Solutions
Development of 1D-model of turbine generator rotor cooling system
The article demonstrates the procedure and results of calculation of 1D-model of turbine generator rotor air cooling system in REPEAT software and comparison of calculation results with thermal-hydraulic calculation in other software in 3D-production.
Development of 1D-model of turbine generator rotor cooling system
Turbine generators serve as energy sources in thermal and nuclear power plants and today retain the largest share in generating capacity worldwide.
Due to the strict design requirements for dimensions and the need to provide a large unit power, turbine generators are the most loaded electrical machines according to the specific power criterion, which is accompanied by significant heat generation in the windings and core.
At the same time, electrical insulating materials are used in the design of any electrical machine, which are extremely sensitive to high temperatures.
In order to ensure the service life of 40 years or more required for turbine generators, it is necessary to strictly monitor temperatures of turbine generators active parts. This is achieved by using extremely complex cooling systems with a large number of small-section channels forming branched hydraulic circuits.
Thermal-hydraulic calculations of such cooling systems in 3D formulation are extremely demanding on computing power, 1D modeling can be alternative options in this case.
The advantages of this approach compared to 3D simulation include:
Thermal-hydraulic calculations of such cooling systems in 3D formulation are extremely demanding on computing power, 1D modeling can be alternative options in this case.
- less demanding on computing resources;
- less labor input when modeling systems consisting of a large number of similar components;
- greater flexibility and ease of editing.
This allows to simulate significantly more complex systems compared to 3D production, as well as significantly reduce the design time of electrical machines, especially during the preliminary design stage.
Study objectives:
1. Development of simulation 1D-model for determination of parameters of turbine generator rotor cooling system;
2. Analysis of the possibility of using 1D models to evaluate the operation of cooling systems of electrical machines.
1. Development of simulation 1D-model for determination of parameters of turbine generator rotor cooling system;
2. Analysis of the possibility of using 1D models to evaluate the operation of cooling systems of electrical machines.
Initial data
| Parameter | Unit of measurement | Value |
| Current in each conductor | А | 1240 |
| Cooling air temperature at the inlet to the underflow channel | °C | 40 |
| Arithmetic mean roughness of axial channel walls | mm | 0,1 |
| Arithmetic mean roughness of radial channel walls in conductors | mm | 0,5 |
| Volumetric air flow rate through all channels: for design point 1 | m3/s | 0,020 |
| Volumetric air flow rate through all channels: for design point 2 | m3/s | 0,025 |
| Volumetric air flow rate through all channels: for design point 3 | m3/s | 0,030 |
| Volumetric air flow rate through all channels: for design point 4 | m3/s | 0,035 |
| Volumetric air flow rate through all channels for design point 5 | m3/s | 0,040 |
Table 1 - Model parameters
Figure 1. Sketch of the design area
Figure 2. General view of the design area in other software
Figure 3. Calculation results in other software
Simulation model description
A single-mass model with averaged characteristics is chosen to simulate the design area shown in Figure 1, Figure 2 and Figure 3.
The combination of conductors and insulation is a single thermal mass with channels for intensive air cooling.
The temperature distribution inside the thermal mass was not taken into account.
The design area substitution diagram is given in Figure 4.
Heat release in conductors is simulated by “Heat flow source” block, the input of which receives a value in accordance with the following equation describing the changes in the amount of heat due to the passage of electric current
\( Q = I^2 \cdot R = \frac{I^2 \cdot r_t \cdot L}{S} = \frac{I^2 \cdot \left( r_{20} \cdot \left( 1 + 0.004 \cdot (t - 20) \right) \right) \cdot L}{S}, \)
where \( I \) — conductor current, А;
\( R \) — conductor resistance, Ohm
\( r_t \) — resistivity \( (\text{Ohm} \cdot \text{mm}^2)/\text{m} \);
\( r_{20} \) — resistivity at temperature 20 °C, \( (\text{Ohm} \cdot \text{mm}^2)/\text{m} \);
\( t \) — conductor temperature, °C;
\( L \) — conductor length, m;
\( S \) — - conductor cross-section area, mm\(^2\).
Temperatures in the design area were determined by simulating convective heat transfer between the channel walls and the cooling air flowing therein.
The model was calculated using the cosimulation method in SAPFIR and REPEAT software products.
The task is divided into two components: calculation of air flow in rotor winding channels and calculation of convective heat exchange of a set of conductors and air in channels, each of which is solved in the corresponding software product.
SAPFIR
SAPFIR simulates and calculates the air flow taking into account the specified geometry of the channels. According to the initial data, the pressure profile is determined.
Pressure losses in the design area are due to friction, rotation, diameter change and tee losses.
Rotation losses [1, p. 287] and diameter changes [1, p. 126, 165] are calculated in accordance with [1].
Impulse equation used in SAPFIR to determine gas flow rate [3].
\( \frac{l}{s} \cdot \frac{df}{d\tau} - \frac{f^2}{2 \rho s^2} \left( 1 + \xi \right) + kf + \Delta p + \rho g \Delta z = 0 \)
where:
\( L \) — section length;
\( f \) — mass flow rate;
\( \frac{df}{d\tau} \) — flow rate derivative in time;
\( s \) — cross-section;
\( \rho \) — density;
\( \xi \) — hydraulic loss factor;
\( k \) — coefficient proportional to \( \sqrt{p} \), entered to linearize the flow rate relationship at \( \Delta p \to 0 \);
\( \Delta p \) — pressure decrease in the circuit section;;
\( g \) — gravity factor;
\( \Delta z \) — height difference in chain section.
\( \xi = \xi_m + \xi_{тр} \)
where \( \xi_m \) — coefficient of local hydraulic losses (losses in constrictions/extensions, turns and tees), \( \xi_{тр} \) — friction loss factor.
Coefficient of hydraulic friction losses is calculated by the formula:
\( \xi_{тр} = \lambda \frac{L}{d} \)
where:
\( \lambda \) — friction factor,
\( d \) — hydraulic diameter of the channel.
Friction factor [2]:
\( \lambda = \frac{1}{\left(1.8 \log_{10}\left(\frac{6.9}{Re} + \left(\frac{r}{d}\right)^{1.11}\right)\right)^2} \)
where \( Re \) — Reynolds number;
\( \frac{r}{d} \) — relative roughness of the channel.
Air flow in rotor winding channels is simulated using CMS standard library blocks: “Node”, “Channel”, “Boundary condition”, “Makeup”, “External heat source” (Figure 5).
REPEAT
Convective heat transfer is calculated in REPEAT software.
Air parameters (temperature, speed) are transferred from SAPFIR to “Convective heat transfer with heat transfer coefficient calculation” blocks, where the amount of heat transferred is calculated. The resulting amount of heat removed by air from the surface of the conductors is transmitted to SAPFIR, thus completing the calculation of heat transfer equations.
In order to calculate it, the corresponding block properties shall be filled in: “Surface Area”, “Convection Type”, “Wrap Type”, “Feature Size”, “Pipe Length”, “Wetted Perimeter” and “Flow Area”.
The simulation model executed in REPEAT is given in Figure 6.
Figure 4. Equivalent circuit
where:
\( Q_1 \) — amount of heat generated in conductors during current flow;
\( Q_k \) — amount of heat removed from the set of conductors due to air cooling (13 channels);
\( Q_1 \) — amount of heat generated in conductors during current flow;
\( Q_k \) — amount of heat removed from the set of conductors due to air cooling (13 channels);
Figure 5. Thermal-hydraulicmodel of cooling channels in SAPFIR
Figure 6. Convective heat transfer model in REPEAT software
1 - Calculation of heat flows from cooling channels; 2 - Calculation of heat flow from current flow; 3 - Thermal mass of conductors
Simulation results
The results of parameters calculation (average temperature of conductors, total heat flow, pressure drop in channels, air temperature at the outlet from channels, parameters of axial and radial channels) and deviations from test data are given in Tables 2 - 8. The results of CFD calculation in other software were used as verification data.
Table 2 - Average temperature of conductors
Table 3 - Total heat flux
Table 2 - Average temperature of conductors
