Blade Element Momentum Research Articles

Adjoint-Based High-Fidelity Concurrent Aerodynamic Design Optimization of Wind Turbine

To evaluate novel turbine designs, the wind energy sector extensively depends on computational fluid dynamics (CFD). To use CFD in the design optimization process, where lower-fidelity approaches such as blade element momentum (BEM) are more popular, new tools to increase the accuracy must be developed as the latest wind turbines are larger and the aerodynamics and structural dynamics become more complex. In the present study, a new concurrent aerodynamic shape optimization approach towards multidisciplinary design optimization (MDO) that uses a Reynolds-averaged Navier–Stokes solver in conjunction with a numerical optimization methodology is introduced. A multidisciplinary design optimization tool called DAFoam is used for the NREL phase VI turbine as a baseline geometry. Aerodynamic design optimizations in terms of five different schemes, namely, cross-sectional shape, pitch angle, twist, chord length, and dihedral optimization are conducted. Pointwise, a commercial mesh generator is used to create the numerical meshes. As the adjoint approach is strongly reliant on the mesh quality, up to 17.8 million mesh cells were employed during the mesh convergence and result validation processes, whereas 2.65 million mesh cells were used throughout the design optimization due to the computational cost. The Sparse Nonlinear OPTimizer (SNOPT) is used for the optimization process in the adjoint solver. The torque in the tangential direction is the optimization’s merit function and excellent results are achieved, which shows the promising prospect of applying this approach for transient MDO. This work represents the first attempt to implement DAFoam for wind turbine aerodynamic design optimization.

In-Hover Aerodynamic Analysis of a Small Rotor with a Thin Circular-Arc Airfoil and a Convex Structure at Low Reynolds Number

This study focused on the in-hover aerodynamics of a small rotor with a thin circular-arc airfoil and a convex structure at a low Reynolds number. The method combined computational fluid dynamics (CFD) with the blade element momentum theory (BEMT). The former was used for studying the two-dimensional parametric aerodynamics of the airfoil at a low Reynolds number and the latter was used for the prediction of the rotor's hover performance. A novel thin circular-arc airfoil with a convex structure with a high aerodynamic performance, high structural strength, light weight and easy manufacturing process is presented in this paper. A convex curve on the upper surface was adopted to increase the thickness of the airfoil at partial chord, and a stiffener in the airfoil was installed to improve the structural strength of rotor span-wise. The aerodynamic performance of the airfoil was numerically simulated by the two-dimensional steady and incompressible Navier-Stokes equations. The in-hover performance of the rotor for small-scale vehicles was predicted by an improved version of the blade element momentum theory (BEMT). Finally, a carbon-fiber rotor with the presented airfoil was manufactured that had a diameter of 40 cm and a pitch of 6.2 inches. The analysis results were verified by experiments. It was shown that the maximum calculation errors were below 6%. The improved BEMT can be used in the analysis of in-hover micro-rotor aerodynamics at low Reynolds numbers.

Shape sensing of NREL 5 MW offshore wind turbine blade using iFEM methodology

In this study, the shape sensing of a blade of the NREL 5 MW offshore wind turbine is presented by using the inverse Finite Element Method (iFEM) under real loading conditions. Among the applied forces, the aerodynamic forces are calculated based on the Blade Element Momentum Theory (BEMT). The results of iFEM with full sensors and reduced sensors are compared with the reference Finite Element Method (FEM) analysis to test the accuracy of the iFEM analysis. The practical distribution of the iFEM elements with sensors is explored and the effects of different wind velocities are investigated to make the analysis more practical. Based on numerical results, it is concluded that iFEM is a suitable technique for shape sensing of offshore wind turbines.

Wind turbine electrohydraulic transmission system control for maximum power tracking with pump fault

The wind power generation system plays a significant role in the power sector as it is an environment-friendly green power system, increasing power demand, and technological development in wind power systems. Wind turbine systems are exposed to the harsh environment with continuous variation of wind speed with gusts causing damage and failure in system components along with the fluctuation of generated power. The hydrostatic transmission system has become one of the promising solutions over the gear transmission system for transmitting power from the turbine rotor to the generator. Further to reduce power generation costs in wind power systems, a suitable control system with parametric uncertainty and system fault plays a significant role. In this study, the 5 MW wind turbine model has been developed with the combination of blade element momentum theory and the electrohydraulic transmission system model. Moreover, the wind turbine system model has been imposed fault in the pump of electrohydraulic transmission system. The proposed wind turbine system model has been validated with the existing result. The blade element momentum theory has been used to estimate the optimum pump turbine couple rotational speed for maximum power tracking. Double loop controller has been used for wind turbine power transmission system control. The first controller loop has been used for pump and wind turbine system speed control for maximum power tracking, as a passive fault tolerance controller and the second control loop for motor and generator system speed control to regulate the frequency of the generated power. Interval type 2-fuzzy proportional–integral–derivative controller are suitable for high degree of uncertain system like wind power system due to their footprint of uncertainties. Proper choice of footprint of uncertainty provides robust performance against uncertainties and dynamic performance. Hence, the primary and secondary controller has been developed as interval type 2-fuzzy proportional–integral–derivative with inertial weight local search–based teaching–learning-based optimization controller. The inertial weight local search–based teaching–learning-based optimization interval type 2-fuzzy proportional–integral–derivative controller performance has been studied with benchmark sinusoidal test signals. The proposed inertial weight local search–based teaching–learning-based optimization interval type 2-fuzzy proportional–integral–derivative controller performance has been also compared with conventional proportional–integral–derivative and interval type 2-fuzzy proportional–integral–derivative controller. The proposed system performance has been compared with contemporary reported digital hydrostatic transmission wind turbine system and recently reported controller with consideration of fault in the pump. The proposed inertial weight local search–based teaching–learning-based optimization interval type 2-fuzzy proportional–integral–derivative controller performance has been compared through integral absolute error with interval type 2-fuzzy proportional–integral–derivative controller and recently reported proportional–integral–derivative sliding mode controller obtained as 0.0016, 0.0029, and 0.0031, respectively.

Progress in the validation of rotor aerodynamic codes using field data

Abstract. Within the framework of the fourth phase of the International Energy Agency (IEA) Wind Task 29, a large comparison exercise between measurements and aeroelastic simulations has been carried out featuring three simulation cases in axial, sheared and yawed inflow conditions. Results were obtained from more than 19 simulation tools originating from 12 institutes, ranging in fidelity from blade element momentum (BEM) to computational fluid dynamics (CFDs) and compared to state-of-the-art field measurements from the 2 MW DanAero turbine. More than 15 different variable types ranging from lifting-line variables to blade surface pressures, loads and velocities have been compared for the different conditions, resulting in over 250 comparison plots. The result is a unique insight into the current status and accuracy of rotor aerodynamic modeling. For axial flow conditions, a good agreement was found between the various code types, where a dedicated grid sensitivity study was necessary for the CFD simulations. However, compared to wind tunnel experiments on rotors featuring controlled conditions, it remains a challenge to achieve good agreement of absolute levels between simulations and measurements in the field. For sheared inflow conditions, uncertainties due to rotational and unsteady effects on airfoil data result in the CFD predictions standing out above the codes that need input of sectional airfoil data. However, it was demonstrated that using CFD-synthesized airfoil data is an effective means to bypass this shortcoming. For yawed flow conditions, it was observed that modeling of the skewed wake effect is still problematic for BEM codes where CFD and free vortex wake codes inherently model the underlying physics correctly. The next step is a comparison in turbulent inflow conditions, which is featured in IEA Wind Task 47. Doing this analysis in cooperation under the auspices of the IEA Wind Technology Collaboration Program (TCP) has led to many mutual benefits for the participants. The large size of the consortium brought ample manpower for the analysis where the learning process by combining several complementary experiences and modeling techniques gave valuable insights that could not be found when the analysis is carried out individually.

A comparison of dynamic inflow models for the blade element momentum method

Abstract. With the increase in rotor sizes, the implementation of innovative pitch control strategies, and the first floating solutions entering the market, the importance of unsteady aerodynamic phenomena in the operation of modern offshore wind turbines has increased significantly. Including aerodynamic unsteadiness in blade element momentum (BEM) methods used to simulate wind turbine design envelopes requires specific sub-models. One of them is the dynamic inflow model, which attempts to reproduce the effects of the unsteady wake evolution on the rotor plane induction. Although several models have been proposed, the lack of a consistent and comprehensive comparison makes their relative performance in the simulation of large rotors still uncertain. More importantly, different dynamic inflow model predictions have never been compared for a standard fatigue load case, and thus it is not clear what their impact on the design loads estimated with BEM is. The present study contributes to filling these gaps by implementing all the main dynamic inflow models in a single solver and comparing their relative performance on a 220 m diameter offshore rotor design. Results are compared for simple prescribed blade pitch time histories in uniform inflow conditions first, verifying the predictions against a high-fidelity free-vortex-wake model and showing the benefit of new two-constant models. Then the effect of shed vorticity is investigated in detail, revealing its major contribution to the observed differences between BEM and free-vortex results. Finally, the simulation of a standard fatigue load case prescribing the same blade pitch and rotor speed time histories reveals that including a dynamic inflow model in BEM tends to increase the fatigue load predictions compared to a quasi-steady BEM approach, while the relative differences among the models are limited.

Effects of blade design linearization on aerodynamic performance of horizontal axis wind turbine

AbstractThe optimized chord and twist angle of the preliminary blade design through Blade Element Momentum theory are non-linear distributions, which adds to the complexity of blade manufacture and does not always guarantee the best aerodynamic performance. In this paper, the effect of the linearization on aerodynamic performance using Prandtl-Glauert correction model was investigated through four cases: case 1 and case 2 and case 3, where the chord and the twist angle are linearized and case 4, where sole chord is linearized. The effect of the linearization using Shen correction model while making a comparison to the linearization using Prandtl-Glauert correction model was also studied. The simulation is conducted for S809 wind turbine blade profile. The results show that case 4 using Shen correction model represents the best technique of linearization in terms of higher aerodynamic performance and easy manufacturing process.

Multi-fidelity aerodynamic design and analysis of propellers for a heavy-lift eVTOL

This paper presents a multi-fidelity propeller design and analysis process, and demonstrates it for the preliminary design of a heavy-lift eVTOL vehicle proposed by GKN aerospace, known as Skybus. The multi-fidelity framework integrates tools and results of variable fidelity levels. A global scan of the design space was first carried out at the low-fidelity stage. The low-fidelity output was converted to 3D shapes and grids through an automatic meshing tool, and high-fidelity CFD simulations and gradient-based optimisation were launched to deliver further improved designs. The method was first verified using a benchmark multi-modal test function. The framework was then demonstrated for the propeller design of the Skybus vehicle. Rectangular blade designs with linear twist were first derived through the Blade Element Momentum Theory and used as the input to the low-fidelity stage for simplicity. Upon the baseline design, the low-fidelity stage managed to find an improved shape with 3% reduced power, while the high-fidelity optimisation further reduced the power by 2.2% under the equality thrust constraint. In addition, this work also reports the propeller pitch-RPM performance map tool that has effectively supported the Skybus development through fast performance predictions and operating condition determination. For propellers with both pitch and RPM regulation, the performance map explicitly correlates various performance scopes and to aid optimisation. The multi-fidelity construction of the performance map and demonstrations of its usage are then presented.

Heat Transfer Correlations for Smooth and Rough Airfoils

Low-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The present study develops correlations for an average heat transfer over smooth and rough airfoil. The correlation coefficients were obtained from a CFD database using RANS equations and the Spalart–Allmaras turbulent model. This work studies the NACA 0009, NACA 0012, and NACA 0015 with and without the leading roughness representative of a small ice accretion. The numerical results are validated against lift and drag coefficients from the literature. The heat transfer at the stagnation point compares well with the experimental results. The database indicates a negligible dependency on airfoil thickness. The work presents two correlations from the database analysis: one for the smooth airfoils and one for the rough airfoils. For the zero lift coefficient, the average Nusselt number is maximum. This increases with Re0.636 for the smooth surface and with Re0.85 for the rough surface. As the lift increases, the average Nusselt is reduced by values proportional to the square of the lift coefficient for the smooth surface, while it is reduced by values proportional to Re and the square of the lift coefficient for the rough surface.

Optimal design of horizontal axis tidal current turbine blade

As the tidal current energy has become a significant replacement for conventional energy, the efficiency of the tidal current turbine is highly stressed. An optimal design of the turbine blades can greatly boost the energy conversion efficiency of the turbine. This study focused on the key technologies of hydraulic turbine geometric modeling and reconstruction. The blade element momentum theory was adopted to obtain the distribution of the twist angle and chord of blade, based on which a parameterized model of the original rotor was established. Further, the artificial neural network and the Genetic Algorithm (GA) were utilized to optimize the performance of the original blades. Meanwhile, the approximate model trained by Artificial Neural Network (ANN) was used as the objective function of GA optimization, which greatly improved the iterative speed. Then, an error reactive mechanism was established to ensure the accuracy of the performance prediction. According to numerical simulations based on Computational Fluid Dynamics (CFD), the energy conversion efficiency of the optimized rotor was higher than that of the original rotor under the blade-tip speed ratios considered. The efficiency was improved by 8.5% at most. And the thrust coefficient increased significantly in the optimized model.

Extended Blade Element Momentum Theory for the Design of Small-Scale Wind Turbines

Blade element momentum theory (BEMT) has been widely used in the design of the small scale wind turbine (SSWT). However, the original BEMT has weaknesses in providing the final design values of the wind turbine blade partly due to inaccurate assumptions of infinite number of blades made in deriving the theory. As such, the theory has to be amended in certain areas to form the so called the extended BEMT. In this study, a SSWT blade is designed using the extended BEMT method considering 3 factors: tip loss, low thrust at high axial induction factor, and high angle of attack in post-stall region where 5 correction models applying also the tip loss correction factor have been compared to the original BEMT model. The SSWT rotor has a diameter of 3m. An airfoil, SG6043 known for its suitability for SSWTs is used in this study. Furthermore, the blade geometry prior to the conduct of the shape optimization process are calculated using polynomial obtained from experimental procedures. The effect of infinite number of blades can be seen here to change the axial induction factor, especially at the tip of the blade and as a result increases the lift coefficient, and overpredicts the overall power coefficient and power of the wind turbine. With the Prandtl’s tip loss factor along with the correction model, the corrected final values of aerodynamic performances have been determined.

Extended scaling approach for droplet flow and glaze ice accretion on a rotating wind turbine blade

This paper presents and analyzes a non-dimensional model of the flow field and droplet trajectories with glaze ice accretion on a rotating wind turbine blade. The formulation leads to similitude relationships for glaze ice accretion to evaluate new scaling parameters corresponding to the rotation of the blade. New scaling parameters are developed to determine ice scaling conditions based on the geometry scale factor of a wind turbine blade. The scaling methodology can be used to determine alternative test conditions and predict glaze icing conditions on a full-scale wind turbine blade. Numerical CFD icing simulations are performed using ANSYS FENSAP ICE software. A wind blade model is developed using blade element momentum theory (BEM). Each blade size is tested at specific flow conditions using the scaling equations. Scaled conditions for velocity (streamwise and rotational), droplet size, and icing time are tested. CFD solutions for the flow field are obtained for comparisons of the velocity, droplet trajectories, pressure coefficient distributions, ice thickness, and ice shapes. Recommended parameters to be used for glaze ice scaling on a rotating blade are presented and numerical results are reported to support these recommendations. The paper provides new insights into modeling of glaze ice accretion on large wind turbine blades based on smaller scaled blade sections tested in a laboratory setting.

Comparison studies on aerodynamic performances of a rotating propeller for small-size UAVs

A better prediction of key aerodynamic parameters of a propeller is necessary to improve the performances of unmanned aerial vehicles (UAVs) in different operating environments. In this work, we conduct a systematic investigation on an APC 1045 multi-rotor propeller to analyze its aerodynamic performances with wind tunnel tests, blade element momentum theory (BEMT) and 3D computational fluid dynamics (CFD). The theoretical BEMT model provides accurate and reliable estimation at the advance ratios ≤0.567, whereas the method begins to stall at advance ratios ≥0.661. Conversely, the results obtained from CFD simulations agree well with the experiments at all advance ratios, with the differences in thrust- and power coefficients around 5% and 4%, respectively. The present work compares the aerodynamic parameters while varying the freestream velocity to investigate the limitations and advantages of the use of the aforementioned three different methods. Given the limitation of the BEMT, it is found to be reliable enough to estimate the aerodynamic parameters of a small-scaled fixed-pitch propeller. In addition, a more comprehensive investigation of the BEMT shows that increasing advance ratio decreases the lifting portion of the propeller blade, i.e. incurring more losses associated with the hub and tip.

Coupled dynamic analysis of horizontal axis floating offshore wind turbines with a spar buoy floater

Coupled dynamic analysis of a floating offshore wind turbine (FOWT) is predicted with in-house ITU-WAVE computational tool. The hydrodynamic parameters are approximated with time marching of boundary integral equation whilst aerodynamic parameters are solved with unsteady blade element momentum method. In addition, forces on FOWT due to mooring lines are predicted with quasi-static analysis whilst hydrodynamic viscous effects are included with Morison equation. FOWT’s blades are considered as an elastic structure whilst tower is considered as a rigid structure. The effects of steady wind speed on surge motion spectrum decrease the spectrum amplitude over wave frequency ranges, but this effect is not significant. The duration of time domain simulation plays significant role in the region of surge and pitch resonant frequencies. The numerical results of in-house ITU-WAVE computational code for eigenfrequencies of blades, aerodynamics and hydrodynamics parameters are validated against other numerical results which shows satisfactory agreements.

Rapid Blade Shape Optimization for Contra-Rotating Propellers for eVTOL Aircraft Considering the Aerodynamic Interference

The rising interest in the evolvability of electric vertical takeoff and landing (eVTOL) promises substantial potential in the field of urban air mobility (UAM). Challenges in energy storage density and geometry restriction both emphasize the propeller efficiency for endurance and takeoff weight, whereas the contra-rotating propellers (CRP) advantage is balancing high thrust and efficiency over a single propeller. The aim of this paper is twofold: (i) to present a novel rapid CRP blade shape optimization framework and (ii) to study the impact of the dual propellers revolution speed allocations on the overall CRP power efficiency. The core of the framework is the blade element momentum theory (BEMT)-based blade shape optimization considering the wake effect of the upper propeller by the rotational CFD (computational fluid dynamics) actuator-disc simulation method. The results show that for the same thrust, the optimized CRP at the equal revolution speed is superior to the original (upper-lower-identical) one by 5.9% in thrust-to-power ratio. The overall efficiency can be additionally lifted by 5.3% when the dual propellers share similar torques. By excluding the integral propeller CFD simulation and empirical parameters estimation, the framework enables the swift obtaining of an optimized CRP scheme while maintaining robustness as well.

Uncertainty quantification study of the aerodynamic performance of high-altitude propellers

Performance evaluations for propellers operating at high altitudes are subject to increased uncertainty due to scarce experimental or flight data and difficulties in modeling low Reynolds number flows. For this reason, the Polynomial Chaos Expansion (PCE) method is used in this paper to assess the performance uncertainty of propellers operating at high altitudes. Aleatoric (i.e. linked to the geometry or operating conditions) and epistemic (i.e. linked to the mathematical model describing the flow) uncertainty variables are included in this study to estimate the total uncertainty related to performance predictions made by two physical models, namely 3D RANS with the use of γ−Reθ transition model and Blade Element Momentum Theory (BEMT). In order to validate the proposed method, multipoint uncertainty quantification (UQ) studies are performed for two benchmark propeller geometries under various operating conditions for which experimental data are available. The UQ method is further illustrated on a propeller operating at high altitude. The efficacy of UQ with Computational Fluid Dynamics (CFD) and BEMT is compared and the most influential uncertain variables are found using Sobol's total order indices. As a result of the CFD-based uncertainty quantification studies, two major uncertain variables are identified, providing a direction for more computationally affordable UQ studies.

Design and Mass Optimization of Numerical Models for Composite Wind Turbine Blades

In this paper, a constrained optimization by linear approximation (COBYLA) algorithm is used to optimize the design of a 5 MW wind turbine blade. In the process of blade material modeling, the actual manufacturing conditions are considered, and the load of blades under 50 m/s wind conditions is analyzed based on the blade element momentum (BEM) method. Mass optimization was achieved by removing material from the shear webs. In addition, constraints such as tip displacement, stress, and frequency during blade design were considered. The results show that the mass is reduced by about 1.7% after removing material from blade webs, while the structural response of the blade remains unchanged. This case provides a practical reference for commercial wind turbine blades.

Blade element momentum theory for a skewed coaxial turbine

A coaxial turbine under skew with significant rotor spacing has the potential for increased power output compared to a flow-aligned turbine due to a portion of the downstream rotor experiencing freestream velocity, referred to as a fresh flow region. A lab-scale prototype was designed and built to investigate the skew-to-power relationship of a coaxial turbine system as it compared to a blade element momentum theory model with multiple, sheared streamtubes representing the downstream rotor fresh flow region. The inclusion of the downstream rotor fresh flow region in the theoretical analysis is compared to the experimental data. The results support that the torque and power performance of the downstream rotor and overall skewed coaxial turbine system are predicted more accurately.

An investigation of the Steady-State and Fatigue Problems of a Small Wind Turbine Blade Based on the Interactive Design Approach

A wind turbine blade is an essential system of wind energy production. During the operation of the blade, it is subjected to loads resulting from the impact of the wind on the surface of the blade. This leads to appear large deflections and high fatigue stresses in the structure of blades. In this paper, a 5 kW horizontal axis wind turbine blade model is designed and optimized using a new MATLAB code based on blade element momentum (BEM) theory.The aerodynamic shape of the blade has been improved compared with the initial design, the wind turbine power has been increased by 7% and the power coefficient has been increased by 8%. The finite Element Method was used to calculate the loads applied to the blade based on Computational Fluid Dynamics (CFD) and BEM theory.High agreements were obtained between the results of both approaches (CFD and BEM).The ANSYS software was also used to simulate and optimize the structure of the blade by applying variable static loads 3.3, 6, and 8.3 kg and compared the results with the experimental results. It was reduced the maximum deflectionswith 37%, 42.85%, and 42.61% when using CFRP material and 4.5%, 15.45%, and 16.19% for GFRP material that corresponds to the applied forces. Based on the results, the mass of the optimized model decreased by 47.86% for GFRP and 71.24% for CFRP. IEC 61400.2 standard was used to estimate thefatigue loads, damage, blade life prediction, and verify blade safety usinga Simplified Load Model(SLM) and FAST software. It was found that the blade will be safe under extreme wind loads, and the lifetime of the wind blade (GFRP) is 5.5 years and 10.25 years,according to SLM and FAST software, respectively. At the same time, the lifetime of the wind blade (CFRP)is more than 20 years, according to the two applied methods.

XFOIL Performance Validation for Medium-Scale Variable Pitch UAV Rotor Systems

This study focuses on experimentally validating the performance of XFOIL, a sophisticated software airfoil analysis tool used for approximating lift and drag coefficients. XFOIL output data was incorporated into a theoretical model simulating a variable pitch rotor system operating in a hovering state. The output of the Blade Element Momentum Theory (BEMT) rotor model is compared to thrust and power output performance data collected from a constructed rotor test bench and analysed in MATLAB. Using XFOIL as input, the BEMT rotor model was observed to yield good robust results when compared to experimental data, but demonstrated sensitivity to airfoil performance characteristics, laying the groundwork for future empirical validation. In comparing BEMT model performance, it was interesting to find that thrust performance remained within tolerance in contrast to an overprediction of rotor power output resulting from XFOIL drag at high blade pitch angles. Upon further interrogation by means of variable isolation, XFOIL demonstrated instability resulting from sensitivity to variability of model constraints. Modification of rotor geometry definitions or environmental constants beyond the test environment framework showed simulated systems may not necessarily behave reliably nor enhance output performance. This highlights the critical importance and utility of experimentation for understanding theoretical model behaviour or validating simulation output performance.