In an oil-filled power transformer the ageing rate of the insulating paper rises exponentially with temperature. What sets the life is therefore not the mean but the hottest spot — and that spot is usually in the upper part of the winding, in a place that cannot be instrumented.
How the oil flows
Natural circulation (ONAN). The oil warms in the winding, rises, cools in the radiator and descends. It is driven entirely by buoyancy, so this is a classic natural convection problem giving a slow, stratified flow.
Forced circulation (OFAF/ODAF). With a pump. It provides higher cooling capacity, but how the flow distributes between the winding channels becomes critical.
The reverse-flow trap
In directed forced cooling the winding is divided into sections separated by horizontal channels. If the pressure distribution is unfavourable, the flow in some channels reverses or stops. The winding section in that channel is barely cooled at all, and the hot spot forms there.
This is entirely invisible in a calculation that looks at the total flow rate — it is a classic distribution problem, solved by the placement of the channel washers.
Oil properties vary strongly with temperature
The viscosity of transformer oil changes by orders of magnitude with temperature. At a cold start the circulation is very weak; a naturally-cooled transformer can heat more than expected on a cold start-up. A constant-property model misses this behaviour.
Modelling
The problem is conjugate: conductor, insulation, oil and tank together. Solving the winding turn by turn is not practical; an anisotropic equivalent region is used.
The loss distribution comes from the electromagnetic analysis and is not uniform — stray flux produces local peak losses at the winding ends and in the tank wall. A uniform-loss assumption misses the hot spot.
The air flow over the radiators belongs in the model too; if the radiators breathe each other's warm air, capacity falls. See the heat pump outdoor unit note.
References
- Churchill, S. W. & Chu, H. H. S. (1975). Correlating equations for laminar and turbulent free convection from a vertical plate. International Journal of Heat and Mass Transfer, 18(11), 1323–1329. DOI: 10.1016/0017-9310(75)90243-4
- Shah, R. K. & Sekulić, D. P. (2003). Fundamentals of Heat Exchanger Design. John Wiley & Sons. DOI: 10.1002/9780470172605