Influence of the reaction on the performance of the Crossflow turbine

Abstract

The crossflow turbine is a hydraulic where the water crosses the region of the rotor blades twice. In the first passage, the water goes from the rotor outside to an empty space defined by the blades, while the second passage takes the water from the inside space to the outside. The main advantage of this turbine is the ease of manufacture, which translates into a low cost of production. However, the value of its peak efficiency tends to be lower than what is achievable with the other hydraulic turbines, restricting its application to instances with low power. To minimize this drawback, both experimental and theoretical studies have been conducted in the past. The experimental analysis consisted in the measurement of the turbine efficiency as a function of the rotor rotational speed, for different geometries (diameter ratio, number of blades, angles, etc.). These tests showed conclusively that the crossflow turbine tends to behave like an action turbine for the smaller values of the rotational speed, but as this parameter is increased, some degree of reaction sets in, i.e., the water flow through the rotor starts to be accompanied by a decrease in pressure. The different geometric parameters influence the point where the reaction begins to appear. On the theoretical front, there are examples of the use of computational codes to calculate the two-dimensional flow inside the turbine, but this approach tends to be quite expensive in terms of computational resources, and so does not allow the study of large number of different geometric configurations. An alternative consists in the use of one-dimensional models to analyse quickly and inexpensively the dependency of the peak efficiency value with the turbine geometric parameters. In the open literature there are some examples of this strategy, but all of them assume the turbine to behave like an action turbine, i.e., consider the water flow inside the rotor to be at constant pressure. To address this shortcoming, a one-dimensional model of the flow through a crossflow turbine that considers the reaction is described in the present paper. The results of this modelling show that the peak efficiency values can be affected by the reaction, depending on the geometric parameters being used, the runaway speed being strongly influenced. This study shows the utility of this refined analysis for the correct choice of the geometric parameters of a crossflow turbine, eventually leading to improved designs, with better performance.