Blade Element Momentum Method Research Articles

Simulation of unsteady ice accretion on horizontal axis wind turbine blade sections in turbulent wind shear condition

This study presents a comprehensive simulation approach to quantify power losses in horizontal axis wind turbines under environmental icing conditions. It investigates how wind shear and turbulence affect a 2.5 MW wind turbine's performance, particularly under ice accretion. Turbulence intensity, ranging from 1% to 20%, impacts the relative flow fluctuations and angle of attack on the blade sections, influencing the aerodynamic penalty ratio. The incoming wind speed and the flow angle at various blade sections were determined using the unsteady blade element momentum method, considering vortex induction effects and Prandtl and Glauert corrections. For ice accretion analysis, a fully unsteady simulation of computational grid motion due to ice accretion was performed, along with the solution of the multiphase flow of water dispersed particles in cold air, derived from the psychrometric chart. The findings highlight the significant impact of the incoming turbulent wind fluctuations on the dispersion of the ice shape formed at sections corresponding to their radial position on the blade according to the momentary angle of attack fluctuations. The formation of ice profiles along the blade has led to a subsequent degradation in the aerodynamic efficiency of the blade sections, which is directly proportional to the escalation in turbulence intensity. This phenomenon leads to a continual reduction in the power output of the wind turbine. This research provides valuable insights into the performance of wind turbines under icing conditions in real wind fluctuations.

The influence of the rotor spacing distance and rotating speed ratio on the power production of dual rotor wind turbines using a modified two-way interaction blade element momentum method

The present study aims to develop an accurate and fast improved blade element method (BEM) with two-way rotor-rotor interaction model which can account for two-way rotor-rotor interaction and the influence of rotor spacing while most previous BEM models for co-axis dual rotor wind turbines (DRWT) ignore the rear to front rotor interaction effect. A modified BEM model distinct from computationally intensive Computation Fluids Dynamics (CFD) model, is proposed for DRWTs. Validation of the present model is conducted by comparing it with experimental data from referenced literature for both co- and counter-rotating configuration. In our case study, for both co- and counter-rotating configurations, the power coefficient (CP) maps exhibit a double-hump shape instead of a single peak on the power output -λ curve observed in a single rotor wind turbine system. This characteristic may lead the DRWT to a local CPmax condition rather than the global CPmax while pursing the optimum operational condition. Although the counter-rotating DRWT can achieve a higher CPmax for most rotor spacing ratio (S/R) cases, it exhibits inferior power output than the single rotor for the S/R = 0.1 case. The present model can serve as a rapid and accurate model for configuring and control strategy evaluating DRWTs.

A Comparison of a Three Blade and Five Blade Wind Turbine in Terms of the Mechanical Properties Using the Q-Blade Software

يمكن لتوربينات الرياح المنتشرة في مزارع الرياح على نطاق المرافق أن تدعم تلبية رغبات الطاقة المستقبلية وتقليل انبعاثات ثاني أكسيد الكربون عن طريق تقليل متطلبات الطاقة من الوقود الأحفوري. مع ارتفاع درجة حرارة الهواء على مدار اليوم، تزداد سرعة الرياح بسبب تدرجات درجة الحرارة، والتي تنتج تدرجًا في الكثافة / الضغط، مما يؤدي إلى حركة الهواء التي تواجهها توربينات الرياح. اعتمادًا على تضاريس الأرض، يمكن أن تواجه الرياح وتوجه في الوديان بين التلال وفوقها حيث تتدفق وتتبع منحنيات الأرض. تنتج هذه التضاريس زيادة في سرعة الرياح في القمم والتلال. في هذا العمل، تم تصميم شفرة دوار توربينات الرياح الأفقية الصغيرة للعمل في ظل سرعة الرياح المنخفضة، باستخدام برنامج (Q-Blade). استنادًا إلى نظرية عنصر الشفرة (BEM). مع الجنيح NACA3712. تم استخدام دوار ثلاثي الشفرات ودوار بخمس شفرات بناءً على نوع التوربين وحجم الدوار لتوليد الطاقة الميكانيكية من طاقة الرياح. تم إجراء مقارنة وتحليل قوة التوربين ومعامل القدرة ومعامل عزم الدوران عند سرعة رياح منخفضة ((1m/s-8m/s وتم الحصول على نتائج دقيقة للغاية. وجد أن أفضل أداء يمكن أن يعمل فيه دوار توربيني ثلاثي الشفرات بقدرة توربينية تبلغ (955W) كما تم الحصول على قدرة التوربين ((582W للدوار خماسي الشفرات. وجد أن تصميم توربينة رياح أفقية صغيرة بخمس ريش أفضل من التوربين بثلاث ريش ومناسب للعمل في المناطق ذات سرعة الرياح المنخفضة وبكفاءة عالية مقارنة بحجم التوربين.

Aerodynamic efficiency assessment of a cross-axis wind turbine integrated with an offshore deflector

The present work examines the performance of an offshore cross-axis wind turbine (CAWT) with a flow deflector by integrating numerical and analytical methods. The deflector's geometry redirects flow in all directions, causing it to exit vertically and collide with the wind turbine's horizontal blades. In contrast, the blades of a vertical axis wind turbine (VAWT) harness the power of horizontal wind flow. The total power absorbed by the horizontal and vertical turbine blades represents the power of CAWT. In this study, the speed of the outflow from the deflector was initially determined through numerical simulation. The numerical simulation output was then utilized as an input for analytical Double Multiple Stream Tube (DMST) and Blade Element Momentum (BEM) methods to evaluate the vertical and horizontal turbine blades, respectively. This approach reduces the overall simulation time and establishes an offline coupling between analytical and numerical approaches. The findings of this research have unveiled a promising future for offshore wind energy generation. Through the implementation of a modeled deflector on a Cross-Axis Wind Turbine (CAWT), the power output reached a remarkable 19 KW with a power coefficient of 0.35 at an 8.4 m/s wind speed. The results indicate that the CAWT with the deflector produced a power output 35 % higher and was 45 % more efficient than a single Vertical-Axis Wind Turbine (VAWT). These outcomes illustrate the potential for greater energy production and efficiency in offshore wind farms.

RMSE POWER COEFFICIENT OF WIND TURBINES WITH INVERSE TOQUE-SPEED CONTROL

The Blade Element Momentum (BEM) method stands out among various turbine modelling techniques due to its integration of airfoil aerodynamics with momentum theory, allowing detailed force calculations on blade elements. While traditional methods like BEM and Wake Models are efficient for initial turbine design, advancements in computational power have enabled the use of Computational Fluid Dynamics (CFD) for more accurate simulations. Although these models are precise, they are computationally intensive, leading to the continued use of simpler empirical methods, such as the static power coefficient approach, in power system studies. Future research aims to validate and implement dynamic estimation models to account for wind variability and turbine control dynamics. Traditional constant torque-speed control strategies maintain a constant generator speed by using a fixed electromagnetic torque command and adjusting the pitch angle when wind speed exceeds the rated value. However, if the pitch control does not respond quickly enough, rotor acceleration can occur, leading to increased power beyond the generator’s rating. To mitigate this, the pitch control mechanism must react promptly to adjust the turbine's torque profile, ensuring convergence to the rated operating point and avoiding prolonged generator overload. To reduce the burden on the pitch-control system, an inverse torque-speed control approach is proposed, where the electromagnetic torque is dynamically adjusted based on real-time rotor speed data. This method aims to achieve rated power operation with improved responsiveness and reduced stress on the pitch-control mechanism.

Circuit representation of ducted hydrokinetic turbines based on blade element momentum method

Hydrokinetic turbines are designed and deployed worldwide due to the vast scale of hydrokinetic energy existing in tidal streams, ocean currents, and riverine flow. Duct augmentation is a design feature potentially to improve power extraction, reduce maximum stresses, and reduce the cost of electricity. However, there is a lack of computationally efficient and accurate predictive models to evaluate and compare ducted and open turbines. This research proposes a lumped circuit representation model for ducted hydrokinetic turbines. The equivalent duct, rotor, and wake resistances are derived from the control volume analysis based on the axial momentum theory and blade element momentum method. The wake resistance, which represents the viscous mixing loss in the very far wake, is critical for turbine farm design. The duct resistances, which depend on the duct thrust, efficiency, and duct-rotor interactions are identified by computational fluid dynamics. Based on the proposed model, parametric investigations of distributed rotor thrust, torque, power, and wake loss for different duct and blade geometries are conducted. The model can facilitate preliminary parametric design, co-design, real-time control to enhance power extraction and dynamic stabilities, and turbine farm design. A design optimization case is demonstrated to illustrate the utility of the proposed model.

How does the blade element momentum method see swept or prebent blades?

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.

A correction model for the effect of spanwise flow on the viscous force contribution in BEM and Lifting Line methods

Design optimization and aeroelastic load evaluation for wind turbines are still infeasible for CFD due to computational cost. These tasks are carried out using 3D engineering aerodynamic methods, where the local aerodynamic loads are obtained from tabulated 2D aerodynamic polars, which makes the models fast. With recent developments such as highly flexible blades, coned/prebent/swept blades, the relative inflow direction to the “inner” 2D airfoil section systems can have a significant component in the spanwise direction. The Crossflow Principle (CP) is used to treat the effects of this in a physically consistent manner. Cases dominated by pressure forces are described well with the CP method, but it is shown in the paper that CP fails to describe the part of the forces stemming from the friction forces correctly. It is shown in the paper that the power loss due to friction forces will be underestimated with the crossflow principle for rotors with significantly swept blades or other designs with a significant amount of local crossflow on the blades. The present work presents a simple model to correct the baseline crossflow principle method to take into account also the friction force part in a consistent manner. The model is validated with 3D CFD results on a 2D airfoil section. It is shown that the new model successfully corrects for the addition of the viscous forces due to spanwise flow component. The paper includes examples of the effect of using the model on rotor designs with different amounts of blade sweep simulated using a blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods.

Enhanced Modeling of Joint Yaw and Axial Induction Control Using Blade Element Momentum Methods

Wind turbine control via concurrent yaw misalignment and axial induction control has demonstrated potential for improving wind farm power output and mitigating structural loads. However, the complex aerodynamic interplay between these two effects requires deeper investigation. This study presents a modified blade element momentum (BEM) model that matches rotor-averaged quantities to an actuator disk model of yawed rotor induction, enabling analysis of joint yaw-induction control using realistic turbine control inputs. The BEM approach reveals that common torque control strategies such as K − Ω2 exhibit sub-optimal performance under yawed conditions. Notably, the power-yaw and thrust-yaw sensitivities vary significantly depending on the chosen control strategy, contrary to common modeling assumptions. In the context of wind farm control, employing induction control which minimizes the thrust coefficient proves most effective at reducing wake strength for a given power output across all yaw angles. Results indicate that while yaw control deflects wakes effectively, induction control more directly influences wake velocity magnitude, underscoring their complementary effects. This study advances a fundamental understanding of turbine aerodynamic responses in yawed operation and sets the stage for modeling joint yaw and induction control in wind farms.

Uncertainty Quantification Analysis in the Blade Element Momentum Method

The blade element momentum (BEM) method is a widely used non-linear model for the efficient performance evaluation and design of wind turbines. The aim of this paper is to quantify the uncertainty related to BEM model inputs and sub-models, and investigate how these propagate through the model. Uncertainties related to viscous dissipation in the wake, aerofoil force coefficients, and tip-loss models are considered. Global sensitivity to these parameters is analysed using non-intrusive polynomial chaos expansion, which provides a structured method for uncertainty propagation and sensitivity quantification. Sobol indices are employed to rank the relative importance of each factor to the overall uncertainty in the system. By analysing the NREL 5 MW and DTU 10 MW reference wind turbines, we observe that the different rotors may exhibit different levels of sensitivity to input parameters. The effect of viscous mixing in the turbine wake is found to have a significant impact on predicted rotor performance. Uncertainty in tip-loss model coefficients is also found to generally be important, particularly when evaluating spanwise variations in rotor loads. Uncertainty quantification has the potential to improve understanding of BEM modelling, and provide guidance on the importance of sub-model improvements.

Multi-fidelity, steady-state aeroelastic modelling of a 22-megawatt wind turbine

In this work we present multi-fidelity steady-state aeroelastic framework that leverages the state-of-the-art simulation tool HAWC2 for the structural model, and a variety of aerodynamic models, comprising of the low fidelity blade element momentum (BEM) method, the medium fidelity blade element vortex cylinder (BEVC) method and the coupled near wake and vortex cylinder method, and finally the high-fidelity CFD solver EllipSys3D. The aeroelastic framework is part of AESOpt, an aerostructural framework for design of wind turbine blades. The different aerodynamic models are applied to compute the aeroelastic steady state of the newly designed IEA 22 MW Reference Wind Turbine. The results show a very good agreement between the medium- and high-fidelity aerodynamic models with a maximum of 2.7% difference between the high-fidelity aeroelastic response and that of the lower fidelities.

Reduced-order modelling of floating offshore wind turbine: Aero-hydro-elastic stability analysis

A reduced-order aero-hydro-elastic analysis tool for performing the stability analysis on floating offshore wind turbines is presented. In this work, a high-order non-linear aero-elastic model initially developed for onshore wind turbines is extended by utilizing a super-element body, which models the floating platform, the mooring system and the hydrodynamic contributions. The turbine structure is modelled by a Finite beam Element Method, and the aerodynamic loads are modelled by the Blade Element Momentum method coupled with a Beddoes-Leishman type dynamic stall model in a state-space formulation. The linearization is performed around steady state equilibrium at any given mean wind speeds, rotor speeds and collective blade pitch angles utilizing Coleman transformation to remove the periodic terms. The order reduction is based on two projections to reduce the number of structural states and aerodynamic states separately using the structural modal project matrix and the aerodynamic shape functions. Concurrently, we investigate the effect of unsteady aerodynamic states on the stability analysis of a floating wind turbine. The results show the low-order aero-hydro-elastic model expands the scope of numerical tools available for conducting structural modal analysis and aero-hydro-elastic stability analysis on floating wind turbines.

Efficient prediction of tidal turbine fatigue loading using turbulent onset flow from Large Eddy Simulations

To maximise the availability of power extraction from a tidal stream site, tidal turbines need to be able to operate reliably when located within arrays. This requires a thorough understanding of the operating conditions, which include turbulence, velocity shear due to bed proximity and roughness, ocean waves and due to upstream turbine wakes, over the range of flow speeds that contribute to the loading experienced by the devices. High-fidelity models such as Large Eddy Simulation (LES) can be used to represent these complex flow conditions and turbine device models can be embedded to predict loading. However, to inform micro-siting of multiple turbines with an array, the computational cost of performing multiple simulations of this type is impractical. Unsteady onset conditions can be generated from the LES to be used in an offline coupling fashion as input to lower-fidelity load prediction models to enable computationally efficient array design. In this study, an in-house Blade Element Momentum (BEM) method is assessed for prediction of the unsteady loads on the turbines of a floating tidal device with unsteady inflow developed with the in-house LES solver DOFAS. Load predictions are compared to those obtained using the same unsteady inflow to the commercial tool Tidal Bladed and from an Actuator Line Model (ALM) embedded in the LES solver. Estimates of fatigue loads differ by up to 3% for mean thrust and 11% for blade root bending moment for a turbine subject to a turbulent channel flow. When subjected to more complex flows typical of a turbine wake, the predictions of rotor thrust fatigue differ by up to 10%, with loads reduced by the inclusion of a pitch controller.

Hydro- and aero-elastic response of floating offshore wind turbines to combined waves and wind in frequency domain

An analytical approach and numerical solution to determine coupled aeroelastic and hydroelastic response of floating offshore wind turbines of arbitrary shape to combined wind and wave loads is presented. The model considers simultaneously the aerodynamic and hydrodynamic loads on an FOWT and integrates these with finite element method for structural analysis due to the combined loads. The hydrodynamic and aerodynamic loads are determined based on the linear wave diffraction theory and steady blade element momentum method, respectively, and the solution is obtained in frequency domain. The structure may be fixed or floating, located in arbitrary water depth, and may host single or multiple wind towers. The model captures the complete translational and rotational motions of the body in three dimensions, and the elasticity of the blades, tower and the floating platform. To assess the performance of the model, rigid and elastic responses of a FOWT to combined wave and wind loads are computed and compared with available laboratory measurements and other theoretical approaches where possible, and overall very good agreement is observed. The model developed in this study addresses directly three shortcomings of existing approaches used for the analysis of FOWTs, namely (i) determination of the elastic responses of the entire structure including the floating platform, (ii) analysis of the motion and elastic response of FOWTs in frequency domain, and (iii) assessment of responses of FOWTs with single or multiple wind towers.

Inviscid analysis of horizontal axis wind turbines using distributed vorticity elements

The primary tool currently used for a wind turbine preliminary design is the blade element momentum method, which lacks a detailed wake model and relies on an assumption of non-interacting streamtubes. These simplifications limit the designer's ability to tailor the blade shape to minimize the induced power loss of the rotor. Improved prediction of the induced velocity distribution on the blades can be achieved through the use of vortex-based models at a computational cost low enough for use in design processes requiring many iterations. This paper presents the implementation of a potential flow, lifting-surface methodology using elements of distributed vorticity. The use of such elements provides several advantages including higher resolution than filament-based methods, simulation of non-planar blade planforms, and avoids the need for empirical corrections. Because the wake has a strong influence on the flow at the rotor, the accurate prediction of its geometry is highly important for wind turbine analysis. To this end, a force-free relaxed-wake model is presented as well as less numerically intensive fixed-wake and hybrid-wake models. Comparison is made to the blade element momentum method and Goldstein's theoretical solution for the ideal lightly loaded rotor.

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

Field-data-based validation of an aero-servo-elastic solver for high-fidelity large-eddy simulations of industrial wind turbines

Abstract. To design the next generations of wind turbines, engineers from the wind energy industry must now have access to new numerical tools, allowing the high-fidelity simulation of complex physical phenomena and thus a further calibration of lower-order models. For instance, the rotors of offshore wind turbines, whose diameters can now exceed 200 m, are highly flexible and fluid–structure interactions cannot be neglected any longer. Accordingly, this paper presents a new aero-servo-elastic solver designed to perform high-fidelity large-eddy simulation (LES) of wind turbines, as well as of rotor–wake interactions classically occurring in wind farms. In this framework, the turbine blades are modeled as flexible actuator lines. In terms of operating parameters (rotation speed and pitch angles) and power output, the solver is first validated against field data from the Westermost Rough offshore wind farm, for three different operation points. A very good agreement between the numerical results and field data is obtained. To push the validation further, additional results are compared to those given by a certified aero-servo-elastic solver used in the industry, which relies on a blade element momentum (BEM) method. The internal loads throughout the first blade and the deflections at the tip are studied in detail, and some discrepancies are observed. Of a reasonable amplitude overall, those are legitimately related to intrinsic modeling differences between the two solvers.

The effect of airfoil type and wind speed on HAWT wind turbine performance using QBlade software

Energy transition is critical in the context of the current global climate situation. It is also important for Indonesia to achieve Sustainable Development in the Clean and Affordable Energy sector; given that the country’s primary energy mix is still dominated by fossil energy, which accounts for around 90% of energy production. Wind is a new renewable energy that can be utilized to produce electrical energy through energy conversion. In addition, wind power is a type of renewable energy that has the lowest price compared to other types. This study aims to determine the characteristics of the selected airfoil types, including; NACA 2412, NACA 4412, NACA 6409 and SG6043. These characteristics included lift and drag coefficient. The BEM (Blade Element Momentum) method approach was used to obtain the performance parameter values of the airfoil and wind turbine, which include; lift and drag coefficient, lift-to-drag ratio, power coefficient, torque coefficient, turbine rotation, and power with variations ranging from angle of attack, tip speed ratio and wind speed. The results obtained for the highest lift coefficient value produced by SG6043 airfoil of 1.838 at an angle of attack of 16 °, and the lowest value produced by NACA 2412 of 1.529 at an angle of attack of 16 °. For the drag coefficient value, all types of airfoils produced values that increased as the angle of attack increased. Then, the highest power coefficient value produced by the SG6043 airfoil of 0.496 at TSR 5, and the lowest value produced by the NACA 6409 airfoil of 0.481 at TSR 5. Then, the power generated was based on the results of the power coefficient, where the SG6043 airfoil produced the greatest power for each wind speed used, and the NACA 6409 airfoil produced the lowest power. From the results of this study, it can also be concluded that the SG6043 airfoil produced the best performance compared to other types used.

Two-body dynamic simulations of a combined semi-submersible floating offshore wind turbine and torus wave energy converter

Dynamic responses of a combined wind and wave energy system which consist of a 5MW semi-submersible floating offshore wind turbine (FOWT) and a torus-shaped wave energy converter (WEC) are investigated. In the investigated configuration, the torus WEC is constrained to move only in the heave direction with respect to the FOWT. This results in a two-body dynamic system that allows for the extraction of wave energy through the relative heave motion. A Modelica-based multi-body system (MBS) code is used to perform fully coupled dynamic analyses of the combined system. The wind turbine loads are calculated using the state-of-the-art Blade Element Momentum (BEM) method, while the wave power take-off (PTO) system is modelled as a linear spring and a viscous damper. A case study is presented where the mass of the torus is varied to investigate the impact on the two-body dynamics of the combined system. The system performance is assessed in terms of the maximum wave power absorption and the quality of wind power production.

Numerical Modeling and Application of Horizontal-Axis Wind Turbine Arrays in Large Wind Farms

The global supply of energy is still tight, even with the rise of renewable energy utilization and abundant wind energy. More and more large wind farms have been installed globally. As of 2020, China’s total installed capacity accounted for 38.8%, far ahead of other countries. The layout of horizontal-axis wind turbine (HAWT) arrays in large wind farms poses three main issues: (1) How to select a site. (2) How to arrange the HAWT arrays to achieve greater power extraction at a specific wind farm. (3) How to reduce the noise generated by HAWTs. The numerical simulation of a HAWT wake field generally includes the analytical method (AM), vortex-lattice or vortex particle method (VM), panel method (PM), blade element momentum method (BEM), generalized actuator method (GAM), and direct modeling method (DM). Considering the computational cost, this paper combines DMs and mainly adopts the BEM-CFD coupling method, including uniform and non-uniform loading of axial force. Forty specially designed numerical experiments were carried out, which show that: (1) the BEM-CFD method greatly improves the calculation speed within the accuracy range of a thrust coefficient less than 2.5%, making it very suitable for the calculation of large wind farm HAWT arrays; (2) for regular HAWT arrays, it is reasonable to choose a 6D spacing in the wind direction and a 4D spacing in the crosswind direction for simplicity in practice.