deceleration and arrest. Viscosity acts like an internal source of heat for the fluid, and a significant heat transfer arises from the low speed flow closer to the body surface (at high static temperature) the flow at higher speed and lower temperature far from the wall. As a consequence, the adiabatic wall temperature will be slightly lower than the total gas temperature, and its magnitude can be related to the total flow temperature TT and the static flow temperature Tg by the recovery factor r:
r = Tw,ad− Tg TT − Tg
(1.14)
At the stagnation point of a body, that is the point of the surface at which the fluid fully arrests, the recovery factor is close to 1 and the difference between the adiabatic wall temperature and the total temperature can be neglected. On the contrary, in surface regions where the boundary layer (both of velocity and temperature) develops, a recovery factor lower than 1 should be considered. A consequence of this fact, is that
1.2 Earliest Works
Figure 1.4: Example of data interpolation and linear regression
if the flow is not perfectly aligned with the probe i.e. thin films do not measure the flow temperature perfectly at the probe stagnation point, the measured temperature would not be the flow total temperature but the recovery one. The sensitivity of the thin film measurements with the flow angle of attack is referred to as yaw angle sensitivity.
Finally, a last clarification is necessary for the unserstanding of the probe’s working principle. The use of the adiabatic wall temperature and HTC as invariant descriptors of the heat transfer implies the linearity of the relation in Equation (1.15).
˙
qw00 = had(Tw,ad− Tw) (1.15)
This means that the flow adiabatic wall temperature can be found performing a series of measurements at different Tw of the body and performing a linear regression of
the data extracted from experiments in a heat-temperature graphic. The adiabatic wall temperature is found with the intercept of the interpolating linear function with the temperature horizontal axis, that corresponds to the condition of null heat flux. This procedure is graphically explained in Figure 1.4, where also the HTC is pointed out as the slope of the interpolating line.
1.2
Earliest Works
The development of thin film gauges started in the 50’s for the investigation of heat transfer in hypersonic facilities such as shock tubes and gun tunnels. The potentiality of thin films became soon clear also for the application in larger research areas, and in particular for short duration facilities and turbomachinery applications. Even if thin films were originally designed for surface temperature measurements, their application as heat transfer gauges for transient facilities spread thanks to the studies carried on by Vidal at the Cornell Aeronautical Laboratory [37].
Introduction
Figure 1.5: Typical analogue circuit used with thin film heat transfer gauges [26]
The first attempt to provide an unified theoretical treatment of heat transfer mea-surement in short-duration transient facilities dates back to 1973 and is ascribed to Shultz and Jones from Oxford University [30]. The work presents a detailed description of the functioning of several types of gauges, including thin films, calorimeters, pyro-electric and optical gauges. For what concerns thin film sensors and the 1D semi-infinite theory, the basic equations are introduced, along with the data reduction techniques for the derivation of heat flux from wall temperature measurements.
In early experiments, data reduction was accomplished using an analog circuit con-nected to the probe. The circuit was built on the assumption that a flow of heat in a semi-infinite material is directly analogous to a flow of current through a resistance-capacitance (R-C) transmission line. The circuit performed the transformation of the voltage coming from the thin films into a current directly proportional to q˙w00. A
schematic of the circuit is depicted in Figure 1.5, in which it is possible to identify a current supply, an analogue network and an amplifier. The limited bandwidth of the output signal was overcome by Oldfield [26], with the design of wide-bandwidth ana-logue circuit for measurements up to 100 kHz. Calibrating the circuitry it is possible to find the unsteady heat flux as in Equation (1.16), that express the proportionality between the circuit output voltage signal and the requested heat flux:
˙ qw00 Vout = β √ ω/K αfVf (1.16)
Being β = √ρck the thermal product of the substrate material,√ω/K the calibra-tion constant of the circuit and αf the thin film temperature coefficient of resistivity
and Vf its operating voltage.
Other techniques of data reduction have been introduced later in the years: since the 80’s thanks to the increasing power of computers and the development of numerical tools, the surface temperatures could be recorded and used directly as input for a numerical heat conduction model. An example of numerical data reduction for heat transfer calculation is illustrated in [12], where the heat transfer into the gauge substrate is modeled trough an electric analogy with discrete lumped elements distributed through the gauge substrate. The thermal properties of the substrate are replaced by a series of resistance-capacitance elements on n nodes, and a system of equation is then solved using the Rounge-Kutta method to find the heat flux from the wall temperature history.
1.2 Earliest Works
Digital methods have the advantage that less hardware is required and the effects of temperature-dependent thermal properties of the substrate can be easily included if needed. It is important to remember that all these data reduction techniques relied on the assumption of the semi-infinite 1D medium for heat conduction. This approximation is reasonable only if the temperature at substrate interior is essentially uninfluenced by the change of surface temperature, and no bi-dimensional heat conduction effects are present: this condition has to be checked and respected for the extraction of accurate measurements.
Three single layer thin film probes were manufactured and tested at the Oxford University by Buttsworth and Jones. All these probes base their functioning on the dual thin film principle: two thin films are used at different substrate temperatures Tw
for the same test, supposing a constant HTC between the two. One thin film is heated up, and is referred to as hot thin film as the other, referred to as cold thin film, remains at ambient temperature. The flow total temperature and HTC are inferred solving the system of Equations reported below, in which subscripts 1 and 2 allude to the hot and cold thin films.
( ˙ q100= h(TT− Tw1) ˙ q200= h(TT− Tw2) (1.17) (1.18) The first probe built in 1996 was composed by two cylindrical quartz prongs of 3 mm diameter with hemispherical heads for the positioning of thin films. The hot probe was preheated prior to each test using an external heater positioned onto the hot prong and that could swing away before each run; thin films were fed with constant current. The numerical data reduction technique was studied for taking into account the conduction and radiation from the hot probe as well as the curvature effect of the hemispherical head. The probe was tested for temperature between 400 K and 700 K, and provided the uncertainty in the temperature measurements of ± 3 K with a frequency response up to 50 kHz.
The considerable distance between the two prongs of the probe prevented its appli-cations in situation with steep gradients, for which the equality of HTC perceived by the hot and cold probe could not be guaranteed. Moreover, the spatial accuracy, i.e. the precision of the measurement with respect to space and the ability to resolve small fluctuations, resulted unsatisfactory because of the probe’s encumbrance. To overcome this problem, a second probe was manufactured in 1997 with the two prongs closer to each other and distanced only by a 0.2 mm gap, so that the distance between the two sensors was about 3 mm. The hot prong was heated internally by a 12 Ω resistance placed inside the substrate. The uncertainty was also improved to ± 1 K as well as the cutoff frequency to 85 kHz. A picture of this probe is provided in Figure 1.6, in which the two quartz prongs are well recognizable mounted on the perspex (plastic) body and on the steel support plate of the probe.
For the third probe Buttsworth and Jones improved even more the spatial resolution [7] using a single hemispherical blunted fused quartz rod with the two thin films painted close to its stagnation point. Figure 1.7 represents a schematic of this second probe. Thin films have a room temperature resistance of 44 Ω and 58 Ω and are distanced by a gap of 0.7 mm, as the rod has a diameter of approximately 3 mm. Temperature
differ-Introduction
Figure 1.6: Total temperature probe designed by Buttsworth and Jones at Oxford University in 1997 [9]
Figure 1.7: Schematic of the single prong probe designed by Buttsworth and Jones at Oxford University [7]
ence was achieved using two different feeding currents for the thin films and exploiting the heating by Joule effect: the hot film is fed with a relatively large current of 70 mA as the cold one is fed with 15 mA. In order to reduce the interaction and the heat flux between the hot and the cold film, the authors adopted a solution called ”Pulsed Heating Technique”, that means that the 70 mA current is activated only shortly before the flow commences. The heat fluxes for both films have been calculated using a finite difference routine, and results were corrected to take into account the lateral conduction effects that arouse for the presence of a strong temperature gradient between the hot and the cold thin films. In particular, this effect was evident for signals coming from the hot thin film, that showed a positive heat flux even when the probe was no more exposed to the flow. This effect is due to the heat traveling in the substrate and driven by the temperature gradients created by thin films Joule effect. A lateral conduction correction is derived from the heat diffusion equation in hemispherical substrates. The corrected heat flux is obtained in an iterative way using the finite difference routine, adding or subtracting an additional term to the uncorrected heat flux, until a zero-heat flux is obtained when the probe is no more subjected to the flow. The recovery factor at the location of the thin films on the hemispherical head has been considered as well, and the film recovery temperature was estimated to be within 1% of the total gas
1.2 Earliest Works
perature. The frequency response of this probe reached 100 kHz.
In the same historical period, researches concerning heat transfer measurements in transient facilities have been carried on also at the NASA Lewis Research Center. In particular, the probe presented by O’Brien [25] 1990 shows geometrical and manufac-turing similarities, in particular for the choice of materials, with the probe presented in this thesis. The probe, depicted in Figure 1.8 is obtained from a 12.7 mm diameter cylindrical Macor (ceramic) rod with 7 platinum thin film gauges (0.25 mm wide and 2.5 mm long) fired onto its lateral surface. Thin film resistances at ambient temperature had a nominal value of 50 Ω, and the sensors operated in constant current mode with a current intensity of 8 mA. The probe was tested at midspan of an ambient temperature annular flow wind tunnel, that is a steady flow facility equipped for the occasion with a wake generator rotor for the simulation of turbine guide vanes wakes. In order to pro-vide the necessary driving temperature difference for heat transfer between air stream and the probe, the cylinder was uniformly preheated in a small oven connected to the test section, and as a temperature difference of approximately 100 °C was reached the probe was injected into the flow by means of a pneumatic actuator. This study provides an example of application of thin film gauges in steady state facilities, such as wind tunnels, in which the unsteady component is introduced by means of moving elements, that in this case are the wake generator bars mounted on the rotor. The time averaged signals from the high frequency probe have been compared with the signals from con-ventional steady state probes (i.e. thermocouples), and results matching demonstrated the reliability of the time resolved measurements and of the data reduction technique. This technique, however, suffered from the drawback of non-continuous heat flux sig-nals, since as the probe gradually cooled down to ambient temperature, the heat flux signal slowly went to zero and the probe had to be heated up another time.
Figure 1.8: Cylindrical probe with platinum thin films developed at Lewis Research Center, NASA [25]
The idea of exploiting two different current intensities for feeding the sensors was used also in 2008 by Mansour [23] at the Turbomachinery Laboratory at the ETH, Zurich, for the construction of an an entropy probe, which consisted in a pressure transducer combined with a total temperature thin film sensor. Entropy measures were inferred from pressure and temperature ones, as reported in the formula below:
∆s = Cpln T Tref − R ln p pref
Introduction
Figure 1.9: Photograph of the entropy probe developed at ETH: on the left the pressure probe is visible, as on the right side the thin films and the quartz rod are positioned [23]
The probe was constructed from a cylindrical fused quartz rod of 1.8 mm diameter, on which two serpentine-shaped sensors are obtained removing nickel with a 20 µm Nd:YAG laser. The serpentines are 30 µm wide for a resulting spatial accuracy of approximately 1.5 mm. A picture of the fast temperature probe assembled with the pressure probe is reported in Figure 1.9, in which the two films are visible along with the silver electrical connections. The data reduction technique adopted was again an unsteady, semi-infinite numerical model based on an electrical analogue. The relative error for the total temperature was estimated as 2.5%, as the frequency response of the probe proved to reach 70 kHz. The probe was tested at ETH in a single stage centrifugal compressor facility equipped with an impeller followed by a vaneless diffuser, and the time resolved contours of total pressure and temperature have been extracted on a measurement plane in correspondence of the exit of the impeller. Thanks to these measurements, a deeper insight on the losses mechanisms for the radial compressor could be inferred: as example, the jet region appears almost loss free, as higher losses are observed for the flow closer to the shroud, where velocity relative to the casing is high.
1.3
Researches at the Von Karman Institute for Fluid
Dy-namics
The investigation on the heat transfer mechanism in short duration facilities falls among the Von Karman Institute for Fluid Dynamic research occupations since the 80’s. More precisely, the interest for this research area was pioneered with the installation, in 1978, of the first Isentropic Light Piston Compression Tube of the Institute for tests on linear cascades (CT-2). That was soon followed, in 1990, by the construction of a large annular cascade tunnel (CT-3), that remains even nowadays one of the biggest in the world. Light Piston isentropic Compression Tubes, first developed at the Oxford University by Schultz et Al., are a class of facilities able to compress and therefore heat up a volume of air, contained into a tubular reservoir, thanks to the slow and quasi-static motion of a piston. The air is then released in a low pressure ambient where the test section, that can be either a linear or annular gas turbine cascade, is located. Those facilities proved to be invaluable for the detailed study of the performances of
1.3 Researches at the Von Karman Institute for Fluid Dynamics
Figure 1.10: On the left: VKI CT-3 ro-tor blade equipped for heat flux measure-ments. On the right: inserts carrying 5 to 6 gauges, from [32]
turbine airfoils in relation to flow conditions, such as Mach number (M ), Reynolds number (Re), turbulence intensity (TU) and incidence angle. Instrumented blades and inserts have been tested as well as specifically developed probes such as the one designed in this thesis. A comprehensive summary of instruments and techniques used at the Von Karman Institute for short duration blowdown tests, not only involving thin film probes, can be found in [32]: the most relevant experimental campaigns for this work are reported in this Section.
In 1994 Arts and Heider [2] studied the thermal and aerodynamic behavior of a three dimensional nozzle guide vane of an annular cascade, equipped with local surface pressure transducer an painted platinum thin film gauges. The aerodynamic losses as well as the flow angle in the blade-to-blade plane were fully determined, providing an excellent test case for numerical models predictions. Examples of equipped blades built at the VKI are shown in Figure 1.10.
Figure 1.11: Turbine stage tested by Sieverding et Al: Thin film gauges used in stator and rotor (above) and measure-ment locations along the airfoil (below), from [27]
Introduction
In 1996 Sieverding, Arts, Denos and Martelli [34] investigated the performance of a transonic turbine guide vane with trailing edge coolant flow ejection, in CT-3 facility. Thin film sensors were used to monitor the surface temperature on both stator and rotor: in Figure 1.11 the white macor insert equipped with 5 thin films is visible on the rotor blade, as on the statoric airfoil an array of double layer thin film printed on a polyamide sheet is recognizable. In more recent times, A. J. Carvalho [10], designed at the Institute a dual double layer thin film probe. This probe was conceived for measurements in turbine rotor tip region, therefore as for the last Oxford dual thin film probe, an adequate spatial resolution was achieved using a single cylindrical Macor prong. A second layer of Kapton was added to the Macor cylinder to ease the thin film manufacturing. The final design of the probe and its geometry have been validated using the finite element software COMSOL, in order to verify the semi-infinite and 1D assumption at the basis of the data reduction technique. A photograph of the probe is reported in Figure 1.12. Unfortunately, the probe showed a lack of robustness as the Kapton layer exhibited the tendency to detach from the substrate. This problem was already observed at Oxford University by Doorly for the construction of a double layer thin film instrumented metal blade. Therefore, in all those cases involving geometries with small radii of curvature, the single layer gauges demonstrate to be more resistant and reliable.
Figure 1.12: Potograph of the probe designed by Carvalho [23]
To conclude, Solano and Panigua performed transient blade-surface measurements exploiting a thin film array printed on a Upilex-S polyamide sheet and then glued on a turbine rotor blade at 15% height [35]. This study is cited for the interesting approach used in the numerical investigation of the heat transfer between airfoil and the hot gas. The surface heat flux on the blade profile was calculated exploiting a FEM numerical code. For the data processing, the 2D unsteady heat conduction equation was directly solved in the double layered cross sectional area of the airfoil, using as input for the finite element solver the initial temperature distribution of the blade and the recorded tem-perature histories from the thin films. In this way, the need of assuming a semi-infinite substrate was unnecessary, and bi-dimensional effect could have been precisely
1.3 Researches at the Von Karman Institute for Fluid Dynamics
lated. The cross section of the blade has been discretized with 170’000 finite elements and can be observed in Figure 1.13, in which two distinct layers of material is visible, along with the two internal cooling ducts. The study, demonstrated the shortcomings of the purely 1D approach when complex and curved geometries are considered: in the trailing and leading edge of the blade a reduction in the heat flux up to the 8% was observed with respect to the one predicted with the 1D approach, confirming therefore the importance of considering the lateral conduction caused by curvature of the profile. Moreover, the effect of a non-uniform temperature distribution in the substrate prior to the blowdown was examined, along with the possibility of applying the superposition method for the data reduction. All these results are particularly valuable for the work presented in this thesis.
Figure 1.13: 2D mesh of the tur-bine blade blade tested by Solano and Paniagua at the VKI [35]
2.
Probe Design
The design of a complex engineering device such as a thin film temperature probe is an expensive and iterative process, involving several validations and corrections that start long before its manufacturing. Firstly, the encumbrance of the probe and all the components for its connection to the facility should be dimensioned. After that, it is necessary to to calculate the expected performance of the probe and to verify its agreement with the project requisites, both via numerical and analytical calculations. In the meanwhile, the technical feasibility of the project should be assessed considering the machining methods available, the costs related to them, the materials that are accessible in the market and and working hours required by the technicians. If any of these passages fails, corrective solutions must be implemented and probably one or more steps of the project should be reviewed. For the reasons explained above, the gauge that we designed and present in this thesis is not born from scratch, but it is the result of an accurate tuning process on previous works performed at the Von Karman Institute. In particular, the thermal characterization of a probe with a simplified geometry as well as the fluid-dynamic study of the flow around it has been carried out by Bassignana [4]. A preliminary dimensioning of the probe was accomplished by Tarazona [36]. The aim of this Chapter is that of illustrating the design passages that we performed and that were still necessary for the finalization of the probe, along with the reasons that lie beyond many of its features.
2.1
CT-3 Facility
As already mentioned in Chapter 1, the probe of this work is designed for its application in the Isoentropic Light Piston Compression Tube Facility CT-3 of the Von Karman Institute for Fluid Dynamic. In order to better understand the projects requisites and the design goals, a brief description of the facility is provided in this Section. As explained in [27], CT-3 is a short duration blowdown tunnel that consists of three elements: a compression tube (upstream reservoir), the test section where rotating cascades are assembled and a dump tank (downstream reservoir). The air blowdown in the facility is actuated via a shutter valve that connects the upstream reservoir to the test section. An adjustable sonic throat is located downstream of the test section, and acts to regulate the volumetric flow rate through the facility in order to match the desired pressure and temperature conditions. Figure 2.1 represents a schematic of the facility.
Typical test cycle operations start with the shutter valve closed. The pressure in the upstream tank is regulated to the initial level of 300 bar. The pressurized air coming
Probe Design
Figure 2.1: Technical scheme of the CT-3 facility with components indications and dimensions [27]
from the upstream reservoir is expanded at the back of the piston, that slowly starts to slide performing a quasi-static isentropic compression of the air in the cylinder. As the pressure rises, also the gas temperature increases for the effect of compression. In the meanwhile, in the test section a vacuum pump acts to bring the pressure at 25 mbar. As soon as the desired pressure is reached in the cylinder, the shutter valve opens and the hot and pressurized air is discharged in the test section, where the annular cascade has been operated to the regime rotational speed.
The facility is designed for the aerodynamic characterization of a HPT (vane + rotor), and can be regulated adjusting independently Mach (M ) and Reynolds (Re) numbers. Real engine flow conditions are scaled in the facility exploiting the similar-ity approach, while the geometrical similarsimilar-ity is guaranteed and keeps the flow angles constant. The typical flow blowdown lasts for approximately 0.7 s, with 0.5 s of stable flow condition. Typical Mach numbers reached in the test section are within 0.2 - 0.6, with an average temperature of 365 K. The complete list of the flow thermodynamic quantities achievable in the facility can be found in [6], as a summary table is provided here in Table 2.1.
2.2
Aim of the Experimental Campaign and Design
Re-quirements
The fast response total temperature probe designed in this thesis (GTP-A) will be on duty in a measurement plane located at 50% of the axial chord downstream of the rotor trailing edge in CT-3 facility, in the context of a wide and important experimental campaign that will be accomplished in the year 2020.
The goal of the experimental campaign is the quantification of the performance
2.2 Aim of the Experimental Campaign and Design Requirements
MEASUREMENT PLANE Min Max Mean TT [K] 315 415 365 PT [P a] 42000 50000 46000 T [K] 314 395 359 ρ [Kg/m3] 0.461 0.371 0.421 M 0.13 0.5 0.29 v [m/s] 44.8 200.5 109.8 Re/L [1/m] 1.1 ·106 3.3 ·106 2.2 ·106
Table 2.1: Minimum, maximum and average flow quantities in the measurement plane behind the CT-3 rotor
of innovative blade tips for a HPT stage, composed by 34 vane and 48 rotor blades. Simultaneous testing of multiple geometries is achieved by setup of a rainbow rotor configuration with different tip profiles. The influence of each blade tip on heat transfer mechanism between the hot gas of the HPT and the casing will be studied with fast response temperature and heat-flux gauges integrated in the casing. Moreover, an as-sessment of the blade tips geometry in their ability of controlling the leakage flows, that are well known loss sources in HPT stages, will be performed. In particular, the inter-action of head leakage flows with secondary flows in the blade to blade channels will be observed in the measurement plane downstream of the rotor, thanks to the application of the GTP-A along with fast response pressure probes. The complete characterization of the downstream flow field will also provide a valuable foundation for the validation of further numerical simulations.
The GTP-A has to reach a series of measurements points placed in a grid composed by 25 points in radial direction and 10 points in the circumferential one. The grid covers entirely the blade to blade channel from 0% to 100% of the blade span. The total span length to be characterized is 70.3 mm. In total, 250 measurement points for the grid are determined. The GTP-A should infer the total gas temperature from the wall temperature and heat flux, performing a linear regression of the data as explained in Section 1.1. For an accurate linear regression, we expect at least 5 different wall temperatures for each measurement location and in order to do that, the probe should be heated by a resistive heater inserted in the substrate. As a consequence, it is necessary to maximize the number of thin films on the probe to reduce the overall number of tests: a total of 3 radial displacements at 10 different circumferential locations along one full vane pitch will allow the complete coverage of the grid, for a total number of 150 tests. For the reasons explained in Chapter 1, one of the most important requirements for the probe is a wide bandwidth. The high frequency response is needed to catch correctly the temperature and heat flux fluctuations driven by the blade passage and action on the flow. The rotor operational speed is set at 5925 rpm, and considering the number of blades mounted in the rotor, the blade passing frequency for the rotor results in 4.74 kHz. Therefore, in order to correctly catch the phenomena related to the rotor blades movement and the rotor-stator interaction, a frequency response up to 25 kHz at least
Probe Design
Figure 2.2: Picture and exploded sketch of the first full-probe assembly GTP-A1
is needed. Another important requirement is the spatial resolution of the probe that should be adequate for the experimental grid.
Other requirements not mentioned until now are those related to the probe man-ufacturing. The probe is entirely built at The Von Karman Institute, and its design must be such that the manufacturing results as much simplified as possible. Moreover, the probe has to resist when exposed to the blowdown flow: its mechanical properties must be adequate in order not to break or soften when subjected to high speed and high temperature jets. The substrate material must be machinable but not too fragile. The electrical leads must be robust as well. The overall structure must be reliable to withstand severe thermal and mechanical loads.
Last but not least, the probe has to guarantee an accuracy in the gas temperature measurement of 1K.
2.3
Gauge Components and Geometry
A picture of the first completely assembled gas temperature probe (GTP-A1) is provided in Figure 2.2, along with a schematization of its three main components: the probe’s head, the insulating insert and the support stem. The aim of the stem is to facilitate the probe positioning and to bring the electrical connections from inside to outside the facility. The electrical cables must in fact pass through the stem, that consists of a hollow cylindrical beam, in order to be connected to the acquisition system. Since the stem is metallic and the probe will be heated up during the tests, an insulating insert is necessary to limit the temperature gradient and heat flux in the probe axis direction. As already mentioned, an electrical heater is placed inside the Macor head. The heater as well is completely built at the Von Karman Institute and consists of a series of electric wire loops that work exploiting the Joule heating principle. All the three parts are glued together with a heat-resistant glue in order to ensure sufficient rigidity to the probe.
The choice of materials was done considering the expertise and the previous projects done at the Institute. As regards the thin films substrate, the choice fell on Macor, a machinable glass ceramic material that can be easily shaped with conventional work-shop tools. Macor was already used at the institute by Iliopoulou and Arts [3] for the construction of a double thin film probe similar to the Oxford double prong one, and
2.4 Probe’s Head
also by Carvalho [10] for a double layer probe. The material and its resistance are there-fore well known by the Institute’s technicians. Reference properties for Macor, that are used for numercal simulations reported in Chapters 3 and 4, are summarized in Table 2.2.
ρ [Kg/m3] c [J/KgK] k [W/mK] α [m2/s] 2520 752 1.672 8.82 · 10−7
Table 2.2: Macor reference thermophysical properties
As regards the choice of thin films’ material, according to [30], one of the best options is the use of platinum. The choice is made considering the resulting sensitivity in terms of voltage over temperature of the sensors, that can be expressed as:
∆V
∆T = V0αR (2.1)
Where αR is the thin film temperature coefficient, ∆V and ∆T the voltage and
temperature variations with respect to a reference condition, that is usually the ambient one, and V0the reference voltage at ambient temperature. From the formula in Equation
(2.1), it is clear that increasing the voltage supplied to the sensors also their sensitivity increases. However, it is also important to keep the dissipated electrical (and as a consequence thermal) power as low as possible, in order not to damage the material and to avoid undesired overheating in the thin film area. As explained by Schultz and Jones in [30], platinum is the material that allows the highest sensitivity [V/K] with respect to the power dissipated per unit area. This means that using platinum films it is possible to obtain high sensitivity even with a low supplied voltage or, in other words, considering the same power dissipated by joule effect, a platinum thin film will have a higher sensitivity with respect to another made of any other material.
Electrical leads are made of gold painting, and are welded to the thin films through silver welding spots. The stem is made of brass, and it is obtained shaping and adjusting the standard 8 mm diameter probe’s support used at the Institute. Brass provides sufficient rigidity to the probe stem and is at the same time simple to machine. The insulating insert between stem and probe’s head is made of Iglidur® W300, that is chosen for its mechanical rigidity and softening temperature of 90 °C.
A prospective exploded view of the probe is visible in Figure 2.3, in which the insulating insert with the cable passage slot is visible, as well as the heater hole on the probe’s head and the plane for the cables welding. These features will be explained in the following Sections.
2.4
Probe’s Head
The final shape for the head is the result of some adjustments on the preliminary dimensioning made by Tarazona [36]. The Von Karman Institute’s technicians have been consulted to understand the difficulties that could arise in the manufacturing of the
