Influence of Complex Fluid Flow on Temperature Distribution in the Rotor Region of Large Hydrogenerator under the Rotor Rotation

Ventilation cooling design is one of the key technologies during the design of large hydrogenerator. With the increase of hydrogenerator capacity, the overheating problem of rotor region become more and more serious. In this paper, a 250 MW hydrogenerator is analyzed. The transient electromagnetic field of the hydrogenerator is calculated. The losses (heat sources) of rotor components in the rotor region of the hydrogenerator are determined. Three-dimensional fluid and thermal coupled mathematic model of the hydrogenerator rotor region is established. The rotor rotation of the hydrogenerator is considered. The distribution of complex fluid velocity in the rotor region is calculated using the finite volume method. The influence of fluid velocity in the different directions on the temperature of the rotor excitation winding is studied under the different flow rates in the rotor region. The surface heat-transfer coefficient distribution of the rotor components is determined. The temperature distribution of the rotor excitation winding, rotor pole body, rotor press plate, rotor damping bar, and rotor end ring is obtained. The calculated temperature results match well with test values. These provide an important reference for the rotor structural design and optimization of larger hydrogenerator.


I. INTRODUCTION
Hydroelectric power generation is one of the cleanest methods of power generation. Hydrogenerator is the core equipment in the entire hydropower system, which plays a vital role. With the rapid development of hydroelectric power generation technology, the capacity of hydrogenerator continues to increase. The efficiency of hydrogenerator and the utilization of materials improve obviously. However, as the capacity of hydrogenerator increases, the overheating problem of hydrogenerator rotor region becomes more and more serious. It has seriously threatened the stability, safe operation, and service life of hydrogenerator. Furthermore, the heat of the rotor components is taken away by the complex fluid flow in the rotor region. Therefore, a study of influence of complex fluid flow on temperature distribution in the rotor region of large hydrogenerator is of great significance when the rotor rotation is considered.
In recent years, numerous studies researched on the physical field in the large generator. For example, C. Carounagarane et al studied the temperature distribution of the hydrogenerator under 10% and 20% continuous overloads through the coupling thermal and fluiddynamical analysis [1]. H. C. Dirani et al studied the impact of rotor interturn short circuit on radial flux density, radial force density, unbalanced magnetic pull, and electromagnetic torque of a 74-MVA industrial large hydrogenerator with 76 poles [2]. G. Traxler-Samek et al describes an analytical algorithm for the calculation of currents and corresponding losses in the damper winding [3]. M. Ranlöf et al proposed a permeance model that can be employed to estimate the no-load damper current loss and voltage waveform harmonics in large hydrogenerators [4]. A. Z. Gbé gbé et al studied a large hydrogenerator modeling method that provides an excellent compromise between accuracy and speed [5]. S. E. Dallas et al presents an investigation of the behavior of a 200-MVAsynchronous hydrogenerator during interturn stator fault. It focuses on the affection to the electromagnetic magnitudes, such as the currents and the electromagnetic torque [6]. J. C. Akiror et al studied rotational flux distribution in the stator of the hydrogenerator under different operating conditions [7]. T. Øyvang et al proposed and verified an air-cooled hydrogenerators heating network for real-time monitoring and optimal control [8]. S. Li et al studied the flux and loss distributions in the end region of large generators by transient 3-dimensional finite-element method. The in-plate loss contribution from the flux in the Z direction on the out most several packets of the stator laminations is considered. Parametric study is carried out to evaluate the effectiveness of various candidate designs in reducing the losses in the end region of large generators [9]- [13]. Some other experts extensively studied hydrogenerator [14], [15], but very few focused on the influence of complex fluid flow on temperature distribution in the rotor region of large hydrogenerator under the rotor rotation.
This paper is the continuation of the reference [16]. In reference [16], it focused on the influence of different rotor structures on the temperature distribution in the rotor region of hydrogenerator. However, this paper focuses on the influence of fluid velocity in the different directions on the temperature distribution of the rotor components under the different flow rates in the rotor region of hydrogenerator. In this paper, a 250 MW hydrogenerator is analyzed. The transient electromagnetic field of the hydrogenerator is established. The losses (heat sources) of rotor components in the rotor region of the hydrogenerator are determined. Three-dimensional fluid and thermal coupled mathematic model of the hydrogenerator rotor region is established. The rotor rotation of the hydrogenerator is considered. The distribution of complex fluid velocity in the rotor region is calculated using the finite volume method. The influence of fluid velocity in the different directions on the temperature of the rotor excitation winding is studied in detail under the different flow rates in the rotor region. The surface heattransfer coefficient distribution of the rotor components is determined. The temperature distribution of the rotor excitation winding, rotor pole body, rotor press plate, rotor damping bar, and rotor end ring is obtained. It provides an important reference for the rotor structural design of larger hydrogenerator. Fig. 1 gives this 250MW hydrogenerator unit. Fig. 1(a) shows the hydrogenerator unit. Fig. 1(b) shows the hydrogenerator rotor. According to the actual structure of the 250MW hydrogenerator, the mathematical model of two-dimensional transient electromagnetic field is established in the 250MW hydrogenerator [17]. Fig. 2 gives the solved region of the two-dimensional transient electromagnetic field of the hydrogenerator. Fig. 3 shows the meshing map. Table 1 shows the basic parameters of this hydrogenerator.      Table 2 shows the additional loss of the rotor magnetic pole surface.

III. ESTABLISHMENT OF THREE-DIMENSIONAL FLUID AND THERMAL COUPLED MATHEMATIC MODEL OF HYDROGENERATOR
Fig. 5 shows the ventilation system of this hydrogenerator. It includes the stator core, stator winding, rotor exciting winding, rotor yoke ventilation duct, magnet yoke, rotor support, wind plate, cooler, etc. According to the actual structure of the hydrogenerator rotor region, threedimensional fluid and thermal coupled model of rotor region is established, as shown in Fig. 6. Fig. 6(a) shows the solving region of hydrogenerator rotor. Fig. 6(b) gives the rotor components. It includes mainly the rotor excitation winding, rotor magnetic yoke, rotor support plate, rotor pole body, rotor damper bar, rotor end ring, rotor press plate, and rotor pole body insulation, etc. In Fig. 6(a), x direction represents the circumferential direction of the hydrogenerator, y direction represents the radial direction of the hydrogenerator, and z direction represents the axial direction of the hydrogenerator. Cold air from cooler enters into the inlet of the rotor region. After cooling the rotor components, the hot air flows out from the outlet of the rotor region. The rotation speed of the hydrogenerator rotor is 68.2r/min. The fluid temperature of the rotor region inlet is 40°C under the rated load condition. In the hydrogenerator rotor region, the equations for the 3-D fluid and thermal coupled analysis model in the hydrogenerator rotor region are given as follows [18]- [21]: where v is velocity vector,  is fluid density, t is time, p is static pressure, g  and F are gravitational body force and external body forces,  is stress tensor, I is the unit tensor,  is the molecular viscosity, j J is the diffusion flux of species j , h S includes the heat of chemical reaction and any other volumetric heat sources, k is kinetic energy of turbulence, t  is the turbulent viscosity coefficient, eff k is the effective conductivity, k G is the generation rate of the turbulence,  is diffusion factor, k  and   are Planck constants, 1 G  and 2 G  are constants.

IV. 3-D FLUID AND THERMAL COUPLED ANALYSIS MODEL IN THE HYDROGENERATOR ROTOR REGION
This paper focuses on the loss of rotor magnetic pole surface, the loss of rotor exciting winding, complex fluid velocity, and temperature distribution of rotor components in the rotor region of large hydrogenerator. When the problems of fluid flow and heat transfer are solved, the finite element method is not as mature as the finite volume method in terms of the discrete processing method of convection term and the original variable solution method of incompressible fluid. The complex fluid velocity and the temperature distribution of rotor components are calculated using the finite volume method in this paper. In the 3-D fluid and thermal coupled analysis model in the rotor region of hydrogenerator, the loss values from electromagnetic field calculation are applied to the rotor components as heat sources in the temperature field. The rotor rotation of the hydrogenerator is considered. After solving the fluid and thermal equations of fluid-solid conjugated heat transfer, fluid velocity and temperature distribution are obtained in the rotor region of hydrogenerator [22]- [27]. The influence of fluid velocity in the different directions on the temperature of the rotor excitation winding is studied under the different flow rates in the hydrogenerator rotor region. In Fig. 7, the highest fluid velocity is 80m/s and it appears in the outlet of the rotor region. The highest temperature of the hydrogenerator rotor region appears in the rotor excitation winding. The fluid velocity between the rotor magnetic poles affects directly the temperature distribution of the rotor excitation winding. When the hydrogenerator rotor rotates, the distribution of fluid velocity between the rotor magnetic poles is very complicated. In order to study the influence of fluid velocity in the different directions on the temperature of the rotor excitation winding, three sample lines are selected between the rotor magnetic poles, respectively. Three black sample lines A, B, C locate around the leeward side of the rotor excitation winding. Three red sample lines D, E, F locate around the windward side of the rotor excitation winding, as shown in Fig. 8. The synthetic fluid velocity and the fluid velocity in different directions on these sample lines are obtained when the fluid velocity of rotor region inlet is v1=2.5m/s, v2=2m/s, and v3=1.5m/s, respectively. The influence of fluid velocity in different directions on the temperature of the rotor excitation winding is studied in detail.  In Fig. 9 and Fig. 10, fluid velocity fluctuates up and down along the axial direction. Since cooling fluid flows out from the rotor yoke ventilation duct, it results in a higher fluid velocity around the outlet of the rotor yoke ventilation duct. The fluid velocity is also relatively high near the rotor end region. As the fluid rate of rotor region inlet increases, the fluid velocity around the leeward side and windward side of the rotor excitation winding increase accordingly at the same position. When the hydrogenerator rotor rotates, the fluid velocity around the windward side of the rotor excitation winding changes obviously along the axial direction.

A. DISTRIBUTION OF FLUID VELOCITY IN THE
The temperature of the rotor excitation winding is relatively high in the rotor region of the hydrogenerator. In order to study the contribution of fluid velocity in the radial direction, circumferential direction, and axial direction to the cooling of the rotor excitation winding, Fig. 11-Fig. 16 give the distribution of fluid velocity in the radial direction, circumferential direction, and axial direction around the windward side and leeward side of the rotor excitation winding. Fig. 11 and Fig. 12 show the distribution of fluid velocity in the circumferential direction around the leeward side and windward side of the rotor excitation winding. The rotor rotation direction is clockwise and fluid velocity in the circumferential direction is negative. The distribution of the fluid velocity in the circumferential direction is basically the same along the axial direction under the different flow rates. The rotor rotation drives the fluid flow in a circumferential direction. The change of the fluid velocity of rotor region inlet has little effect on fluid velocity in the circumferential direction. There is a certain difference of fluid velocity in the circumferential direction around the windward side and the leeward side of the rotor excitation winding. The fluid velocity in the circumferential direction fluctuates obviously around the windward side of the rotor excitation winding, while the fluid velocity in the circumferential direction is relatively stable around the leeward side of the rotor excitation winding along the axial direction within the range of 0m~0.98m. The fluid velocity in the circumferential direction drops obviously near the rotor end region.   It can be seen from Fig. 9-Fig. 16 that the change of the fluid velocity between the rotor magnetic poles affects directly the temperature distribution of the rotor excitation winding as the fluid velocity of the rotor region inlet increases. The average values of the synthetic fluid velocity, fluid velocity in the circumferential direction, fluid velocity in the radial direction, and fluid velocity in the axial direction are compared under the different flow rates, as shown in Table 3. It can be seen from Table 3 that the fluid velocity in the circumferential direction accounts for a large proportion of the synthetic fluid velocity around the leeward side and windward side of the rotor excitation winding. The fluid velocity in the circumferential direction remains basically unchanged as the fluid velocity of the rotor region inlet increases. It plays a major role in the cooling of the rotor excitation winding. The fluid velocity in the radial direction is relatively high around the windward side, which cannot be ignored in the cooling of rotor excitation winding. The fluid velocity in the axial direction has little effect on the cooling of rotor excitation winding. The fluid velocity in the radial direction and axial direction accounts for a small proportion of the synthetic fluid velocity around the leeward side and windward side of the rotor excitation winding.  Fig. 17 shows the temperature distribution of rotor pole body, rotor press plate, rotor damping bar, rotor pole shoe, and rotor end ring in the hydrogenerator rotor region. The highest temperature of these components appears in the rotor press plate and it is 120°C. The temperature of the rotor pole body is low around the outlet of the rotor radial ventilation duct. Fig. 18 shows the surface heat-transfer coefficient distribution of the rotor excitation winding when the fluid velocity of rotor region inlet is 2m/s. The maximum surface heat-transfer coefficient of the rotor excitation winding is 120 W· (m 2 ·°C) -1 . The surface heat-transfer coefficient distribution of the rotor excitation winding is uneven along the axial direction. Fig. 19 shows the temperature distribution of the rotor excitation winding when the fluid velocity of rotor region inlet is 2m/s. The highest temperature of the rotor excitation winding appears on the leeward side and it is 132°C. The average temperature of the rotor excitation winding is 106°C. The measured average temperature of the rotor excitation winding is 108.6°C. The measured value and calculated result of the temperature of rotor excitation winding are shown in Table 4. The calculated result is close to the measured value. It shows the calculated result is accuracy and the calculated method is reliable.

Rotor pole body
Rotor press plate Rotor end ring

V. CONCLUSION
In this paper, the influence of fluid velocity in the different directions on the temperature of the rotor excitation winding is studied under the different flow rates in the rotor region. The calculated temperature result agrees well with the measured value. Fluid velocity in the circumferential direction accounts for a large proportion of the synthetic fluid velocity around the leeward side and windward side of the rotor excitation winding. The fluid velocity in the circumferential direction remains basically unchanged as the fluid velocity of the rotor region inlet increases. It plays a major role in the cooling of the rotor excitation winding.
The fluid velocity in the radial direction is relatively high around the windward side, which cannot be ignored in the cooling of rotor excitation winding. The fluid velocity in the axial direction has little effect on the cooling of rotor excitation winding. The fluid velocity in the radial direction and axial direction accounts for a small proportion of the synthetic fluid velocity around the leeward side and windward side of the rotor excitation winding.
The highest temperature of rotor press plate is 120°C. The temperature of the rotor pole body is low around the outlet of the rotor radial ventilation duct. The maximum surface heat-transfer coefficient of the rotor excitation winding is 120 W· (m 2 ·°C) -1 . The surface heat-transfer coefficient distribution of the rotor excitation winding is uneven along the axial direction. The highest temperature of the rotor excitation winding appears on the leeward side of the rotor excitation winding and it is 132°C. The average temperature of the rotor excitation winding is 106°C.