Numerical Analysis of Convective Cooling in Hydro Generators

Hydroelectric power is currently the most common form of renewable energy and plays a very important role in global electric power generation. It accounts for approximately 17.5% of total electricity production, and almost 85% of electricity produced from renewable sources (Internaltional Energy Agency, 2017).

Hydro-generators are high performance electrical machines, they have an efficiency rate up to 98%. However, during the conversion from the mechanical energy into electricity, a certain amount of energy is lost (Traxler-Samek et al., 2010a). The power losses associated with the electricity production by hydro-generators include:
– Electrical losses: the losses generated as a result of the electrical resistance in the rotor and stator windings.
– Magnetic losses: the losses generated as a result of the rotating magnetic field, appeared due to the motion of the rotor core relatively to the stator core.
– Mechanical losses: consists of the bearing loss and the windage losses caused by the air friction on the solid surface.

These losses manifest mainly in the form of volumetric heat source and cause the temperature rise in the solid components of hydro-generators. It is well known that the thermal performance and lifetime of the generator depend strongly on the maximum temperature of solid components, particularly thermally-limited dielectric insulators. As a result, it is required to consider the thermal aspect, besides the mechanical and electromagnetic analysis in the design and upgrading of hydro-generators.

In order to maintain the maximum temperature within the critical value, the heat generated must be extracted away from the machine. The cooling of the generator is conventionally assured by a forced convection using a closed-loop cooling air circuit passing over solid components. After passing through the active components of the generator (rotor ventilation ducts, salient pole surfaces, stator ducts, windings, etc.), the air directs towards the radiators, where the accumulated heat is dissipated. The energy required to maintain this flow induces the windage loss, that accounts for 20%-30% of total losses in the generator (Toussaint et al., 2011). As a consequence, an efficient ventilation system is also an important attribute in the generator’s design and uprating.

The province of Québec benefits from an abundant water resource in the form of 500,000 lakes and 4,500 rivers that cover 12% of its surface area, which motivates the installation of many hydroelectric power plants over provincial territory. Hydro-Québec is currently operating 63 hydroelectric power units with an output capacity of 36 908 MW, accounting for 99% capacity of its total production (Hydro-Québec, 2017). The majority of hydroelectric power plants in Québec were built before the 1970s. At that time, the electrical machine designers did not benefit from the highly accurate measurement instruments, nor the numerical analysis techniques which are now widely available, such as the finite element analysis (FEA) or computational fluid dynamics (CFD). Instead, engineers mainly relied on past experience and on empirical approach to build the machines. Consequently, large safety factors have been assigned to the electrical machines due to the uncertainty of the calculation method. With the aid of novel technologies, these factors of safety can be reduced, allowing for an improvement of the power rating of existing generators.

For this reason, Hydro-Québec started the project AUPALE (Augmentation de la Puissance des Alternateurs Existants) in 2002 at the company’s research center, Institut de Recherche d’Hydro-Québec (IREQ). The ultimate goal of this project is to evaluate the potential of increasing the rated maximum capacity of certain existing generators without compromising the machines’ lifetime. As the power of generators increases, the power losses consequently elevate and result in a temperature rise, which might damage the generator or cause an overheating problem. The AUPALE project therefore has also been required to assess the impact of this power upgrading on the lifetime of generators. This project is a multi-physics consideration of the hydro-generator as an entire single unit, involving the electromagnetic, structural, and thermo-fluid aspects. The electromagnetic simulations allow one to calculate the power losses in the active components of the machine, then transferred to an in-house code developed at IREQ to calculate the temperature field in solid components. In order to accomplish the thermal analysis, one requires an understanding of convective cooling on the surfaces of the active solid components of the generator. An investigation of the ventilation flow in the machine is thus important to fully predict the thermal performance of the machine. Due to safety reasons, the access to power plants to carry out flow measurements is very limited. Moreover, it is frequently necessary to stop or remove a part of the generator to install measurement instruments. Since a halt of the generator’s operation is highly costly, the instrumentation must be synchronized with a maintenance period, which is strictly time-bounded. To date, the measurement of the air ventilation flow rate at power plants is insufficient to fully analyze the ventilation circuit.

Numerical models

Turbulence models

Most fluid motions found in engineering applications are turbulent flows, which are characterized by many physical properties (Ferziger & Peric, 2002). Historically, turbulent flows were primarily studied using experimental approaches, in which overall quantities such as timeaveraged friction coefficients or heat transfer are quantified. However, there are some parameters that are almost impossible to measure even using cutting-edge instruments, and others cannot be made with sufficiently desired precisions. Consequently, the numerical approach to model turbulent flows is required for engineering applications.

Direct numerical simulation (DNS)
DNS is considered the most accurate approach to characterize turbulence because it solves the Navier-Stokes equations without any approximation other than the numerical discretization. In such simulations, all length and time scales involved in the flow are resolved. In order to assure that all significant structures of the turbulence have been captured, on the one hand the computational domain must be at least as large as the largest turbulent eddy or the integral scale L, on the other hand the mesh size must be no larger than the smallest length scales, the Kolmogorov scale η. Tennekes (1972) proved that the number of computational nodes in each direction must be proportional to at least L/η ≈ Re ³/⁴ L , where ReL is the Reynolds number based on an integral scale. Since the number of nodes must be used in each three coordinate directions, and the time step is related to the grid size, the cost of simulation scales is Re ³ L. Because the number of grid points used in computation is limited by the processing speed and memory, direct numerical simulation is only possible for flows at a low Reynolds number and for geometrically simple cases. For the case of hydroelectric generators that have an extremely complex geometry, a Reynolds number of 2.6 × 10⁴ is typically found, the DNS are thus not applicable for this application.

Large eddy simulation (LES)
An alternative approach of DNS is the large eddy simulation approach, which was firstly proposed and developed by Smagorinsky (Wilcox, 1988). In LES approach, the large scale motions of the turbulent flow are directly solved meanwhile small scale ones (sub-grid scale) are modelled, which results in a significant reduction in computational cost in comparison with DNS. LES approach is more accurate than the Reynold-averaged Navier-Stokes (RANS) simulations since the large eddies of the turbulent flow are much more energetic and provide most of momentum transport and turbulent mixing. Furthermore, compared to the large eddies the small scale motions are more isotropic and homogeneous, and therefore modelling the sub-grid scale eddies is less computational costly than modelling all scales in a single closure as in the RANS approach. LES is not applicable for the current configuration since it is too computationally expensive.