On the design of propeller hydrokinetic turbines: the effect of the number of blades

Abstract

A design study of propeller hydrokinetic turbines is explored in the present paper, where the optimized blade geometry is determined by the classical Glauert theory applicable to the design of axial flow turbines (hydrokinetic and wind turbines). The aim of the present study is to evaluate the optimized geometry for propeller hydrokinetic turbines, observing the effect of the number of blades in the runner design. The performance of runners with different number of blades is evaluated in a specific low-rotational-speed operating conditions, using blade element momentum theory (BEMT) simulations, confirmed by measurements in wind tunnel experiments for small-scale turbine models. The optimum design values of the power coefficient, in the operating tip speed ratio, for two-, three- and four-blade runners are pointed out, defining the best configuration for a propeller 10 kW hydrokinetic machine.

Propagation of uncertainties

The experimental uncertainties of this work are given by the sum of instrumental and random errors. For the digital sensors, the instrumental errors are given by the smallest scale value displayed by the instrument and for the analog instruments by the smallest half scale. Random uncertainties were defined as being the standard deviation a set of realizations under the same conditions. In this work, the derived uncertainties can be expressed according to the following primary measurements errors: wind velocity ($\delta V_0$), rotational speed ($\delta \omega$) and torque ($\delta T$). The uncertainty in Cp measurements ($\delta Cp$) is computed with the general formula for error propagation [30], as it is given in Eqs. 47, 47 and 48.

$$\begin{aligned} \delta P= & {} \sqrt{\omega ^2\delta \tau ^2+\tau ^2\delta \omega ^2}, \end{aligned}$$

(47)

$$\begin{aligned} \delta P_\mathrm{flow}= & {} \sqrt{(3/2\rho A \ V_0^2 \delta V_0)^2}, \end{aligned}$$

(48)

$$\begin{aligned} \delta Cp= & {} \sqrt{(P_\mathrm{flow}^{-1} \delta P)^2+(P P_\mathrm{flow}^{-2}\delta {P_\mathrm{flow}})^2}. \end{aligned}$$

(49)