Core-duct flow follows the pressure and density balance of the connected oil loop [1]. Include the heated winding and both duct openings before solving for flow direction, then use that signed flow in the thermal model. [2] [3]
Allow the duct flow to have either sign. Prescribing upward flow from the outset prevents the model from answering the reversal question.
Compare the competing vertical paths
Trace the core duct from its lower opening to its upper opening, then trace the available return paths. Record the oil-temperature profile and hydrostatic head in each. The circulation-driving difference depends on the density profiles around the loop, not simply on the hottest surface temperature.
| Quantity on the flow map | Evidence needed | Interpretation |
|---|---|---|
| Lower and upper opening pressures | Common pressure reference and elevations | External forcing on this branch |
| Duct oil-temperature profile | Core heat input and incoming-oil condition | Density and buoyancy along the branch |
| Neighbouring winding/return path | Its heat input and hydraulic resistance | Competing head that sets loop circulation |
| Signed local velocity | Resolved model or suitable test evidence | Upward, stagnant or downward state |
In a branch pressure balance, keep hydrostatic contribution and friction consistent with the elevation and flow sign. A friction term should oppose the calculated flow. Treating it as a fixed positive drop can make the reverse solution impossible numerically.
Vary the mixed heating duty
Examine core excitation and winding load separately within their permitted combinations. At low load, core heating can remain relevant while the winding contribution changes substantially. Under another duty, winding-driven circulation can dominate the boundary conditions beside the core.
Use temperature-dependent oil properties over the credible range. A constant-property or linearized-density approximation needs a stated application range, especially when the paths have very different temperatures.
Treat zero and reverse flow as candidate states of this loop. Establish common elevation/pressure references and the density distribution in each branch; an imposed positive inlet velocity cannot test whether natural circulation reverses. [1]
Verify the zero-flow boundary
Locate cases where the predicted branch flow approaches zero and perturb the relevant heating and boundary conditions around them. Examine stability and whether the model changes upstream thermal conditions correctly after reversal. A solver that uses the old inlet temperature for negative flow can misrepresent the new state.
Assume a 20 kg 23ZH90 region: its catalogue 0.90 W/kg at 1.7 T, 50 Hz gives an 18 W strip-source screen [4]. Hydraulic assumptions: two 2 m vertical paths, mean duct density 875 kg/m³, return density initially 885 kg/m³, no other imposed head, g = 9.81 m/s² and resistance Δp = Kṁ|ṁ| with K = 10⁶ Pa·s²/kg². Upward-positive driving head is gH(ρreturn − ρduct) = 196.2 Pa, giving ṁ = +0.0140 kg/s. If adjacent winding heat lowers mean return density to 870 kg/m³ while duct density is held fixed for this comparison, head becomes −98.1 Pa and ṁ = −0.00990 kg/s [1]. The changed return path reverses this simplified loop. Reassign the upstream temperature at the new inlet; near zero flow, solve the coupled heat/conduction problem rather than divide 18 W by a vanishing mass flow.
Spacer openings, packet alignment and winding-to-core passage geometry determine the connected buoyancy loop. Verify their installed state when investigating reversal; a changed guide or support can alter the branch before the magnetic source changes.
Map where flow changes direction, which external path drives it and the resulting packet temperature. Judge the reversed or stagnant case on its actual heat removal and thermal duty.
References
- U.S. Department of Energy, DOE-HDBK-1012/3-92, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 3, 1992.
- 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.