{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T00:56:30Z","timestamp":1769907390314,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,12,28]],"date-time":"2018-12-28T00:00:00Z","timestamp":1545955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51506107"],"award-info":[{"award-number":["51506107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51476082"],"award-info":[{"award-number":["51476082"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In unshrouded turbine rotors, the tip leakage vortices develop and interact with the passage vortices. Such complex leakage flow causes the major loss in the turbine stage. Due to the complex turbulence characteristics of the tip leakage flow, the widely used Reynolds Averaged Navier\u2013Stokes (RANS) approach may fail to accurately predict the multi-scale turbulent flow and the related loss. In order to effectively improve the turbine efficiency, more insights into the loss mechanism are required. In this work, a Delayed Detached Eddy Simulation (DDES) study is conducted to simulate the flow inside a high pressure turbine blade, with emphasis on the tip region. DDES results are in good agreement with the experiment, and the comparison with RANS results verifies the advantages of DDES in resolving detailed flow structures of leakage flow, and also in capturing the complex turbulence characteristics. The snapshot Proper Orthogonal Decomposition (POD) method is used to extract the dominant flow features. The flow structures and the distribution of turbulent kinetic energy reveal the development of leakage flow and its interaction with the secondary flow. Meanwhile, it is found that the separation bubble (SB) is formed in tip clearance. The strong interactions between tip leakage vortex (TLV) and the up passage vortex (UPV) are the main source of unsteady effects which significantly enhance the turbulence intensity. Based on the DDES results, loss analysis of tip leakage flow is conducted based on entropy generation rates. It is found that the viscous dissipation loss is much stronger than heat transfer loss. The largest local loss occurs in the tip clearance, and the interaction between the leakage vortex and up passage vortex promotes the loss generation. The tip leakage flow vortex weakens the strength of up passage vortex, and loss of up passage flow is reduced. Comparing steady and unsteady effects to flow field, we found that unsteady effects of tip leakage flow have a large influence on flow loss distribution which cannot be ignored. To sum up, the current DDES study about the tip leakage flow provides helpful information about the loss generation mechanism and may guide the design of low-loss blade tip.<\/jats:p>","DOI":"10.3390\/e21010021","type":"journal-article","created":{"date-parts":[[2018,12,28]],"date-time":"2018-12-28T11:52:42Z","timestamp":1545997962000},"page":"21","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Entropy Analysis of the Flat Tip Leakage Flow with Delayed Detached Eddy Simulation"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8787-113X","authenticated-orcid":false,"given":"Hui","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Xinrong","family":"Su","sequence":"additional","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Xin","family":"Yuan","sequence":"additional","affiliation":[{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1115\/1.3262090","article-title":"Effects of Tip Clearance on Blade Loading in a Planar Cascade of Turbine Blades","volume":"109","author":"Sjolander","year":"1987","journal-title":"J. Turbomach."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1115\/1.3262162","article-title":"Tip leakage flow in a linear turbine cascade","volume":"110","author":"Moore","year":"1988","journal-title":"J. Turbomach."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1115\/1.2927987","article-title":"Prediction of Tip-Leakage Losses in Axial Turbines","volume":"114","author":"Yaras","year":"1992","journal-title":"J. Turbomach."},{"key":"ref_4","first-page":"817","article-title":"Numerical Simulation of Tip Leakage Flows in Axial Flow Turbines, with Emphasis on Flow Physics: Part I?Effect of Tip Clearance Height","volume":"123","author":"Tallman","year":"2000","journal-title":"J. Shenyang Jianzhu Univ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"111004","DOI":"10.1115\/1.4041514","article-title":"Aerodynamic Interaction between an Incoming Vortex and Tip Leakage Flow in a Turbine Cascade","volume":"140","author":"Zhou","year":"2018","journal-title":"J. Turbomach."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, J., Du, K., and Song, L. (2016). Effects of tip cavity geometries on the aerothermal performance of the transonic turbine blade with cavity tip. Proc. Inst. Mech. Eng. Part A J. Power Energy, 230.","DOI":"10.1177\/0957650915626833"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.ijheatmasstransfer.2016.03.121","article-title":"Effects of squealer rim height on heat\/mass transfer on the floor of cavity squealer tip in a high turning turbine blade cascade","volume":"99","author":"Kang","year":"2016","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_8","first-page":"589","article-title":"Tip Leakage Flow and Heat Transfer Predictions for Turbine Blades","volume":"4","author":"Yang","year":"2007","journal-title":"Proc. ASME Turbo Expo"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.ijheatmasstransfer.2017.12.017","article-title":"An aerothermal study of the influence of squealer width and height near a HP turbine blade","volume":"120","author":"Senel","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1016\/j.ijheatmasstransfer.2016.12.026","article-title":"Heat\/mass transfer over the cavity squealer tip equipped with a full coverage winglet in a turbine cascade: Part 2? Data on the cavity floor","volume":"108","author":"Lee","year":"2017","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.energy.2014.05.041","article-title":"Heat transfer and film cooling effectiveness on the squealer tip of a turbine blade","volume":"72","author":"Park","year":"2014","journal-title":"Energy"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"052506","DOI":"10.1115\/1.4035175","article-title":"Cooling Injection Effect on a Transonic Squealer Tip Part I: Experimental Heat Transfer Results and CFD Validation","volume":"139","author":"Ma","year":"2017","journal-title":"J. Eng. Gas Turb. Power"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"052507","DOI":"10.1115\/1.4035200","article-title":"Cooling Injection Effect on a Transonic Squealer Tip Part II: Analysis of Aerothermal Interaction Physics","volume":"139","author":"Ma","year":"2017","journal-title":"J. Eng. Gas Turb. Power"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1016\/j.applthermaleng.2016.08.173","article-title":"Investigations of Film Cooling and Heat Transfer on a Turbine Blade Squealer Tip","volume":"110","author":"He","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_15","unstructured":"Stefano, C., and Shahrokh, S. (2016, January 13\u201317). Enter Multi-Disciplinary Analyses for The Design of a High Pressure Turbine Blade Tip. Proceedings of the ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, Korea."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Stefano, C., Shahrokh, S., and D, C.J. (2016). Numerical investigations of different tip designs for shroudless turbine blades. Proc. Inst. Mech. Eng. Part A J. Power Energy, 230.","DOI":"10.1177\/0957650916661459"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Du, K., Li, Z., and Li, J. (2016, January 13\u201317). Numerical Investigation of the Blade Tip and Overtip Casing Aerothermal Performance in a High Pressure Turbine Stage. Proceedings of the ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition, Seoul, Korea.","DOI":"10.1115\/GT2016-56709"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Kelly, R., Jemcov, A., Cameron, J.D., Morris, S.C., Coffman, J., and Malak, M.F. (2017, January 26\u201330). GT2017-64979 Very Large Eddy Simulation (VLES) of a Squealer Tipped Axial Turbine Stage. Proceedings of the Igti Turbo Expo, Charlotte, NC, USA.","DOI":"10.1115\/GT2017-64979"},{"key":"ref_19","unstructured":"Yaglom, A.M., and Tatarski, V.I. (1967). The structure of inhomogeneous turbulence. Atmospheric Turbulence & Wave Propagation, Nauka."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0022112088001818","article-title":"The dynamics of coherent structures in the wall region of a turbulent boundary layer","volume":"192","author":"Aubry","year":"1988","journal-title":"J. Fluid Mech."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1017\/S0022112002007991","article-title":"A low-dimensional model for simulating three-dimensional cylinder flow","volume":"458","author":"Ma","year":"2002","journal-title":"J. Fluid Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2493","DOI":"10.1063\/1.1483300","article-title":"Models for turbulent plane Couette flow using the proper orthogonal decomposition","volume":"14","author":"Moehlis","year":"2002","journal-title":"Phys. Fluids"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/j.combustflame.2009.12.013","article-title":"POD-based analysis of combustion images in optically accessible engines","volume":"157","author":"Bizon","year":"2010","journal-title":"Combust. Flame"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.ijheatfluidflow.2012.03.010","article-title":"LES of turbulent jet in cross flow: Part 2 \u2013 POD analysis and identification of coherent structures","volume":"36","author":"Dalibor","year":"2012","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.3390\/en11082091","article-title":"Computational Modeling of Gurney Flaps and Microtabs by POD Method","volume":"11","author":"Unai","year":"2018","journal-title":"Energies"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Spalart, P.R., and Allmaras, S.R. (1992, January 6\u20139). A one-equation turbulence model for aerodynamic flows. Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.1992-439"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00162-006-0015-0","article-title":"A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities","volume":"20","author":"Spalart","year":"2006","journal-title":"Theor. Comput. Fluid Dyn."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Su, X., Yamamoto, S., and Yuan, X. (2013, January 30). On the accurate prediction of tip vortex: Effect of numerical schemes. Proceedings of the ASME Turbo Expo 2013, San Antonio, TX, USA.","DOI":"10.1115\/GT2013-94660"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1002\/fld.3655","article-title":"On the efficient application of weighted essentially nonoscillatory scheme","volume":"71","author":"Su","year":"2013","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"5275","DOI":"10.1007\/s12206-016-1046-0","article-title":"Numerical investigation on the effects of real industrial bleeding geometry in a high-speed compressor stage","volume":"30","author":"Gou","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lin, D., Yuan, X., and Su, X. (2017). Local Entropy Generation in Compressible Flow through a High Pressure Turbine with Delayed Detached Eddy Simulation. Entropy, 19.","DOI":"10.3390\/e19010029"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.2514\/3.12149","article-title":"Two-equation eddy-viscosity turbulence models for engineering applications","volume":"32","author":"Menter","year":"1994","journal-title":"AIAA J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1016\/B978-008043328-8\/50064-3","article-title":"Detached-eddy simulation of an airfoil at high angle of attack","volume":"4","author":"Shur","year":"1999","journal-title":"Eng. Turbul. Model. Exp."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1002\/fld.2111","article-title":"Implicit solution of time spectral method for periodic unsteady flows","volume":"63","author":"Su","year":"2010","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Vatsa, V.N., Carpenter, M.H., and Lockard, D.P. (2010, January 4\u20137). Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications. Proceedings of the 48th AIAA Aerospace Sciences Meeting, Orlando, FL, USA. Number 20100002944.","DOI":"10.2514\/6.2010-122"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wang, H., Lin, D., Su, X., and Yuan, X. (2017). Entropy analysis of the interaction between the corner separation and wakes in a compressor cascade. Entropy, 19.","DOI":"10.3390\/e19070324"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1080\/10618562.2016.1156095","article-title":"All-speed Roe scheme for the large eddy simulation of homogeneous decaying turbulence","volume":"30","author":"Li","year":"2016","journal-title":"Int. J. Comput. Fluid Dyn."},{"key":"ref_38","first-page":"213","article-title":"The Minimal Flow Unit in Near-Wall Turbulence","volume":"225","author":"Javier","year":"2006","journal-title":"J. Fluid Mech."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/0021-9991(92)90046-2","article-title":"Boundary conditions for direct simulations of compressible viscous flows","volume":"101","author":"Poinsot","year":"1992","journal-title":"J. Comput. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1088\/1367-2630\/6\/1\/035","article-title":"Ten questions concerning the large-eddy simulation of turbulent flows","volume":"6","author":"Pope","year":"2003","journal-title":"New J. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Pope, S.B. (2000). Turbulent Flows, Cambridge University Press.","DOI":"10.1017\/CBO9780511840531"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Pinnau, R. (2008). Model Reduction via Proper Orthogonal Decomposition, Springer.","DOI":"10.1007\/978-3-540-78841-6_5"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"V002T14A001","DOI":"10.1115\/1.2929299","article-title":"Loss Mechanisms in Turbomachines","volume":"115","author":"Denton","year":"1993","journal-title":"Trans ASME J. Turbomach."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1115\/1.3451063","article-title":"A Study of Entropy Generation in Fundamental Convective Heat Transfer","volume":"101","author":"Bejan","year":"1979","journal-title":"J. Heat Transf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1002\/er.1107","article-title":"Entropy-based metric for component-level energy management: application to diffuser performance","volume":"29","author":"Adeyinka","year":"2010","journal-title":"Int. J. Energy Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"144","DOI":"10.3390\/e15010144","article-title":"Numerical Study of Entropy Generation in a Flowing Nanofluid Used in Micro- and Minichannels","volume":"15","author":"Mohammadreza","year":"2013","journal-title":"Entropy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.ijheatmasstransfer.2013.10.063","article-title":"Turbulent flow and heat transfer in channels with shark skin surfaces: Entropy generation and its physical significance","volume":"70","author":"Jin","year":"2014","journal-title":"Int. J. Heat Mass Transf."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:36:28Z","timestamp":1760196988000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/1\/21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,28]]},"references-count":47,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["e21010021"],"URL":"https:\/\/doi.org\/10.3390\/e21010021","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,28]]}}}