Predictions of unsteady HAWT aerodynamics in yawing and pitching using the free vortex method
Introduction
Horizontal-axis wind turbines (HAWTs) operate in unsteady conditions with yaw, shear and gust conditions, among others. Because of the unsteady inflow conditions, the fatigue and extreme loads forced on the blades are generated affecting the life time and the security of wind turbines. Modern large-scale wind turbines use active control techniques (e.g., active pitch or yaw) to control the aerodynamic loads on the blades. Researchers have shown that the advanced active control techniques (e.g., individual pitch control) of HAWTs may play an important role in reducing the fatigue and extreme loads [1]. Therefore, it is necessary to improve the existent methods for the prediction of unsteady wind turbine aerodynamics in the control process.
Due to the high cost and computing time involved, the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations remain difficult to use for unsteady simulations of HAWTs in engineering applications. The conventional method, the Blade-Element-Momentum (BEM) method, is still widely used. To predict the rotor aerodynamics in pitching processes, dynamic wake models (DWMs) are presented [2], [3], [4]. Jose [5] used a modified BEM method with a DWM to couple with a controller to optimise the HAWT's control strategies. However, based on empirical equations, the BEM method lacks the physics to model the complex flow fields. Researchers have presented some correction equations to overcome this limitation. However, the accuracy of the BEM method remains unsatisfactory in complex inflow conditions [6].
The Free-Vortex Method (FVM) is based on the assumption of potential flow. In essence, the FVM is composed of the blade aerodynamic model and the wake model. The blade aerodynamic model describes the flow fields around the blade and computes the circulation strength of the trailing and shed vortices released to the blade wake. The wake model describes vorticity fields in the wake through the use of vortex filaments. These vortex filaments are trailed by each blade and are convected into the downstream wake. As the blade rotates, the spiral wake is generated. The free-vortex method simulates the unsteady flow fields around the blade more accurately than the BEM method. Furthermore, the computational efficiency of the FVM is also higher than that of the CFD method.
Regarding the blade aerodynamic model, the blade could be modelled by the lifting line method [7], the lifting surface method [8], [9] and the panel method [10], [11]. Because the use of the lifting surface method and the panel method to consider the viscous effects is difficult and complex, the nonlinear lifting line method is more widely used for wind turbine aerodynamics. In this method, the aerofoil aerodynamic data, which are usually obtained from experiments or CFD simulations, are used to solve the blade aerodynamic loads and the vortex circulation strengths. Therefore, this method is simpler and more efficient. In the references [12], [13], [14], [15], for the nonlinear lifting line method, the iterative method called the simple iterative method is used to solve the vortex circulation strengths. The iterative method is widely used in the existing lifting line method. However, the simple iterative method may cause a poor convergence. In the iterative method, the iterative process to solve the circulation is independent on each bound vortex filament. Thus, the relevance of the iterative process between different bound vortex filaments is not considered.
With reference to the wake model, two types of wake models are generally used. One is the vortex sheet wake model. The entire wake is modelled by the vortex sheet, which is composed of trailing and shed vortex filaments. Based on the Helmholtz and Kelvin law, the model is highly accurate. Sebastian et al. use the model to simulate the unsteady aerodynamic loads on an offshore floating wind turbine [12], [13], [14]. Jeong et al. [9] use the model to research the aeroelastic characteristics of a wind turbine blade under yawed conditions. Gebhardt et al. [16] use the model to simulate tower shadow effects. However, there are too many vortex filaments in the wake model. The work of Sant [17] has shown that the computational time increases rapidly with the extension of the vortex wake. Thus, a simplified wake model is needed. The wake model is simplified by using tip vortex filaments, which consider trailing vortices and neglect shed vortices. Leishman et al. [8] use the simplified wake model to predict the aerodynamics of a helicopter's rotor. Shen et al. [18] use this model to research the unsteady wind turbine aerodynamics under shear wind conditions.
In this paper, an improved free-vortex method (IFVM) is proposed. The nonlinear lifting line method is used for the blade aerodynamic model. To improve the convergence of the equations for the nonlinear lifting line method, the Newton–Raphson method is used. To increase the computational efficiency and maintain the accuracy of the wake model, a hybrid wake model is proposed. The wake near the rotor is modelled by the vortex sheet model, which consists of the trailing vortex filaments and the shed vortex filaments. In the far wake region, as the vortex sheets roll up at the blade tip, the tip vortex filaments displace the vortex sheet model. The viscous vortex core model is used to consider the viscous effects in the wake. Vortex filaments are numerically solved by the second-order backward difference (PC2B) method. The method is presented by Bagai et al. [19], [20].
The paper is organised as follows: In Section 2, the improved iterative algorithm for the nonlinear lifting line method, the hybrid wake model and the solution process are presented. In Section 3, the testing wind turbines (NREL Phase VI, the TU Delft model turbine and the Tjæreborg wind turbine) and the testing programs are introduced. In Section 4, the IFVM is validated through comparison with the experiments, the BEM method, the FVM [18] and the GDW method [4]. The observed computed loads on the blades in pitching and yawing processes are analysed.
Section snippets
Nonlinear lifting line method
The blade aerodynamic model is based on the nonlinear lifting line method. The blade is modelled by multiple bound vortex filaments, which are located at quarter-chord locations (c/4). The trailing and shed vortices are modelled by trailing and shed straight-line vortex filaments in Fig. 1. The bound vortex filaments are discretised by the cosine segmentation, which gives refinement in the blade tip and root in Fig. 2.
The refined mesh is obtained from
Applications in classical wind turbines simulations
To verify and validate the method, three scales of wind turbines are used here as testing examples:
NREL Phase VI is a stall-regulated turbine. This turbine was designed by the National Renewable Energy Laboratory (NREL). The experiments were performed in the NASA Ames wind tunnel (24.4 × 36.6 m) [25] and is considered a benchmark for the evaluation of wind turbine aerodynamic methods [26].
The TU Delft model turbine was designed for wind tunnel tests. The experiments were performed in the 2.24-m
Convergence history of bound vortex circulations
An iterative algorithm is presented, based on the Newton–Raphson method for solving bound vortex circulations. To validate the method, spanwise distributions of the ΓB and ΔΓB with respect to the iterative step are investigated. The ΓB is the blade bound vortex circulation, and the ΔΓB is the difference of ΓB in the iterative process.
The NREL Phase VI rotor is computed at a yaw angle of 60°, a pitch angle of 3° and a wind speed of 7 m/s. The number of bound vortex filaments of a blade is 28 and
Conclusions
A novel method, which is based on the free-vortex method, for predictions of unsteady aerodynamic loads on a HAWT's blades in yawing and pitching processes is presented in this paper. Three classical wind turbines are computed in the conditions of given yaw and pitch angles and during pitching or yawing processes. The computed results are compared to the experimental data as well as to the results of other methods. The variations of the aerodynamic loads and wakes are analysed.
The results show
Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant No. 51176046) and the National High-tech R&D Program (863 Program, Grant No. 2012AA051303). The authors are grateful for these supports.
References (29)
- et al.
Review of state of the art in smart rotor control research for wind turbines
Prog Aerosp Sci
(2010) - et al.
Predictions of unsteady hawt aerodynamics by lifting line theory
Math Comput Modell
(2001) - et al.
Development of a free vortex wake method code for offshore floating wind turbines
Renew Energy
(2012) - et al.
Numerical simulations of the aerodynamic behavior of large horizontal-axis wind turbines
Int J Hydrogen Energy
(2010) - et al.
Wind turbine aerodynamics and loads control in wind shear flow
Energy
(2011) - et al.
An insight into the separate flow and stall delay for HAWT
Renew Energy
(2011) - et al.
Theoretical predictions of dynamic inflow derivatives
Vertica
(1981) Application of dynamic inflow theory to wind turbine rotors
(2000)Survey of induction dynamics modelling within BEM like codes: dynamic inflow and yawed flow modelling revisited
Control of wind turbines for power regulation and load reduction
(2007)
Comparison of momentum and vortex methods for the aerodynamic analysis of wind turbines
Free-vortex filament methods for the analysis of helicopter rotor wakes
J Aircr
The impact of yaw error on aeroelastic characteristics of a horizontal axis wind turbine blade
Renew Energy
A panel method free-wake code for aeroelastic rotor predictions
Wind Energy
Cited by (68)
Effects of blade torsion on IEA 15MW turbine rotor operation
2023, Renewable EnergyYaw system restart strategy optimization of wind turbines in mountain wind farms based on operational data mining and multi-objective optimization
2023, Engineering Applications of Artificial IntelligenceResearch on the rotor speed and aerodynamic characteristics of a dynamic yawing wind turbine with a short-time uniform wind direction variation
2022, EnergyCitation Excerpt :The dynamic yawing process is formed from continuous static yawed processes. The traditional engineering method for dealing with the dynamic yawing problem is to use a series of load data at the static yawed angle to approximately replace the load in the dynamic yawing process [4]. It can be seen that static yaw research is the basis of dynamic yawing.