An Aerodynamic Optimization Approach for Wind Turbine Blades Using Proper Generalized Decomposition

Low-center-of-gravity wind turbines (LCGWTs) characterized by tapered blades whose chord length c increases nonlinearly from the top (where c = 0.11 m) to the bottom (where c = 0.17 m) of each blade. Further, turbines featuring these blades do not need any arms, or even a center pole in the rotor. Two experimental LCGWTs (diameter: 0.4 m; height: 0.25 m) with symmetrical blades (NACA 0018) and cambered blades were built. A dead band, which is a band of tip speed ratio (TSR) where the rotor has negative torque at TSR lower than that where the maximum power-coefficient condition is achieved, was observed when symmetrical blades were subjected to low wind speed. In contrast, no dead band was observed for the cambered blades. Under high wind speeds and over a wide range of TSR values, performance of the LCGWTs was better with cambered blades than with symmetrical blades. Computational fluid dynamics (CFD) analysis of 2-dimensional rotors whose blade sections corresponded to the blade sections at the equatorial planes of both types of LCGWTs showed the same tendency. Performance predictions by the blade element momentum (BEM) method using aerodynamic data on the NACA 0018 blades showed some agreement with the CFD analysis. For the cambered blade rotor, Wilson and Walker’s empirical correction of the thrust coefficient, a correction that is typically used in simulations of horizontal axis wind turbines, brought the BEM prediction closer to the CFD prediction than Glauert’s correction did. However, the agreement between the BEM prediction with Wilson and Walker’s correction and the CFD prediction of the cambered blade rotor was thought to be just a coincidence due to large difference on the torque variations between BEM and CFD. At least, the Wilson and Walker’s correction predicts larger torque than the Glauert’s correction at high TSR region. : Wind power, Vertical axis wind turbine, Low center of gravity, Cambered blade, Flow curvature, Conformal mapping, Blade element momentum method, Computational fluid dynamics

ABSTRACTThe blade element momentum (BEM) method is widely used for calculating the quasi‐steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now be obtained in the blade root and tip sections. It is expected that this will lead to small changes in optimum blade designs. In this work, has been implemented, and the spanwise load distribution has been optimized to find the highest possible power production. For comparison, optimizations have been carried out using BEM as well. Validation of shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using , and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM. In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd.

Wind turbine blades perform the most important function in the wind energy conversion process. It plays the most vital role of absorbing the kinetic energy of the wind, and converting it to mechanical energy before it is transformed into electrical energy by generators. In this work, National Advisory Committee for Aeronautics (NACA) 4412 and SG6043 airfoils were selected to design a small horizontal axis variable speed wind turbine blade for harvesting efficient energy from low wind speed areas. Due to the low wind profile of the targeted area, a blade of one-meter radius was considered in this study. To attain the set objectives of fast starting time and generate more torque and power at low wind speeds, optimization was carryout by varying Reynolds numbers (Re) on tip speed ratios (TSR) values of 4, 5, and 6. The blade element momentum (BEM) method was developed in MATLAB programming code to iteratively find the best twist and chord distributions along the one-meter blade length for each Re and tip speed ratio (TSR) value. To further enhance the blade performance, the twist and chord distributions were transferred to Q-blade software, where simulations of the power coefficients (Cp) were performed and further optimized by varying the angles of attack. The highest power coefficients values of 0.42, 0.43, and 0.44 were recorded with NACA 4412 rotor blades, and 0.43, 0.44, and 0.45 with SG6043 rotor blades. At the Re of 3.0 × 105, the blades were able to harvest maximum power of 144.73 watts (W), 159.69 W, and 201.04 W with the NACA 4412 and 213.15 W, 226.44 W, 245.09 W with the SG6043 at the TSR of 4, 5, and 6 respectively. The lowest cut-in speed of 1.80 m/s and 1.70 m/s were achieved with NACA 4412 and SG6043 airfoils at TSR 4. At a low wind speed of 4 m/s, the blades were able to harness an efficient power of 79.3. W and 80.10 W with both rotor blades at the TSR 4 and 6 accordingly.

The blade element momentum (BEM) method is among the mostly used engineering aerodynamic models for wind turbine rotors. Even though the BEM method is strictly only applicable to straight blades forming a planar rotor, it is in practice used for load calculation and design optimization of blades with relatively large sweep, prebend or coning. The present work aims to answer the question: How does the BEM method see swept or prebent blades? The blade element part of the method can be adapted for swept or prebent blades by projecting the velocity and loads between the 2-D airfoil section and the 3-D blade geometry under the cross-flow principle. However, momentum theory considers the 3-D wake and the induction of a planar actuator disc with straight blades. There could be significant differences between the results calculated from different implementations of the BEM method, while the details of the implementations are often omitted in the literature. In the present work, a consistent implementation including the definition of airfoil section alignments and the coordinate systems is provided. It is shown that for a given circulation distribution, the BEM method will predict approximately the same local aerodynamic loads for non-straight blades as if the blades were straight and the rotor was planar. This means using the BEM method to perform aerodynamic optimization of modern rotors with curved blades and/or rotors that are not planar can only have little meaningful result. In order to model the impact of the wake geometry on the induction, more advanced models that take into account the wake geometry on the induction are necessary.

Disadvantages of electrical energy generation by fossil fuels, beside renewable energy benefits, cause the growth of this form of power generation. Among various forms of renewable energies, wind energy have had a significant growth in recent years. Wind turbines convert kinetic energy of air particles to electricity. Due to changes in wind characteristics based on global wind regime, local wind regime, and also terrain in any geographical area, each turbine cannot be exploited optimally in every area. By selecting a turbine which has the closest match to the installation location, the cost of electricity can be minimized and energy production can be maximized as possible. In this paper, the blade element momentum (BEM) method with intelligent multi-objective optimization algorithms is used to extract the best power curve, which can be applied to the desired site. In site, from the existing turbines, the turbine which fits this power curve will be selected. The result is compared to the turbine installed by trial and error method and mounted at site. In this paper, BEM method is used to synthesize the optimum power curve for the turbine to be installed in Tabriz.

The output aerodynamic power from a wind turbine is estimated through a classical c1 - c6 formulae in most of the research works especially when it is considered for the generation of electrical power. This approach sometimes may not be useful where the actual aerodynamic power with better accuracy is required. This paper investigates the blade element momentum (BEM) method in-depth with the impact of wind speed, turbine speed and air-foil geometry. An artificial intelligence model (AIM) of BEM for its use in simulation has also been proposed in this paper. AIM helps to reduce the computational time significantly since the BEM when run in whole takes a lot of time during simulation. A neural network has been made and trained with the data obtained from the BEM method. Further, the turbine power resulted from the BEM approach through AIM has been used for the generation of the electrical power with its maximum power tracking. The simulation has been performed on NREL's 5-MW test wind turbine.

Three design strategies for low pressure axial fans are compared. Benchmark fans are designed with the blade element momentum (BEM) method. All common validity limits are respected. Optimized fans are designed according to design guidelines obtained in earlier studies by the authors of this work. Here, “optimal” always means maximum possible total-to-static efficiency at exact fulfillment of a specific design point. One typical difference between the benchmark and optimized fans is that the optimization yields considerably smaller hub-to-tip ratios. The two design methodologies are combined for a third series of fans. These fans are also designed with the BEM method, but with the same hub size and blade number as obtained from the optimization. As a consequence of the smaller hub size, the aforementioned validity limits are violated. All three design strategies are applied at three distinct design points which are supposed to outbid the bounds of axial fans according to Cordier’s diagram. The nine resulting fans are simulated by means of steady CFD (Reynolds-averaged Navier Stokes method, RANS). Quality assurance is considered by a grid independence study and a comparison with transient simulations (SAS method). The aerodynamic comparison reveals the weaknesses of the BEM designs which suffer from high exit losses (if designed with common validity limits) or from high hydraulic losses (if designed with small hub). Additionally, BEM designs with small hubs still have unnecessary exit losses which originate from an uneven distribution of flow velocity downstream of the fan. In contrast, the optimized designs enable a small hub without increased losses resulting in a total-to-static efficiency improvement by 2–14 percentage points depending on the design point. The flow fields of all fans are analyzed in detail to find reasons for the superiority of the optimized designs. It is found that optimized fans benefit from an evenly distributed meridional velocity profile downstream of the fan. Reasons are given why such a flow field is hardly achievable by BEM designs. Further advantages of optimized fans are found in the blade shape near the hub which strictly avoids flow separations which in standard designs often compromise the efficiency in the complete blade channel.

The present work compares non-planar rotors designed using the blade element momentum (BEM) method and a vortex cylinder model. In a previous work, it is shown that blade element theory coupled with the superposition of the vortex cylinder model (BEVC) is able to model the loads of non-planar rotors. The result predicted by the BEVC model is in significantly improved agreement with higher-fidelity models than the loads as predicted using the BEM method. In this work, the BEM method and the BEVC method are integrated into a gradient-based optimization framework for aerodynamic planform optimization, in which the analytical gradients are obtained using the algorithmic differentiation (AD) method. In the present study, the rotor is assumed to be stiff for all cases such that the pure aerodynamic effects are highlighted. Loads of the optimized non-planar rotors with different geometries under different constraints designed from both methods are calculated using the BEM method, the BEVC method and also the higher-fidelity lifting-line (LL) method. Within the constraints of the present work it was found that the advantage of the BEVC method is not significant when comparing the integrated aerodynamic loads: the non-planar rotor designed using the BEM method gives similar total thrust and power as the rotor designed using the BEVC method when the designs are evaluated with the higher-fidelity LL method. However, the results confirmed that the distributed aerodynamic loads of the non-planar rotors predicted by the BEVC method are in improved agreement with the LL method compared to the BEM method.

In spite of the enlarging interest in wind turbines development, the design optimization of wind turbine blades has not been studied in the past as gas or steam turbines optimization. Due to its reduced computational cost, Blade Element Momentum (BEM) method has been employed up to now to estimate the power output of the turbine. However, BEM method is not able to predict complex three dimensional flow fields or the performance of profiles for which drag and lift coefficients are not available. Theoretically, Computational Fluid Dynamics (CFD) can be more useful in these cases, but at the price of a much higher overall computational cost. In a past work, the authors developed and validated a simplified CFD process (including meshing) capable to assess the aerodynamic loads acting on a wind turbine with acceptable computational resources. Starting from that, in this work a full 3D CFD optimization of a small wind turbine is presented, both with constrained single- and multi-objective. Twist and chord distributions of a single blade have been varied keeping fixed the aerodynamic profile, and the obtained optimums have been compared with a benchmark case. The results demonstrate that CFD optimization can be effectively employed in a wind turbine optimization. As expected, stalled conditions of the blade are more likely to be improved than those characterized by attached flow. Future works will focus on multi-disciplinary optimization and will include also aerodynamic profile variation.

Wind turbine blades experience excessive load due to inaccuracies in the prediction of aerodynamic loads by conventional methods during design, leading to structural failure. The blade element momentum (BEM) method is possibly the oldest and best-known design tool for evaluating the aerodynamic performance of wind turbine blades due to its simplicity and short processing time. As the turbine rotates, the aerofoil lift coefficient enhances, notably in the rotor’s inboard section, relative to the value predicted by 2D experimentation or computational fluid dynamics (CFD) for the identical angle of attack; this is induced by centrifugal pumping action and the Coriolis force, thus delaying the occurrence of stall. This rotational effect is regarded as having a significant influence on the rotor blade’s aerodynamic performance, which the BEM method does not capture, as it depends on 2D aerofoil characteristics. Correction models derived from the traditional hard computing mathematical method are used in the BEM predictions to take into account stall delay. Unfortunately, it has been observed from the earlier literature that these models either utterly fail or inaccurately predict the enhancement in lift coefficient due to stall delay. Consequently, this paper proposes a novel stall delay correction model based on the soft computing technique known as symbolic regression for high-level precise aerodynamic performance prediction by the BEM process. In complement to the correction model for the lift coefficient, a preliminary correction model for the drag coefficient is also suggested. The model is engendered from the disparity in 3D and 2D aerofoil coefficients over the blade length for different wind speeds for the NREL Phase VI turbine. The proposed model’s accuracy is evaluated by validating the 3D aerofoil coefficients computed from the experimental results of a second wind turbine known as the MEXICO rotor.

It is shown in the literature that wind turbine designs with different load distributions have different wake features. To systematically study how different load distributions affect turbine wakes, a method for designing variants of blades with different radial load distributions, but with approximately the same power (CP) or thrust coefficient (CT), is needed. In this work, an inverse design method based on the blade element momentum method and the multi-dimensional Newton’s method, with the normal and tangential force coefficients as the design objective and iterations for satisfying the CP or CT constraint, is developed. The proposed method is validated using the two-bladed small-scale NREL phase VI S809 wind turbine blade design and the three-bladed utility-scale NREL 5 MW wind turbine blade design. Four variants of the NREL 5 MW wind turbine, i.e., the Root-CP, Tip-CP, Root-CT, and Tip-CT designs, which represent the variants of the original design (NREL-Ori) with a higher load near the blade root and tip regions with approximately the same power coefficient (CP) or thrust coefficient (CT) as that of the NREL-Ori design, respectively, are then designed using the proposed method. At last, the flapwise blade bending moment and the power coefficients from different variants of the NREL 5 MW turbine are compared for different tip speed ratios, showing that the “Root” designs are featured by a wider chord near the root, lower blade bending moment, and higher power coefficients for tip-speed ratios greater than nine.

In the present work, a computationally efficient engineering model for the aerodynamic load calculation of non-planar wind turbine rotors is proposed. The method is based on the vortex cylinder model, and can be used in two ways: either as a correction to the currently widely used blade element momentum (BEM) method, or used as the main model, replacing the BEM method in the engineering modelling complex. The proposed method needs the same order of computational effort as the ordinary BEM method, which makes it ideal for time-domain aero-servo-elastic simulations. The results from the proposed method are compared with results from two higher-fidelity aerodynamic models: a lifting-line method and a Navier-Stokes solver. For planar rotors, the aerodynamic loads are identical to the current BEM model when the drag force is excluded during the calculation of the induced velocities. For non-planar rotors, the influence of the blade out-of-plane shape, measured by the difference of the load between the non-planar rotor and the planar rotor, is in very good agreement with higher-fidelity models. Meanwhile, the existing BEM methods, even with a correction of radial induction included, show relatively large deviations from the higher-fidelity method results.

The BEM method is extensively used for analyzing the aerodynamic performance of wind turbines and marine propellers. It is computationally fast and is easily implemented while it can give fairly accurate results. Application of the BEM method to predict the forces acting on rotor blades for a model scale axial shaft-driven Counter-Rotating Pump-Turbine (CRPT) is investigated. Some modifications have been proposed to adopt the classical BEM method for CRPT machine and the results are validated against results from Computational Fluid Dynamics (CFD). The results display that the proposed modifications can improve the loading predicted by BEM. However, the improvements are more pronounced in pump mode rather than turbine mode.

Abstract. In the present work, a computationally efficient engineering model for the aerodynamic load calculation of non-planar wind turbine rotors is proposed. The method is based on the vortex cylinder model and can be used in two ways: either used as a correction to the currently widely used blade element momentum (BEM) method or used as the main model, replacing the BEM method in the engineering modeling complex. The proposed method needs the same order of computational effort as the ordinary BEM method, which makes it ideal for time-domain aero-servo-elastic simulations. The results from the proposed method are compared with results from two higher-fidelity aerodynamic models: a lifting-line method and a Navier–Stokes solver. For planar rotors, the aerodynamic loads are identical to the current BEM model when the drag force is excluded during the calculation of the induced velocities. For non-planar rotors, the influence of the blade out-of-plane shape, measured by the difference of the load between the non-planar rotor and the planar rotor, is in very good agreement with higher-fidelity models. Meanwhile, the existing BEM methods, even with a correction of radial induction included, show relatively large deviations from the higher-fidelity method results.

Significant research in the field of Floating Offshore Wind Turbine (FOWT) rotor aerodynamics has been documented in literature, including validated aerodynamic models based on Blade Element Momentum (BEM) and vortex methods, amongst others. However, the effects of platform induced motions on the turbine wake development downstream of the rotor plane or any research related to such areas is rather limited. The aims of this paper are two-fold. Initially, results from a CFD-based Actuator Disc (AD) code for a fixed (non-surging) rotor are compared with those obtained from a Blade Element Momentum (BEM) theory, as well as previously conducted experimental work. Furthermore, the paper also emphasises the effect of tip speed ratio (TSR) on the rotor efficiency. This is followed by the analysis of floating wind turbines specifically in relation to surge displacement, through an AD technique implemented in CFD software, ANSYS Fluent®. The approach couples the Blade Element Theory (BET) for estimating rotating blade loads with a Navier Stokes solver to simulate the turbine wake. With regards to the floating wind turbine cases, the code was slightly altered such that BET was done in a transient manner i.e. following sinusoidal behaviour of waves. The AD simulations were performed for several conditions of TSRs and surge frequencies, at a constant amplitude. Similar to the fixed rotor analysis, significant parameters including thrust and power coefficients, amongst others, were studied against time and surge position. The floating platform data extracted from the AD approach was compared to the non-surging turbine data obtained, to display platform motion effects clearly. Data from hot wire near wake measurements and other simulation methods were also consulted.