Module Turbine

Overview

Module Turbine is in charge of calculating the force exerted by turbines in the water flow as well as the power and energy extraction. This implementation is available for 2D and 3D simulations being, in the 3D model, only discretised in the vertical domain. There is no discretisation of the turbine geometry (and force) in the horizontal domain, the model computes the force as a punctual force in the cell where the turbine is placed.

For the moment, the model is thought for horizontal bidirectional turbines, with pitch control and free rotation in the vertical axis (the perpendicularity between flow and turbine is implicit in the model as the force is introduced into the hydrodynamic model as a punctual force).

Implementation

Forces

Failed to parse (Cannot write to or create math temp directory): \text{F}_{T} = \frac{1}{2}\rho A_{T} C_{T} U^{2}

Failed to parse (Cannot write to or create math temp directory): \text{P}_{T} = \frac{1}{2}\rho A_{T} C_{P} U^{3}

Thrust force produced by the turbine rotor due to the energy extraction

F_{T} = (1/2)ρA_{T}C_{T}U^{2}

The power extracting by the turbine

P_{T}=(1/2)ρA_{T}C_{P}U^{3}

Where ρ is the water density, A_{T} is the area swept by the blades, C_{T} is the thrust coefficient that quantifies the force exerted by the turbine to the flow and C_{P} is the power coefficient that quantifies the amount of power extracted from the flow.

Coefficient parameterisation

C_{T}=

• 0 if U≤U_{C}
• C_{T_0} if U_{C}<U≤U_{D}
• C_{T_0}U_{D}^{3}/U^{3} if U>U_{D}

C_{P}=

• 0 if U≤U_{C}
• C_{P_0} if U_{C}<U≤U_{D}
• C_{P_0}U_{D}^{3}/U^{3} if U>U_{D}

Where C_{T_0} and C_{P_0} are the design values for each coefficient and U_{C} and U_{D} are the cut-in and design speed, respectively