Study of a Taylor-Couette-Poiseuille Flow in an Annular Channel with a Slotted Rotor N. Lancial, F. Torriano, F. Beaubert, S. Harmand, G. Rolland
I. I NTRODUCTION Abstract—This paper investigates a Taylor-Couette-Poiseuille flow in an annular channel of a slotted rotating inner cylinder, corresponding to a salient pole hydrogenerator. The purpose of this study is to improve the understanding of flow and thermal phenomena in electrical machines using a simplified scale model. Some numerical tests are first shown to investigate the influence of certain numerical parameters. Finally, CFD and CHT studies of the flow regimes are presented in the slotted rotor geometry and compared to experimental and literature data. Index Terms—Hydrogenerator, rotating machines, CFD, RANS simulations, CHT.
N OMENCLATURE Latin Symbols CFD, CHT, Dh , e=R2 -R1 , h, H, l, Lf er , n, p, R1 , R2 , Rea =Vz Dh /ν, T, Ta=ω 2 R1 ( D2h )3 /ν 2 , SST, ,
Computational Fluid Dynamics. Conjugate Heat Transfer. Hydraulic diameter (m). Air gap (m). Heat transfer coefficient (W/m2 K). Rotor height (m). Pole width (m). Rotor height (m). Number of poles. Pole depth (m). Rotor radius (m). Stator inner radius (m). Axial Reynolds number. Temperature (°C). Taylor number. Shear Stress Transport. Mean axial velocity (m/s).
Greek Symbols θ, ν, ω,
Angle (°). Kinematic viscosity (m2 /s). Rotational speed (rad/s).
This work was supported by the EDF R&D company with the help of financing from the Regional Council Nord-Pas-de-Calais and the European Regional Development Funding, in the framework of the MEDEE program. Nicolas Lancial is associated with UVHC, TEMPO/DF2T and EDF R&D, France (e-mail:
[email protected]). Federico Torriano is associated with Institut de Recherche d’Hydro-Québec, Canada (e-mail:
[email protected]). François Beaubert is associated with UVHC, TEMPO/DF2T, France (email:
[email protected]). Souad Harmand is associated with UVHC, TEMPO/DF2T, France (e-mail:
[email protected]). Gilles Rolland is associated with EDF R&D, France (e-mail:
[email protected]).
978-1-4799-4775-1/14/$31.00 ©2014 IEEE
ALIENT pole synchronous machines are essential equipment for converting the mechanical energy of water turbines into electrical energy. Insulation life expectancy is directly linked to temperature and decreases as the latter increases. Temperature limits are a key factor affecting the efficiency and capacity of hydrogenerators. Because overheating is often caused by poor circulation of the cooling fluid, it is necessary to understand the flow dynamics of the cooling fluid and their effect on the heat transfer mechanisms in the various generator components (i.e., end-winding, pole face, etc.). Comparisons between experimental measurements and numerical simulations are needed to improve the understanding of the thermofluid phenomena as the numerical methods have not yet achieved a sufficient degree of maturity to be used alone. The use of a laboratory scale model is the best solution to acquire data in order to validate numerical models. This approach was chosen by EDF (Électricité de France), TEMPO/DF2T (Université Lille Nord-de-France) and IREQ (Institut de Recherche d’Hydro-Québec), where a common strategy was established to share knowledge in the field of hydrogenerator thermofluid analysis. The basic air gap geometry is composed of two smooth concentric cylinders. Flow and heat transfer phenomena have been extensively studied over the years for this configuration (Taylor-Couette flows). Studies found in the literature have shown the existence of different flow structures in a smooth and closed annular gap. Those structures mainly depend on rotational speed with Ta=ω 2 R1 e3 /ν 2 , where Dh = 2e. Below the critical value T ac ' 1700, the flow is considered laminar and steady. The larger the air gap or the smaller the length of the cylinders is, the higher the value of T ac . For this regime, heat transfer from one cylinder to the other can be considered constant and is dominated by conduction, as described in [1]. Above the critical value T ac , the rotational instability of the flow causes the appearance of vortices known as Taylor vortices. In this case, the rate of heat transfer increases in accordance with an increasing Taylor number. The flow becomes more complex with increasing rotational speed: random fluctuations progressively start to dominate the flow, which finally becomes turbulent. For a Taylor-Couette-Poiseuille flow, where an axial flow is superimposed on the rotation, four types of flow are encountered ([2]): laminar flow with or without Taylor vortices and turbulent flow with or without Taylor vortices (for 0 ≤ Rea ≤ 104 and 0 ≤ Ta ≤ 106 ). For this configuration, an increase in the axial flow delays the transition from laminar to turbulent regime.
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S
TABLE I F LOW REGIMES IN OUR SLOTTED ANNULAR CHANNEL Vz (m/s) Rea ω (rad/s) Ta
Fig. 1.
Laminar 0.5 750 1.05 723
Laminar with vortices 0.5 750 52.36 1797700
Turbulent 2 3000 1.05 723
Turbulent with vortices 2 3000 52.36 1797700
Demarcation lines for flow regimes in smooth annulus, according to [1].
The increase in the rotational speed deforms the Taylor vortices. Heat transfer depends on rotation, axial speed and geometrical parameters, such as the annular channel length and width. Unfortunately, industrial configurations such as salient pole synchronous machines present a more complex geometry. The main difference is due to the presence of salient magnetic poles separated by longitudinal slots. The salient poles are mainly present in the rotor and their size and number may vary. Given the large number of parameters, it is difficult to generalize the results for different slotted configurations. The Taylor number is defined here by Ta=ω 2 R1 ( D2h )3 /ν 2 ([3]). In such slotted gaps, heat transfer results are often contradictory. For example, the presence of slots in the stator or rotor has no effect on the Nusselt number according to [4], but the Nusselt number increases at the rotor and stator, as described in [5]. The differences between the results found in these studies can be explained by different geometries or velocity entrance profiles. Recently, [6] investigated the use of an infrared camera in an annular channel with an open four-pole synchronous motor. Nusselt correlations were given for various axial and rotational Reynolds numbers in different rotor (e.g., leading side, trailing side and pole face) and stator regions. CFD is the most recent technique applied to hydrogenerators and was made possible by the increase in available computing capabilities ([7]). Some papers have been published on CFD simulations of electrical machines which simulated the cooling airflow and calculated the convective heat transfer in different components ([8]). Guidelines for choosing suitable thermal and flow network formulations depending on the studied electrical machines are presented in [9]. The calculation of the heat transfer coefficient distribution from temperature measurements on the pole face of a hydrogenerator scale model
using FEM and CFD was performed in [10]. A comparison was made in [11] between CFD and network models, and good agreement was found. CFD accurately predicted the trend of the heat transfer coefficient on the pole surface, but the computed values were up to 30 % lower compared to experimental data. According to [12], more accurate solutions can be obtained via a CHT computation in which the flow and thermal simulations are coupled. Furthermore, [13] have accurately simulated the flow field of the rotor ventilation system and the temperature of the excitation winding using a CHT computation. Finally, [14] suggests different methods for thermal analysis of a high-speed permanent-magnet machine and compares them with experimental data. The authors conclude that a 2D axisymmetric CHT model gives the most realistic results. This paper continues the investigation of the effect of a Taylor-Couette-Poiseuille flow on the convection heat transfer at the surface of a slotted rotating inner cylinder. The goal is to improve the understanding of flow and thermal transfer phenomena on electrical machines, using CFD and CHT simulations. With the EDF/TEMPO scale model of a hydrogenerator, temperature profiles on the rotor pole face are experimentally and numerically obtained with Ansys-CFX, and Code_Saturne 3.0 coupled with SYRTHES 4.0. The final objective is to study all main flow regimes in the annulus (see Fig. 1) through the cases studied (listed in TABLE I). This paper is subdivided into four sections. The scale model design is first presented. Then, the numerical models are presented and validation tests are shown to choose the most appropriate numerical method. An experimental and numerical comparison is also performed for a specific configuration. Finally, a numerical analysis of the flow regimes in the air gap and their influence on rotor temperatures are presented.
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(a) Full view of the scale model. Fig. 2.
(b) View of the rotor and stator, which is removable and made of Lexan.
Generator scale model.
II. S CALE MODEL DESIGN Understanding complex phenomena such as heat transfer in rotating parts of the machine is quite challenging, especially with available experimental data, which are limited. However, these data can serve to validate numerical models, which allow a better comprehension of thermal and flow dynamics in generators. Due to limited access and difficulties of performing measurements on actual generators, scale models are needed. Thus, a hydrogenerator scale model was designed at EDF/TEMPO. This model is based on actual generators in EDF production plants, but is a simplified version of the prototype because the active electromagnetic elements are absent. As illustrated in Fig. 2, the scale model is in an open loop ventilation circuit. The air is drawn by a fan and is directed by two air guides located upstream and downstream of the rotor/stator system. The main simplifications in the scale model include omission of the coils and the ducts in the stator. The stator is a transparent cylindrical plate where a flat section (made of fluorine) is present in order to have optical access to the rotor components and to avoid optical aberration for the IR Jade III MWIR camera and for flow visualization with Particle Image Velocimetry. A uni-directional hot wire is also used to measure axial velocity upstream of the rotor/stator system. Simplifications were also made to facilitate measurements and to reduce geometric complexity in order to ease the meshing process of the numerical study. The rotor shaft is driven by an ABB 1.1 kW engine. TABLE II shows the main scale model characteristics. TABLE II S CALE MODEL CHARACTERISTICS Characteristics Rotor radius, R1 Rotor height, Lf er Pole width, l Pole depth, p Air gap, e Number of poles, n Stator inner radius, R2
Dimensions (mm) 119 186 55 20 10 10 129
The overall dimension is scaled down (1:6 in the radial
direction and 1:12 in the axial direction). The main components have been dimensioned to maintain similarity with the L prototype for the following parameters: pl , Rp1 and Rf er . The 1 hydraulic diameter is calculated using the following equation, π(R2 −R2 )−nlp Dh =2 π(R22 +R11 )+np = 0.02289 m. The rotor turns clockwise up to a maximum speed of 1500 rpm and the fan can generate an axial velocity up to 10 m/s (0 ≤ Rea ≤ 14250, 0 ≤ Ta ≤ 1.7 × 107 ). The objective is to maintain prototype similitude of the Reynolds number in the hydrogenerator air gap. The operating air temperature in the enclosure can exceed 30 °C due to heat generated by windage losses. Sufficient cooling is provided to maintain temperatures within 70 °C in the rotor pole. The scale model is also used to analyse heat transfer phenomena occurring on the surface of a rotor pole. A slip ring on the rotor shaft connects 10 cartridge heaters to a power source. Each heater has a maximum output of 300 W and is equipped with a J-type thermocouple. The power output can be varied and the rotor surface temperature is measured with the IR camera. Some temperatures inside the scale model are measured with K-type thermocouples and are acquired by a two-channel slip ring connected to a data logger system. III. N UMERICAL MODEL Before calculating the temperature distribution through CHT, some preliminary tests were completed via CFD, using Code_Saturne, to verify the flow dynamics in the scale model. As shown in Fig. 3, a CAD model that includes the air guide boxes and the associated mesh were built for this purpose. A structured hexahedral mesh was generated with SALOME 6.6. The main turbulence model used was the first order k-ω SST model. The mesh refinement near the no-slip walls was set to obtain a y + value close to 1. A mesh-independence study was performed to ensure that the grid resolution was appropriate. A frozen rotor interface was applied to the full domain: additional rotational effects (Coriolis and centrifugal terms) are included in the rotating regions. Several interfaces were tested: one before and one after (BA) the studied domain (Fig. 4 (a)) and inside the air gap (AG, Fig. 4 (b)).
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Stator e l R1
p
Rotor
R2
(a) CAD model.
(b) CFD periodic mesh used during numerical simulations.
CAD model and its mesh used during numerical calculations.
Note that the air gap (AG) interface is divided into three domains according to its radial position: in the middle of the air gap (AG - 12), at one quarter of the rotor (AG - 14) and at three-quarters of the rotor, closer to the stator (AG - 34).
in Fig. 5 (a), the steady solution can be obtained for ω ≤ 2.09 rad/s when no axial velocity is applied. However, when ω > 2.09 rad/s, the steady solution can not be reached (Fig. 5 (b)). The CFD code Ansys-CFX gives a similar conclusion.
Downstream Stator Z
0,2
Air gap
Rotor
0,03
0,15
Z
Vz (m/s)
Rotor Upstream
(a) Before and after the rotor/stator domain, named BA. Fig. 4.
0,04
Stator
(b) Interface in the air gap, named AG.
Vz (m/s)
Fig. 3.
0,01
0,1
0,05
Influence of the interface positions. 0 0
For the two air guide boxes, which are stationary, a counterrotating velocity was set to have a static wall in the absolute reference frame. Compared to the experimental scale model, the outlet air guide box is artificially extended in order to limit the effect of the boundary conditions. Before presenting the considered cases (shown in TABLE I), the influence of the numerical parameters is studied in the next section. The objective is to select the most appropriate numerical method and have an optimal balance between the computational cost and the accuracy of the results. For the steady state algorithm, first order schemes for time and space discretization are used. For unsteady calculations, a Crank-Nicholson time scheme with a time step of 5 × 10−5 s (CFL ' 2) and a second-order scheme in space are used. Convergence is reached when all residuals are below 10−4 . IV. P RELIMINARY NUMERICAL TESTS Some numerical tests are presented, including the possibility of using a steady state analysis, the influence of the computational domain with or without periodic condition, the influence of the interfaces and the turbulence models. For these sensitivity studies, no axial velocity is applied; the rotational speed is set to ω = 500, unless otherwise specified. A. Steady state At first, a test is performed in order to check whether the flow can be calculated with a steady state model. As presented
104
2×104 3×104 Iterations
4×104 5×104
(a) ω = 2.09 rad/s: in the middle of the rotor, for k-ω SST turbulence model. Fig. 5.
0 5×104
6×104
7×104 8×104 Iterations
9×104
105
(b) ω = 5.24 rad/s: in the middle of the rotor, for k-ω SST turbulence model.
Study of the steady state convergence.
However, as the main numerical calculations have to be run at higher rotational speeds, an unsteady solver has to be used and the influence of the integration period on the mean flow values must be investigated. The computation of the mean quantities begins after 2 s of simulation time, when the fully developed regime is reached. An error of 2% is observed between the values averaged over a period of time from 6 s to 13 s. The characteristic time Dh is Tω = ωR =0.0037 s. So, the mean values are computed over 1 an integration time of 6 s which consist of 1622Tω . B. Periodic calculations The comparison between the periodic and full domains indicates that the results are similar. Although calculation convergence was difficult due to flow instabilities, the streamlines of Fig. 6 show that the mean flow enters from both ends of the slotted rotor up to the middle of the rotor, creating two main recirculations. Thus, without axial velocity, the flow is symmetric in the middle of the rotor, for both cases. As illustrated in Fig. 7, the axial velocity distribution along the axial and radial directions is quite similar and a maximum error of 5 % is observed between both cases. Therefore, all subsequent simulations can be run with the periodic domain.
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(a) Contour and streamlines of in periodic domain in the y-z plane, in the middle of the notch. Fig. 6.
Comparison of the flow topology between periodic and full domains.
3
0,5
2
(m/s)
(m/s)
0
Periodic Full domain
1
0
Periodic Full domain
−1
−1 −1,5
−2
−3 0
(b) Contour and streamlines of in full domain in the y-z plane, in the middle of the notch.
0,05
0,1 Z (m)
0,15
−2 0,095
0,2
(a) Axial distribution of in the middle of the rotor (x = 0 m, y = 0.108778 m).
0,1
0,105 0,11 0,115 0,12 0,1250,13 Y (m)
(b) Radial distribution of in the middle of the rotor, at the outlet (x = 0 m, z = 0.186 m).
The same conclusion is reached in [15] when analysing a frozen rotor model. Moreover, no differences are observed between the first order (k-ω SST, v2f-BL-v2/k) and second order (Rij-EBRSM) low Reynolds models. Similar conclusions can be drawn for the high Reynolds models (k-ε, Rij-SSG). However, differences can be observed between the low and high Reynolds models for all flow variables. In conclusion, an experimental study must be performed to better evaluate the accuracy of low and high Reynolds models. However, according to the literature, low Reynolds models are preferred as the flow is strongly unsteady and as the main goal is to evaluate heat transfer coefficient.
Fig. 7. Comparison of the mean velocity distribution between periodic and full domain.
V. R ESULTS AND ANALYSIS A. Comparison between experimental and numerical results
C. Effect of interface type and turbulence models In this section, different rotor/stator interface positions as well as several turbulence models are tested: low Reynolds (k-ω SST, v2f-BL-v2/k and Rij-EBRSM) and high Reynolds models (k-ε and Rij-SSG). The overall mesh size is 4431900 elements for low Reynolds models. A separate mesh (124350 elements) was used for high Reynolds models (y + ' 30). The results of Fig. 8 illustrate the influence of the rotor/stator interface type as well as the turbulence models. When the rotor/stator interface is placed closer to the rotor, the results differ more from the case without interface. 4
4 Periodic Periodic Periodic Periodic Periodic
3
3
1 0
1 0
−1
−1
−2
−2
−3 0
0,05
0,1 Z (m)
0,15
0,2
(a) Influence of the interfaces: axial distribution of in the middle of the rotor (x=0, y=0.108778 m). Fig. 8.
k-ω SST k-ε v2f-BL-2v/k Rij-SSG Rij-EBRSM
2 (m/s)
(m/s)
2
- no interface BA AG - 12 AG - 14 AG - 34
−3 0
0,05
0,1 Z (m)
0,15
0,2
(b) Influence of the turbulence models: axial distribution of in the middle of the rotor (x=0 m, y=0.108778 m).
Numerical influence of the interfaces and the turbulence models.
The CHT simulations are performed with two CFD software codes: Code_Saturne 3.0 coupled with the thermal software, SYRTHES 4.0, and Ansys-CFX. For both solvers, a tetrahedral mesh is used for the solid domain, whereas a hexahedral mesh is used for the fluid domain. The overall solid domain size is 5400000 cells including the rotor, the cartridge heaters, the insulation and the shaft. A mesh independence study was made for both domains, and a similar mesh size is specified at the interface. The inlet velocity profile obtained from the hot wire measurement (< Vz >max = 2.15 m/s, Rea = 3225) is imposed as a boundary condition at 6Dh upstream of the rotor/stator system. The rotational speed is set to ω = 500 rpm (T a = 1797700). The total heat power is set to P = 507.6 W, and the operating air temperature is approximately 21 °C. As the thermal characteristic time is much higher than the fluid characteristic time, the time step in SYRTHES is set to 1 s to guarantee a steady state temperature field. For Ansys-CFX, the time step for the fluid and solid domains must be the same. A time-averaging of the global fluid variables was performed, according to the recommendations given before. The average flow field obtained from the CFD calculation is then used to compute the temperature distribution in the solid and fluid by solving the energy equation. Convergence in SYRTHES and Ansys-CFX is reached when the energy residual is below 10−6 and when all monitor points signal have stabilized. The comparison of the normalized temperature contours is presented in Fig. 9. The two codes predict quite accurately the rotor temperature distribution since the maximum temperature is about 0.9 °C higher for Ansys-CFX and 1.2 °C lower for SYRTHES compared to experimental data (about 69.8 °C).
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It should be noted that as the measurements with the IR camera were made from a fluorine window, some experimental approximations are unavoidable, especially close to the rotor ends and between each window measurement. To account for this, grey bands are placed in the regions where an interpolation was performed. The results show that the pole leading side is more effectively cooled than the trailing side because the flow impinges the former surface, whereas a large recirculation region is present near the trailing side wall (see Fig. 10). The temperature contours indicate an axial temperature gradient on the pole surface, where the minimum pole surface temperature is found on the bottom corner of the leading edge. This distribution occurs because the axial fan generates a flow in the positive z-direction, and cooler air is thus present at the entrance of the notch region. Conversely, the hot spot is located at the downstream end of the rotor notch because low flow velocities are found in this region (see Fig. 10), and the cooling fluid has been warmed by its passage along the heated pole surfaces.
Fig. 10. Relative velocity contours and pathlines along the air gap and notch regions.
Near the notch entrance region, a strong velocity gradient is observed due to the presence of a large recirculation zone adjacent to the pole trailing edge (Fig. 10).
Fig. 9. Normalized temperature contours on the pole face, obtained from experimental and numerical data.
The pathlines in Fig. 10 illustrate the presence of a strong vortex in the notch region, generated at the upstream end of the pole trailing edge and extends up to 3/4 of the pole length. A secondary vortex starts at the upstream end of the pole leading corner and is diagonally convected along the pole. The presence of the latter vortex causes a decrease in the heat transfer coefficient, as shown in Fig. 11 by the indent near θ = 5◦ and θ = −12◦ on the lines located at z = 0.005 m and z = 0.049 m, respectively. The presence of these vortices is predicted by both numerical codes, although they seem to dissipate slightly faster with Ansys-CFX. The plots of Fig. 11 show that the heat transfer coefficient decreases from the leading edge to the trailing edge of the pole face and this behaviour has also been observed in the studies carried out in [6] and [10]. In the notch region, the heat transfer coefficient profiles are quite uniform in the circumferential direction θ: the values are close to those observed near the trailing edge of the pole, except for the profiles located at z = 0.005 and 0.049 m.
Fig. 11. Heat transfer coefficient profiles on the pole face (Ansys-CFX: solid lines; SYRTHES 4.0: dashed lines).
Finally, the heat transfer coefficient on the pole face and in the notch region decreases with increasing z due to the growth of thermal boundary layers. In summary, the CHT simulations performed with SaturneSyrthes and Ansys-CFX have predicted a temperature distribution quite close to the measured one, and the heat transfer profiles on the pole face have been extrapolated. Overall, the values given by these codes are in good agreement except at z = 0.005 m where Code_Saturne predicts a significantly higher heat transfer coefficient. This is not so surprising since even a small change in the dynamics of the pole leading edge tip vortex (see Fig. 10) can greatly affect the local heat transfer. This comparison has validated both numerical codes, and a parametric study of the flow regimes can now be performed.
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(a) Laminar (Rea = 750, Ta = 723).
(b) Laminar with vortices (Rea = 750, Ta = 1797700).
(c) Turbulent (Rea = 3000, Ta = 723).
(d) Turbulent with vortices (Rea = 3000, Ta = 1797700).
Fig. 12. Contours of the mean axial velocity and velocity vectors at different flow regimes (a skip factor of 50 vectors is applied for clarity purposes).
B. CFD study of flow regimes In this section, the numerical calculations are done using Code_Saturne. A parametric study of the flow regimes in the slotted rotor configuration is presented (see Fig. 12). Compared to the study presented in [1], a similar description of the flow can be provided, either in the smooth or slotted annular configuration. Although the study presented in [1] was performed for a smooth annular configuration, a similar flow is obtained for the current slotted annular case. As the flow is similar between the laminar and turbulent regimes without vortices, it clearly means that the effect of the axial velocity overcomes the effect of rotation. In Fig. 6, it was shown that without any axial velocity, the air is drawn in at both ends of the slotted rotor, and two symmetric recirculation zones are present. A similar behaviour is observed in the results of laminar or turbulent flows with vortices, although the main recirculation zone is shifted further downstream of the rotor. This indicates that the effect of rotation is not negligible and that Vz has a weak effect. Consequently, the rotational speed, ω, promotes the formation of vortices which produce chaotic movements, whereas the axial velocity, Vz , prevents their creation.
C. CHT study of the rotor temperature distribution The CHT studies are shown in Fig. 13 and depict the effect of the flow on the rotor temperature. The numerical calculations presented were computed using SYRTHES. As expected, near the notch entrance region, a better cooling can be observed. Moreover, the cooling is higher in the leading edge, especially for the highest Taylor numbers. In the pole face, for laminar and turbulent flows at low rotational speed, the temperature profile is almost symmetric between the trailing and the leading edge. On the opposite, for laminar and turbulent flows at high rotational speed, the leading edge is better cooled than the trailing edge. For all cases, the location of the high temperature area is found at the downstream end of the rotor, in the notch region.
750,
(b) Laminar with vortices (Rea = 750, Ta = 1797700).
(c) Turbulent (Rea = 3000, Ta = 723).
(d) Turbulent with vortices (Rea = 3000, Ta = 1797700).
(a) Laminar (Rea Ta = 723).
Fig. 13.
=
Temperature contours on the rotor pole.
VI. C ONCLUSION AND P ERSPECTIVES The effect of a Taylor-Couette-Poiseuille flow in an annular channel of a slotted rotating inner cylinder was investigated. Numerical sensitivity tests have shown that an unsteady solver needs to be used for the flow regimes studied here. It has also been proved that a domain with periodic boundary conditions can be utilized. Furthermore, if a rotor/stator interface is placed in the airgap, it should be placed far away from the rotor.
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A comparison of numerical results with experimental data has shown a very good agreement. It was observed that a hot spot is located near the downstream end of the rotor notch. The distribution of the heat transfer coefficient shows that the leading edge is better cooled than the trailing edge and that the presence of vortices in the notch region affects its distribution. The same type of flow can be depicted in the smooth or slotted annular channel: the predominance of the axial and the tangential velocity depends on Rea and T a, respectively. This study improves the understanding of flow and heat transfer phenomena on electrical machines. In the near future, an inverse method using temperature measurements will be used to experimentally deduce the distribution of the heat transfer coefficient and compare it to the numerical results. This method has already been validated in 1D by [16] in a backward-facing step study and in 3D by [10] in a hydrogenerator scale model study. PIV measurements may also be appropriate to further validate the CFD results. R EFERENCES [1] K. Becker and J. Kaye, “Measurements of diabatic flow in an annulus with an inner rotating cylinder,” Journal of Heat Transfer, 1962. [2] J. Kaye and E. Elgar, “Modes of adiabatic and diabatic fluid flow in an annulus with an inner rotating cylinder,” Transactions of ASME 80, pp. 753–765, 1958. [3] M. Fénot, Y. Bertin, E. Dorignac, and G. Lalizel, “A review of heat transfer between concentric rotating cylinders with or without axial flow,” International Journal of Thermal Sciences, vol. 50, pp. 1138– 1155, 2011. [4] C. Gazley, “Heat-transfer characteristics of the rotational and axial flow between concentric cylinders,” Journal of Heat Transfer, vol. 80, pp. 79– 90, 1962. [5] T. Yanagida and N. Kawasaki, “Pressure drop and heat-transfer characteristics of axial air flow through an annulus with a deep-slotted outer cylinder and a rotating inner cylinder,” Heat transfer. Japanese Research, vol. 21, 1992. [6] M. Fénot, E. Dorignac, A. Giret, and G. Lalizel, “Convective heat transfer in the entry region of an annular channel with slotted rotating inner cylinder,” Applied Thermal Engineering, vol. 54, pp. 345–358, 2013. [7] A. Boglietti, A. Cavagnino, D. Staton, M. Shanel, and M. Carlos, “Evolution and modern approaches for thermal analysis od electrical machines,” IEEE Transactions on Industrial Electronics, vol. 56, 2009. [8] H. Lang, C. Kral, A. Haumer, M. Haigis, and R. Schulz, “Investigation of the thermal behavior of a salient pole synchronous machine,” in Proceedings of the 17th International Conference on Electrical Machines (ICEM), (Chania (Greece)), 2006. [9] D. A. Staton and A. Cavagnino, “Convection heat transfer and flow calculations suitable for electric machines thermal models,” IEEE Transactions on Industrial Electronics, vol. 55, pp. 3509–3516, 2008. [10] F. Torriano, N. Lancial, M. Lévesque, G. Rolland, C. Hudon, F. Beaubert, J. Morissette, and S. Harmand, “Heat transfer coefficient distribution on the pole face of a hydrogenerator scale model,” Applied Thermal Engineering, vol. 70, pp. 153–162, 2014. [11] R. Dépraz, R. Zickermann, A. Schwery, and F. Avellan, “Cfd validation and air cooling design methodology for large hydro generator,” in Proceedings of the 17th International Conference on Electrical Machines (ICEM), (Chania (Greece)), 2006. [12] M. Shanel, S. Pickering, and D. Lampard, “Conjugate heat transfer analysis of a salient pole rotor in an air cooled synchronous generator,” Proc. IEEE-IEMDC, 2003. [13] L. Weili, G. Chunwei, and Z. Ping, “Calculation of a complex 3-d model of a turbogenerator with end region regarding electrical losses, cooling, and heating,” IEEE transactions on energy conversion, vol. 26, 2011. [14] Z. Kolondzovski, P. Sallinen, and A. Arkkio, “Thermal analysis of a high-speed pm machine using numerical and thermal-nterwork method,” in Electrical Machines (ICEM), 2010 XIX International Conference On, pp. 1–6, 2010.
[15] K. Toussaint, F. Torriano, F. Morissette, C. Hudon, and M. Reggio, “Cfd analysis of ventilation flow for a scale model hydro-generator,” in Proceedings of the ASME 2011 Power Conference, 2011. [16] N. Lancial, F. Beaubert, S. Harmand, and G. Rolland, “Effects of a turbulent wall jet on heat transfer over a non-confined backward-facing step,” International Journal of Heat and Fluid Flow, vol. 44, pp. 336– 347, 2013.
B IOGRAPHIES Nicolas Lancial is currently a Ph.D. student in Mechanical Engineering at EDF R&D and at TEMPO lab. in France, which collaborates with IREQ in Canada. He is studying the effects of rotation on the fluid dynamics and heat transfer in large-sized rotating electrical machines. He obtained his Master’s degree in Mechanics and Energetics at the ENSIAME Engineering School in Valenciennes, France. Federico Torriano is currently a researcher at HydroQuébec research institute (IREQ). He is a graduate of Laval University in Québec city, where he studied physical engineering. He received his M.Sc. in CFD from Laval University in 2006. His main research interests are numerical simulations of thermal and flow phenomena in power transformers and hydrogenerators. He is currently studying the numerical validation of the flow in a hydrogenerator scale model through PIV measurements in addition to other subjects. François Beaubert is currently an Associate Professor in the Engineering School ENSIAME at the University of Valenciennes, France. He is a graduate of Pierre and Marie Curie University (UPMC) in Paris where he studied mechanical engineering and applied numerical methods. He received his Ph.D. in fluid mechanics from the University of Nantes in 2002. His research interests include scientific computing and CFD with an emphasis on turbulence modelling (RANS, LES), wall bounded flow, and heat and mass transfer. He is currently working on the modelling and enhancement of heat exchangers in complex geometries as well as turbulent heat transfer modelling in rotor/stator flows. Souad Harmand is a Professor at the University of Valenciennes, France. She graduated from the Engineering School Ecole des Mines and received her Ph.D. from the University of Valenciennes. Her research area is strongly focused on the convective heat transfer on rotating systems and on the heat and mass transfer in heat pipes. She is currently working on the optimization of the cooling of electrical components as well as the enhancement of the evaporation of nanofluids. Gilles Rolland is currently a Research Engineer for EDF (EDF-Lab Les Renardières). He is a graduate of ENIB (Ecole Nationale d’Ingénieurs de Brest) where he studied mechatronics. He received his Ph.D. in material science from Mines ParisTech in 2010. His research field is related to CFD applied to electrical machines, thermal spray and powder metallurgy, and advanced analysis for material characterization.
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