LARGE EDDY SIMULATION OF TIP LEAKAGE FLOW IN A LINEAR TURBINE CASCADE GRADUATION PROJECT. Abdurrahman Gazi YAVUZ

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3 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS LARGE EDDY SIMULATION OF TIP LEAKAGE FLOW IN A LINEAR TURBINE CASCADE GRADUATION PROJECT Abdurrahman Gazi YAVUZ Faculty of Aeronautics and Astronautics Aeronautical Engineering JANUARY 2018

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5 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS LARGE EDDY SIMULATION OF TIP LEAKAGE FLOW IN A LINEAR TURBINE CASCADE GRADUATION PROJECT Abdurrahman Gazi YAVUZ ( ) Faculty of Aeronautics and Astronautics Aeronautical Engineering Thesis Advisor: Asst. Prof. Ayşe Gül Güngör JANUARY 2018

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7 İSTANBUL TEKNİK ÜNİVERSİTESİ UÇAK VE UZAY BİLİMLERİ FAKÜLTESİ DOĞRUSAL BASAMAKLI BİR TÜRBİNİN UÇ SIZINTI AKIŞININ BÜYÜK GİRDAP BENZETİMİ İLE SİMÜLASYONU BİTİRME ÇALIŞMASI Abdurrahman Gazi YAVUZ ( ) Uçak ve Uzay Bilimleri Fakültesi Uçak Mühendisliği Tez Danışmanı: Asst. Prof. Ayşe Gül Güngör OCAK 2018

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9 Abdurrahman Gazi YAVUZ, an Undergraduate student of ITU Faculty of Aeronautics and Astronautics, successfully defended the thesis entitled LARGE EDDY SIMULATION OF TIP LEAKAGE FLOW IN A LINEAR TURBINE CASCADE, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below. Thesis Advisor : Asst. Prof. Ayşe Gül Güngör... Istanbul Technical University Jury Members : Prof. Dr. Mehmet ŞAHİN... Istanbul Technical University Asst. Prof. Bayram ÇELİK... Istanbul Technical University... Date of Submission : 3 January 2019 Date of Defense : 15 January 2019 v

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11 vii To all and none,

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13 FOREWORD Foreword January 2018 Abdurrahman Gazi YAVUZ ix

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15 TABLE OF CONTENTS Page FOREWORD... ix TABLE OF CONTENTS... xi ABBREVIATIONS... xiii SYMBOLS... xv LIST OF TABLES...xvii LIST OF FIGURES... xix SUMMARY... xxi ÖZET... xxv 1. INTRODUCTION Problem Definition Literature Overview Motivation and Outline NUMERICAL METHODOLOGY Mathematical Modeling Computational Domain RESULTS Two Dimensional Analysis Statistical Results Instanteneous Results Three Dimensional Analysis Statistical Results Instanteneous Results DETAILED FLOW ANALYSIS Interaction Mechanisms Blockage of Upstream Flow CONCLUSION AND FUTURE WORK REFERENCES CURRICULUM VITAE xi

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17 ABBREVIATIONS LPT : Low Pressure Turbine CFD : Computational Fluid Dynamics LES : Large Eddy Simulation DNS : Direct Numarical Simulation APG : Adverse Pressure Gradient FPG : Favorable Pressure Gradient ZPG : Zero Pressure Gradient N-S : Navier-Stokes OpenFOAM : Open Field Operation and Manipulation PISO : Pressure Implicit with Splitting of Operators FTT : Flow Through Time rms : Root Mean Square TKE : Turbulent Kinetic Energy SGS : Sub-grid Scale xiii

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19 SYMBOLS i, j : Cartesian Tensor Indices x, y, z : Cartesian Coordinate Indices u i, u j : Velocity Field in the x i and x j Directions t : Time ρ : Density U re f : Reference Velocity P : Instanteneous Pressure P out : Reference Outlet Pressure P re f : Reference Pressure P T : Total Pressure ν : Kinematic Viscosity u i : Filtered Velocity Field in the x i Direction u i : Sub-grid Scale Velocity in the x i Direction P : Filtered Pressure τ sgs i j : Sub-grid Scale Stress Tensor S i j : Filtered Strain Rate Tensor : Characteristic Filter Width ν τ : Sub-grid Scale Viscosity C ax : Axial Chord h : Span C p : Time-averaged Static Pressure Coefficient : Skin Friction Coefficient C f xv

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21 LIST OF TABLES Page Table 2.1 : T106 blade specifications... 7 xvii

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23 LIST OF FIGURES Page Figure 1.1 : Typical high-bypass turbomachinery and close view to the LPT blades REFERENCE HERE... 1 Figure 1.2 : (a) Two dimensional view of leakage mechanism, (b) reattached and non-reattached leakage flow... 2 Figure 2.1 : Computational domain, inlet (blue), casing wall (green) and periodic surfaces (red)... 7 Figure 2.2 : Two dimensional view of computational domain with non-dimensional lengths and T106 blade profile... 8 Figure 3.1 : Mean static pressure coefficient for two dimensional analysis compared with experimental [7] and DNS [7] data Figure 3.2 : Mean velocity contours for two dimensional analysis Figure 3.3 : Instanteneous pressure and velocity contours for two dimensional analysis Figure 3.4 : T106 cascade sketch with incoming wakes [8] Figure 3.5 : Mean static pressure coefficient compared with experimental [7], DNS [7] data and previous study [43] Figure 3.6 : Two dimensional rms velocity and TKE contours, %50, %25, %1.25 of the blade span from (a) to (c) respectively Figure 3.7 : Two dimensional velocity contours, %50, %25, %1.25 of the blade span from tip clearance from (a) to (c) respectively Figure 3.8 : Tip leakage flow streamlines demonstrated with different colors, 0.6x, 0.7x, 0.8x, 0.9x from red to blue respectively Figure 3.9 : Two dimensional contours demonstrated with corresponding U z magnitudes, (a) 0.5x, (b) 0.7x, (c) 0.9x, (d) 1.1x Figure 3.10: Two dimensional pressure and velocity contours, %50, %25, %1.25 of the blade span according to the design span length from (a) to (c) respectively Figure 4.1 : Passage and leakage separation interaction [27] Figure 4.2 : Passage and leakage separation interaction in the present study at 0.8x, (a) passage flow zone, (b) buffer zone, (c) leakage flow zone Figure 4.3 : Surface flow visualisation on the casing wall, (a) %1 clearance, (b) %2 clearance, (c) %3 clearance [27] Figure 4.4 : Flow field near the casing wall for present study Figure 4.5 : Zoomed in view of flow field near the casing wall Figure 4.6 : Flow field near the casing wall Figure 4.7 : Passage flow separation with no clearance [27] xix

24 Figure 4.8 : (a) and (c) Streamlines on the blade suction side surface, mm off the wall, (b) C fx over blade suction surface, (d) cells containing negative value of C fx and C fz Figure 4.9 : Close view to the critical interaction zone Figure 4.10: (a) Mean pressure coefficient close to the tip clearance compared with experimental [7] and DNS [7] data, (b) corresponding slices on the blade surface demonstrated with the streamlines 0.01 mm off the wall, vertical two white lines indicates the 0.2x and 0.3x Figure 4.11: U z contours (a) without and (b) with streamlines, ω x contours (c) with and (d) without streamlines, 0.2x, 0.25x and 0.3x Figure 4.12: Three dimensional vortices with related streamlines from three different views Figure 4.13: Blockage of upstream flow Figure 4.14: (a) C fx on blade tip, (b) cells containing negative value of C fx, (c) tip leakage cross flow, 0.05x, 0.1x and 0.15x from blue to green Figure 4.15: (a) C fx on casing wall, (b) cells containing negative value of C fx xx

25 LARGE EDDY SIMULATION OF TIP LEAKAGE FLOW IN A LINEAR TURBINE CASCADE SUMMARY 1 line spacing must be set for summaries. For theses in Turkish, the summary in Turkish must have 300 words minimum and span 1 to 3 pages, whereas the extended summary in English must span 3-5 pages. For theses in English, the summary in English must have 300 words minimum and span 1-3 pages, whereas the extended summary in Turkish must span 3-5 pages. A summary must briefly mention the subject of the thesis, the method(s) used and the conclusions derived. References, figures and tables must not be given in Summary. Above the Summary, the thesis title in first level title format (i.e., 72 pt before and 18 pt after paragraph spacing, and 1 line spacing) must be placed. Below the title, expression ÖZET (for summary in Turkish) and SUMMARY (for summary in English) must be written horizontally centered. It is recommended that the summary in English is placed before the summary in Turkish. Before to begin, one must understand the concept it occupies in the terminology, thusly what means "leakage" exactly. Yet, some notions sound uncertain due to their collective nature though they are spreadly used somehow in the language. The dictionary defines the term leakage as "the accidental admission or escape of liquid or gas through a hole or crack". As a result, the problem discussed here refers to an inevitable concept occuring in the turbines, which causes unintentional losses. However, the physical nature of such loss will be discussed rather than fixing it, which is beyond that study. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. xxi

26 Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus xxii

27 dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Morbi massa orci, luctus at vulputate lacinia, vestibulum sed libero. Ut accumsan tortor vulputate dolor semper id dignissim augue semper. Proin ac purus mi. xxiii

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29 DOĞRUSAL BASAMAKLI BİR TÜRBİNİN UÇ SIZINTI AKIŞININ BÜYÜK GİRDAP BENZETİMİ İLE SİMÜLASYONU ÖZET Özet hazırlanırken 1 satır boşluk bırakılır. Türkçe tezlerde, Türkçe özet 300 kelimeden az olmamak kaydıyla 1-3 sayfa, İngilizce genişletilmiş özet de 3-5 sayfa arasında olmalıdır. İngilizce tezlerde ise, İngilizce özet 300 kelimeden az olmamak kaydıyla 1-3 sayfa, Türkçe genişletilmiş özet de 3-5 sayfa arasında olmalıdır. Özetlerde tezde ele alınan konu kısaca tanıtılarak, kullanılan yöntemler ve ulaşılan sonuçlar belirtilir. Özetlerde kaynak, şekil, çizelge verilmez. Özetlerin başında, birinci dereceden başlık formatında tezin adı (önce 72, sonra 18 punto aralık bırakılarak ve 1 satır aralıklı olarak) yazılacaktır. Başlığın altına büyük harflerle sayfa ortalanarak (Türkçe özet için) ÖZET ve (İngilizce özet için) SUMMARY yazılmalıdır. Türkçe tezlerde Türkçe özetin İngilizce özetten önce olması önerilir. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Praesent imperdiet, nisi nec aliquam cursus, dui turpis mollis nisl, ac consequat tellus sapien sit amet magna. Duis vel venenatis velit. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Proin malesuada risus nec metus dapibus eu tincidunt lectus dignissim. STATISTICS RELIABILITY COMMENTS COULD BE ADDED. xxv

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31 1. INTRODUCTION 1.1 Problem Definition Most of the turbomachines have rotating elements settled on a shaft and those rotating elements are enclosed with a surface, could be called casing-wall as seen from Figure 1.1. In order those components to rotate and function properly, there must be a gap in between such enclosing surface and rotating elements tip, otherwise there would be a contact such that elements of the turbine could not work. As a result of such clearance, some of the flowing air leaks through that gap while it goes from upstream to the downstream of the turbine blade. That leaking air flow phenomena is called "tip leakage" in the literature and the main reason why that air leaks through the gap is basically the pressure difference between upstream and downstream of the rotating elements. Figure 1.1 : Typical high-bypass turbomachinery and close view to the LPT blades REFERENCE HERE. Figure 1.2 shows the typical behaviour of tip leakage flow. As seen from the figure, the flow separates from the sharp corner of the blade s pressure side and creates a separation bubble on tip surface along the pressure side corner of the blade. Then, the fluid flows through the small region between separation bubble layer and the boundary layer occured on casing-wall. Flow accelerates through that region so that thickness 1

32 of that separation bubble region decreases, which means that flow tends to reattach to the blade tip as it progresses along clearance. Flow reattaches to the blade tip if the thickness is quite enough, otherwise, it goes through the gap and behaves as a jet flow (Figure 1.2). Reattachment location is about 2.4 times of the clearance size relative to the pressure side sharp corner [3]. Storer and Cumpsty [4] figured out that flow would not reattach to the blade unless the thickness of the blade is more than about 2.5 times of the clearance size. That non-reattached, jet fluid behaviour means that there is no pressure recovery for the thin blade case [2]. Besides, the more mass of the fluid would leak for the same driving pressure [3]. (a) (b) Figure 1.2 : (a) Two dimensional view of leakage mechanism, (b) reattached and non-reattached leakage flow. 1.2 Literature Overview Tip leakage has several side effects on turbomachines. Denton [2] explained them as two main effects, of which one is that tip leakage causes capability of fluid to produce work on blade to reduce, the other is that tip leakage disturbs main passage flow since it mixes with main passage flow, hence, up to 30 percent of aerodynamic losses might occur. One of the most effective modification could be done to reduce tip leakage flow mass and side effects on the turbomachine is basically to decrease clearance size on the blade tip because 1% change in the clearance size causes 1-3% on stage efficiency [5,6]. The 2

33 most of the researches have used tip clerance sizes varying from 1% of the span size to 4% of the span size to investigate that flow phenomena. The 1% clearance is the one that is used in practical fields, real turbines, but there is no clearance size less than that of 1% probably to prevent physical rubbing between blades and casing wall. Due to the higher tip leakage mass, larger tip clearance sizes causes stronger leakage vortexes and aerodynamics losses as expected. 1.3 Motivation and Outline Aerodynamic losses in turbines are amongst the most crucial problems in modern turbomachineries [2]. Engineering tools play a vital role to probe nature of complex flow physics in turbines, thusly to preclude inevitable losses such as tip leakage. Accordingly, considerable progress in the development of computational fluid dynamics (CFD) applications into turbomachineries have been achieved for last decades. It has been proved that CFD, nowadays, overcomes most of the engineering problems in the aerospace industry. On contrary to experimental approaches demanding particular places and implementation of specific instruments, CFD is applicable just through computers that makes it mostly preferable. Whereas, some CFD approaches, such as direct numerical simulation (DNS), are not suitable on some occasions since they require quite detailed domain with numerous amount of grid points, which makes them computationally expensive. Yet, large eddy simulation (LES), that is operable with less computational cost in comparison with DNS, could take place to investigate flow problems in turbines since it outputs reliable information on flow physics, which are in good agreement with both DNS and experimental results, as seen in the literature [9, 11]. From the tip leakage point of view, there exists also papers in the literature, in which the effect of clearance height [18] or viscous losses [10] was studied with the help of LES. To contribute further understanding of tip leakage flow mechanism, the present study is aimed to simulate tip leakage flow over a LPT blade T106. Hence, remarks about flow features such as upstream flow blockage near casing wall and local APG on suction surface near tip clearance caused by flow interactions was found out. Capabilities of LES in tip leakage aerodynamics containing complex turbulent flow structures were sought alongside. Results were compared with DNS and experimental results. 3

34 Structure of the following chapters are as follows: Numerical methodology about the problem and explanation about the computational domain and selected LPT blade profile are given in Chapter 2. Statistical and instanteneous results for both two dimensional and three dimensional flow cases are given with comments in Chapter 3. Detailed analyses about interaction mechanisms between leakage flow, secondary cross flow and horseshoe vortices, alongside the remarks about blockage of upstream flow are given in Chapter 4. And finally, conclusion and future work expectations are remarked in Chapter 5. 4

35 2. NUMERICAL METHODOLOGY Due to the fact that there is no analytical solution to the full Navier Stokes Equations since there exists some nonlinear variables within such as convection terms, some numerical methodologies and techniques were developed for last decades in order to be able to solve such equations. However, the scientists or engineers are still incapable of solving a Navier Stokes Equation, which contains all the different flow cases being in the nature at the same time. Yet, the methodological thinking human brain gave rise to the researchers to approach fluid problems in such a way that lacks chaotic behaviour of the fluids out of the problem but keeps the most critical behaviours of the fluid in the problem. That is to neglect some unnecessary fluid properties in the fluid problems. To decide whether a property is necessary in a flow case - negligible in other words, is an easy task thanks to the great development of the aerospace science. For instance, the fluid might be assummed as though it is an incompressible one where the flow velocity is barely slow such that the Mach number is less than 0.3 [1]. Besides, one would discard the energy equation so that would not need to solve it aside continuity and momentum equation, which means less complexity and time cost. That type of easy and witty solutions of deducing the complexity of flow problems caused lots of fluid mechanics problems to be computed easier with negligible amount of error. From that point of view, some neglections were also done in this work. Incompressible Navier Stokes Equations were selected due to the fact that operating velocity of the low pressure turbine blade is in incompressible range. Therefore, one would deal with the 3D incompressible Navier Stokes Equations in the present study. 2.1 Mathematical Modeling Incompressible continuity equation is defined to be; u i x i = 0 (2.1) 5

36 incompressible momentum equation is defined to be; u i t + u ju i = 1 P + ν 2 u i (2.2) x j ρ x i x j x i where i and j indices take values of 1, 2, 3 and velocity component u i could be written as; u i = u i + u i (2.3) u i here corresponds to filtered resolvable scale and u i corresponds to sub-grid scale in velocity term. After substition of such velocity terms into N-S equations, these decomposition of velocity term links to LES; u i t + u iu j x j = 1 ρ P x i + ν 2 u i x j x i (2.4) the term u iu j x j is not possible to calculate, while the term u i u j x j would be possible. As a result, such filtered N-S equation could be written in a new form; u i t + u i u j = 1 P + ν 2 ( u i ui u j u ) i u j (2.5) x j ρ x i x j x i x j x j sub-grid scale tensor is defined to be τ sgs i j u i t + u i u j x j = 1 ρ = u i u j u i u j such that; P + ν 2 u i τ sgs i j (2.6) x i x j x i x j this filtered last form of N-S equation is solvable when sub-grid scale tensor τ sgs i j modeled. One of the most common and simplest model, Smagorinsky model is utilized in the present study. Following equations are determined to model eddies in sub-grid scale; τ sgs i j τkk 3 δ i j = 2ν τ S i j (2.7) ν τ = (C s ) 2 S i j (2.8) S i j = 1 ( (ui ) + (u ) j) (2.9) 2 x j x i S = 2S i j S i j (2.10) ν τ is sub-grid scale viscosity, is the characteristic filter width, S i j is the rate of strain tensor for the resolved scale and finally, C s is defined to be Smagorinsky constant. is 6

37 2.2 Computational Domain Figure 2.1 illustrates the domain of the present case having 1.3 million grid point with uniform inlet. Rotational LPT blade having unshrouded tip is settled on an infinitely long linear cascade as was first offered by Bindon and Morphis [22], just to simplify the problem. Thereby, cyclic boundary conditions were defined along pitch-wise direction, no-slip boundary conditions were specified at the blade surface and the tip end wall. Symmetry boundary condition was assigned at hub end wall to succeed 200 mm span length, which is design span length as seen in Table 2.1. Reference Reynolds number was determined to be 8x10 4 based on axial chord length, inlet flow velocity and kinematic viscosity values. Full structured hexahedral mesh is maintained in the computational domain EXPLAIN YPLUS ALSO HERE. Finally, incompressible LES solver utilizing PISO algorithm is used to solve the problem in OpenFOAM and Smagorinsky model is selected. Figure 2.1 : Computational domain, inlet (blue), casing wall (green) and periodic surfaces (red). Table 2.1 : T106 blade specifications. Chord 198 [mm] Axial chord 170 [mm] Blade stagger 30.7 [ ] Pitch 158 [mm] Span 200 [mm] Suction surface length [mm] Pressure surface length [mm] Inlet flow angle 37.7 [ ] Design exit flow angle 63.2 [ ] 7

38 Figure 2.2 : Two dimensional view of computational domain with non-dimensional lengths and T106 blade profile. 8

39 3. RESULTS 3.1 Two Dimensional Analysis LES deals with the turbulent flow structures and accordingly three-dimensional analysis must be performed. However, the analyses were operated from two dimensional simple case to the complex three-dimensional cases just to overcome the complexity of the problem step-by-step. Yet, OpenFOAM solver acquires at least a uniform width perpendicular to the two dimensional surface, which makes it still three-dimensional though the case is two dimensional. Thereby, LES could be performed still over the two-dimensional case as is done in the present study. The two-dimensional case theoretically gives results as if the dimension of the case is infinitely long through empty defined unit width, whereas it practically does not mean anything from the turbulence point of view Statistical Results Figure 3.1 : Mean static pressure coefficient for two dimensional analysis compared with experimental [7] and DNS [7] data. 9

40 Figure 3.2 : Mean velocity contours for two dimensional analysis Instanteneous Results (a) (b) (c) Figure 3.3 : Instanteneous pressure and velocity contours for two dimensional analysis. 10

41 3.2 Three Dimensional Analysis Statistical Results What makes the analysis done by computational fluid dynamics reliable is the fact that the results are in good agreement with experimental results, or at least with DNS results. Therefore, that results in some properties to be compared with the others. Such properties have to be the ones corresponding to the instantaneous properties during the analysis. The statistical results are the ones containing all the information as mean ones while the solver iterations converge. If such mean informations are compatible with the results of the other researches, it could be said that the CFD results are reliable. Thereby, some of the statistical values such as velocity, pressure, etc. were collected throughout the iterations. Since the initial iterations deviates from the physical results since the simulation is incapable of convergence yet, they must be discarded or simply not collected. As a result, statistics were collected in 5 FTT after first 2 FTT and their agreements with other results are discussed here. Investigators [7,8,11,13,15,16] approached in different ways to obtain time-averaged static pressure coefficient. They also explained whether a numerical method (i.e DNS or LES) suffers to give the most reliable plot and what is the reason of that if such. All of them come to the similar point that boundary layer resolution at the suction side of the surface is very critical such that the statistical mean pressure coefficient would deviate beyond the 0.6 x/c ax for T106 blade. Such blade encounters very strong APG beyond such location and as a result, even the plot obtained by DNS could not finely overlay on the measurement results obtained from experiments in the C p graph as seen at Koschichow [7]. They had a slight difference in the C p graph and explained that as a result of incompressible approach. Koschichow s results are used also here to compare the present results. Since the researchers preferred a disturbed flow at the inlet but not in the present study, the first difference occurs at the suction side around leading edge of the blade. Due to the fact that they put moving bars at the inlet domain or experimental setup, or at least put varying inlet turbulence levels, the flow has a strong APG at the very near leading edge region of the suction side of the blade [7, 8, 11, 16]. That wake effect was illustrated in Figure 3.4. As a result of disturbed flow and wakes, transition occurs 11

42 Figure 3.4 : T106 cascade sketch with incoming wakes [8]. in a short region on the suction side near leading edge. Beyond the x/c ax 0.03 flow quickly becomes laminar on the suction side [8]. Besides, they used moving bars to create that inlet effect and Chen et all [16] explained that the presence of the moving bars causes inlet velocity angle to slightly deviate, which also could affect the static pressure coefficient on the blade surface. Kalitzin et all [15] also mentioned similar things for their incompressible DNS analysis. Boundary layer on the suction side is laminar on the large part of the suction side for uniform inlet case than that of disturbed one since the inlet turbulence results in a local amplification of turbulence near leading edge stagnation point. They also explained slight difference between their and experimental case as a compressibility effect. From LES point of view, parameters affecting the static pressure coefficient remains same as DNS analyses above and there are a few more. In LES study of Michelassi et all [11], they found noticeable differences in the suction side boundary layer. To resolve viscous sub-layer finely, they preferred a y + value less than 3 at the leading 12

43 edge, which approaches to 1 about half axial chord and remains same beyond. They linked the low pressure level found by LES comparing to DNS to the boundary layer state. LES predicted the transition %10 delayed and they conclude that the boundary layer resolution is not sufficient to obtain fine scale fluctuations and turbulent spots. Medic et all [17] also explained that LES suffers from difficulties in predicting boundary layer transition and capturing the delay of laminar separation with varying inlet turbulence, which is one of the main reason why there seems differences at the suction side separation region on the C p plot. All those researchers also preferred different equations to obtain time-averaged static pressure. The most common one they offered was the simple C p = 2(p p re f ) [8, 11, Ure 2 f 13, 15]. U re f and p re f here are the inlet and outlet parameters, which are 1 m/s and 0 m 2 /s 2 for the present case respectively. However, when it is plotted according to that equation, curve is slighly shifted. The second one offered by Chen et all [16] is more accurate than the traditional one, which is C p = (p p re f ) (p T p re f ). However, p re f is not the defined inlet pressure but is the pressure chosen from the first grid point. p T is the total pressure which could be taken from stagnation point. Those two equation above results in y axis (C p ) to be in a range of [-3.5 : 1]. Third one is offered by Koschichow et all [7], which is the one also utilized here, that is; C p = (p p out) (p T p out ) (3.1) The p T value is similar to the one offered by Chen et all [16] and p out is the static pressure taken from anywhere beyond the trailing edge. For the most accuracy, it was taken at 1.45 x/c ax beyond the trailing edge. Unlike two equations above, one offered by Koschichow et all [7] results in y axis to be in a range of [-0.4 : 1]. The results were compared with the experimental and DNS results performed by Koschichow et all [7]. As seen from the figure, there is no strong APG around leading edge of the suction side in the present study high probably due to the facts explained previously. The flow experiences a FPG around 0.03 < x/c ax < 0.6. Then, the flow immediately encounters an APG. The differences is noticeable at such region. LES predicts the APG location a bit further upstream than those of DNS and experimental results. Besides, the APG obtained by DNS and experimental results is weaker than the LES results for mid-span, for example. That strong mid-span APG found by LES result then turns to the ZPG and slight FPG beyond the x/c ax 0.8. The result of that could be the fact that LES is 13

44 poor to obtain small fluctuations around near trailing edge of suction side (1), absence of the inlet turbulence and compressibility effect at the present study results in LES to obtain different flow properties around that part (2) and finally, the mesh resolution around suction side wall and the beyond was not enough to resolve important flow properties for the present study. Above, at the pressure side, both curves overlay on the DNS results fine. (a) (b) Figure 3.5 : Mean static pressure coefficient compared with experimental [7], DNS [7] data and previous study [43]. Aside to the mean static pressure coefficient, other statistics such as mean velocities, turbulent kinetic energy, rms velocities are also collected and given as xy-plane 14

45 contours for three different spanwise locations in Figure 3.6. contours were non-dimensionalised. All corresponding (a) (b) Figure 3.6 : Two dimensional rms velocity and TKE contours, %50, %25, %1.25 of the blade span from (a) to (c) respectively. 15

46 (a) (b) Figure 3.7 : Two dimensional velocity contours, %50, %25, %1.25 of the blade span from tip clearance from (a) to (c) respectively. 16

47 3.2.2 Instanteneous Results Apart from the statistical results, the instanteneous results are given in that section and will be discussed to better imply the complex turbulent flow structure of the linear cascade. All given instanteneous informations here and in the further section correspond to the last iteration. Flow separates from the sharp corner of the blade pressure side when leakage process occurs [2 4, 18 20, 22, 24 26, 35]. Then, depending on the clearance height or the blade thickness, it tends to reattach on blade tip. Reattachment location is about 2.4 times of the clearance size relative to the pressure side sharp corner [3]. Storer [4] emphasized that the flow would not reattach and blow like jet flow if the fraction of the tip clerance height to the blade thickness is more than about %40. That would cause pressure difference between blade surfaces to be decreased, which causes no pressure recovery. Such non-reattached jet flow mechanism was not observed in the present study since the clearance was maintained to be %1 of the span, which is most widely preferred in the aerospace industry [18]. Another tip leakage separation occurs after the leaking fluid reaches to the suction side of the blade [2, 3, 18 21]. Such fluid separates from the corner between the blade suction side and the tip gap and then reattaches to the blade suction side surface. Then, those separated flow rolls through opposite direction according to the leakage vortex direction as seen from Figure 3.8. Denton [2] figured out that a vortex sheet occurs when the leakage and the main passage flow run into each other at the suction side of the blade since they both have different velocity vectors- different magnitude and direction in other words. Therefore, that causes a mixing process which triggers both flow to create a concentrated vortex. That could be the most probable reason why flow rolls through opposite direction after reattachment. For example, that reattachment of leakage flow resulting in reattachment line is clearly seen in Figure 4.8(a). Figure 3.9 was contoured with the corresponding U z magnitudes in order to imply leakage vortex mechanisms in a different manner. Each slice demonstrates specific chordwise locations. As the leakage process occurs along the chordwise direction, the mixing process, in which the leakage and mainstream interaction is very high, also 17

48 Figure 3.8 : Tip leakage flow streamlines demonstrated with different colors, 0.6x, 0.7x, 0.8x, 0.9x from red to blue respectively. occurs simultaneously [2, 18, 19, 24, 26 31] such that the particular vortical structures belong to the mixing process can be seen on the each contour slice from 0.5x to 0.9x of the chordwise direction. From the contour belonging 0.5x to the one corresponding 0.9x, the vortex structure expands and there is double negative spanwise moving flow spots especially at, for example, 0.9x. Upstream vortices are pushed off the suction surface beyond some axial position in between 0.7x and 0.9x. Such zone is also where pressure side leg of horseshoe vortex from the adjacent blade mixes up with passage vortex. Which means that velocity spots on very right hand side on contour at 0.9x correspond to such vortex core, whose three dimensional isosurfaces are demonstrated in the Figure Moreover, those mixture vortex cores have particular moving spots up to trailing edge position. Then, there exists many eddies beyond the traling edge, at 1.1x, as seen from negative and positive moving flow spots, which links fully turbulent flow. That is most likely due to the fact that main passage flow at the pressure side decomposes leakage vortex and suction passage mixture beyond the trailing edge after they run into each other. Besides, two dimensional xy planes having instanteneous results of pressure and velocity magnitudes are given in Figure

49 (a) (b) (c) (d) Figure 3.9 : Two dimensional contours demonstrated with corresponding U z magnitudes, (a) 0.5x, (b) 0.7x, (c) 0.9x, (d) 1.1x. 19

50 (a) (b) Figure 3.10 : Two dimensional pressure and velocity contours, %50, %25, %1.25 of the blade span according to the design span length from (a) to (c) respectively. 20

51 4. DETAILED FLOW ANALYSIS 4.1 Interaction Mechanisms In typical high cambered blade profiles, a so-called "stagnation line" or "attachment line" forms on the casing wall of the turbine cascade. Such line, which is almost parallel to the blade pressure side profile, divides the cascade flow such that some of the fluid leaks through the clearance gap or just advances through the downstream of the blade. Therefore, it might be said that there are two of the different flow zones could be called "passage flow zone" and "leakage flow zone". However, the leakage flow encounters an interaction with the passage flow after it forms a leakage vortex at the suction side of the turbine blade. That leakage flow might separate from the casing wall as seen from the Figure 4.1. On the other hand, the passage flow might also separate from the casing wall of turbine cascade and that leads an interaction with the leakage flow vortex, which creates a separated flow zone called "buffer zone" in the literature [27 30]. That "buffer zone" is a critical interaction area. Figure 4.1 : Passage and leakage separation interaction [27]. Similar to the representation in Figure 4.1, such flow zone occurs in the present study as well. The fluid at the pressure side of the blade leaks through the tip gap, separates from the sharp corner of the pressure side along tip and reattaches to the tip surface on the clearance and leaks to the suction side of the cascade. The leakage vortex 21

52 encounters a strong passage vortex after the fluid leaks through tip gap, as seen from the Figure 4.2. Then, those two vortexes mixes up. Figure 4.2 : Passage and leakage separation interaction in the present study at 0.8x, (a) passage flow zone, (b) buffer zone, (c) leakage flow zone. To better understand the leakage separation, the passage separation and their interaction at the buffer zone, the whole flow field on the casing wall should be analysed. From the experimental point of view, surface oil visualization method is a good one to track streamlines on a solid object and to visualise the separation regions if exist. Lee and Kim [27] carried out some experiments and they obtained the flow fields for three different linear cascades having different clearance heights, %1, %2, %3, and compared results with the tip modified case. Eventhough the blade profile they preferred is different than the present study, those flow fields near the casing wall are very typical for high cambered blade profiles regardless of the blade tip modification [28 31] or the tip clearance height [27] so that some of the flow properties on the casing wall inevitably occurs, such as attachment line (or called stagnation line), passage separation line, stagnation zone, which is formed upstream of the leading edge and causes two different attachment line to form upstream of it, which meet each other at the buffer zone. Therefore, such properties are also expected in the present study since the blade profile is a high cambered one and the clearance height is defined to be %1, in which the leakage and passage flow interaction is high according to the literature [18, 33, 35]. As viewed in the Figure 4.3, there is a flow region, which is encircled with the white dashed line upstream of the buffer zone. The passage flow coming through separates from the casing wall there and it causes a passage flow separation line advances to the 22

53 upstream. As the clearance height is raised, the effect of the such region decreases and it almost vanishes at the case having %3 clearance, as seen from the Figure 4.3(c). Figure 4.3 : Surface flow visualisation on the casing wall, (a) %1 clearance, (b) %2 clearance, (c) %3 clearance [27]. In order to track the fluid particles near the casing wall of the present study, velocity vectors very close to the casing wall are demonstrated below. Very similar flow properties occurs in the present study as well. Region "A" corresponds to the passage flow zone, "B" corresponds to the buffer zone and "C" corresponds to the leakage flow zone in Figure 4.4. The zoomed in view for the critical areas are demonstrated in the following. Figure 4.4 : Flow field near the casing wall for present study. As seen from the Figure 4.4, similar flow patterns and properties are obtained in the present study, which means reliable information on flow physics. Besides, since the white dashed encircled area is not in the interest of the other studies, they did not name it. However, such region is called "Interaction Zone" here and it is encircled with yellow line in Figure 4.5. Figure 4.6 demonstrates the main buffer zone, in which the passage separation and the leakage separation on the casing wall are highly interacted. Some of the velocity 23

54 Figure 4.5 : Zoomed in view of flow field near the casing wall. vectors on the right figure are encircled with the green line, which flows to the upstream, meaning the leakage separation [23]. Figure 4.6 : Flow field near the casing wall. In the Figure 4.7 [27], the interaction of the blade suction surface and incoming passage flow near the casing wall is shown. As seen from the figure, passage flow separation creates a separation line regardless of the clearance and moreover, the fluid penetrates to the blade surface through spanwise direction, a bit tilted. Therefore, regardless of whether inlet turbulence exist [7, 11, 14, 15, 34] or not [43], the forming passage vortex affects the flow on the suction side of the blade so it decelerates the fluid flowing on the blade suction surface, which creates a local APG near the endwall. For example, those penetrating flow is clearly seen at the streamlines shown in Fig.34 of reference [34]. Figure 4.7 gives rise a further analysis, which should be performed on the blade surface since the passage flow obviously affects the flow on the blade suction surface. As a result, the streamlines very close to the blade surface are tracked by some iterations and the streamlines being mm off the wall were obtained. Figure 4.8(a) and (c) indicate such streamlines on the blade suction side surface. The instanteneous flow feature is quite complex. Far from the tip clearance, flow advances in a smooth path 24

55 Figure 4.7 : Passage flow separation with no clearance [27]. through downstream of the blade and then it separates from the blade surface, whose separation line on the blade surface is visible. At the separated flow zone, the flow behaviour is very turbulent and vortices impinging on the blade surface causes some cross flow structures. On the other hand, a suction side reattachment line of the leakage flow appears close to the tip clearance, where reattached flow mixes up with the main passage flow afterward. Aside to the wall-bounded streamlines, skin friction coefficient on the blade surface is also contoured, just to remark separation zones. Figure 4.8(b) demonstrates non-dimensional skin friction coefficient along x-axis over the blade suction surface. Additionally, cells containing negative C fx values were demonstrated, which is a good proof to emphasize flow separation. Since the leakage separation does not occur along x-axis but z-axis, cells containing C fz values were also added to view not only main stream flow separation but also leakage separation. Close view to the interaction zone, where local APGs occurs, could be seen on the Figure 4.9. Passage flow penetration to the blade surface occurs as it was observed in the study of Lee and Kim [27]. The flow penetration at such zone is a bit tilted to downstream. Due to the fact that the streamlines are directed inclined through, the local APG is expected at downstream in the C p plot as the z/h is increases along the spanwise direction- according to the clearance gap. As seen from mean pressure coefficient plot in Figure 4.10, such behaviour clearly occurs. The local APG at the first half of the suction side occurs at upstream as the plotted pressure coefficient data is taken from the slice closer to the tip clearance. 25

56 (a) (b) (c) (d) Figure 4.8 : (a) and (c) Streamlines on the blade suction side surface, mm off the wall, (b) C fx over blade suction surface, (d) cells containing negative value of C fx and C fz. Figure 4.9 : Close view to the critical interaction zone. Moreover, the effect of the vortex and cross flow interaction decreases as moving to the negative spanwise direction (i.e %3). 26

57 (b) (a) Figure 4.10 : (a) Mean pressure coefficient close to the tip clearance compared with experimental [7] and DNS [7] data, (b) corresponding slices on the blade surface demonstrated with the streamlines 0.01 mm off the wall, vertical two white lines indicates the 0.2x and 0.3x. Due to the complexity of the flow feature, detailed streamline track and vortex identification are performed to give more detailed information about flow features. The followed streamlines are given alphabetical nomenclature to simplify the explanations. Those nomenclatures refers to the streamlines in the Figures 4.11 and instance, L1, L2 and L3 are three different followed streamlines, which leakes through the blade clearance and they are in the interest since L1 and L2 forms leakage vortex and interact with the passage vortex, whose streamlines were called P1, P2 and P3 as nomenclature. Streamlines belong to the L3 leakes further downstream so that they do not contact with the leakage and the passage vortex interaction but mixes up with the cross flow passage streamlines, which are PS1, PS2, PS3, PS4 and PS5, in the so-called buffer zone. Furthermore, BP1 and BP2 are the streamlines, which influences neither local APG -interaction- zone nor buffer zone, simply bypass the suction surface. H is the streamlines forming pressure side leg of the horseshoe vortex. Besides, each streamline group contains 100 streamlines and was tracked from the domain inlet in circular areas having 0.1 mm radius to emphasize where the flow uniformity is deformed. Some spanwise velocity and axial vorticity contours with some of the streamlines are indicated in Figure As seen from the contours, which are at 0.2x on both figures, that the spanwise velocity and vorticity magnitudes are low in comparison with the further downstream for the region close to the interaction zone. Then, for instance, L s For 27

58 streamlines mixes up with the P s streamlines at the suction side, which causes both streamlines to form interaction vortex and to be pushed through negative spanwise direction. That behaviour is frankly identified in the contours as well, the areas of negative spanwise velocity spots and axial vorticity spots close to the interaction zone raises from 0.2x to 0.3x. BP s streamlines are close to the L s and P s streamlines, which means they must have influenced each other. However, BP s streamlines bypasses interaction zone through a "hole" and mixes up with the interaction vortex at the further downstream, which was demonstrated in the followings. (a) (b) (c) (d) Figure 4.11 : U z contours (a) without and (b) with streamlines, ω x contours (c) with and (d) without streamlines, 0.2x, 0.25x and 0.3x. A further analysis, which contains three-dimensional vortical structures and streamlines, is done along the computational domain around LPT blade since the flow physics is quite complex. From that point of view, the cascade with vortices and vortices with related streamlines are given from three different perspectives in Figure Vortex identification criteria was selected to be Q-criterion, which is a better option for the present study [41, 42]. 28

59 P1 and P2 streamlines directly go through the local APG zone but P3 streamlines forms horseshoe vortex first and then directs through such region. Meanwhile, L1 and L2 streamlines go through pressure side of the blade and then leak upon blade tip. Then those two streamlines groups mix up at so-called interaction zone to form passage and leakage interaction vortex. They are pushed downward -through negative spanwise direction- immediately after interaction. That results in such interaction vortex to be detached and different one than main passage vortex -secondary flow vortex, which is formed due to the passage flow near casing wall. However, there are two forming horseshoe vortexes off the leading edge, one of which in comparison is predominantly smaller than the other, which impinges on the region where leading edge and blade tip meets each other. Suction side leg of such small vortex goes downstream through the interaction zone since its direction of motion is along the similar path with mainstream flow on the leading edge through suction surface. As a result, its isosurface is seen clearly on the Figure 4.12(a) and (b). Then, such vortex mixes up with the passage and leakage interaction vortex. That means that the passage and leakage interaction vortex is not only due to the L s and P s streamlines interaction but also in the negative influence of suction side leg of such small horseshoe vortex. To predict which one has the most negative on the local APG in comparison is a competitive study. L1 and L2 streamlines, for example, advances along the blade tip almost perpendicular to the mainstream flow, which could trigger the local APG. Incoming cross secondary flow near casing wall from adjacent blade impacts on the blade surface on such local APG zone, which penetrates through direction off the tip clearance. Suction side leg of small horseshoe vortex enlarges itself across the local APG zone, where it together with others turn into the interaction vortex after running into each other at such interaction zone. On the other hand, pressure side leg of such small horseshoe vortex impinges on the corner, where pressure side surface and tip clearance meet near leading edge. Due to the different direction of motion with respect to the mainstream flow and mixing process with the leakage flow, such structure having negative angle of attack is blown upon tip clearance by leakage flow, which creates separation bubble along the pressure side sharp corner of the blade, whose schematic is shown in Figure 1.2. As a result of 29

60 being blown, pressure side leg of such small vortex is barely seen on Figure 4.12(a) and (b). (a) (b) (c) (d) (e) (f) Figure 4.12 : Three dimensional vortices with related streamlines from three different views. 4.2 Blockage of Upstream Flow Aside to the small horseshoe vortex explained in the previous sub-section, relatively big horseshoe vortex is also in the interest since vortex results in negative 30

61 circumstances, as is well known. Figure 4.13 presents that the flow has a particular behaviour as the followed streamlines get closer to the casing wall of the domain. Two blades were put apart each other and one of them was transformed to the position of its corresponding cascade location just to demonstrate them very similar to the way how they are settled in a linear cascade. The incoming flow, that is going from upstream to the downstream of the turbine blades could either be blocked and directs to a different path or advances through blade passage, as viewed in the streamlines. The ones belonging to the group 1 slow down across the leading edge of the blade and roll around the leading edge, which forms suction side leg of horseshoe vortex off the leading edge. Those streamlines afterward mixes up with the over tip leakage flow of the same blade in the suction side region. Their corresponding isosurface in Figure 4.12 diminishes in size as it moves with mainstream flow. The ones belong to the group 2 follows the path which is almost as same shape as the pressure side of the blade along the chordwise direction. Then that decelerating flow leakes through the tip gap due to the suction effect along the tip region caused by suction side of the same blade, as is well known. The last incoming flow ones belong to the group 3 decelerates across the very near region of the leading edge of the blade, forming the other leg of the horseshoe vortex created also by group 1 streamlines and immediately turns across the neighbourhood region belonging to the adjacent blade. That turning flow rolls and mixes up with the leakage flow and ones belonging to group 1 of the adjacent blade. Such horseshoe vortex seen in Figure 4.12 is formed upstream of the leading edge near casing wall, so upstream of clearance above blade tip. Therefore, some physical flow properties should be obtained in order to find out the reason of such formation. Accordingly, non dimensional skin friction coefficient on blade tip and casing wall and cells having negative values are contoured in Figure 4.14 and Negative value of C fx links to boundary layer separation for flow along x-axis, as is well known, so cells having negative value of C fx on Figure 4.14(b) link to local separation on blade tip for almost all quarter chord, could be thought. However, such negative values of C fx on blade tip and tip casing wall do not present boundary layer separation when inlet flow angle is considered. That is because defined global axis of the domain is not perpendicular to the inlet flow angle. Thereby, they correspond to the tip cross flow such that resulting in blockage of upstream flow and relatively big horseshoe vortex 31

62 Figure 4.13 : Blockage of upstream flow. upstream of leading edge close to the casing-wall. Due to the high camberness of the LPT blade, cross flowing tip leakage occur on blade tip near leading edge so that it results in blockage of upstream flow and a strong horseshoe vortex. 32

63 (a) (b) (c) Figure 4.14 : (a) C fx on blade tip, (b) cells containing negative value of C fx, (c) tip leakage cross flow, 0.05x, 0.1x and 0.15x from blue to green. (a) (b) Figure 4.15 : (a) C fx on casing wall, (b) cells containing negative value of C fx. 33

64 34

65 5. CONCLUSION AND FUTURE WORK Large eddy simulation of tip leakage flow in a linear turbine cascade was simulated in OpenFOAM. Time-averaged static pressure coefficient was in good agrement with other studies except than the separation region because of the absence of inlet turbulence and due to the fact that mesh resolution was poor for LES to resolve small fluctuations. From the flow physics point of view, local APG caused by flow interactions was observed on blade suction surface close to the clearance. That is most likely due to the fact that leakage flow, suction side leg of small horseshoe vortex and secondary cross flow from adjacent blade VERBHERE around such region. The flow field on the casing wall and the streamlines off the blade profile agreed with other studies. Another big horseshoe vortex was formed upstream of the leading edge, which mixes up with vortices formed around adjacent blade suction side. For further studies, following detailes could be performed; Grid effect, which is critical for LES, should be investigated since total grid number was maintained to be 1.3 million for the present study. Turbulent flow should be defined at the inlet such that flow field upstream of the LPT blades has about %5 turbulence intensity in practical REFERENCE. Turbulence energy spectrum should be plotted and compared with Kolmogorov scale, which is another proof for LES in terms of reliablity. 35

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71 CURRICULUM VITAE Name Surname: Abdurrahman Gazi Yavuz Place and Date of Birth: Adıyaman, 11/07/ EDUCATION: B.Sc.: 2018, Istanbul Technical University, Faculty of Aeronautics and Astronautics, Aeronautical Engineering 41