Loss Mechanisms in Turbine Tip Clearance Flows by Arthur Huang Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2011 (cid:13)c Arthur Huang, MMXI. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. Author .............................................................. Department of Aeronautics and Astronautics May 19, 2011 Certified by.......................................................... Edward M. Greitzer H.N. Slater Professor of Aeronautics and Astronautics Thesis Supervisor Certified by.......................................................... Choon S. Tan Senior Research Engineer Thesis Supervisor Certified by.......................................................... Steven G. Gegg Manager, Turbine Aerodynamics, Rolls-Royce Corporation Thesis Supervisor Accepted by......................................................... Eytan H. Modiano Associate Professor of Aeronautics and Astronautics Chair, Graduate Program Committee 2 Loss Mechanisms in Turbine Tip Clearance Flows by Arthur Huang Submitted to the Department of Aeronautics and Astronautics on May 19, 2011, in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics Abstract Numerical simulations of tip clearance flow have been carried out to define the loss generationmechanismsassociatedwithtipleakageinunshroudedaxialturbines. Mix- ing loss between the leakage, which takes the form of a strong embedded streamwise vortex (u /u ≥ 1 in the vortex core), and the mainstream flow is found to be the θ x main source of loss. Vortex line contraction, and consequent vortex core expansion, and also vortex breakdown, are identified as the two important mechanisms that determine mixing loss. Because of these vortex dynamic features, the behavior is different from the conventional view of the effect of pressure level on mixing of non- uniform flows. More specifically, it is shown, through control volume arguments and axisymmetric computations, that as a strongly swirling flow passes through a pres- sure rise, the mixed-out loss can either decrease or increase, the latter occurring if the deceleration becomes large enough to initiate vortex breakdown. It is further shown that tip vortices in turbines experience pressure rises large enough to cause vortex breakdown. The effect of pressure distribution on tip leakage losses is illus- tratedthroughexaminationoftwoturbineblades, onedesignedwithaforwardloaded tip and one with an aft loaded tip. The computations show a 16% difference in tip clearance loss between the two, due to the lower pressure rise encountered by the clearance vortex, and hence lower vortex breakdown losses, with the forward loaded blade. Other computational experiments, on the effects of blade loading, incidence, and solidity, are also shown to be consistent with the ideas developed about blade pressure distribution effects on vortex breakdown and hence clearance mixing loss. Thesis Supervisor: Edward M. Greitzer Title: H.N. Slater Professor of Aeronautics and Astronautics Thesis Supervisor: Choon S. Tan Title: Senior Research Engineer Thesis Supervisor: Steven G. Gegg Title: Manager, Turbine Aerodynamics, Rolls-Royce Corporation 3 4 Acknowledgments “Come unto me, all you who are weary and burdened, and I will give you rest” -Matthew 11:28 This work was carried out with the support of the Rolls-Royce Whittle fellowship, in collaboration with the Turbine Aerodynamics group at Rolls-Royce Corporation in Indianapolis. I would like to thank my thesis advisors, Prof. Edward Greitzer and Dr. Choon Tan, without whom this work would not have been possible. Their constructive critiques never let me settle for less, and their encouragement let me know that I was capable of more. I am also indebted to Prof. Nick Cumpsty for his helpful comments on this work. ThanksisalsoduetoseveralengineersatRolls-Roycefortheirfriendshipanddeep technicalinvolvementinthiswork. EdTurner, SteveGegg, andEugeneClemenshave allcontributedvitallytothetechnicalthoughtbehindthisthesis. Specifically, Iwould like to thank Steve for his great advice and management of the Whittle Fellowship program, Ed for his help in designing new airfoil geometries, and Eugene for putting up with all the times I went running to him with CFD issues. Likewise, I’d like to thank Kurt Weber, who good-naturedly endured my countless questions about CFD. I would also like to thank my colleagues at the Gas Turbine Lab for their friend- ship, advice, and support. I am especially grateful to Dorian Colas and David Hall for enlightening discussions on vortex dynamics, mixing losses, and basketball. My time at MIT would have been far less meaningful if I had never become friends with Yunji Wu, Justin Lai, Jeremy Lai, Orton Huang, James Won, Yu Xu, Albert Chi and Ed Kao. Thank you for sharing your lives with me. In addition, thanks to Joey Sung and Eddie Wu for their friendship which has continued since childhood. Finally, I want to thank my family for their support and love through the years. Alex and Allen have been the best of brothers, each in his own way. I never see my dad so excited as when he discusses research with me, and I am grateful for his love, patience, and wisdom. As for my mom, I know that no one loves me more, and it is to her that this thesis is dedicated. 5 6 Contents Nomenclature 19 1 Introduction 23 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.2 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2 Features of Tip Clearance Flows 29 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2 Computational Study of Tip Clearance Flow . . . . . . . . . . . . . . 29 2.3 Loss Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4 Characterization of Gap Exit Flow . . . . . . . . . . . . . . . . . . . 33 2.4.1 Gap Pressure Ratio and Discharge Coefficient . . . . . . . . . 35 2.4.2 Gap Exit Area . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.3 Leakage Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.4.4 Leakage Flow Modeling . . . . . . . . . . . . . . . . . . . . . . 39 2.5 Characterization of Tip Clearance Vortex . . . . . . . . . . . . . . . . 39 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3 Estimation of Tip Clearance Mixing Losses with Control Volume Analysis 43 7 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 Description of Control Volume Model . . . . . . . . . . . . . . . . . . 43 3.3 Assessment of Control Volume Model in Rectangular Ducts . . . . . . 46 3.4 Assessment of Control Volume Model of Mixing in Turbine Environments 51 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4 Effect of Pressure Changes on Vortex Mixing Losses 57 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Mixing Losses for a Wake in a Pressure Gradient . . . . . . . . . . . 58 4.3 ControlVolumeModelforRankineVortexResponsetoPressureGradient 59 4.4 Mixing Losses for a Vortex in a Pressure Gradient . . . . . . . . . . . 62 4.5 Criteria for Vortex Breakdown . . . . . . . . . . . . . . . . . . . . . . 66 4.6 Computational Study of Vortex in Pressure Rise . . . . . . . . . . . . 66 4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5 Effect of Turbine Pressure Rise on Clearance Loss 75 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Tip Design Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.1 Overall Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.2 Leakage Mass Flow . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.3 Tip Clearance Vortex . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.4 Loss Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6 Effect of Overall Blade Loading, Incidence and Solidity 89 6.1 Effect of Blade Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.1.1 Computational Details . . . . . . . . . . . . . . . . . . . . . . 90 6.1.2 Blade Loading Study Results . . . . . . . . . . . . . . . . . . 90 6.1.3 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . 94 6.2 Effect of Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 8 6.3 Effect of Solidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 6.3.1 Leakage Massflow . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.3.2 Mixing Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 7 Conclusions and Recommendations for Future Work 105 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 107 9 10