Blade Element Momentum Method Research Articles

Numerical study of icing impact on the performance of pitch-regulated large wind turbine

This paper presents a study of the impact of icing on the performance of a pitch-regulated large wind turbine. Numerical simulations of six blade sections of the NREL 5 MW wind turbine at various free stream velocities are performed. Blade Element Momentum (BEM) method along Computational Fluid Dynamics (CFD) bases multiphase numerical simulations are used for this study. Analysis shows that the simulated parameters are in good agreement with the real conditions for each blade element during operation, except for the three-dimensional effects. The analysis of accreted ice shapes and air/droplet flow fields around the blade profile sections was carried out, and the calculation of aerodynamic performance, and energy production degradation was also performed. The tip of the blade is most affected by icing, it is characterized by the greatest changes in the aerodynamic performance. Maximum reduction in the wind turbine performance is estimated to be around 24%.

Atmospheric rotating rig testing of a swept blade tip and comparison with multi-fidelity aeroelastic simulations

Abstract. One promising design solution for increasing the energy production of modern horizontal axis wind turbines is the installation of curved tip extensions. However, since the aeroelastic response of such geometrical add-ons has not been characterized yet, there are currently uncertainties in the application of traditional aerodynamic numerical models. The objective of the present work is twofold. On the one hand, it represents the first effort in the experimental characterization of curved tip extensions in atmospheric flow. On the other hand, it includes a comprehensive validation exercise, accounting for different numerical models for aerodynamic load prediction. The experiments consist of controlled field tests at the outdoor rotating rig at the Risø campus of the Technical University of Denmark (DTU), and consider a swept tip shape. This geometry is the result of an optimized design, focusing on locally maximizing power performance within load constraints compared to an optimal straight tip. The tip model is instrumented with spanwise bands of pressure sensors and is tested in atmospheric inflow conditions. A range of fidelities of aerodynamic models are then used to aeroelastically simulate the test cases and to compare with the measurement data. These aerodynamic codes include a blade element momentum (BEM) method, a vortex-based method coupling a near-wake model with a far-wake model (NW), a lifting-line hybrid wake model (LL), and fully resolved Navier–Stokes computational fluid dynamics (CFD) simulations. Results show that the measured mean normal loading can be captured well with the vortex-based codes and the CFD solver. The observed trends in mean loading are in good agreement with previous wind tunnel tests of a scaled and stiff model of the tip extension. The CFD solution shows a highly three-dimensional flow at the very outboard part of the curved tip that leads to large changes of the angle of the resultant force with respect to the chord. Turbulent simulations using the BEM code and the vortex codes resulted in a good match with the measured standard deviation of the normal force, with some deviations of the BEM results due to the missing root vortex effect.

Novel Machine-Learning-Based Stall Delay Correction Model for Improving Blade Element Momentum Analysis in Wind Turbine Performance Prediction

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.

Multi-Objective Optimization of a Small Horizontal-Axis Wind Turbine Blade for Generating the Maximum Startup Torque at Low Wind Speeds

Generating a high startup torque is a critical factor for the application of small wind turbines in regions with low wind speed. In the present study, the blades of a small wind turbine were designed and optimized to maximize the output power and startup torque. For this purpose, the chord length and the twist angle were considered as design variables, and a multi-objective optimization study was used to assess the optimal blade geometry. The blade element momentum (BEM) technique was used to calculate the design goals and the genetic algorithm was utilized to perform the optimization. The BEM method and the optimization tools were verified with wind tunnel test results of the base turbine and Schmitz equations, respectively. The results showed that from the aerodynamic viewpoint, the blade of a small wind turbine can be divided into two sections: r/R < 0.52, which is responsible for generating the startup torque, and r/R ≥ 0.52, where most of the turbine power is generated. By increasing the chord length and twist angle (especially chord length) in the r/R < 0.52 section and following the ideal chord length and twist angle distributions in the r/R ≥ 0.52 part, a 140% rise in the startup torque of the designed blade was observed with only a 1.5% reduction in power coefficient, compared with the base blade. Thereby, the startup wind speed was reduced from 6 m/s for the base blade to 4 m/s for the designed blade, which provides greater possibilities for the operation of this turbine in areas with lower wind speeds.

An efficient blade sweep correction model for blade element momentum theory

AbstractThis article proposes an efficient correction model that enables the extension of the blade element momentum method (BEM) for swept blades. Standard BEM algorithms, assuming a straight blade in the rotor plane, cannot account for the changes in the induction system introduced by blade sweep. The proposed extension corrects the axial induction regarding two aspects: the azimuthal displacement of the trailed vorticity system and the induction of the curved bound vortex on itself. The extended algorithm requires little additional processing work and maintains BEM's streamtube independent approach. The proposed correction model is applied to simulations of swept blade geometries based on the IEA 15 MW reference wind turbine. Results show good agreement with lifting line simulations that inherently can account for the swept blade geometry.Blade sweep couples bending and torsion deformations by curving the blade axis in the inplane direction. As such, it can be used to passively alleviate loads and, thus, aeroelastically tailor wind turbine blades. The implementation of aeroelastic tailoring techniques, and the aeroelastic analysis in general, becomes increasingly significant with the size of wind turbine rotors continually rising. Due to its low computing complexity, BEM remains a crucial tool in the aerodynamic and aeroelastic analysis of wind turbine rotors. Thus, the proposed correction model contributes to a fast and accurate evaluation of swept blade designs.

Development of blade element momentum (BEM) method for hydropower

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.

Motion and elastic response of wind-tracing floating offshore wind turbines

A multi-unit floating offshore wind turbine concept, the wind-tracing floating offshore wind turbine, is introduced. In this concept, the floating structure is a triangular platform that hosts three 5 MW wind turbines and is moored to the seabed with a turret-bearing mooring system. This mooring system allows the structure to rotate about the turret such that the total yaw moment by the environmental load on the turret is minimized. In this study, the optimum properties of the mooring lines and the location of the turret are determined. To identify the preferred location of the turret, the responses of the structure to combined co-directional and misaligned wind and wave loads are computed. The motions of the structure are obtained with a frequency-domain numerical model integrated with structural finite-element method for hydroelastic and aeroelastic analyses. The hydrodynamic and aerodynamic loads are obtained by wave diffraction theory and steady blade element momentum method, respectively. Finally, with the optimum configuration of the mooring system, the motion and aero- and hydroelastic responses of the fully flexible wind-tracing floating offshore wind turbines to combined waves and wind loads are determined and discussed.

Coupled BEM and two-phase mixture model for surrounding flow of horizontal axial turbine over sediment seabed

Horizontal axial turbine (HAT) is widely used to extract kinetic energy from tidal current. The power absorption of HAT is largely decided by the surrounding flow. A two-phase, sediment-laden mixture model is coupled with the blade element momentum method (BEM) for the impact of HAT on surrounding flow over sediment seabed. The mixture model incorporates theoretical relative velocity, turbulence enhancement from particle wake flow and turbulence damping from high concentration sediment. A blade-induced turbulence (BIT) term is introduced into the mixture model to represent the turbulence production at blade edge. The computed velocity and turbulence are improved by the BIT term in the wake region of HAT. Three turbine hub heights are adopted to investigate the impact of the turbine on sediment seabed and the surrounding flow. Results show that with low turbine hub height, long wake region is generated after the turbine, force exerted on the turbine is asymmetric vertically and thrust and power coefficients decrease. The pattern of bed shear stress is highly dependent on the turbine hub height. The bed shear stress is enhanced under the turbine and strong scour and sediment transport tend to occur on the sediment seabed with low turbine hub height.

Review on validation techniques of blade element momentum method implemented in wind turbines

There are two broad kinds of energy sources: renewable and non-renewable. In the renewable energy sector, significant advancements have been made in wind energy, the world’s fastest-growing renewable energy production technology. Despite this rapid development, the wind industry must still strive to ensure that any device designed for commercial use is reliable and its performance satisfies its economic projections. The critical factor in achieving this target is rotor aerodynamics because the rotor is the part that mainly reacts with the wind. When designing a wind turbine, the assessment of the aerodynamic characteristics of the blades must be accurate. Errors may result in wrong estimates of the turbines’ performance and economic projections. If experimental measurements cannot determine these characteristics, a designer will use alternative methods. Several modeling methods have proven viable solutions for design and analysis purposes, like Blade Element Momentum (BEM) methods. BEM methods analyze the aerodynamic performance of wind turbines, but it requires validation to examine the accuracy of its results. This paper highlights and reviews BEM validation techniques implemented in wind turbine aerodynamics analyses. BEM is validated against experimental data and other advanced models, namely, higher-order vortex and CFD (Computational Fluid Dynamics) models. Nevertheless, the experimental data are essential in wind turbine studies for both understanding the aerodynamic mechanisms and validating all these models.

Increasing power coefficient of small wind turbine over a wide tip speed range by determining proper design tip speed ratio and number of blades

This paper proposes a design strategy based on an understanding of basic rotor aerodynamics principles to achieve aerodynamically efficient small wind turbine rotor by determining proper design tip speed ratio (TSR) and number of blades. In the design and performance analyses of rotors, the blade element momentum (BEM) method was employed in conjunction with the Viterna-Corrigan post-stall model and Buhl’s wake state model. BEM simulations use the Re number dependent airfoil aerodynamic coefficients derived through Xfoil panel code. Reduced design tip speed ratio increased rotor solidity and hence blade Reynolds number. The width of the optimum TSR range, on the other hand, was found to decrease when the design TSR was less than a certain threshold. At high tip speeds, rotors with optimum design TSR were able to maintain an almost constant and near-ideal axial induction factor, resulting widest optimum TSR range for high aerodynamic efficiency. Increasing number of blades ( B) increased CP,max, but further increase in B lowered rotor efficiency due to reduced blade Re number. Based on CFD results, 5-blade SD7032 rotor with a design TSR of 4 achieved 12.3% higher CP,max compared to 0.9 m diameter 3-blade experimental reference rotor. Maximum achievable power coefficient of infinitely many-bladed ideal rotor with design TSR of 4 is 0.559, while CP,max of 5-blade SD7032 rotor is 0.492.

Including the power regulation strategy in aerodynamic optimization of wind turbines for increased design freedom

AbstractIn wind turbine optimization, the standard power regulation strategy follows a constrained trajectory based on the maximum power coefficient. It can be updated automatically during the optimization process by solving a nested maximization problem at each iteration. We argue that this model does not take advantage of the load alleviation potential of the regulation strategy and additionally requires significant computational effort. An alternative approach is proposed, where the rotational speed and pitch angle control points for the entire operation range are set as design variables, changing the problem formulation from nested to one‐level. The nested and one‐level formulations are theoretically and numerically compared on different aerodynamic blade design optimization problems for AEP maximization. The aerodynamics are calculated with a steady‐state blade element momentum method. The one‐level approach increases the design freedom of the problem and allows introducing a secondary objective in the design of the regulation strategy. Numerical results indicate that a standard regulation strategy can still emerge from a one‐level optimization. Second, we illustrate that novel optimal regulation strategies can emerge from the one‐level optimization approach. This is demonstrated by adding a thrust penalty term and a constraint on the maximum thrust. A region of minimal thrust tracking and a peak‐shaving strategy appear automatically in the optimal design.

Equilibrium Behavior of a Tethered Autogyro: Application in Extended Flight and Power Generation

Abstract In this article, we study the characteristics of steady autorotation of a tethered autogyro. The phenomenon of autorotation refers to the natural spinning of a rotor in a wind field. We explore the viability of tethered autogyros as unmanned aerial vehicles (UAVs) for long-duration and energy efficient hovering applications, such as in monitoring or surveillance. The tether provides mooring and can be used to power the rotor and to transmit wind power to the ground when suitable. This is a novel application of autorotation. It requires a generalized formulation and modeling of autorotation, beyond what is reported in the literature. We adopt a model-based approach where the blade element momentum (BEM) method and catenary mechanics are used to model the aerodynamics and the tether, respectively. The resulting model is highly nonlinear and numerical methods are proposed to solve for the equilibria. The model is validated against existing simulation and experimental results in the literature. It is extended to incorporate new features that are pertinent to our application, such as low rotor speeds, regenerative torque for power generation, combining catenary mechanics with aerodynamics, and varying atmospheric conditions with altitude. We characterize the autorotational equilibria over a range of operating conditions involving multiple independent variables. The analysis reveals an optimal operating range of the tip speed ratio of the autogyro under equilibrium. It also indicates the possibility of power generation in large autogyros stationed at high altitudes.

How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?

Abstract. In the present work, a consistent method for calculating the lift and drag forces from the 2-D airfoil data for the dihedral or coned horizontal-axis wind turbines when using generalized lifting-line methods is described. The generalized lifting-line methods refer to the models that discretize the blade radially into sections and use 2-D airfoil data, for example, lifting-line (LL), actuator line (AL), blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods. A consistent interpretation of classic unsteady 2-D thin airfoil theory results reveals that it is necessary to use both the relative flow information at one point on the chord and the chordwise gradient of the flow direction to correctly determine the 2-D aerodynamic force and moment. Equivalently, the magnitude of the force should be determined by the flow at the three-quarter-chord point, while the force direction should be determined by the flow at the quarter-chord point. However, this aspect is generally overlooked, and most implementations in generalized lifting-line methods use only the flow information at one calculation point per section for simplicity. This simplification will not change the performance prediction of planar rotors but will cause an error when applied to non-planar rotors. In this work this effect is investigated using the special case, where the wind turbine blade has only out-of-plane shapes (blade dihedral) and no in-plane shapes (blade sweep), operating under steady-state conditions with uniform inflow applied perpendicular to the rotor plane. The impact of the effect is investigated by comparing the predictions of the steady-state performance of non-planar rotors from the consistent approach of the LL method with the simplified one-point approaches. The results are verified using blade-geometry-resolving Reynolds-averaged Navier–Stokes (RANS) simulations. The numerical investigations confirmed that the full method complying with the thin airfoil theory is necessary to correctly determine the magnitude and direction of the sectional aerodynamic forces for non-planar rotors. The aerodynamic loads of upwind- and downwind-coned blades that are calculated using the LL method, the BEM method, the BEVC method and the AL method are compared for the simplified and the full method. Results using the full method, including different specific implementation schemes, are shown to agree significantly better with fully resolved RANS than the often used simplified one-point approaches.

Comparison of aerodynamic planform optimization of non-planar rotors using blade element momentum method and a vortex cylinder model

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.

An engineering modification to the blade element momentum method for floating wind turbines

The design of next-generation offshore wind rotors for floating applications carries large uncertainties that make it harder to bring costs down. A significant share of this uncertainty is associated with the use of Blade Element Momentum (BEM) methods to run aeroelastic design and loadcase calculations, because the assumptions underlying the momentum theory are violated by the floater motion. This work presents an engineering method for BEM that allows to model generic floater motions and improves the aerodynamic modelling of floating wind turbines. The new model overcomes the challenge of estimating the apparent wind caused by the platform motion in a simple way, which proves to be very effective for rigid aerodynamic simulations. To verify its impact, BEM results with and without the proposed correction are compared to high-fidelity free vortex wake simulations, imposing the same harmonic motion first to the pitch and then to the yaw degree of freedom of the platform. While little differences are found for the yaw motion, the new floating model clearly improves predictions for the platform pitch case in terms of both aerodynamic loads and induction, finding a very good match with the high-fidelity results. An analysis of the verification data provides new valuable insights on the effect of these motions on aerodynamic loads and performance of a floating wind turbine.

Effect of blade contamination on power production of wind turbines

Wind turbines suffer from considerable power losses because of contamination on their blades, that can be due to erosion, wear, smog, insect, sand and dust particle impact. Blade contamination, its effects on the flows over the wind turbine blades and consequent power production losses form the main focus of the present study. These effects are mainly due to increased roughness on the blades leading to earlier laminar-turbulent transition and consequently, thicker boundary-layers on the blades. Early laminar-turbulent transition leads to a larger part of the flow over a blade being turbulent, thus increasing skin friction drag. Thicker boundary-layer on a blade results in blade profile being effectively modified, rendering the flow over the blade depart from ideal. In the present study, the effects of blade contamination on power output of contaminated wind turbine blades is investigated numerically using an in-house computational tool. Blade Element Momentum Method (BEM) combined with the Panel Method is used to calculate the local velocity and angle of attack at the blade sections, together with the power produced by the blade. Trajectories of particles causing contamination are calculated using Lagrangian approach, also yielding the impingement pattern of the particles on the blade surface, i.e. particle collection efficiency distribution. The effects of roughness on the boundary-layer flow are investigated by using an Integral Boundary-Layer Method, which yields the characteristics of the boundary-layer, i.e. laminar-turbulent transition location, increased skin-friction and thickening of the boundary-layer. The blade shape is modified due contamination thickness, the local height of which is assumed to be proportional to the local collection efficiency. Also, the roughness height distribution used in the boundary-layer calculations is assumed to be equal to the contamination thickness distribution on the blades. Power production and consequent losses of wind turbines with contaminated wind turbine blades are studied with respect to variations in particle size, wind speed and roughness height.

Comparison of different fidelity aerodynamic solvers on the IEA 10 MW turbine including novel tip extension geometries

Lifting-line based solvers could supersede the blade element momentum (BEM) method as the industry standard in the near future as rotor sizes of modern wind turbines and computational resources continue to increase. A comparison study between both methods is presented where the IEA 10 MW wind turbine is evaluated in the aero-servo-elastic simulation tool QBlade, comparing the lifting-line free vortex wake method to an unsteady blade element momentum solver. Besides the baseline rotor of the IEA 10 MW turbine, the comparison includes several blade tip extensions, including a swept and a dihedral geometry, to further differentiate capabilities between both methods in aerodynamically complex flow fields. As a reference serve results from equivalent simulations performed with multiple fidelity solvers of the simulation tool HAWC2. Results of a rigid load case demonstrate considerable improvement regarding the aerodynamic accuracy of lifting-line based methods in below rated conditions over BEM codes. The aerodynamic loads on geometrically complex tip extensions in steady conditions prove good capabilities of lower fidelity codes to predict out-of-plane bend shapes but also clear limitations regarding loads on swept geometries. A quasi-steady aeroelastic load case further demonstrates the capability of both QBlade codes to produce comparable results to similar fidelity solvers of the HAWC2 tool on an integral level. A detailed comparison in the time domain shows a larger dependency of the results on the type of structural solver that is used in contrast to the fidelity level of the aerodynamic method.

Comparing wind turbine aeroelastic response predictions for turbines with increasingly flexible blades

Highly flexible blades are becoming more prevalent designs as a potential solution to the transportation challenges associated with large-scale wind turbine rotors. However, there is currently no quantitative definition of “highly flexible” blades. To further develop turbines with highly flexible blades, a precise definition of the term and accurate simulations of turbines with such blades are required. Assumptions made in the traditional aerodynamic model, Blade Element Momentum (BEM) theory, are violated in turbines with flexible blades. However, Free Vortex Wake (FVW) methods can more accurately model these turbine designs. Though more computationally expensive than BEM, FVW methods are still computationally tractable for use in iterative turbine design. The purpose of this work was to determine the blade flexibility at which BEM and FVW methods begin to produce diverging aeroelastic response results. This was accomplished by simulating the BAR-DRC reference turbine with increasingly flexible blades in a range of steady, uniform inflow conditions using OpenFAST, the National Renewable Energy Laboratory’s physics-based turbine engineering tool. Blade-tip deflections confirmed that BEM and FVW results diverge as blade flexibility increases. For the 212 m rotor diameter turbine used in this study, the two methods largely agreed for smaller blade deflections. But their results differed by an average of 5% when the out-of-plane blade-tip deflections exceeded 5% of the blade length and in-plane blade-tip deflections exceeded 1.25% of the blade length, with percent differences approaching 25% at the largest deflections.

Design and Optimization of a Small-Scale Horizontal Axis Wind Turbine Blade for Energy Harvesting at Low Wind Profile Areas

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.

An Inverse Method for Wind Turbine Blade Design with Given Distributions of Load Coefficients

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.