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Friction Losses and Heat Transfer in High-Speed Electrical Machines

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Friction Losses and Heat Transfer in High-Speed Electrical Machines XK'Sj Friction losses and heat transfer in high-speed electrical machines Juha Saari DJSTR10UTK)N OF THI6 DOCUMENT IS UNLIMITED Teknillinen korkeakoulu Helsinki University of Technology Sahkotekniikan osasto Faculty of Electrical Engineering Sahkomekaniikan laboratorio Laboratory of Electromechanics Otaniemi 1996 1 50 2 Saari J. 1996. Friction losses and heat transfer in high-speed electrical machines. Helsinki University of Technology, Laboratory of Electromechanics, Report 50, Espoo, Finland, p. 34. Keywords: Friction loss, heat transfer, high-speed electrical machine Abstract High-speed electrical machines usually rotate between 20 000 and 100 000 rpm and the peripheral speed of the rotor exceeds 150 m/s. In addition to high power density, these figures mean high friction losses, especially in the air gap. In order to design good electrical machines, one should be able to predict accurately enough the friction losses and heat-transfer rates in the air gap. This report reviews earlier investigations concerning frictional drag and heat transfer between two concentric cylinders with inner cylinder. rotating. The aim was to find out whether these studies cover the operation range of high-speed electrical machines. Friction coefficients have been measured at very high Reynolds numbers. If the air-gap surfaces are smooth, the equations developed can be applied into high-speed machines. The effect of stator slots and axial cooling flows, however, should be studied in more detail. Heat-transfer rates from rotor and stator are controlled mainly by the Taylor vortices in the air-gap flow. Their appearance is affected by the flow rate of the cooling gas. The papers published do not cover flows with both high rotation speed and flow rate. Furthermore, the effect of stator and rotor slots cannot, be predicted by the existing methods. ISBN 951-22-3119-0 ISSN 0784-4662 TKK OFFSET ,3 Preface The report gives a literature review concerning friction losses and heat transfer between concentric cylinders. This information is very essential in the design of high-speed electrical machines. This study is one part of a research work dealing with cooling of high-speed electrical motors. The work belongs to a project aiming at increasing the performance of high-speed electrical motors developed in 1991-1994. The research is financed by High Speed Tech Ltd. I would like to express my gratitudes to Dr Jaakko Laijola and Dr Antero Arkkio for their advices concerning this work. Financial supports from Graduate School of Electrical Power Engineering, as well as foundations “Tekniikan edistamissaatio” and “Suomen Kulttuurirahasto, Hameen rahasto” are gratefully acknowledged. Espoo, 22.05.1996 Juba Saari 4 Contents Abstract ......................................................................................................................................... 2 Preface............................................................................................................................................3 Contents......................................................................................................................................... 4 List of symbols ............................................................................................................................. 5 1 Introduction............................................................................................................................. 7 2 Fluid flow in the air gap.........................................................................................................8 2.1 Tangential and axial velocity distributions ...................................................... 8 2.2 Taylor vortices.......................................................................................................10 3 Friction torque........................................................................................................................12 4 Heat transfer.......................................................................................................................... 18 5 Discussion............................................................................................................................... 26 5.1 Friction torque.......................................................................................................26 5.2 Heat transfer......................................................................................................... 27 6 Conclusions.............................................................................................................................29 References................................................................................................................................... 30 Appendix A: Friction coefficient...........................................................................................33 Appendix B: Nusselt number ................................................................................................34 DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document 5 List of symbols Cf Friction coefficient h1 Heat-transfer coefficient of inner cylinder h2 Heat-transfer coefficient of outer cylinder hl2 Heat-transfer coefficient between inner and outer cylinders k Thermal conductivity l Length of the inner cylinder Nu-i Nusselt number of inner cylinder Nu2 Nusselt number of outer cylinder Nu12 Nusselt number between inner and outer cylinders Pr Prandtl number qm Mass flow rate of cooling fluid r Radius rx Radius of inner cylinder (rotor) r2 Radius of outer cylinder (stator) rm Mean air-gap radius: r^=0.5(r^+rg) Rea Axial Reynolds number for axial flow Res Couette Reynolds number for tangential flow ReT Tip Reynolds number of rotating cylinder T Torque Ta Taylor number Tam Modified Taylor number Tae Critical Taylor number u Tangential fluid velocity between the cylinders Peripheral speed of inner cylinder um Mean tangential fluid velocity between the cylinders v Tangential fluid velocity between the cylinders ve Effective fluid velocity between the cylinders vm Mean axial fluid velocity between the cylinders y Radial location between the cylinders z Axial location between the cylinders 8 Length of the clearance between cylinders % Eddy diffusivity of momentum fi Dynamic viscosity v Kinematic viscosity p Density T Shear stress xl Shear stress on the inner cylinder co Angular velocity 6 7 1 Introduction High-speed electrical machines usually rotate between 20 000 and 100 000 rpm and the peripheral speed of the rotor exceeds 150 m/s. These machines have high power densities but also high loss densities. Especially the friction losses are very large and effective cooling methods are needed. In order to design good high-speed machines, the designer has to know how the friction losses and heat transfer depend on the machine geometry, rotation speed, and cooling method. The performances of high-speed electrical machines have been reported, for example, by Boglietti et al. (1992), Gilon (1994), and Saari et al. (1995a and 1995b). The most critical friction losses for the electrical machine are located in the air gap. The rotor is cooled mainly by the air-gap gas and, therefore, the temperature of rotor is increased by the friction losses. On the other hand, one can lower the air-gap temperature by introducing an axial cooling flow through the air gap. In addition to losses, the rotor temperature depends on the heat-transfer coefficient on the rotor surface. This parameter is set by the peripheral speed of the rotor and axial velocity of the cooling gas. Naturally, the temperature of the stator depends also on the losses and heat-transfer coefficients in the air gap. This report reviews the earlier investigations concerning friction losses and heat transfer between concentric cylinders. The aim of the study was to find out whether one can apply these calculation methods on high-speed electrical machines. Only analytical methods were considered because they are preferred in the cooling design by thermal networks. The analysis was focused on the turbulent flow which is the case of high-speed machines. Friction losses and convection heat transfer are set by the velocity field in the air gap. This includes the tangential and axial flows as well as Taylor vortices discussed in Chapter 2. In Chapters 3 and 4, the most important research works concerning friction generation and heat transfer between concentric cylinders are reported. The papers are summarised in chronological order and the experimental setups are listed at the end of the corresponding chapter. In Chapter 5, the applicability of analysis methods on high-speed machines is discussed. Chapter 6 gives the conclusions of this study. 8 2 Fluid flow in the air gap Friction losses and heat transfer are set by the velocity field. The velocity distribution in the air gap of electrical machines is controlled by the following flows: 1. Tangential flow due the rotor rotation. 2. Axial flow of the cooling gas through the air gap. 3. Taylor vortices due to centrifugal forces. The importance of each flow depends on the peripheral speed of the rotor, flow rate of the cooling gas, gas properties and air-gap geometry. Typical peripheral speeds of rotors are 150-500 m/s and the axial velocity of the cooling gas is 20-60 m/s. 2.1 Tangential and axial velocity distributions The nature of a fluid flow is determined by the ratio between the inertia and viscous forces,
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