Power Estimation of an Experimental Ocean Current Turbine Based on the Conformal Mapping and Blade Element Momentum Theory

Abstract

Abstract Conformal mapping techniques have been used in many applications in the two-dimensional environments of engineering and physics, especially in the two-dimensional incompressible flow field that was introduced by Prandtl and Tietjens. These methods show reasonable results in the case of comprehensive analysis of the local coefficients of complex airfoils. The mathematical form of conformal mapping always locally preserves angles of the complex functions but it may change the length of the complex model. This research is based on the design of turbine blades as hydrofoils divided into different individual hydrofoils with decreasing thickness from root to tip. The geometric shapes of these hydrofoils come from the original FX77W121 airfoil shape and from interpolating between the FX77W121, FX77W153, and FX77W258 airfoil shapes. The last three digits of this airfoil family approximate the thickness ratio times 1000 (FX77153 => 15.3 % thickness ratio). Of the different airfoil shapes specified for the optimal rotor, there are 23 unique shapes.[15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 28] This study describes the advantage of using at least one complex variable technique of transformation conformal mapping in two dimensions. Conformal mapping techniques are used to form a database for sectional lift and drag coefficients based on turbine blade design to be used in Blade Element Momentum (BEM) theory to predict the performance of a three bladed single rotor horizontal axis ocean current turbine (1.6-meter diameter) by considering the characteristics of the sea-water. In addition, by considering the fact that in the real ocean, the underwater ocean current turbines encounter different velocities, the maximum brake power will be investigated for different incoming current velocities. The conformal mapping technique is used to calculate the local lift coefficients of different hydrofoils with respect to different angles of attack: −180 ≤ AOA ≤ +180. These results will be compared to those from other methods obtained recently by our research group. This method considers the potential flow analysis module that follows a higher-order panel method based on the geometric properties of each hydrofoil cross section. The velocity and pressure fields are obtained directly by the applications of Bernoulli’s principle, then the lift coefficients are calculated from the results of the integration of the pressure field along the hydrofoil surface for any angle of attack. Ultimately, the results of this research will be used for further investigation of the design and construction of a small-scale experimental ocean current turbine to be tested in the towing tank at the University of New Orleans.