This is the second paper in a two-part series, examining a methodology to positioning stator vent positions in through-flow ventilated generators.

Stator vents have been used in through flow generators for almost 100 years to reduce operating temperature. As the airflow through the vents and their cooling behaviour is complex and difficult to predict, the number of stator vents to use and exact positioning has required a trial and error approach.

Part one of the paper series discussed the Computational Fluid Dynamics (CFD) simulations, which provided data on the airflow rate and heat transfer coefficients within the generator under different vent positions and baffling.

Using the Reduced Order Models determined from the CFD data, the second part of the paper series deals with calculating the key generator temperatures. The Lumped Parameter Thermal Model (LPTM) approach allows temperatures of different design variants to be calculated very quickly, allowing an optimal vent and baffle setup to be determined.

**Lumped Parameter Thermal Models**

At the early stage of design, a method which can provide temperature predictions very quickly in order to consider many design parameters is usually preferred. The speed of these calculations come at the cost of solution accuracy and detail. At this stage, trends in the temperature are as important as being able to predict temperature very precisely. Lumped Parameter Thermal Model (LPTM) approaches are widely popular to achieve this.

Using Lumped Parameter Thermal Models (LPTMs), temperature predictions are made for the range of vent locations and housing-passage baffling considered. The Reduce Order Models (ROMs) allow air flow and heat transfer coefficients to be determined inside the generator for any combination of vent position and baffle. Therefore, the impact of these parameters on the cooling network can be accurately applied to this simplified thermal model.

This methodology serves an example of how CFD and LPTMs can be successfully used together. The ROMs obtained from the CFD modelling are specific to the generator and are therefore significantly more accurate compared to using generic correlations that do not account for specific electrical machine configurations.

The LPTM method is widely used and its methodology well documented. Described succinctly, the geometry at hand is discretised into lumps, each represented by a node. It is assumed that the temperature is uniform through each lump. The decision on the number of model nodes comes down to a trade-off between model speed (both setup and solve), versus solution accuracy and resolution.

The thermal resistances between adjacent nodes is calculated based on the geometric and material properties.

Node temperatures are then calculated by balancing the heat equation: the heat lost to adjacent nodes due to temperature difference must be equal to that entering the node both from adjacent nodes and any internal heat generation.

As the heat node of each node depends on the adjacent node temperatures, an iterative solution must be sought. An alternative method for determining the model temperatures is a direct matrix solver, which is usually preferred as it is not iterative and therefore quicker,

The LPTM approach is used for the thermal predictions in this paper.

**Generator Geometry**

As a reminder, the generator has a 500mm diameter stator, with a 500mm core length is used as the example machine. The 4-pole field wound rotor has a diameter of 356mm, the airgap being 2mm.

Specific attributes of the machine are unimportant, as this paper serves to present a method that could be applied to any generator of any size and operating conditions.

Various views of the generator are shown between Figure 1 and Figure 2.

**Node Arrangement**

The node arrangement for the model is determined based on the resolution of results required. Both symmetry and cyclic patterns can be assumed to reduce the size of the model: half of one stator slot and half of one rotor pole are modelled.

In the active core region, a radial arrangement of nodes is created that can be duplicated axially. Each radial plane consists of nine nodes in the half stator slot and two nodes in the stator lamination region, plus one for the housing. A further nine winding nodes and 4 lamination nodes are distributed in the rotor.

Additional nodes are placed in the rotor and stator windings.

**Losses**

Temperatures are predicted based upon the loss distribution inside the generator, and therefore to accurately predict operating temperatures the loses must be well understood. This is usually determined from electromagnetic FEA.

In this example case, losses are taken from a known similar machine, for which electromagnetic analysis has been performed. These losses are distributed to each node, accordingly, based on the volume and location of the nodes.

In reality, there is an impact on the generator losses when a stator vent is placed. The removal of active lamination material reduces the active core length. To maintian the same output, the core length must either be lengthened by the same amount, or the rotor must induce a greater flux to make the reamining core compensate.

This change is not very significant, and no adjustemnt in the losses is made for the presence of a vent. Nor is there any compensation to the losses according to the operating temperatures as there would be in practice due to the impact on electrical resistance. The practical pupose of the papers is to demonstarte a methodology, which can be achieved whilst making these modelling simplifcations.

With these results, it is possible to hone into the best performing regions and perform a more refined analysis.

A further analysis of the results can be made by comparing the axial stator winding temperature profiles in the core region for different scenarios.

Figure 5 compares the profile along the stator core of each stator vent position when no baffling is applied. In each case the hottest winding node is plotted.

This demonstrates a variance in the shape of the curve with a dip in the curve corresponding to the position of the vent. The hottest location is typically around three-quarters along the core. When the vent is located near this position, it has the greatest cooling impact on the hot-spot.

A similar comparison can be made using Figure 6 which shows the temperature profile when the vent is located at 75% along the core for the three baffle scenarios considered. Here the profile shapes are very similar due to the vent location being equal. However, the reduced airflow through the housing-passage has negative impact in terms of Heat Transfer Coefficient and rate of air temperature increase.

**Optimal Configuration**

From Figure 3 we can determine that the region of the design field with the lowest stator temperatures is for vent positions close to 75% along the core and with little or no baffling.

An additional batch of models were run, this time considering vent positions between 68 and 74% along the core, and baffle amounts of 0% and 10%.

The generated stator winding temperatures can be seen in Figure 4. These results indicate the best configuration is for a vent position at 72% along the core length and no baffle.

**Assumptions and Model Improvements**

This demonstration of the methodology to derive at an optimal stator vent location has been simplified for reasons of conciseness. Additional details can easily be added, such as making losses temperature dependent.

In this case, the baffle shown to not have a positive impact on temperature. However, considering different positions of the baffle (locating it immediately before the vent will have the greatest impact) would render further results and would make an interesting parameter to consider for a similar investigation.

This second and final part of the White Paper series has demonstrated how thermal predictions can be made based on the Reduce Order Models (ROMs) generated in the first paper.

Using Lumped Parameter Thermal Models (LPTMs), temperature predictions were made for the range of vent locations and housing-passage baffling considered. The ROMs allowed air flow and heat transfer coefficients to be determined inside the generator for any combination of vent position and baffle. Therefore, the impact of these parameters on the cooling network can be accurately applied to a simplified thermal model.