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Based on a finite control volume analysis, a coupled thermal model is developed to investigate the two-dimensional hot-spot temperature field in the disks for oil-filled transformer windings. The model consists of two submodels: the heat conduction submodel and the nonisothermal hydraulic submodel. The heat conduction submodel for the temperature distribution in the winding disks includes a nonuniform heat-generation rate, and axisymmetry of the disk geometry. A successive over-relaxation method is adopted to accelerate numerical convergence. Taking into account the temperature-dependent fluid properties, the nonisothermal hydraulic model can predict the flow and temperature distributions in the fluid. The cooling oil flow is treated as a thermally developing laminar flow for the determination of the local heat-transfer coefficient, due to the low-flow Reynolds numbers (20-200), high oil Prandtl numbers (150-50), and relatively short flow channel length encountered in the oil-filled transformers. The two submodels are coupled through the heat-transfer boundary condition, and an iterative method is used to solve the coupled thermal model.

Effects of various design and operating parameters on the hot-spot temperature are analyzed in disk-type forced oil-cooled transformer windings. The results indicate that a two-dimensional thermal analysis in the disks is necessary to determine the temperature and location of the hottest spot, and that the cooling oil-flow arrangement has a significant influence on the cooling of disk windings. The maximum disk temperature for each pass is proportional to the oil entrance temperature and, therefore, the heat transfer in the radiator should be improved as much as possible. A larger total oil-flow rate through the pass can increase the cooling capacity and, hence, improve the cooling of the disks, but increases the pressure loss. Although a uniform distribution of cooling oil flow among the various horizontal cooling ducts within a pass is beneficial to decrease the hottest spot temperature, the best cooling results can be obtained when the cooling flow distribution matches the distribution of heat generation in each disk of the pass.

A comprehensive resistance network-based hydraulic model for mass flow distribution and pressure loss in disk-type oil-cooled transformer windings with zigzag cooling flow passages is presented. The number, size, and location of the horizontal ducts and fluid properties are considered variable, and the distribution of mass flow rates is determined by associated pressure losses, including the so-called "minor losses". Axisymmetry of the winding geometry is taken into consideration, and the pressure loss calculation is based on the discretization of flow domains in order to tackle the nonuniformity of the cross-sectional area in the horizontal ducts and to provide easy coupling with thermal analysis for the cooling of winding disks. Successive under relaxation method is used for numerical convergence.

For pt.1, see ibid., vol.19, no.1, p.186-93, January 2004. The effects of total mass flow rate, flow arrangement, and geometrical parameters in ONAN transformer windings are investigated. It is found that the conventional minor losses are predominant in determining the mass flow distribution and pressure losses for the present flows. The sizes of the cooling ducts and the number of disks per pass have strong influence on both the mass flow distribution and the pressure loss. Flow arrangement in the horizontal ducts can have significant influence on the flow distribution, hence on the hot spot formation. Since the rate of heat generation increases in the vertical direction, a corresponding increase in the cooling oil flow rate vertically will optimize winding performance.