A sensitivity analysis of the Winter-Kennedy method

Abstract: Hydropower is among the lowest-cost electrical energy sources due to its long lifespan and lower operation and maintenance cost. The hydro-mechanical components of hydropower plants generally last about four to five decades, then they are either overhauled or replaced. The major upgrades and refurbishments of the hydropower plants that are ongoing have also been motivated by the introduction of new rules and regulations, safety or environmentally friendly and improved turbine designs. Whatever are the drivers, the refurbishments are usually expected to increase efficiency, flexibility and more power from the plant.Efficiency measurement is usually performed after refurbishments. While it is relatively straightforward to measure efficiency in high head machines due to the availability of several code-accepted methods, similar measurements in low head plants remain a challenge. The main difficulty lies in the discharge/flow rate measurement. The reason is due to the continuously varying cross-section and short intake, as a result, the flow profile or parallel streamlines cannot be established. Among several relative methods, the Winter-Kennedy (WK) method is widely used to determine the step-up efficiency before and after refurbishment. The WK method is an index testing approach allowing to determine the on-cam relationship between blade and guide vane angles for Kaplan turbine as well. The method utilizes features of the flow physics in a curvilinear motion. A pair of pressure taps is placed at an inner and outer section of the spiral case (SC). The method relates discharge (Q) as Q=K(dP)^n, where K is usually called as the WK constant and n is the exponent whose value varies from 0.48 to 0.52. dP is the differential pressure from the pair of pressure taps placed on the SC.  Although the method has very high repeatability, some discrepancies were noticed in previous studies. The reasons are often attributed to the change in local flow conditions due to the change in inflow conditions, corrosions, or change in geometry. Paper A is a review of the WK method, which includes the possible factors that can influence the WK method. Considering the possible factors, the aim of this thesis is to study the change in flow behavior and its impact on the coefficients. Therefore, a numerical model of a Kaplan turbine has been developed. The turbine model of Hölleforsen hydropower plant in Sweden was used in the study. The plant is considered as a low head with 27-m head and a discharge of 230 m3/s. The 1:11 scale model of the prototype is used as the numerical model in this study, which has 0.5 m runner diameter, 4.5 m head, 0.522 m3/s discharge and 595 rpm at its best efficiency point. A sensitivity analysis of the WK method has been performed with the help of CFD simulations. The numerical results are compared with the previously conducted experiment on the model. The study considers four different WK configurations at seven locations along the azimuthal direction. The simulations have been performed with different inlet boundary conditions (Paper B and Paper C) and different runner blade angles (Paper C). The CFD results show that the WK coefficients are sensitive to inlet conditions. The study also concludes that to limit the impact of a change in inflow conditions, runner blade angle on the coefficients, the more suitable WK locations are at the beginning of the SC with the inner pressure tap placed between stay vanes on the top wall.