NUMERICAL SIMULATION OF HEAT TRANSFER TO GAS TURBINE BLADES
N. ASOK KUMAR
THESIS SUBMITTED
IN FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF
DOCTOR OF PHILOSOPHY
SOT[ Or
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Department of Mechanical Engineering INDIAN INSTITUTE OF TECHNOLOGY, DELHI
NEW DELHI-1 10016, INDIA JULY, 1995
CERTIFICATE
This is to certify that the thesis entitled "Numerical Simulation of Heat Transfer to Gas Turbine Blades" being submitted by N. ASOK KUMAR for the award of degree of DOCTOR OF PHILOSOPHY is a record of bonafide research work carried out by him in Mechanical Engineering Department of Indian Institute of Technology, Delhi.
Mr. N. Asok Kumar worked under my guidance and supervision and has fulfilled the requirements for the submission of this thesis, which to my knowledge, has reached the requisite standard.
The results obtained here in have not been submitted in part or in full to any other University or Institute for the award of any degree.
Dr. S.R. Kale Associate Professor
Mechanical Engineering Department I.I.T. Delhi, Hauz Khas,
New Delhi-110016, India
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ACKNOWLEDGEMENTS
I wish to express my deepest sense of gratitude to Dr. S.R. Kale who gave me guidance for my Ph.D. Research work at IIT Delhi. An informal and friendly relationship which he made a point to develop between us gave me courage to carry on with the work with confidence even during the hours of stress. Notwithstanding his busy schedule in his office his top priority has always been my research work. He made efforts for the smooth progress of my work. I am indebted to him for this work and also for the advice and moral support he rendered to me in abundance.
I am grateful to Prof. J.S. Rao, who showed interest in my research work and has been a constant source of encouragement.
I wish to put on record my gratitude to Prof. M.K. Radhakrishnan and Prof. R.S.
Moni, Principals, Government College of Engineering, Kannur, who helped me in their official capacity for the pursuit of this work after my joining that college.
My friends at IIT Delhi are quite large in number. They helped me in making my stay in the campus a pleasant one. It would be difficult to mention them each by name. I am thankful to each and every one of them.
The affection and concern showed by my relatives in Delhi created a homely atmosphere. I especially want to mention Gopimamman who always showed great interest in my studies.
Finally, a special word of thanks goes to Mr. Mahesh Gaur for his quick and efficient typing of this thesis.
July, 1995 (N. ASOK KUMAR)
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ABSTRACT
Gas turbines for civil and military aviation, and for industrial applications are being contemplated with turbine entry temperatures (TETs) approaching 1,500 C or more.
Consequently, hot gas path components, especially first stage blades will experience increased thermal load-mg. In this research, a two-dimensional numerical model has been developed for predicting steady state and transient temperatures in a cooled blade. Gas radiation to blade and thermal barrier coatings (TBCs) are also incorporated in the model.
This code was validated prior to performing simulations on a typical blade.
At elevated lbIs, radiation heat transfer to uncoated blades increases significantly and cannot be ignored. In transients, radiation increases the peak temperature gradients everywhere in the blade. However, for blades with full TBCs, radiation has very marginal effect on blade metal and ceramic temperatures. TBCs were found to be very effective in reducing total heat transfer to the blade, and more so in blocking radiation. In blades with full TBCs, the metal temperatures are lowered significantly when compared .to uncoated
blades even though the TBC itself runs hotter.
Transients produce peak temperature gradients which are significantly larger than steady state gradients. Thus, during heating and cooling, the blade experiences much greater stresses than in normal operation. For uncoated blades, radiation adds to this increased stress. TBCs reduce both the peak and steady state gradients in the blade. Selective coatings were observed to locally suppress blade temperatures significantly.
The code has also been used for studying the effects of coolant to gas side heat transfer ratio, surface emissivity variations and extent of selective coatings on nodal
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temperatures, cooling effectiveness and heat loss to coolant in steady state; and on nodal temperatures and temperature gradients during three different transients. This code can be used for designing blades and vanes, with or without TBCs, at high TETs.
Keywords: Gas turbine; Heat transfer; Simulation; FEM; Finite difference; Blade cooling;
TBC; Radiation; Steady state; Transients.
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CONTENTS
Page No.
Certificate ii
Acknowledgements iii
Contents iv
Abstract viii
List of Symbols
List of Figures xiv
List of Tables xix
Chapter
1. Introduction 1
1.1 Gas Turbine Technology 1
1.2 Blade Heat Transfer 4
1.2.1 Convection Cooling 4
1.2.2 Impingement Cooling 5
1.2.3 Film Cooling 5
1.2.4 Transpiration Cooling 5
1.3 Blade Coatings 5
1.4 Organisation of the Thesis 7
2 Literature Review 14
2.1 Blade Heat Transfer 15
2.1.1 External Heat Transfer 16
2.1.2 Blade Cooling 23
2.2 Thermal Barrier Coatings 31
2.2.1 Heat Transfer Aspects 32
2.2.2 Mechanical and Manufacturing Aspects 39 2.2.3 Related Applications of Ceramics 42
2.3 Numerical Techniques 44
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2.4 Concluding Remarks - Literature Review 48
3 Heat Transfer Modelling 54
3.1 Heat Transfer Equations 54
3.2 Boundary Conditions 55
3.2.1 Pressure and Suction Surfaces 55 3.2.2 Internal Coolant Surfaces 57
3.3 Initial Conditions 57
3.3.1 Cold Start 58
3.3.2 Throttle 59
3.4 Finite Element Formulation 59
3.4.1 Galerkin Approach 60
3.4.2 Steady State with Convection 64 3.4.3 Steady State with Combined Convection and
Radiation 65
3.4.4 Transient Heat Transfer 66
3.4.5 Finite Difference Solution in the Time Domain 67
3.5 Code Development 69
3.5.1 Versatility Features 70
3.5.2 Inputs Required for the Code 70
3.5.3 Code Outputs 71
3.5.4 Automatic Time Stepping Scheme 72
3.5.5 Programs and Subroutines 73
3.6 Modelling Summary 73
4 Code Validation 78
4.1 Geometry for Code Validation 79
4.2 Validation for Steady State -- Hollow Cylinder 79 4.2.1 Exact Analytical Solution (Steady State) 81 4.2.2 FEM Solution (Steady State) 82 4.2.3 Comparison of Exact and FEM Solutions (Steady
State) 83
4.3 Validation for Transient - Solid Cylinder 84 4.3.1 Exact Analytical Solution (Transient) 84
4.3.2 FEM Solution (Transient) 86
4.3.3 Comparison of Exact and FEM Solutions (Transient) 87
4.4 Validations for Blades 87
5 Data For Simulations 95
5.1 Blade Materials - Alloys 96
5.2 Blade Materials - Ceramics and TBCs 97
5.3 Blade Geometry 101
5.4 Convection Heat Transfer Coefficient - Blade Surface 102 5.5 Convection Heat Transfer Coefficient - Cooling Passages . . 103
5.6 Gas and Coolant Temperatures 107
5.7 Transient Forcing Function 108
5.8 Data Summary 109
6 Simulation Results 117
6.1 Steady State Simulations 117
6.1.1. Base Case 117
6.1.2 Effect of Coating 120
6.1.3 Effect of Radiation for Coated
Blade 121
6.1.4 Effect of Radiation for Uncoated
Blade 122
6..1.5 Effect of Coolant to Average Gas Side Heat Transfer Coefficient
Ratio 122
6.1.6 Effect of Surface Emissivity 123 6.1.7 Selectively Coated Blades 124
6.2 Transient 128
6.2.1 Step Change Cold Start 128 6.2.2 Ramp Change Cold Start 132
' 6.2.3 Throttle 135
7 Discussion
7.1 Effect of Radiation 190
7.1.1 Steady State 190
7.1.2 Transient Effects 192
7.2 Effect of TBCs 193
7.2.1 Effectiveness Changes 193 7.2.2 Metal Temperature Comparison 194
190
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7.2.3 Reduction in Heat Loss to Coolant 196
7.2.4 Partial Coatings 197
7.2.5 Transients 198
7.2.6 Modelling of TBC 200
7.2.7 Interface Gradients 201
7.3 Model Applicability and Limitations 202
7.3.1 Radiation Model 203
7.3.2 Convection Model 203
7.3.3 Surface Emissivities 205
7.4 Closure 205
8 Conclusions and Recommendations for Future Work 211
8.1 Conclusions 211
8.2 Recommendations for Future Work 212
References 213
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