{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T16:58:18Z","timestamp":1768669098124,"version":"3.49.0"},"reference-count":52,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,25]],"date-time":"2022-04-25T00:00:00Z","timestamp":1650844800000},"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":["51775025"],"award-info":[{"award-number":["51775025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Labyrinth seals are widely employed in the air system of aircraft engines since they reduce the leakages occurring between blades and shrouds, which affect the entropy generation significantly. Excessive leakage flow of the labyrinth may be reduced the efficiency and performance of the engine. This paper proposes the concept of flow-resistance-increasing vortex (FRIV) on the top of the labyrinth that is based on the flow entropy generation mechanism of the stepped labyrinth and the main flow characteristics that lead to entropy generation. A three-dimensional simulation model of the labyrinth structure was established, and the model was compared and verified with the experimental data of the reference. The relative dissipation strength and vorticity distribution of the FRIV were theoretically analyzed. It was confirmed that the dissipative intensity distribution was the same as the vorticity distribution, and the correlation coefficient was larger in the labyrinth tip region. Therefore, a parametric study was conducted on design parameters related to the FRIV, including the teeth inclined angle, tooth crest width, step inclined angle, and other parameters. The results are beneficial for the construction of a stronger FRIV to reduce the leakage. This research is of great significance for the improvement of engine efficiency and for the reduction of fuel consumption in the future.<\/jats:p>","DOI":"10.3390\/sym14050881","type":"journal-article","created":{"date-parts":[[2022,4,26]],"date-time":"2022-04-26T02:14:39Z","timestamp":1650939279000},"page":"881","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Investigation on the Formation and Evolution Mechanism of Flow-Resistance-Increasing Vortex of Aero-Engine Labyrinth Based on Entropy Generation Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Xiaojing","family":"Liu","sequence":"first","affiliation":[{"name":"Research Institute of Aero-Engine, Aircraft\/Engine Integrated System Safety Beijing Key Laboratory, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuiting","family":"Ding","sequence":"additional","affiliation":[{"name":"Research Institute of Aero-Engine, Aircraft\/Engine Integrated System Safety Beijing Key Laboratory, Beihang University, Beijing 100191, China"},{"name":"Department of Aviation Engineering, Civil Aviation University of China, Tianjin 300300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longtao","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Zhao","sequence":"additional","affiliation":[{"name":"Research Institute of Aero-Engine, Aircraft\/Engine Integrated System Safety Beijing Key Laboratory, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Qiu","sequence":"additional","affiliation":[{"name":"Research Institute of Aero-Engine, Aircraft\/Engine Integrated System Safety Beijing Key Laboratory, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2246-1812","authenticated-orcid":false,"given":"Yu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Research Institute of Aero-Engine, Aircraft\/Engine Integrated System Safety Beijing Key Laboratory, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaozhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shenyang Engine Research Institute, Aero Engine Corporation of China, Shenyang 110015, China"},{"name":"Aero-Engine Thermal Environment and Structure Key Laboratory of Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,25]]},"reference":[{"key":"ref_1","unstructured":"Ludwig, L.P., and Johnson, R.L. (2000). Sealing Technology for Aircraft Gas Turbine Engines, AIAA."},{"key":"ref_2","first-page":"1779","article-title":"Experiment on flow characteristic in rotating labyrinth with consideration of clearance change","volume":"33","author":"Guo","year":"2018","journal-title":"J. Aerosp. Power"},{"key":"ref_3","unstructured":"Hanzlik, H.J. (1931). Labyrinth Packing. (US1831242A)."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1115\/1.3673158","article-title":"A Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem","volume":"83","author":"Vermes","year":"1960","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zimmermann, H., and Wolff, K.H. (1998, January 2). Air System Correlations: Part 1\u2014Labyrinth Seals. Proceedings of the Asme International Gas Turbine & Aeroengine Congress & Exhibition, Stockholm, Sweden.","DOI":"10.1115\/98-GT-206"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"081001","DOI":"10.1115\/1.4047180","article-title":"Effect of Rotation on Leakage and Windage Heating in Labyrinth Seals With Honeycomb Lands","volume":"142","author":"Nayak","year":"2020","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"32","DOI":"10.5293\/kfma.2020.23.1.032","article-title":"Basic Research Trends on Labyrinth Seal of Gas Turbine","volume":"23","author":"Lee","year":"2020","journal-title":"KSFM J. Fluid Mach."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Soemarwoto, B.I., and Kok, J.C. (2007, January 14\u201317). Performance Evaluation of Gas Turbine Labyrinth Seals Using Computational Fluid Dynamics. Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air, Montreal, QC, Canada.","DOI":"10.1115\/GT2007-27905"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1115\/1.3242535","article-title":"Prediction of Incompressible Flow in Labyrinth Seals","volume":"108","author":"Rhode","year":"1986","journal-title":"J. Fluids Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1115\/1.3240315","article-title":"The Prediction and Measurement of Incompressible Flow in a Labyrinth Seal","volume":"111","author":"Demko","year":"1989","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1017\/S0022112080001437","article-title":"Incompressible flow in a labyrinth seal","volume":"100","author":"Stoff","year":"2006","journal-title":"J. Fluid Mech."},{"key":"ref_12","first-page":"429","article-title":"Simulation of Subsonic Flow Through a Generic Labyrinth Seal","volume":"108","author":"Rhode","year":"1985","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"392","DOI":"10.2514\/3.23490","article-title":"New model for flow over open cavities. I-Model development","volume":"8","author":"Rhode","year":"1992","journal-title":"J. Propuls. Power"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"398","DOI":"10.2514\/3.23491","article-title":"New model for flow over open cavities. II-Assessment for seal leakage","volume":"8","author":"Rhode","year":"1971","journal-title":"J. Propuls. Power"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"171","DOI":"10.2514\/3.23240","article-title":"Effect of shaft rotation on the incompressible flow in a labyrinth seal","volume":"6","author":"Demko","year":"1990","journal-title":"J. Propuls. Power"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"011005","DOI":"10.1115\/1.4031748","article-title":"Rounded Fin Edge and Step Position Effects on Discharge Coefficient in Rotating Labyrinth Seals","volume":"138","author":"Rapisarda","year":"2016","journal-title":"J. Turbomach."},{"key":"ref_17","unstructured":"Scherer, T., and Waschka, W. (1994). Numerical Predictions of High-Speed Rotating Labyrinth Seal Performance: Influence of Rotation on Power Dissipation and Temperature Rise. International Symposium on Heat Transfer in Turbomachinery, Begell House Inc."},{"key":"ref_18","unstructured":"Nayak, K., and Ansari, A. (2013, January 14\u201317). The Effect of Rub-Grooves on Leakage and Windage Heating in Labyrinth Seals with Honeycomb Lands. Proceedings of the Aiaa\/Asme\/Sae\/Asee Joint Propulsion Conference & Exhibit, San Jose, CA, USA."},{"key":"ref_19","unstructured":"Musthafa, K.C. (2007, January 8\u201311). The Effects of Tooth Tip Wear and its Axial Displacement in Rub-Grooves on Leakage and Windage Heating of Labyrinth Seals with Honeycomb Lands. Proceedings of the 43rd AIAA\/ASME\/SAE\/ASEE Joint Propulsion Conference & Exhibit (AIAA), Nashville, TN, USA."},{"key":"ref_20","unstructured":"Kaliraj, K.R., and Yepuri, G.B. (2019, January 5\u20136). Parametric Studies on Gas Turbine Labyrinth Seal for the Secondary Air Flow Optimization at Static and Rotating Conditions. Proceedings of the ASME 2019 Gas Turbine India Conference, Chennai, India."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Desando, A., and Rapisarda, A. (2015, January 15\u201319). Numerical Analysis of Honeycomb Labyrinth Seals:Cell Geometry and Fin Tip Thickness Impact on the Discharge Coefficient. Proceedings of the ASME Turbo Expo 2015, Montreal, QC, Canada.","DOI":"10.1115\/GT2015-42106"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"081008","DOI":"10.1115\/1.4049498","article-title":"Transient Aero-Thermo-Mechanical Multidimensional Analysis of a High Pressure Turbine Assembly Through a Square Cycle","volume":"143","author":"Ganine","year":"2021","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_23","unstructured":"Childs, D.W. (1993). Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis. Turbomachinery Rotordynamics Phenomena Modeling and Analysis, John Wiley and Sons."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1115\/1.3227416","article-title":"Scaling Effects on Leakage Losses in Labyrinth Seals","volume":"105","author":"Wittig","year":"1983","journal-title":"J. Eng. Gas Turbines Power"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Denecke, J., and Dullenkopf, K. (2005, January 6\u20139). Experimental Investigation of the Total Temperature Increase and Swirl Development in Rotating Labyrinth Seals. Proceedings of the Asme Turbo Expo: Power for Land, Sea, & Air, Reno, NV, USA.","DOI":"10.1115\/GT2005-68677"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Mcgreehan, W.F., and Ko, S.H. (1989, January 4\u20138). Power Dissipation in Smooth and Honeycomb Labyrinth Seals. Proceedings of the ASME 1989 International Gas Turbine and Aeroengine Congress and Exposition, Toronto, ON, Canada.","DOI":"10.1115\/89-GT-220"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1115\/1.1397304","article-title":"Effects of Reynolds Number and Pressure Ratio on Leakage Loss and Heat Transfer in a Stepped Labyrinth Seal","volume":"123","author":"Willenborg","year":"2001","journal-title":"J. Turbomach."},{"key":"ref_28","unstructured":"Stocker, H.L., and Cox, D.M. (1977). Aerodynamic Performance of Conventional and Advanced Design Labyrinth Seals with Solid-Smooth Abradable, and Honeycomb Lands."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1115\/1.1760555","article-title":"Rub-Groove Width and Depth Effects on Flow Predictions for StraightThrough Labyrinth Seals","volume":"126","author":"Rhode","year":"2004","journal-title":"J. Tribol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1115\/1.2836657","article-title":"Windage Heating of Air Passing Through Labyrinth Seals","volume":"118","author":"Millward","year":"1996","journal-title":"J. Turbomach."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1115\/1.2929166","article-title":"Influence of High Rotational Speeds on the Heat Transfer and Discharge Coefficients in Labyrinth Seals","volume":"114","author":"Waschka","year":"1990","journal-title":"J. Turbomach."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Braun, E., and Dullenkopf, K. (2012, January 11\u201315). Optimization of Labyrinth Seal Performance Combining Experimental, Numerical and Data Mining Methods. Proceedings of the Asme Turbo Expo: Turbine Technical Conference & Exposition, Copenhagen, Denmark.","DOI":"10.1115\/GT2012-68077"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.3390\/pr8111496","article-title":"Effect of clearance and Cavity Geometries on Leakage Performance of a Stepped Labyrinth Seal","volume":"8","author":"Min","year":"2020","journal-title":"Processes"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"e202000212","DOI":"10.1002\/zamm.202000212","article-title":"Mechanical aspects of Maxwell nanofluid in dynamic system with irreversible analysis","volume":"101","author":"Khan","year":"2021","journal-title":"ZAMM J. Appl. Math. Mech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"19378","DOI":"10.1038\/s41598-021-98128-z","article-title":"Mechanical analysis of non-Newtonian nanofluid past a thin needle with dipole effect and entropic characteristics","volume":"11","author":"Ramzan","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_36","first-page":"2021009","article-title":"Investigation on transient dynamics of rotor system in air turbine starterbased on magnetic reduction gear","volume":"1","author":"Yu","year":"2021","journal-title":"J. Adv. Manuf. Sci. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"106626","DOI":"10.1016\/j.ymssp.2020.106626","article-title":"A Novel Blade Tip Clearance Measurement Method Based on Event Capture Technique","volume":"139","author":"Jiang","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Weinberger, T., and Dullenkopf, K. (2010, January 14\u201318). Influence of Honeycomb Facings on the Temperature Distribution of Labyrinth Seals. Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air, Glasgow, UK.","DOI":"10.1115\/GT2010-22069"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"696","DOI":"10.1016\/j.ast.2018.05.017","article-title":"Probabilistic failure risk assessment for aeroengine disks considering a transient process","volume":"78","author":"Shuiting","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_40","first-page":"2305","article-title":"Application of entropy equation in the judgement of flow direction in transient air system","volume":"32","author":"Ding","year":"2017","journal-title":"J. Aerosp. Power"},{"key":"ref_41","unstructured":"Bertin, J., and Cummings, R. (2013). eBook Instant Access\u2014for Aerodynamics for Engineers, International Edition, Pearson."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1103\/PhysRevE.62.845","article-title":"Steady adiabatic state: Its thermodynamics, entropy production, energy dissipation, and violation of Onsager relations","volume":"62","author":"Allahverdyan","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Denecke, J., and Frber, J. (2005, January 6\u20139). Dimensional Analysis and Scaling of Rotating Seals. Proceedings of the ASME Turbo Expo 2005: Power for Land, Sea, and Air. 2005, Reno, NV, USA.","DOI":"10.1115\/GT2005-68676"},{"key":"ref_44","unstructured":"Dagan, A., and Arieli, R. (1992, January 6\u201310). Solutions of the vorticity transport equation at high Reynolds numbers. Proceedings of the Thirteenth International Conference on Numerical Methods in Fluid Dynamics, Rome, Italy."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF02953241","article-title":"Vorticity and viscous dissipation in an incompressible flow","volume":"8","author":"Koh","year":"1994","journal-title":"KSME J."},{"key":"ref_46","unstructured":"Barati, R. (1972, January 7). The numerical solution of the vorticity transport equation. Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, Paris, France."},{"key":"ref_47","unstructured":"ANSYS Inc. (2018). ANSYS CFX 19.0, ANSYS Inc."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.cja.2019.12.001","article-title":"Numerical and Experimental Investigation on Dynamic performance of Bump Foil Journal Bearing Based on Journal Orbit","volume":"34","author":"Yu","year":"2021","journal-title":"Chin. J. Aeronaut."},{"key":"ref_49","unstructured":"ANSYS Inc. (2011). ANSYS CFX-Solver Modeling Guide, ANSYS Inc."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Prasad, B.V.S.S., and Manavalan, V.S. (1997, January 2). Computational and Experimental Investigations of Straight-Through Labyrinth Seals. Proceedings of the Asme International Gas Turbine & Aeroengine Congress & Exhibition, Orlando, FL, USA.","DOI":"10.1115\/97-GT-326"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.jmsy.2020.06.019","article-title":"Digital-twin-driven geometric optimization of centrifugal impeller with free-form blades for five-axis flank milling","volume":"58","author":"Yu","year":"2021","journal-title":"J. Manuf. Syst."},{"key":"ref_52","first-page":"1178","article-title":"Parametric Modeling Method for Integrated Design and Manufacturing of Radial Compressor Impeller","volume":"10","author":"Yu","year":"2020","journal-title":"Int. J. Adv. Manuf. Technol."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/881\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:00:46Z","timestamp":1760137246000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/881"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,25]]},"references-count":52,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14050881"],"URL":"https:\/\/doi.org\/10.3390\/sym14050881","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,25]]}}}