CFD-Parametric Study in Stator Heat Transfer of an Axial Flux Permanent Magnet Machine

Transcription

1 World Acadey of Science, Engineering and Technology CFD-Paraetric Study in Stator Heat Transfer of an Axial Flux Peranent Magnet Machine Alireza Rasekh, Peter Sergeant, Jan Vierendeels Abstract This paper copes with the nuerical siulation for convective heat transfer in the stator disk of an axial flux peranent agnet (AFPM) electrical achine. Overheating is one of the ain issues in the design of AFMPs, which ainly occurs in the stator disk, so that it needs to be prevented. A rotor-stator configuration with 6 agnets at the periphery of the rotor is considered. Air is allowed to flow through openings in the rotor disk and channels being fored between the agnets and in the gap region between the agnets and the stator surface. The rotating channels between the agnets act as a driving force for the air flow. The significant nondiensional paraeters are the rotational Reynolds nuber, the gap size ratio, the agnet thickness ratio, and the agnet angle ratio. The goal is to find correlations for the Nusselt nuber on the stator disk according to these non-diensional nubers. Therefore, CFD siulations have been perfored with the ultiple reference frae (MRF) technique to odel the rotary otion of the rotor and the flow around and inside the achine. A iniization ethod is introduced by a pattern-search algorith to find the appropriate values of the reference teperature. It is found that the correlations are fast, robust and is capable of predicting the stator heat transfer with a good accuracy. The results reveal that the agnet angle ratio diinishes the stator heat transfer, whereas the rotational Reynolds nuber and the agnet thickness ratio iprove the convective heat transfer. On the other hand, there a certain gap size ratio at which the stator heat transfer reaches a axiu. Keywords Axial flux peranent agnet, CFD, agnet paraeters, stator heat transfer. T I. INTRODUCTION HE AFPM achines are highly efficient devices that have been widely used in the applications where the axial length of the achine is a liiting factor []. Due to their copact construction, overheating, which is one of the ain issue in the design of electrical achines, becoes uch ore severe and this needs to be prevented. In fact, deagnetization occurs in the peranent agnet aterials once the teperature exceeds 50 ºC (for SH type NdFeB agnets) []. The resistivity of the copper winding in the stator disk increases with teperature and this deteriorates the efficiency of the achine. Moreover, the lack of insight about the theral perforance of the achine entails the designer to Alireza Rasekh is with the Departent of Flow, Heat and Cobustion Mechanics, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgiu (phone: , fax: ; e-ail: alireza.rasekh@ugent.be,). Peter Sergeant is with the Departent of Electrical Energy, Systes and Autoation, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgiu (e-ail: peter.sergeant@ugent.be). Jan Vierendeels is with the Departent of Flow, Heat and Cobustion Mechanics, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgiu (e-ail: jan.vierendeels@ugent.be). provide excessive cooling by external pup or ventilator to avoid overheating. For these reasons, it is vital to have a deep knowledge of the cooling in the AFPM achines. Theral study of the AFPM achines has gained uch attention over the past few years [], []. Moradnia et al. [5] ipleented the CFD odeling of an electrical achine by MRF ethod. It was reported that this approach is roughly useful as it akes very accurate prediction of the airflow characteristics in the achine. Pyrhönen et al. [6] iproved the cooling of the AFPM achines by using copper bars as extra heat carriers in the construction. Chong et al. [7] perfored the nuerical odeling of the direct-drive AFPM generator operating at 00 rp for power level of 5 kw and built the experiental set up to validate their results. They showed that soe ventilation openings at the side of the achine could enhance the convection heat transfer in the achine. Li et al. [8] conducted an experient to assess the convective heat transfer coefficient in an AFPM achine. They indicated that the effects of natural convection are significant in theral evaluation of the achine. In an AFPM achine, ost heat losses occur in the stator winding and the ain heat transfer echanis to expel the heat fro this region is by convection. Therefore, the convective heat transfer in the stator disk of the AFPM achines has been investigated in the literature. In this regard, Yuan et al. [9] investigated the turbulent heat transfer on the stator surface and the flow characteristics in the gap between the disks. They showed that there is an optiu rotor-stator distance where the heat transfer on the stator side reaches a axiu. Howey et al. [0] easured the stator heat transfer in a discoidal configuration using an electrical heater array. They found that the local Nusselt nuber increases at the periphery due to ingress of air toward the stator. Rasekh et al. [] studied the effects of holes in the rotor side on convective heat transfer on the stator facing rotor in the gap. It was concluded that the presence of holes is beneficiary for the stator heat transfer as air is allowed to enter into the air-gap through the holes, resulting in a net radial flow in the gap region between the rotor and stator. Recently, Rasekh et al. [] presented correlations for the convective heat transfer in the siplified discoidal syste of an AFPM achine. The odel is able to predict the convective heat transfer for different values of the rotational Reynolds nuber and the gap size ratio. The average bulk fluid teperature adjacent of each surface was utilized as the reference teperature instead of the abient teperature to calculate the convective heat transfer coefficient. By doing so, the correlations for the surfaces in the gap becae 6

2 World Acadey of Science, Engineering and Technology independent of the surface teperature as well as the abient teperature. In this paper, the presence of the agnets on the rotor disk of the AFPM achine is taken into account. The objective is to find the correlations for the convective heat transfer coefficients of the stator surfaces according to the geoetrical paraeters of the agnets. A iniization ethod is used to calculate the appropriate value of the reference teperature, which akes these correlations independent of the surface teperatures. Details of the proposed ethod and the results are discussed in the following sections. (a) (b) Fig. (a) Scheatic diagra of the rotor-stator syste in the achine, (b) the real rotor disk with agnets II. DESIGN PROPERTIES OF THE AFPM MACHINE The geoetrical details of the rotor-stator configuration together with the actual rotor disk have been illustrated in Fig.. The syste is coposed of one stator disk encopassed by two rotor disks in which only half of the whole syste is taken into consideration. The radii of the rotor and the stator are 7 and 8, respectively. There are 6 agnets on the rotor disk which are evenly distributed. The space between the agnets creates the radial air-channel, which would be beneficial to the cooling of the achine. This can be further iproved by the annular opening at the entire rotor disk by allowing the cold air to pass the space between the rotor and the stator. Due to the cyclic flow, only one slice of the discoidal syste containing one coplete agnet is studied. The flow and heat transfer characteristics in this syste can be defined through four non-diensional nubers including the air-gap ratio, G=s/R, the rotational Reynolds nuber, Re=ωR /υ, the agnet angle ratio, α =α 6/60, and the agnet thickness ratio, L=t/R, where s is the air-gap thickness, R denotes the radius of the rotor, ω is the angular velocity of the rotor, υ is the kineatic viscosity of air, α is the agnet angle, and t denotes the agnet thickness. For the AFPM achine under study, these paraeters are ranged at G 0.08,.5 0 Re.5 0 5, 0.7 α 0.9 and 0.07 L The theral conductivities of the rotor and the stator surfaces are rather high so that the surfaces are considered isotheral. The variations of air properties such as viscosity and density with teperature are taken into account by the Sutherland s viscosity law and the incopressible ideal gas forulation, respectively. Note that the Reynolds nuber is evaluated at the average teperature of the rotor, the stator and abient, that is, (T r+t s+t ab)/. III. CFD SIMULATION The coercial CFD software ANSYS FLUENT is used to solve the flow field and heat transfer characteristics. The turbulence is odeled through the k-ω SST odel. The MRF which yields the steady state solution, is applied to odel the otion of the rotor. It should be entioned that the coputational esh is fixed in this approach, and the flow in each doain is solved using the oving reference frae equations. The D coputational doain is ade of the hexahedral esh type with,9,000 nodes. It was found that the nuerical odeling is independent of the esh size, by coparing the heat flux on the stator surface in the gap with the coarse and the fine esh sizes including 78,800 and 0,605,50 nodes, respectively. IV. FLOW AND TEMPERATURE PROFILES IN THE GAP To have a better understanding of the heat transfer in this syste, it is necessary to find out the various flow structures being fored in the air-gap between the agnets and also the stator surface. Therefore, Fig. depicts the radial velocity contour in the orthogonal plane through the iddle of the agnets and in the eridional plane through the center of the air-channel for G=0.05, Re= , α =0.8, and L= As seen, the agnets act as a centrifugal fan, accelerating the airflow outward through the air-channel. On the other hand, it is interesting to see the teperature profiles between the agnet and stator surface in the gap. Thus, the variations of the non-diensional teperature profiles along the air-gap between the agnet and the stator surface at different radii and gap size ratios have been illustrated in Fig.. 6

3 World Acadey of Science, Engineering and Technology Fig. Non-diensional radial velocity contour in the orthogonal plane through the iddle of the agnets and in the eridional plane through the center of the air-channel at G=0.05, Re= , α=0.8, and L=0.050 Fig. Non-diensional teperature variations across the air-gap for different G at Re= , α=0.8 and L=0.050 Note that the right side of the horizontal axis represents the area adjacent to the stator surface in the gap, and the left side belongs to the agnet surface. It is clear that the theral boundary layers next to the agnet and the stator surface are erged, whereas for the wide gap thickness, two distinguishable unerged theral boundary layers can be noticed. In addition to that, the slope of the graphs in the vicinity of the stator surface (right side of the horizontal axis) shows that the heat transfer increases at the outer periphery of the gap region. V. CORRELATIONS FOR CONVECTIVE HEAT TRANSFER COEFFICIENT The objective of coencing the CFD siulations is to acquire data to construct correlations for the convective heat transfer coefficient at the stator surfaces; naely, "Stator gap upper" and "Stator gap lower". The proposed correlations are able to assess the average heat flux for the entioned surfaces with respect to the significant non-diensional paraeters including the gap size ratio, the rotational Reynolds Nuber, the agnet angle ratio, the agnet thickness ratio at different surface teperatures of the rotor and the stator. For an isotheral surface, the convective heat transfer coefficient can be given by, h = qɺ ( T sur Tref ) where qɺis the heat flux, T sur is the surface teperature and T ref denotes the reference teperature. The Nusselt nuber can be obtained as, hr Nu = () k R represents the radius of the stator and k is theral conductivity of air. In order to ake the convective heat transfer coefficient independent of the surface teperature, the suitable value of the reference teperature should be considered. Here, it is assued that the reference teperature can be correlated with the surface teperatures and the () 6

4 World Acadey of Science, Engineering and Technology abient teperature through the following linear forulation, as, T = at + bt + [ ( a + b)] T () ref r s ab where the subscripts r, s, and ab denote the rotor, the stator and the abient. The unknown coefficients of a and b are dependent on Re, α and L. By substituting () to (), then the result to (), the Nusselt nuber is rewritten as, qɺ () Nu = ( T at bt [ + ( a + b)] T k sur r s ab) CFD siulations are carried out with the non-diensional paraeters kept at the reference point, i.e. G=0.05, Re= , α =0.8, and L=0.050 at four cobinations of the surfaces teperature, shown in Table I. Given the heat flux fro the nuerical results, the unknowns in () will be a, b, and Nu. The idea is to find certain values of a and b to iniize the standard deviation σ of the Nusselt nuber in () n / σ = ( Nu ) i Nu ] (5) [ n i= TABLE I MINIMIZATION METHOD TO FIND A AND B FOR THE SURFACE "HOLE LOWER" case T s (ºC) T r (ºC) ( w). According to Table I, i= indicates the nuber of surface teperature cobinations. A Pattern-Search algorith fro the MATLAB Optiization Toolbox is eployed to find the global iniu of the standard deviation of Nu in (). The initial points are the results of the solution by setting a and b to 0.00 in the first place. Once the iniization algorith yields the solution, the coefficients a and b will be defined. The ean value of the Nusselt nuber in () will be considered as the desired value for the Nusselt nuber. In this case, so long as the standard deviation resulting fro () is sall, the Nusselt nuber becoes nearly independent of the surface teperatures. Q a b T ref (ºC) Nu i Nu σ Having known a, b, and Nu at the reference point according to Table I, the goal is to find these as Re, α and L as well as the surface teperature of the rotor and the stator vary. To achieve this, a set of CFD siulations are carried out for G= {0.0068, 0.00, 0.070, 0.005, 0.05, & 0.08} at four teperature cobinations of the rotor and the stator, while the other paraeters are kept at the reference point, i.e. Re=. 0 5, α =0.8, and L= Thus, the heat fluxes for stator surfaces at all cases are coputed. Once ore, the iniization algorith is used to assess the appropriate values of a and b for each case separately. As a consequence, variations of the convective heat transfer with G when the other paraeters are fixed at the reference point are given. In the sae way, the cases where Re, α, are L are individually subjected to change will be investigated. Finally, we intend to forulate the variations of a, b, and Nu as follows, a = F( b = G( Nu = Y( It is assued that the above functions of four variables can be written as the product of four functions of one variable as, (6) where the superscript represents the values a, b, and Nu at the reference point. To find all of the above functions with one variable, curve fitting for or each surface should be carried out one after the other. Note that output fro each function at the reference point is alost equal to unity. The details of the forulations for stator surfaces in the gap are presented in Table II. TABLE II CORRELATIONS TO ESTIMATE THE CONVECTIVE HEAT TRANSFER Surface: Stator gap upper Stator gap lower a b Nu f 0.8G G -0.7 f 7.78Re Re f.80α α -0.0α +6. f 0.05L L g G G+ g Re Re+ g α α + g L L+ y -.967G G+.005 y. 0 - Re Re y α α y.86l L a = a f ( G) f b = b g ( G) g Nu = Nu y( G) y (Re) f ( α ) f (Re) g ( α ) g ( L) ( L) (Re) y ( α ) y ( L) (7) VI. CORRECTNESS OF THE CORRELATIONS The correlations presented in this paper have been obtained by varying one non-diensional paraeter while keeping the 6

5 World Acadey of Science, Engineering and Technology rest fixed at the reference point and repeating this for all the other variables. Hence, by coparing the results of the correlations with those obtained by CFD siulation for the cases in which neither Re, α, nor L is at the reference point, the efficacy of the proposed correlations can be ensured. As a result, the coparison has been ade for four different cases, as shown in Table III. TABLE III COMPARISON BETWEEN THE CFD AND THE PROPOSED CORRELATIONS RESULTS FOR HEAT TRANSFER RATE (W). Re= 8.9 0, G=0.00, Re=. 0 5, G=0.008, L=0.08, α =0.77, L=0.06, α =0.8, Surface T s=5ºc, T r=95ºc T s=5ºc, T r=05ºc Correlation CFD Correlation CFD Stator gap upper Stator gap lower It is seen that the correlations presented in this paper are able to assess accurately the convective heat transfer for the stator surfaces in the gap in the practical ranges of the iportant paraeters in AFPM achines with a good accuracy. VII. CONCLUSION The convective heat transfer in the stator disk of an AFPM achine was studied in this paper. CFD siulations have been perfored considering different ranges of the predoinant non-diensional paraeters that govern the heat transfer and fluid flow; naely, the rotational Reynolds nuber, the gap size ratio, the agnet angle ratio and agnet thickness ratio. It was shown that the radial air-channel is constructed between the agnets and also in the gap region. This acts as a centrifugal fan to expel the heat fro the syste. Based on the nuerical results, the objective was to construct correlations to estiate the convective heat transfer coefficient, applicable to the different non-diensional paraeters as well as the surface teperature of the rotor and the stator. To do so, a iniization ethod by eans of Pattern-Search algorith has been eployed to find the proper value of the reference teperature that akes the estiated convective heat transfer coefficient independent of the surface teperature. Afterwards, the correlations for calculating the convective heat transfer for the stator surfaces in the gap were given by using curve fittings. It was concluded that the correlations are scalable and quite versatile tools in the theral odeling of AFPM achines. ACKNOWLEDGMENT The financial support for this study by FWO project G.00. is gratefully acknowledged. [] S. Scowby, R. Dobson, M. Kaper, Theral odelling of an axial flux peranent agnet achine, Appl. Theral Eng, vol., pp. 9 07, 00. [] G. Airoldi, J. Buby, C. Doiny, G. Ingra, C. Li, K. Mahkaov, N. Brown, A. Mebarki, M. Shanel, Air flow and heat transfer odeling of an axial flux peranent agnet generator, World Acad. Sci., Eng. Technol, vol. 58, pp , 009. [5] P. Moradnia, M. Golubev, V. Chernoray, H. Nilsson, Flow of cooling air in an electric generator odel-an experiental and nuerical study, Applied energy, vol., pp. 6-65, 0. [6] J. Pyrhönen, P. Lindh, M. Polikarpova, E. Kurvinen, Heat-transfer iproveents in an axial-flux peranent-agnet synchronous achine, Applied Theral Engineering, vol. 76, pp. 5-5, 05. [7] Y.C. Chong, D.A. Magahy, J. Chick, M.A. Mueller, D.A. Staton, A.S. McDonald, Nuerical odelling of an axial flux peranent agnet achine for convection heat transfer, Renewable Power Generation (RPG) IET Conference, pp. -6, 0. [8] C.H. Li, G. Airoldi, J.R. Buby, R.G. Doiny, G.I. Ingra, K. Mahkaov, N.L. Brown, A. Mebarki, M. Shanel, Experiental validation of CFD odelling for heat transfer coefficient predictions in axial flux peranent agnet generators, International Journal of Theral Sciences, pp. 50, 5-6, 0. [9] Z.X. Yuan, N. Saniei, X.T. Yan, Turbulent heat transfer in the stationary disk in a rotor-stator syste, Int. J. Heat Mass Transf. vol. 6, pp. 07-8, 00. [0] D.A. Howey, A.S. Holes, K.R. Pullen, Radially resolved easureent of stator heat transfer in a rotor stator disc, International Journal of Heat and Mass Transfer, vol. 5 pp. 9 50, 00. [] A. Rasekh, P. Sergeant, J. Vierendeels, A paraetric-cfd study for heat transfer and fluid flow in a rotor-stator syste, th World congress on Coputational Mechanics (WCCM XI) pp. -9, 0. [] A. Rasekh, P. Sergeant, J. Vierendeels, Convective heat transfer prediction in disk-type electrical achines, Applied Theral Engineering, vol. 9, pp , 05. REFERENCES [] H. Hakala, Integration of Motor and Hoisting Machine Changes the Elevator Business, Proceedings of International Conference on Electrical Machines (ICEM), vol., pp. -5, 000. [] C. Ruschettia, C. Verucchib, G. Bossioa, C. De Angeloa, G. García, Rotor deagnetization effects on peranent agnet synchronous achines, Energy Conversion and Manageent, vol. 7, pp. 8, 0. 65