Maria Teodora Pascu Modern Layout and Design Strategy for Axial Fans Moderne Auslegungs- und Entwurfsstrategie für Axialventilatoren Back cover Front cover Modern Layout and Design Strategy for Axial Fans Moderne Auslegungs- und Entwurfsstrategie für Axialventilatoren Der Technischen Fakultät der Friedrich–Alexander–Universität Erlangen–Nürnberg zur Erlangung des Grades DOKTOR–INGENIEUR vorgelegt von Maria Teodora Pascu Erlangen, 2009 Als Disseration genehmigt von der Technischen Fakultät der Universität Erlangen-Nürnberg Tag der Einreichung: 11.12.2008 Tag der Promotion: 24.04.2009 Dekan: Prof. Dr. J. Huber Berichterstatter: Prof. Dr. Dr. h.c. F. Durst Prof. Dr. M. Wensing ii Acknowledgements This work received financial support from the Bavarian Science Foundation in the form of an individual grant, which is gratefully acknowledged. I would like especially to thank my supervisor, Prof. Dr. Dr. h.c. F. Durst, who from the first day we met, during the Summer Academy Kuşadasi 2004, captured my attention for fluid mechanics research, and by supporting my diploma thesis at the Institute of Fluid Mechanics LSTM Erlangen, brought me in close contact with the topic and stirred my interest in further academic education. He has enabled me to work in the field of turbomachines and constantly supported the present work. I would also like to thank Prof. Dr. M. Wensing for his kind acceptance to review the present work. Furthermore, I would like to thank Prof. Dr. A. Delgado, head of the Institute of Fluid Mechanics LSTM Erlangen, who supported and encouraged the present work, always taking a genuine interest in the outcome of the investigations. My deepest acknowledgements go to Dr. J. Jovanović, head of the turbulence research at LSTM, for his sustained moral support, to whom I dedicate the successful turnout of the experimental investigations included in the thesis. I would also like to express my gratitude to Alu Automotive GmbH for the kind support offered to the present work, and especially to the company manager, Mr. Felix Hellmuth. I would especially like to thank Dr. Ph. Epple, head of the Turbomachinery Optimization research group at LSTM Erlangen, for his constant supervision and strong commitment to the present work. iii My warm acknowledgement also goes to Dipl.-Ing. M. Miclea-Bleiziffer for his support and numerous brainstorming sessions that led to the present layout of the work. I warmly acknowledge the technical department of the institute for their continual collaboration, and especially to Mr. F. Kaschak and Mr. C. Bakeberg. Finally, I would like to thank all my colleagues at LSTM for the wonderful and friendly working atmosphere, to the workshop and administration, who all contributed to the achievements in the present work. Şi cel mai important, doresc să îi mulţumesc familiei mele, pentru sprijinul necondiţionat si încrederea deplină pe care mi le-au acordat in permanenţă, si cărora le datorez în întregime tot ceea ce sunt azi. Erlangen, December 2008 Maria Teodora Pascu iv List of Contents 15H 6H Introduction and aim of work 117H 1.18H General9H introduction 1110H 1.21H Classification12H of turbomachines 1113H 1.314H Aim15H of work 1116H 217H 18H Basic equations of fluid mechanics as applied in turbomachines 1119H 2.120H 21H Navier–Stokes equations in rotating systems 112H 2.223H Energy24H transfer in turbomachines 1125H 326H 27H Survey of the available design methods for axial impellers 1128H 3.129H Basic30H features of turbomachinery design 1131H 3.232H Two3H – dimensional cascade theory 1134H 3.2.135H Aerodynamics36H forces and governing equations 1137H 3.338H Design39H methods based on the airfoil theory 1140H 3.3.141H Airfoil42H families. Mean-line and thickness distribution 1143H 3.3.24H Design45H parameters 1146H 3.3.347H Cascade48H losses. Diffusion factor 1149H 3.450H Three-dimensional51H character of the flow in axial turbomachines 1152H 453H 54H Proposed design strategy for axial fans 115H 4.156H Mean-line57H calculation 1158H 4.259H Outlet60H conditions 1161H 4.362H Meridional63H flow analysis for axial fans 1164H 4.465H The6H indirect design problem 1167H 4.568H Parameterization69H of the total pressure in the span-wise direction for an axial fan blade 1170H 4.671H Blade72H shape computation 1173H 4.774H Further75H design assumptions based on profile analysis 1176H 4.7.17H Static-to-static78H cascade efficiency 1179H 4.7.280H Total-to-total81H cascade efficiency 1182H 4.7.383H Profiling84H the camber line 1185H 4.886H Design87H Solver (DS) 118H v 4.989H DS90H output 1191H 592H 93H Numerical flow analysis 1194H 5.195H Mathematical96H model 1197H 5.298H Mesh9H generation 1110H 5.310H Numerical102H models and boundary conditions 11103H 5.4104H Appropriate105H performance indicators 11106H 5.5107H Optimum108H span-wise pressure distribution 11109H 5.610H Profile1H analysis 1112H 5.6.113H Flow14H domain around the profiles 1115H 5.6.216H Mesh17H generation 1118H 5.6.319H Numerical120H results 1112H 612H 123H Experimental validation of the proposed design strategy 11124H 6.1125H Investigated126H impellers 11127H 6.2128H Experimental129H facility 11130H 6.313H Measured132H parameters 1113H 6.4134H Measuring135H equipment 11136H 6.5137H Experimental138H results 11139H 6.6140H Validation14H of the results 11142H 7143H 14H Integrated ideal efficiency for axial fans 11145H 7.1146H The147H Cordier diagram 11148H 7.2149H Ideal150H efficiency for axial fans 1115H 8152H 153H Conclusions and outlook 11154H vi Index of Symbols A [m2] area M [N m] torque P [W] power Q [m3/s] flow rate R [–] degree of reaction b [m/s2] acceleration c [m/s] absolute velocity l [m] blade chord n [rpm] rotational speed r [m] radius u [m/s] peripheral velocity w [m/s] relative flow velocity wm [m/s] meridional component of the relative velocity wu [m/s] tangential (peripheral) component of the relative velocity P [Pa] pressure difference Greek symbols [-] diameter coefficient [o] gliding angle [o] blade angle [–] efficiency [–] flow coefficient (dimensionless flow) [–] pressure ratio between the fan outlet and the inlet static pressures [kg/m3] density vii [o] camber turning angle [–] temperature ratio between the fan outlet and inlet temperatures [–] speed coefficient [rad/s] angular velocity [–] pressure coefficient (loading) [–] circulation [–] vorticity Subscripts 1 blade inlet 2 blade outlet h hub t tip, total s static d dynamic viii Abstract The present work addresses the application of computational fluid dynamics in the research and development process of axial fans of the kind used in numerous fields of engineering and in daily life. In this sense, a modern layout and design strategy for axial impellers are proposed, as basis for optimization in this engineering field. Essentially, the strategy is a combined inverse-direct method, based on a design solver which computes the optimum blade profile according to the flow conditions in the fan, and does not make use of any predefined profiles. When applied in a rigorous manner, the proposed design strategy delivers high- performance design solutions for axial fans, and this is thoroughly confirmed by both numerical and experimental results. The design calculation scheme starts with the one – dimensional hypothesis of the mean streamline, based on which the blade inlet (at all sections) and outlet (at the hub) conditions are determined. Then, by computing the blade as a succession of several cascades, the two-dimensional nature of the flow is considered. Finally, the blade profile is fully resolved by implementing a three-dimensional (meridional) analysis into the design process. By assuming an arbitrary vortex flow, the optimum pressure distribution in the span-wise direction is determined and the parameterization of the outlet blade angle is achieved, as a function of one of the most important constructive characteristics of an axial fan, i.e. the hub ratio. The advantages of employing the suggested design strategy as an optimization tool are first emphasized by fully converged CFD solutions, which show the substantial improvements in efficiency achieved by the new designs over the reference model, i.e. an engine cooling fan currently used in the automotive industry. Moreover, the employment of the non-free vortex assumption at the design stage is proved to be beneficial for the fan performance, since the design obtained accordingly performs efficiently through a wider flow range. Even though modern CFD nowadays achieves excellent flow predictions, phenomena with impact on the performance are neglected, hence the motivation for the experimental confirmation of the proposed designs. The performance curves of the non-free vortex ix flow design against the reference impeller show an absolute increase in the measured (total-to-static) efficiency of 10% for the proposed design. Finally, the present work proposes an analytical computation of the integrated ideal efficiency for axial fans, a concept which was derived as a response to the incapacity of the classical Cordier diagram to predict the actual performance of axial impellers operating in the low-pressure regimes, due to proven inconsistencies for this type of turbomachine with regard to the definitions of the parameters employed. It is shown that the proposed design strategy delivers an axial fan whose performance comes very close to that of the ideal machine. x Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit der Anwendung von numerischen Strömungssimulationen in der Forschungs- und Entwicklungsarbeit