Cross-links between core ducts redistribute oil within the connected cooling network. Represent spacer openings, packet ends and shared cavities to establish whether the local flow requires more than parallel-channel modelling. [1] [2]
Equal total inlet flow does not imply equal cooling along each packet. Oil can leave one duct halfway up and enter another, carrying its temperature with it.
Map the actual hydraulic connections
Divide each duct at the heights where lateral access exists. Assign a pressure and oil-temperature node at those locations. Connect successive axial nodes with duct segments and connect adjacent nodes with the actual cross-links.
| Network element | Geometry to retain | Balance or evidence needed |
|---|---|---|
| Axial duct segment | Length, section and restrictions | Signed flow and pressure change |
| Lateral opening | Opening, approach and exit geometry | Transfer driven by the local pressure difference |
| Mixing node | Connected branches at that height | Mass and incoming enthalpy balance |
| Closed interface | Actual seal or blocked path | Evidence that leakage is negligible for the duty |
A cross-link can carry little flow when its end pressures are nearly equal, even if it looks large. Conversely, a small opening can matter beside unequal axial restrictions. Do not add an arbitrary fixed cross-flow fraction to every pair.
Allow transfer direction to change
Choose a sign convention and let the solution determine the direction. In a simplified linear resistance representation, the cross-flow is proportional to its local pressure difference; the resistance must represent that opening and operating range. Buoyancy and temperature-dependent fluid properties can require a nonlinear, coupled solution.
At a mixing node, use the temperature of the actual incoming branches in the energy balance. A reversal changes which temperature is upstream. Averaging neighbouring temperatures without considering mass flow can invent a cooling benefit.
Test whether the independent-channel model is adequate
Compare the connected and disconnected models under the same external boundary conditions. Examine signed branch flow and local packet temperature, not just total pressure drop. Retain local fluid evidence where the connected model predicts stagnation or reversal.
Target measurements or a detailed flow model at the connections predicted to redistribute the most oil. Check different heat-source distributions and cooling duties, since one successful rated-condition comparison may miss a cross-flow change elsewhere.
Assume a 50 kg 23ZH90 region at 1.7 T, 50 Hz: the catalogue 0.90 W/kg gives a 45 W strip-source screen [3]. Assume cp = 1,900 J/(kg·K) and prescribed steady branch flows from a separate hydraulic solution. Without cross-flow, 0.005 kg/s enters at 40 °C and leaves at 44.74 °C after receiving 45 W. With cross-flow, 0.003 kg/s at 40 °C mixes with 0.002 kg/s at 60 °C, giving the same 0.005 kg/s at 48 °C. The outlet becomes 52.74 °C. Against an assumed 50 °C outlet gate, the independent-channel estimate passes while the connected case fails. Retain the lateral mass and enthalpy exchange; a measured total flow alone cannot justify deleting it.
Spacer breaks, packet offsets and return-path openings establish cross-flow connections. Register these dimensions on the as-built cooling map; nominal channel count alone does not establish hydraulic independence.
Retain cross-links when they materially change hot spots or branch flow. Use the agreed modelling error to define where the simpler parallel-channel model remains justified.
References
- Z. Chen, Z. He and S. Wang, Transformer Iron Core Temperature Field Calculation Based on Finite Element Analysis, Energies 18, 6537, 2025. DOI: 10.3390/en18246537.
- U.S. Department of Energy, DOE-HDBK-1012/2-92, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2, 1992.
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je, April 2020, specification and typical-property tables.