In this study the temperature increase and heat dissipation in the air gap of a cylindrical mini rotor stator system has been analyzed. A simple thermal model based on lumped parameter thermal networks has been developed. With this model the temperature dependent air properties for the fluid-rotor interaction models have been calculated. Next the complete system has also been modeled by using computational fluid dynamics (CFD) with Ansys-CFX and Ansys. The results have been compared and the capability of the thermal networks method to calculate the temperature of the air between the rotor and stator of a high speed micro rotor has been discussed

Aarts, Ronald

Boer, André de

Dikmen, Emre

Hoogt, Peter van der

Jonker, Ben

English

Dikmen, E.

van der Hoogt, Peter

de Boer, Andries

Aarts, Ronald G.K.M.

Jonker, Jan B.

NARCIS 

Thermal modeling of a mini rotor-stator system

In this study the temperature increase and heat dissipation in the air gap of a cylindrical mini rotor stator system has been analyzed. A simple thermal model based on lumped parameter thermal networks has been developed. With this model the temperature dependent air properties for the fluid-rotor interaction models have been calculated. Next the complete system has also been modeled by using computational fluid dynamics (CFD) with Ansys-CFX and Ansys. The results have been compared and the capability of the thermal networks method to calculate the temperature of the air between the rotor and stator of a high speed micro rotor has been discussed.</jats:p

Emre Dikmen

Peter van der Hoogt

Andre´ de Boer

Ronald Aarts

Ben Jonker

Crossref

Thermal Modeling of a Mini Rotor-Stator System

University of Twente Research Information

Proceedings of the ASME 2009 International Mechanical Engi neering Congress & ExpositionIMECE 2009November 13-19, 2009, Lake Buena Vista, Florida,USAIMECE2009-10849THERMAL MODELING OF A MINI ROTOR-STATOR SYSTEMEmre Dikmen ∗, Peter van der Hoogt, Andr é de BoerFaculty of Engineering TechnologySection of Applied MechanicsUniversity of TwenteEnschede, The Netherlandse-mail: e.dikmen@utwente.nlRonald Aarts, Ben JonkerFaculty of Engineering TechnologySection of Mechanical AutomationUniversity of TwenteEnschede, The NetherlandsABSTRACTIn this study the temperature increase and heat dissipationin the air gap of a cylindrical mini rotor stator system has beenanalyzed. A simple thermal model based on lumped parameterthermal networks has been developed. With this model the tem-perature dependent air properties for the fluid-rotor interactionmodels have been calculated. Next the complete system has alsobeen modeled by using computational fluid dynamics (CFD) withAnsys-CFX and Ansys. The results have been compared and thecapability of the thermal networks method to calculate the tem-perature of the air between the rotor and stator of a high speedmicro rotor has been discussed.NOMENCLATUREcf Friction coefficientG Thermal conductance matrixh Convective heat transfer coefficientk Thermal conductivityNu Nusselt numberP Vector of power lossesPf Power loss due to fluid frictionRer Tip Reynolds numberReδ Couette Reynolds numberRia Axial thermal resistanceRir Radial thermal resistancer Rotor radiusT Vector of nodal temperatures∗Corresponding authorTa Taylor numberTr Rotor outer surface temperatureTs Stator inner surface temperatureδ Air gapΩ Rotation speedµ Dynamic viscosityτ Shear stressρ Densityθi Temperature of the i th nodeINTRODUCTIONRecently, there has been a trend to develop mini rotating ma-chinery which operates at high speeds. However as the rotationspeed increases, the heat dissipation due to air friction and thetemperature increase in the air gap between rotor and statorbe-comes more significant. Fig.1 illustrates the simple rotor-s atorwith the air gap in between. Friction losses in the air gap of arotor stator system are resulting from viscous flow. Air frictionloss is determined by the velocity field and air properties. Thefluid velocity field is calculated by Navier-Stokes and continuityequations. These equations can be solved analytically for simplegeometries in laminar flow.However for turbulent flow which is generally observed inhigh speed mini rotating machinery, these equations becomemore difficult to solve. Therefore numerical methods and semi-empirical correlations are frequently used to solve turbulent flowequations.1 Copyright c© 2009 by ASMErotorstatorair gapFigure 1. ROTOR-STATOR AND AIR GAPIn this analysis a thermal model based on thermal networksmethod has been developed to calculate the steady state tempr-ature of the air between rotor and stator. Then a more complexanalysis has been done by using commercially available tools.The lumped parameter thermal networks method has been exten-sively used for a long time for thermal analysis of electric motorsand generators. Advantages of this simple model are: thermalnetworks are easy to construct, and it requires less computationtime compared to other methods. The thermal networks involvenodes describing the mean temperature of each component andresistances between them. Each component is modeled by inde-pendent axial and thermal networks and heat generation in thecomponent is applied to the node describing the mean tempera-ture of the component.In this study the rotor and stator have been modeled by ther-mal networks at steady state, and the air in between has beendescribed by a node. At each rotation speed the heat dissipationdue to air friction has been calculated via empirical friction co-efficients which are functions of Couette-Reynolds number andTaylor number. Then heat dissipation is applied to the node rep-resenting the air in the gap between rotor and stator. In thiswaythe temperature of the air has been calculated at different rotationspeeds. For CFD analysis the air gap is modeled by using An-sys CFX and the rotation speed and estimated steady state tem-perature of the rotor and stator surfaces are applied as boundaryconditions. The temperature in the gap and the convective heattransfer coefficients between the air-rotor and air-statorre cal-culated at each speed with initially assumed rotor and stator sur-face temperatures. Then convective heat transfer coefficients areimported to Ansys and the steady state temperatures of the roorand stator surfaces are calculated. The updated boundary condi-tions (rotor-stator surface temperatures) are imported toCFX andthe air temperature is recalculated. This procedure is continuedtill results converge. Then the results are compared with thermalnetworks and the capability of thermal networks method to cal-culate the temperature of the air between the rotor and stator of ahigh speed micro rotor is discussed.THERMAL NETWORKSAir Friction Loss CalculationFor high speed rotating machinery, most of the total loss oc-curs as a result of friction with the surrounding air. It is impor-tant to estimate the air friction losses in order to determine thetemperature distribution in the machine and design the rotor f rmaximum efficiency. The behavior of the gas flow depends onthe inertia and viscous forces. The ratio of the inertia and viscousforces is the non dimensional Reynolds number. For a rotatingshaft in free space, the relevant Reynolds number is called the tipReynolds number and it is defined as:Rer =ρΩr2µ(1)whereρ is the density,µ is the dynamic viscosity,Ω is the rota-tional speed andr is the shaft radius. However the behavior ofthe flow in the air gap of a rotor-stator system is determined bythe Couette-Reynolds number which is defined as:Reδ =ρΩrδµ(2)whereδ is the air gap in radial direction. Due to the centrifugalforce on the fluid particles, circular velocity fluctuations(Taylorvortices) appear in the air gap. At low speeds the flow is laminrand the creation of Taylor vortices is damped by frictional forces[1]. Taylor vortices occur when the critical Taylor number of1700 is exceeded [2]. The Taylor number is defined as:Ta=Re2δδr=ρ2Ω2rδ3µ2(3)If Reδ < 2000 andTa< 1700, the laminar two-dimensional Cou-ette flow theory is valid, whenReδ < 2000 andTa> 1700, theflow is still laminar, but three-dimensional Taylor vortices arepresent; ifReδ > 2000, the flow is turbulent. Due to high rota-tion speeds, the turbulent regime is widely observed in the airgaps of mini rotating machinery. The shear stress is difficult tosolve in turbulent flows. Therefore empirical friction coefficientsare defined and used to calculate the shear stress and power lossdue to friction. Correlations for empirical frictional coefficientare defined as a function of Reynolds number. The friction coef-ficient and power loss due to friction are:cf =τ12ρΩ2r2(4)Pf = cf πρΩ3r4l (5)2 Copyright c© 2009 by ASMEThere has been a great number of studies available in theliterature for calculation of the friction coefficient of a rotatingcylinder. Saari [3] made a literature review of friction losseand heat transfer between concentric cylinders. One of the ini-tial studies about the friction torque of a rotating cylinder infree space is made by Theodorsen and Regier [4]. In anotherstudy, Bilgen and Boulos [5] have measured the friction torqueof smooth concentric enclosed cylinders. They developed thfollowing correlations for friction coefficient as a function ofCouette-Reynolds number.cf = 0.515(δr)0.3Re0.5δ(500< Reδ < 10000) (6)cf = 0.0325(δr)0.3Re0.2δ(10000< Reδ) (7)In our study, the rotor and stator surfaces are assumed tobe smooth ignoring the roughness effects on the friction. Thecorrelations above are used to determine the heat generation dueto air friction for the simple rotor-stator system. The Couette-Reynolds number is calculated at each rotation speed, then thefriction coefficient and power dissipation due to air friction arecomputed.Thermal Analysis of a Cylindrical Rotor-StatorThe thermal networks method is applied in this study due toits advantages over other methods [1]:- Less computation time is required- Thermal networks are easy to build- Equations for the friction losses and the convection heattransfer coefficients can easily be implementedThermal networks are widely applied for thermal analysis ofelectric motors and generators [6–9]. Perez and Kassakian [10]modeled each component of a high speed synchronous machinein terms of a thermal node that approximates the mean tempera-ture of the component. Mellor [11] et al. described a similarther-mal model for both steady-state and transient analysis. Kylan-der [12] presented a thermal model for enclosed electric motors.The thermal networks involve nodes describing the mean tem-perature of each component. All the heat generation in the com-ponent is applied to the node describing the component. Eachcomponent is modeled with independent axial and radial ther-mal networks with the resistances for conductive and convectiveheat flow. Then thermal networks representing each componentare assembled in order to perform a thermal analysis of the com-plete system. Fig. 2 illustrates independent axial and radial ther-mal networks for a general cylindrical component [11]. The heattransfer equations have been written for each node as:1R1aθ3 + 1R2a θ4 +1R3aθm−(1R1a+ 1R2a +1R3a)θ5 = 01R1rθ1 + 1R2r θ2 +1R3rθm−(1R1r+ 1R2r +1R3r)θ6 = 01R3aθ5 + 1R3r θ6−(1R3a+ 1R3r)θm = −Heat(8)These equations have been written in matrix form and the vectorof the nodal temperatures has been obtained from the equation:P = GT (9)whereG is the matrix of thermal conductances.P is the powerloss vector andT is the temperature vector.The thermal networks method and applications has been ex-plained in detail in many studies [9–14].θ1θ2θ3θ4θmR1aR2aR3aR1rR2rR3rHeatθ1θ2θ3θ4θ5 θ6θmFigure 2. AXIAL AND RADIAL THERMAL NETWORKSThe conductive resistances in the structure are constant,however the convective resistances between the air-rotor and air-stator surfaces change with the rotation speed. The convectiveheat transfer coefficient which is used for the calculation of con-vective resistances is given as [1]:h =2kNuδ(10)where Nu is the Nusselt number and k is the thermal conduc-tivity of the fluid. The Nusselt number for tangential air flowbetween concentric cylinders is given by Becker and Kaye [15]as a function of the Taylor number:Nu= 0.128Ta0.367 (1700< Ta< 104) (11)Nu= 0.409Ta0.241 (104 < Ta< 107) (12)3 Copyright c© 2009 by ASMEIn this study a thermal network corresponding to a simplerotor stator system has been constructed by using the componentresistances developed by Saari [1]. A simple Matlab based codehas been developed for calculation of air friction and tempera-ture increase. The material properties, dimensions and rotationspeed are inputs of the program. The convection heat transfercoefficients are calculated in the program and used for determi-nation of the resistances between air-rotor and air-stator. Thenheat flow equations are solved at each node [16] and the nodaltemperatures are calculated. In this way the mean temperatur sof the rotor-stator, air and heat generation due to air friction arecalculated.ANSYS-CFX COUPLED THERMAL ANALYSISThe thermal analysis of the rotor-stator system has also beenperformed by using the commercial software packages ANSYSCFX and ANSYS Workbench. The rotor and stator are mod-eled in ANSYS Workbench and the air film in between has beenmodeled in ANSYS CFX. In order to calculate the steady stateair temperature in the gap between rotor and stator, rotor outerand stator inner surface temperatures are required in ANSYSCFX. These boundary conditions are initially estimated in AN-SYS CFX and then calculated in ANSYS Workbench. Since onlyone way coupling is possible between these packages initialas-sumptions for the rotor and stator surface temperatures have beenmade, heat generation due to air friction, heat transfer coeffi-cients and air temperature are calculated in ANSYS CFX. Thenheat transfer coefficients are transfered into ANSYS Workbenchto calculate the assumed rotor and stator surface temperatur s.The procedure continues till initial assumptions and final resultsagree each other. The procedure is shown in Fig.3.SurfaceTemperaturesTr,TsCFX - ANSYSTr,TshRotor, StatorCFDFigure 3. ANSYS-CFX COUPLED THERMAL ANALYSIS PROCEDUREThe fluid film has been modeled in ANSYS CFX as shownin Fig.4. The analysis has been run with different mesh sizesFigure 4. CFX MODEL FOR THE AIRand suitable mesh size has been determined as the convergencachieved. The rotation speed of the rotor outer surface, thetem-peratures of the rotor and stator surfaces have been appliedasthe boundary conditions. The total energy formulation includ-ing the viscous terms has been used for heat transfer equationssince it is suitable for flows with Mach number greater than 0.2.The k-ε turbulence model has been used since it is appropriatefor internal flows and offers a good compromise between numer-ical effort and computational accuracy. Simulations have be nperformed at each rotation speed and the air temperature profilehas been obtained. The convective heat transfer coefficients havebeen exported to ANSYS for further analysis to check initiallyassumed boundary conditions.The rotor and stator have been modeled in Ansys Workbench(see Fig. 5). Thermal analysis of the structure has been donebyapplying the ambient temperature to the side walls and importingthe convective heat transfer coefficients from the ANSYS CFXsolutions. The temperature of the rotor and stator surfaceshasbeen computed and the initially assumed temperatures used inANSYS CFX have been updated.SIMULATION RESULTSThe simulations have been performed by using both thermalnetworks and ANSYS CFX based CFD analysis for a rotor witha radius of 25 mm, length of 30 mm and air gap of 0.5 mm. Tab.1compares the CFD analysis with the thermal networks method.The temperature profile in the air gap is computed in ANSYSCFX, then the average of the air temperature profile is calculted4 Copyright c© 2009 by ASMEFigure 5. ROTOR AND STATORTable 1. CFD vs THERMAL NETWORKSCFD THERMAL NETWORKSMany DOF One node for modeling the airLocal Temperature Distribution Global Temperature distributionMuch Computation time Less computation timeand compared to the results obtained by using thermal networks(see Fig.6). For the thermal networks, the air in the gap is mod-eled as a node and the computation time to calculate the tem-peratures corresponding to the mid-rotor, stator and air has been0.06 sec. On the other hand the CFD model constructed usingANSYS CFX involves 3072 elements, 6144 nodes and the com-putation time has been 214 seconds.There is fair agreement between both methods. The differ-ence at higher rotational speeds is a further research issue. Thethermal networks method gives reasonable estimates of the airtemperature. The updated air temperature is used to renew theair poperties at the specific rotation speed for air-rotor coupleddynamic analysis.CONCLUSIONSThermal analysis of a simple cylindrical rotor and stator sys-tem has been performed by using thermal networks and CFD.The thermal networks are simple to construct and can be easilycoupled with other analysis methods. The temperature rise of theair in the gap between a mini rotor and stator due to air frictionhas been calculated by using thermal networks and more compli-cated CFD method. The simulations are performed and accept-able agreement between the results using both methods has beenobtained.40 60 80 100 120 140295300305310315320325330335Rotation Speed (rpm*1000)Temperature (K)  Thermal NetworksCFDFigure 6. THERMAL NETWORK AND CFD RESULTSThus, thermal networks method seems to be appropriate to beimplemented into fluid rotor interaction models to update tem-perature dependent air properties for further analysis.ACKNOWLEDGMENTThe support of MicroNed for this research work is gratefullyacknowledged.REFERENCES[1] Saari, J., 1998. “Thermal analysis of high-speed inductionmachines”. PhD Thesis, Helsinki University of Technol-ogy, Helsinki, Finland.[2] Gazley, C., 1958. “Heat transfer characteristics of therota-tional and axial flow between concentric cylinders”.Jour-nal of Heat Transfer,80(1), pp. 79–90.[3] Saari, J., 1996. Friction losses and heat transfer in high-speed electrical machines: A literature review. TechnicalReport report 50, Helsinki University of Technology, Es-poo, Finland.[4] Theodorsen, T., and Regier, A., 1944. Experiments of dragof revolving disks, cylinders and streamline rods at highspeeds. Technical report 793, Thirtieth annual report ofNational Advisory Committee for Aeronautics(NACA).[5] Bilgen, E., and Boulos, R., 1973. “Functional dependenceof torque coefficient of coaxial cylinders on gap width andreynolds numbers”.Journal of Fluids Engineering,95(1),pp. 122–126.[6] Rouhani, H., Faiz, J., and Lucas, C., 2007. “Lumped ther-mal model for switched reluctance motor applied to me-chanical design optimization”.Mathematical and Com-puter Modelling,45(5-6), pp. 625–638.5 Copyright c© 2009 by ASME[7] Aglen, O., 2003. “Loss calculation and thermal analysisofa high-speed generator”. In IEMDC 2003.[8] Aglen, O., and A.Andersson, 2003. “Thermal analysis ofa high-speed generator”. In Industry Applications Confer-ence, 38th IAS Annual Meeting, ed., pp. 547–554.[9] Boglietti, A., Cavagnino, A., Lazzari, M., and Pastorelli,M., 2003. “A simplified thermal model for variable-speedself-cooled industrial induction motor”.IEEE Transactionson Industry Applications,39(4), pp. 945–952.[10] Perez, I., and Kassakian, J., 1979. “A stationary thermalmodel for smooth air-gap rotating electric machines”.Elec-tric Machines and Electromechanics,3(3), pp. 285–303.[11] Mellor, P., Roberts, D., and Turner, D., 1991. “Lumpedparameter thermal model for electrical machines of tefc de-sign”. IEE Proceedings-B,138(5), pp. 205–218.[12] Kylander, G., 1995. “Thermal modeling of small cageinduction motors”. PhD Thesis, Chalmers University ofTechnology, Gothenburg, Sweden.[13] Roberts, D., 1986. “The application of an induction mo-tor thermal model to motor protection and other functions”.PhD Thesis, University of Liverpool, , UK.[14] Mellor, P. H., 1983. “Improvements in the efficiency andageing of single and parallel machine drives”. PhD Thesis,University of Liverpool, , UK.[15] Becker, K., and J.Kaye, 1962. “Measurements of diabaticflow in an annulus with an inner rotating cylinder”.Journalof Heat Transfer,84(2), pp. 97–105.[16] J.Saari, 1995.Thermal modeling of high-speed inductionmachines. Acta Polytechnica Scandinavica, Helsinki, Fin-land.6 Copyright c© 2009 by ASME

A simpliﬁed thermal model for variable-speed self-cooledindustrial inductionmotor”.

A stationary thermal modelforsmoothair-gaprotatingelectric machines”.

Experiments of drag of revolving disks, cylinders and streamline rods at high speeds. Technical report 793, Thirtieth annual report of National Advisory Committee for Aeronautics(NACA).

Friction losses and heat transfer in highspeed electrical machines: A literature review.

Functional dependence of torque coefﬁcient of coaxial cylinders on gap width and reynolds numbers”.

Heat transfer characteristics of the rotational and axial ﬂow between concentric cylinders”.

Improvements in the efﬁciency and ageing of single and parallel machine drives”.

Lumped parameter thermal model for electrical machines of tefc design”.

Lumped thermal model for switched reluctance motor applied to mechanical design optimization”.

Measurements of diabatic ﬂow in an annulus with an inner rotatingcylinder”.

The application of an induction motor thermal model to motor protectionand other functions”.

Thermal analysis of a high-speed generator”.

Thermal analysis of high-speed induction machines”.

Thermal modeling of high-speed induction machines. Acta Polytechnica Scandinavica,

Thermal modeling of small cage induction motors”.

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Thermal modeling of a mini rotor-stator system

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