Application of Computational Fluid Dynamics (CFD) On

Ventilation-Cooling Optimization of Electrical Machines

Ryuichi Ujiie, Dr. Raphael Arlitt, Hirofumi Etoh Voith Siemens Hydro Power Generation

Ryuichi.Ujiie@vs-hydro.com, Raphael.Arlitt@vs-hydro.com

Abstract Ventilation-Cooling is one of the key-technologies in the design of large electrical machines with significant influence on machine size and performance. On large hydro generators experimental data are difficult to obtain and hence a combination of a scaled model test, network method and three dimensional Computational Fluid Dynamics (CFD) is applied to improve a homogeneous distribution of the air flow rates in the machine which allows to control the temperature avoiding peaks in temperature which would reduce the lifetime of the electrical machine. 1. Introduction

In large hydro generators the maximum current density and induction is limited by material behaviour. Hence the ideal power of the electrical machine scales with a typical length scale to the 4

idPth power:

. Since electromagnetic losses increase with the third

power of a typical length scale

large machines tend to have a better efficiency since

. The electro-magnetic losses correspond to sources of

heat which need to be exchanged to a coolant by convective processes at surfaces, which of course scale with a length scale squared. Hence with larger machines the ratio of losses and heat sources to the heat transferred at surfaces increases linearly with a typical length scale L

. These scalings, see Henneberger [5], show clearly the

rising difficulties of exchanging heat and the need to improve ventilation-cooling in large machines.

Since an increased air flow rate also leads to increased windage losses, the only option is to improve the air flow

rate distribution to obtain a more efficient ventilation-cooling. The final goal is to reach a flat temperature profile and limitation of the maximum temperatures to increase the lifetime of the insulation system and hence the lifetime of the electrical machine.

The above can be reached by doing a scaled model test with an experimental analysis of flow rates, windage losses and temperatures for varying geometries. The obtained design optimizations were then applied to the actual machine, based on experience.

Since it is not possible to build a scaled model for every project due to time limitations and costs, and since only limited details can be obtained in these experiments, the model experiments can only give a basic understanding of the flow and heat transfer processes. There are further difficulties to keep the design homologous with regard to geometry and similar to Reynolds and Mach number. Hence the model experiment has limits to extrapolate statements onto project geometries.

On large scale machines only measurements of temperature at a few locations distributed over the circumference are obtained. For the flow rate only an integral value is measured behind the cooler and does not give information about the distribution of air flow in the machine. Windage losses are also only obtained integrated for the complete generator by a calorimetric method.

Experience from a scaled model, for example flow resistances and heat transfer coefficients, are applied to a flow and heat transfer network model. The network method has been commonly used as an analytical tool, both for ventilation and cooling. In this method, equivalent flow resistances and air flow paths for ventilation analysis, and equivalent thermal resistances and heat flow paths for thermal analysis respectively are defined, and combined through a network.

The model is based on experience and data from experimental investigations and small scaled machine models. The network resistances are based on the models for elements of air flow or thermal transfer as shown in more detail in [2]. Using the network method the air flow

rates in each part and temperature at each node are calculated. The flow network is based on internal flow pressure drops taken from experiments

with a flow resistance of ς , which are at a sufficient high Reynolds number only dependent on geometry. These resistances are taken for example from Idelchick [3], but they are limited for internal flow configurations and cannot be used to describe vortex structures, i.e. in the inlet of the hub and in the recirculation zone. In addition does it limit the thermal transfer model to exchange heat on experimental investigated geometries with a preferred direction of air flow, which is not the case at the end winding. This flow also cannot be modeled by an internal flow pressure drop formulation. Due to the complex geometries and flow field, this method is only a crude estimate of the situation in the electrical machine. The results of the network method could only be calibrated to the integral measurements described earlier.

Thus, since tools and data applied for ventilation-cooling are essentially based on the experiences as mentioned above, new ideas for the improvement could only be proposed and applied limited to the extent of experiences.

Computational Fluid Dynamics can bridge the gap to apply experience to obtain new designs, since CFD is based on first principles, the underlying physical equations, which describe the conservation of mass, momentum and energy. It is an effective tool for design optimization, but since the equations are also solved on some kind of discretization to a finite number of nodes and some equations need to be closed by models, it is of highest importance to have the possibility to compare the results of CFD with the existing approaches. These are experiment and network calculation. In these investigations the knowledge how to discretise to a finite grid and which model closure, for example for turbulence, to take, is built. From these fundaments it is possible to apply CFD to a changed geometry with its general approach.

Table 1: Description of interactions of existing methods with CFD

Table 1 shows the interaction of the existing methods to calculate the temperatures of the critical parts in the machine by knowledge of the losses and air flow. Here CFD is also applied to detailed geometries, where its results are incorporated into the analytical flow and thermal networks, to improve the flow resistances and heat transfer coefficient assumptions.

But CFD enables one further advantage since it allows a tight connection of the loss calculation to the flow field and temperature calculation. This connection, so called Conjugate Heat Transfer (CHT), investigated e.g. by Jilani [4], dismisses the need to fix a boundary condition on the thermal exchange surfaces. Since setting of the boundary condition of either known temperature or fixed or prescribed heat flux at the surface is part of the result that needs to be obtained. Using the conservation equation for energy on fluid and solid and setting the velocities to zero, an heat transfer equation is obtained, in which only the derivative of the thermal conductivity needs to be modeled continuously at the boundary to avoid numerical difficulties. Hence a Fourier equation is obtained:

. Since the heat transfer coefficient alpha and its

dimensionless formulation in Nusselt number (Nu)

depends on the temperature gradient at the wall, it is very important to have a discretization at the wall that corresponds to the near wall turbulence model and wall functions for velocity and temperatures.

Another new possibility is to obtain the windage losses in a simple post processing by analysis of the momentum due to the frictional and normal forces in spite to the empirical formulation based on experiments that has been applied in the past:

, where n stands for the revolution speed and D signifies the stator bore diameter. All the experience is taken into a formulation based on Λ , which may depend on dimensionless flow rates and geometry ratios.

To obtain the windage losses due to the analysis of the wall forces and their moments M multiplied by the angular velocity ω

signifies the step from an empirical formulation in the past to a result directly obtained from analysis based on first principles.

2. Past Methods in Ventilation-Cooling of Electrical Machines

As already mentioned, on site measurements only provide the integral data on the air flow rate, temperature at selected spots and the total windage losses. More details as e.g. air flow and temperature distribution and the windage losses on certain parts of the machine are not available.

But the available data could be applied to calibrate a network air flow and thermal flow model. The air flow network is shown in Figure 1, where the values in the sketch stand for the volume flow rate in /s and the flow resistances are represented by

3m

while the pumping action of the rim due to the Euler relation for a rotating system

caused by the increased circumferential velocity at a larger outer diameter is represented by a fan sketch

2u

, while the distribution of air in the stator duct is done following Hak [1].

Hence the network technique is set up to hit the air flow rate and temperature at one location, after the heat exchanger for the air flow rate and the temperature at a certain location at the stator winding.

Figure 1: Air flow network model of a hydro generator. Still there is no possibility to confirm the assumptions

for the detailed dynamic pressure drop coefficients. Only the application of more detailed measurement devices or more general applicable numerical models could improve this situation.

3. Confirmation of Accuracy of CFD With the application of CFD a more universal

approach based on physical principles of conservation of mass, momentum and energy was followed. Also these general equations need to be solved on a finite number of nodes and certain physical processes like turbulence need closure models. Uncertainty of modeling is shifted from the extrapolation of results of detail models to complex geometries onto the choice of grid resolution and closure models. This uncertainty can only be minimized if the CFD methods are applied to an experimental setup that is investigated in detail and compared to the numerical obtained results. Therefore a scaled model test was built in two configurations, for closed and open ventilation circuit, of which the open setup is shown in Figure 2.

Figure 2: Scaled model test of air cooled generator.

The model was downscaled by a factor of 1:4.5 in all

major dimensions. Revolution speed was increased to obtain the original peripheral speeds. The same Reynolds number could not be adjusted since the flow velocity would have been by a factor of 4.5 higher than in the original machine and compressible effects could not been neglected anymore. To allow access for measuring devices also the height of detail geometries as stator ducts could not be scaled down.

The set up was equipped with measurement devices, as hot wire anemometers, thermocouples, flow velocity anemometers (Figure 3), pressure transducers and an infrared camera to obtain the air flow distribution over the axial height of the machine for each stator core cooling duct, heat transfer coefficients at coil ends and temperatures of the coils.

Figure 3: Air flow measurements devices on each stator core cooling duct.

The results of the velocity distribution over stator

length are shown in Figure 4, where the flow velocity is shown at each air duct number, parameterized and increasing with different hub inlet openings of 26%, 42% and 100%.

Figure 4: Air velocity at each cooling duct for different

hub openings of experimental setup

A CFD calculation for the scaled model was conducted and the detailed results of flow velocities, heat transfer coefficients and temperatures of the experiments were used to confirm the accuracy of the numerical model. The results for velocities at the stator core over axial length are shown in Figure 5. Different mesh resolutions and turbulence model where compared, and final results where obtained with a standard k-ε turbulence model.

To summarize the agreement of numerical and experimental data, a deviation of flow rate of 7%, pressure and core duct velocity at the average of 5% where obtained.

Figure 5: Air velocity at each cooling duct for different hub openings obtained from numerical simulation.

After the CFD calculation its sub models and

resolution is calibrated and accuracy is confirmed in one set up, the method is applicable to other projects. The knowledge for critical regions for resolution is taken from the scaled model and applied to do numerical forecasts of large scale projects which is shown in the following section.

4. Transfer to large scale projects

The accuracy of the universal approach to estimate

flow rates, temperatures and windage losses by CFD was secured on the small scale model test. This knowledge is now taken to predict flow and thermal properties and losses on large scale geometries. Therefore design tools are created to build up a three dimensional geometry shown in Figure 6 on which a combined analysis of solid and fluid is carried out.

Figure 6: Solid geometry of axial half of one pole

pitch.

Figure 7: Solid geometry meshed for thermal analysis. Figure 7 shows the meshed solid geometry. On these

nodes the heat conduction with sources from the electromagnetic losses is solved. This resolution of the grid is less restrictive than the one for the fluid as shown in Figure 8. Special effort is taken to model the boundary layers, so that the wall functions for the turbulent velocity and temperature boundary layer can be applied correctly. Hence the fluid mesh is larger in node number by a factor of 2.

Figure 8: Fluid meshed for flow and thermal analysis.

Since heat sources are not distributed equally on the

solid components, we define regions on stator and rotor components where a mean loss is specified as shown by the different colors in Figure 9 and 10.

Figure 9: Prescription of homogeneous losses on four

different parts of the stator core.

Figure 10: Prescription of homogeneous losses on four

different parts of the stator winding.

Here CFD can supplement the information about the flow and thermal field by enabling the investigation of free flow structures like vortices in the end winding section, hub or recirculation zone. This insight could not be obtained in the past since the resolution of measurement devices is fairly limited, and the network method not applicable to these flow phenomena.

5. Interaction of CFD with existing methods

Geometry optimizations are done using CFD. Effects of these variations can be seen on secondary flow structures, which may cause losses. Virtual measurement devices that cannot be realized experimentally can be set at every node, as shown in the Figures 11 and 12. For example the heat transfer coefficients (Figure 15) follow directly in a post processing of the wall temperature gradient. They can be averaged over homogeneous regions and applied to improve the network method assumptions. Further additional data like windage losses can be evaluated on parts of the geometry as shown in Figure 14, which is used to improve the faster empirical relations.

Figure 11: Velocity component illustrated as vectors.

Figure 12: Velocity illustrated by magnitude.

Main results for the temperature in the pole and stator

winding are obtained in detail and exemplarily shown for the upper half of the stator winding in Figure 13.

Figure 13: Temperature on stator winding.

Figure 14: Windage losses at geometry parts, hub (green), rim (blue) and pole (red).

Figure 15: Heat transfer coefficients on rotor hub, rim and

pole. 6. Summary

It has been demonstrated that CFD is a valuable addition to the network method for the design optimization of electrical machines, if the accuracy is once confirmed on a model test, which is equipped with detailed measurement devices. Then CFD can be used as a standalone tool to compute flow, heat transfer, temperatures and even windage losses. This insight of flow and heat transfer is used to optimize the geometry, to obtain flat temperature profiles, which avoids life-time decreasing temperature peaks. Further more results of this method are used to improve assumptions in the much faster network model, so that these methods supplement each other. 7. References [1] J. Hak, “Kanal mit Abzweigungen; Ein Beitrag zum Ventilationsproblem des Turbogenerators”, Elektrotechnik und Maschinenbau, Heft 15/16, Wien, 1.8.1965, Jahrgang 73 [2] Ali Farschtschi, “Berechnung der Temperaturen in elektrischen Maschinen”, Bosch Technische Berichte, Bosch-Group, Heft 55, 1992 [3] E. Fried and I.E. Idelchick, “Flow Resistance: A Design Guide for Engineers”, Hemisphere Publishing Corporation, 1992 [4] G. Jilani, S. Jayaraj, M. Adeel Ahmed, “Conjugate forced convection-conduction heat transfer analysis of a heat generating vertical cylinder”, International Journal of Heat and Mass Transfer, Elsevier, 45, 2002, p. 331-341 [5] G. Henneberger, “Elektrische Maschinen III, Rechnergestützter Entwurf Elektromagnetischer Felder“