Presented is a new hydrofoil tip loss correction technique.
The technique improves the accuracy of horizontal axis tidal turbine prediction.
This method is validated against experimental flume data.
The work compares and contrasts with industry standard techniques.
Simulating fully resolved Horizontal Axis Tidal Turbine (HATT) geometry for a time period great enough to resolve a fully developed wake, and accurately predict power and thrust characteristics, is computationally very expensive. The BEM-CFD method is an enhanced actuator disk and is able to reduce the computational cost by simulating a time averaged downstream velocity field. Current implementations fall short of accurately determining tip losses, which are a function of the hydrofoil geometry. This work proposes a method of addressing this shortfall by modifying the angle of attack to conform to the constraints outlined in Prandtl’s lifting line theory, i.e. the zero lift angle of attack at the hydrofoil tip. The revised model is compared to existing BEM-CFD methods and validated against experimental data. The revised BEM-CFD method presented in this work shows a significant improvement over previous BEM-CFD methods when predicting power and thrust. The coefficient of power is reduced from 0.57 (approx. 30% above experiment) to 0.44 (approx. 3% above experiment). An increase in turbulence intensity in the rotor region, in particular at the wake boundary, improves the recovery of the wake without the addition of empirical turbulence source terms. Good correlation with experimental results for power, thrust and wake prediction, is observed. The model may also be applied to wind turbines.
- Finite volume;
- Fluid-structure interaction;
- Incompressible flow;
- Marine hydrodynamics;
- Turbulent flow
Tidal stream renewable energy is becoming an increasingly viable source of energy production, as knowledge and technology in this sector develops. Tidal stream power generation has emerged in recent years as a potentially reliable form of renewable energy due to the predictability of tidal periods and magnitudes . While many tidal sites across the world are being identified with economically attractive levels of energy extraction, the UK is of particular interest due to the high concentration of available resource . To meet the growing requirements of this sector, investment in improving current tidal stream power extraction knowledge and technology is necessary. This can be achieved through the study of practical experiment, or numerical and analytical modelling ,  and .
Although laboratory experiments cannot truly mimic complex offshore conditions, they are very convenient due to significantly lower costs compared to offshore deployments. Laboratory experiments provide a platform for collecting accurate and repeatable data. In contrast, Computational Fluid Dynamics (CFD) modelling has the potential to simulate the effect on environmental conditions at significantly lower cost compared to offshore deployments.
To address this a number of Blade Element Momentum Theory (BEMT) techniques, originally derived from Glauert’s propeller theory , have been introduced. BEMT  and  is an analytical approach which uses tabulated aerofoil data to perform analysis. This technique is extensively used in the wind industry due to the simplicity of the model, and the agreement of its results with measured data . The BEMT model has also successfully been applied to Horizontal Axis Tidal Turbines (HATTs). A typical HATT may see several complex flow scenarios throughout its operational range and therefore, a number of empirical corrections have been developed to better correlate the BEMT model with experimental results . These include corrections for yawed rotors, hub losses, tip losses, and heavily loaded rotors.
A significant limitation of the BEMT method is the inability to simulate the local velocity field, and thus perform analysis on the downstream wake characteristics. Where this is required, alternative modelling methods need to be employed. One alternative is the transient CFD simulation of a HATT with fully resolved hydrofoil geometry. However simulating fully resolved HATT geometry for a time period great enough to resolve a fully developed wake, and accurately predict power and thrust characteristics , is computationally very expensive .
An alternative to the transient fully resolved geometry of a HATT is the steady state, or time averaged, Blade Element Momentum CFD (BEM-CFD) computational model ,  and . This model combines elements of BEMT with CFD simulation techniques to resolves the hydrofoil’s effect on the flow in a steady state simulation. This technique significantly reduces the computational cost of simulating HATTs. The advantage of the BEM-CFD method is the prediction of a time averaged downstream velocity field, in particular the downstream wake.
Although the current BEM-CFD methods can predict the power and thrust available at the turbine, recent comparisons with experimental data  and  highlight the need for further investigation into the accuracy of this type of model. Of particular interest is the assumption that correction factors applied to the BEMT analytical model, as discussed in Ref. , are directly transferable to the BEM-CFD numerical model.
In the case of a three dimensional finite hydrofoil geometry, pressure differences between the upper and lower surfaces induce flow spillage at the tip. In turn this motion generates the tip vortices as described in Ref. . This spillage has a knock on effect across the full span of the hydrofoil, and thus reduces its efficiency with the greatest losses towards the tip. The BEM-CFD model averages the effect of a hydrofoil over a complete rotation, therefore there is no upper and lower surface to propagate the flow resulting from a pressure difference. In Ref.  the authors reasoned similarly and thus added the Prandtl tip loss factor to the momentum source terms of the BEM-CFD model. They then compared the power and thrust coefficients to experimental results published in Ref. .
In classical BEMT implementation the model correction factors are applied directly to the axial and tangential induction factors, as demonstrated by Ref. . From this the forces acting on the hydrofoil are computed. In the case of the Prandtl tip loss factor, the effective force on the hydrofoil is reduced towards the tip. If this is applied to BEM-CFD in the same way, as in Ref. , the effect of the hydrofoil on the flow is reduced. If the annular stream tubes close to the tip are considered in detail, the implementation of a tip loss as reduction in reactive force from the hydrofoil allows the fluid to pass the hydrofoil with little momentum change. Although this is not an issue for BEMT as the velocity field is not simulated, this is a significant issue for the BEM-CFD method as accurate results are dependant on the correct flow characteristics in this area.
To address these challenges, this work introduces and investigates the effectiveness of a revised BEM-CFD model based on elements of Prandtl’s analytical lifting line theory as defined in Ref. . This work proposes modifying the angle of attack, and thus the distribution of downwash across the hydrofoil, as a result of the tip constraints outlined in Prandtl’s lifting line theory, i.e. the zero lift angle of attack at the hydrofoil tip. The revised model is compared to existing BEM-CFD methods and validated against experimental data. The revised BEM-CFD method presented in this work shows a significant improvement over previous BEM-CFD methods when predicting power and thrust. This approach deals appropriately with the tip losses encountered with a hydrofoil of finite length, and significantly improves the formation of the local velocity field. The revised BEM-CFD model is compared to; the classical BEMT method, the BEM-CFD with Prandtl tip loss applied directly to the momentum source terms, and experimental data.
This paper introduces the revised model in Section 2, defines a case study in Section 3, discusses the comparative results in Section 3.4, forms conclusions in Section 4, and finally highlights the potential future work in Section 5.
2. The numerical model
This section introduces the revised numerical model for predicting the performance of HATTs (Horizontal Axis Tidal Turbines). The model is a hybrid analytical, BEM, and CFD computational model. First is a short discussion of the CFD process, governing equations and turbulence models (Section 2.1). The following section revisits the standard BEM-CFD approach (Section 2.2), as described by Ref. . Following this a description of the revised model for improving the prediction of potential power and thrust generation (Section 2.3) is provided.
2.1. CFD and the governing equations
CFD simulations are conducted using Physica, a framework for multi-physics Computational Fluid Dynamics and Computational Solid Mechanics . Linking the CFD flow domain to the BEM model is achieved by additional source terms included within the conservation of momentum equations of the Physica finite volume solver. The solver uses steady state Reynolds averaged incompressible Navier-Stokes equations with a range of turbulence model options including K-Epsilon, K-Epsilon RNG, and K-Omega. Physica has been developed by Ref. . An alternate implementation has also been developed in OpenFOAM .