时间步进自由尾迹方法建模及水平轴风力机气动性能分析
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摘要
在风力机的设计和校核过程中,气动性能预测是非常重要的环节。设计出风力机的桨叶气动外形后,计算其气动性能,可以作为对设计结果的评价;反之,气动性能计算结果可以作为反馈,为桨叶气动外形的修正提供依据。但是风力机运行在复杂的自然环境中,风剪切、来流风速及风向的改变以及塔影效应等使得准确预估风轮的气动载荷成为非常困难的工作。因此,在现阶段的风力机设计中,主要采用安全因子来补偿未知载荷,使得风力发电的投资增加,竞争力下降。
风力机在旋转过程中会从桨叶后缘拖出尾迹,形成强烈的卷起涡和内部涡面,这些尾涡旋绕在桨叶附近,会对转子的气动性能产生重要的影响。尾涡的强度由叶素的几何参数、运动参数及桨叶气动载荷决定;反过来,涡的诱导效应又会改变转子的速度场,进而影响涡的强度。因此,桨叶和尾迹之间存在相互干扰,对尾涡的计算是风力机气动载荷分析的关键,也是开展风力机空气动力学研究的基础,具有重要的科学意义和工程实际意义。本文基于时间步进自由尾迹方法对风力机的尾迹及气动性能进行了研究,主要内容包括:
①针对目前风力机气动载荷预测中常用的动量—叶素理论(BEM)不能计入偏航入流影响的缺陷,采用涡柱理论替代动量理论对其进行修正。应用修正的理论对TUDelft模型风力机的气动性能分析表明:即使风力机处于来流风速较小的稳定偏航状态,BEM理论的计算误差仍然较大,不适合于风力机气动载荷分析,因此需要建立新的性能预测方法。
②建立了风力机转子时间步进自由尾迹分析模型。对转子后拖出的尾迹采用自由尾迹方法进行分析,并给出了能处理桨尖涡湍流效应的Vatistas涡模型对Biot-Savart定律进行修正,以消除可能出现的数值奇点;然后对时间步进差分算法展开研究,由待定系数法构造了一种新的3步3阶预估校正差分格式,以提高尾迹求解的精度。对风力机桨叶涡系采用Weissinger-L升力面模型进行描述,并推导了桨叶附着环量的求解方程及桨尖涡强度、释放位置的确定方法。最后建立了完整的风力机转子自由尾迹分析模型,该模型既能用于风力机定常气动性能分析,也能用于复杂来流时的非定常气动性能分析。
③风力机桨叶产生动态失速时,采用二维静态翼型数据进行载荷预测会低估风轮的动力产生,从而对风轮的结构设计产生严重的影响,因此在设计、校核过程中必须认真考虑动态失速的作用。本文将原本用于直升机旋翼分析的动态失速Beddoes-Leishman半经验模型进行相应的修改后,应用于S809翼型的正弦俯仰振荡计算,并与实验数据进行比较,结果表明:在平均攻角较小时计算值与实验数据吻合较好,随着平均攻角的增大,计算误差增大,但总体趋势是正确的,从而验证了模型的有效性。然后将失速模型耦合入②所建立的时间步进自由尾迹模型,以更准确地预测桨叶的气动载荷。
④对数值离散算法的精度和稳定性进行分析。采用根轨迹法对几种差分格式的线性稳定性进行分析,结果表明:Euler显式是不稳定的,PCC格式是中性稳定的,而PC2B及本文推导的PC3B格式均满足稳定性条件。由修正方程的推导对离散差分格式的精度及非线性稳定性的分析表明:本文推导的3阶PC3B格式能够减小尾迹时间步进计算时的误差累积,从而提高尾迹求解精度,且方程中包含与速度梯度无关的耗散项,离散格式是强稳定,具有明显的优势。
⑤应用时间步进自由尾迹分析模型对TUDelft风力机和NREL PhaseⅥ风力机在轴流和偏航时的尾迹形状和气动性能进行计算,并与文献实验数据进行比较,结果表明:当风力机处于来流风速较小的轴流工况时,尾迹涡不能被输运到下游较远的地方,使得涡-涡干扰较大,桨尖涡的位置及气动载荷的计算误差较大,随着风速的增大,涡的诱导影响减小,计算值与实验值吻合非常好;稳定偏航时,本文模型能够在不添加任何修正模型的情况下较好地预测偏航引起的尾迹结构的非对称性及周期载荷,从而验证了模型的有效性。
⑥对风力机处于变桨、稳态风剪切、极端动态来流等非定常风况时的气动性能计算表明:复杂来流时,转子尾迹会出现瞬时畸变,同时桨叶上的涡在脱落并向下游传输的过程中,需要一定的时间才能使尾迹从一个流态变成另一个流态,导致诱导速度的时间滞后响应,本文的自由尾迹模型能够较好的体现这种滞后响应对气动性能的影响,具有明显的优势。在此基础上,得到了一些有意义的结论,为风力机的优化设计及选型提供支持。
During Horizontal Axis Wind Turbine (HAWT)’s design and checking process, aerodynamic performance prediction is very important. Calculation of blades’aerodynamic performance after the design of aerodynamic shape is an evaluation for design results; conversely, aerodynamic performance results can be used as feedback for the amendment of aerodynamic shape of blades. But the load prediction is very difficult, because HAWT operates in complex natural environment, such as wind shear, variation of wind speed and direction, tower influence and so on. Currently, wind turbine designers rely on safety factors to compensate for the effect of unknown loads acting on the turbine, which results in components that are overdesigned because precise load level and load paths are unknown. In order to advance wind turbine technology, the forces acting on the turbine structure must by accurately characterized.
When HAWT is rotating, wake vortices are released from blades’trailing edge, form an inboard vortex sheet and rolled up to strong tip vortex. The strength of the vortex is determined by the geometry and motion parameters of airfoils, also the aerodynamic loads on blades, conversely; the induced effect of the vortex changes the velocity field around the rotor, consequently effect the strength of vortex, which means that blades and vortex interference each other. The calculation of the vortex wake is the key factor to wind turbine’s aerodynamic load analysis, and also carry out wind turbine’s aerodynamics research. It also has important scientific and practical significance when in-depth research of vortices wakes. In this paper, a time-marching free wake method was developed to analyze aerodynamic load of HAWT, the major contributions of the author’s word are as follows:
①The widely used method in aerodynamic airload prediction of HAWT is blade element theory (BEM theory), but which cannot account for yaw inflow’s influence. Aiming at this shortcoming, vortex cylinder theory is used to replace momentum theory in BEM. Aerodynamic performance of TUDelft based on the modified BEM model is put forward, which shows large error even turbine works at low wind speed and steady yaw condition. So develop a new method for aerodynamic performance prediction of HAWT is urgent needed.
②An integrated HAWT rotor wake model is developed by combination of free vortex wake model and blade aerodynamic model. Free vortex wake model is used to represent the wake behind the rotor, and Vatistas turbulence vortex core model, which is suitable for the turbulent effects of tip vortex, is introduced to eliminate numerical singularity of Biot-Savart law. Then a general method used to deduce multi-step differencing scheme is given, and base upon this method, a new 3-step 3-order accurate predictor-corrector with backward difference algorithm—named PC3B is deduced to improve the accuracy of wake solution. On the other hand, blade aerodynamic model is based on Weissinger-L lifting surface model, which can be used to deduce blades bound circulation distribution, tip vortices strength and release point. The integrated rotor wake model is not only suitable for turbine’s aerodynamic performance analysis during steady inflow conditions, but also complex inflow, which is absolutely unsteady.
③Using 2-D static airfoil data to calculate airloads on HAWT’s blades will underestimate turbine’s power generation seriously when blades experiencing dynamic stall, so dynamic stall phenomena’s influence must be considered seriously during design and checking process. The Beddoes-Leishman dynamic stall model, which is used for helicopter rotor’s dynamic stall analysis originally, is introduced to HAWT’s dynamic stall model after some modification. Good agreement is obtained between the predictions and the experimental results for pitch oscillations of S809 at several mean angles of attack and reduced frequencies.
④The linear stability, accuracy, nonlinear stability and convergence are analyzed by deduced modified equations, which provide key insight into the nonlinear behavior of the numerical solution. Results shows that 3-step 3-order difference algorithm is stable for all values of time discretization, and which introduces extra implicit dissipation that is independent of the velocity gradients. Finally, numerical experiments were performed for a wind turbine to better understand the concept of the nonlinear stability and wake convergence of the time-marching method.
⑤The time-marching free wake model is comprehensively validated against experimental measurements for rotor wake geometry and aerodynamic performance of TUDelft and NREL PhaseⅥ, with which operate under axial and yaw inflow condition. The results shows that: when the wind turbine suffers small axial inflow wind, the wake vortex can not be transported to distant places downstream, vortex-vortex interferences are significant, resulting in the blade tip vortex location and aerodynamic loads calculation error, but with wind speed increases, the vortex induced effects on the blade reduce, and the calculated values are good agreement with experimental data; when turbine suffers steady yaw, the present model needn’t any amendments to predict asymmetric wake structure and cyclic loading caused by yaw error, which verify the validity of the free wake model.
⑥When wind turbine suffers pitch operation, steady wind shear or extreme dynamic inflow conditions, the aerodynamic performance predicted by the free wake model shows that: there will be instantaneous rotor wake distortion, and the vortex shedding and transmitting to the downstream will take some time to make the wake from one flow pattern into another, resulting in induced velocity response lag, and the free wake model is able to reflect the lagged response of the aerodynamic performance. In additional, wind shear and dynamic inflow will create substantial asymmetries and non-periodicities in the structure of the wake. Conclusions reached by the calculation could support the optimized design and selection of HAWTs.
风力机在旋转过程中会从桨叶后缘拖出尾迹,形成强烈的卷起涡和内部涡面,这些尾涡旋绕在桨叶附近,会对转子的气动性能产生重要的影响。尾涡的强度由叶素的几何参数、运动参数及桨叶气动载荷决定;反过来,涡的诱导效应又会改变转子的速度场,进而影响涡的强度。因此,桨叶和尾迹之间存在相互干扰,对尾涡的计算是风力机气动载荷分析的关键,也是开展风力机空气动力学研究的基础,具有重要的科学意义和工程实际意义。本文基于时间步进自由尾迹方法对风力机的尾迹及气动性能进行了研究,主要内容包括:
①针对目前风力机气动载荷预测中常用的动量—叶素理论(BEM)不能计入偏航入流影响的缺陷,采用涡柱理论替代动量理论对其进行修正。应用修正的理论对TUDelft模型风力机的气动性能分析表明:即使风力机处于来流风速较小的稳定偏航状态,BEM理论的计算误差仍然较大,不适合于风力机气动载荷分析,因此需要建立新的性能预测方法。
②建立了风力机转子时间步进自由尾迹分析模型。对转子后拖出的尾迹采用自由尾迹方法进行分析,并给出了能处理桨尖涡湍流效应的Vatistas涡模型对Biot-Savart定律进行修正,以消除可能出现的数值奇点;然后对时间步进差分算法展开研究,由待定系数法构造了一种新的3步3阶预估校正差分格式,以提高尾迹求解的精度。对风力机桨叶涡系采用Weissinger-L升力面模型进行描述,并推导了桨叶附着环量的求解方程及桨尖涡强度、释放位置的确定方法。最后建立了完整的风力机转子自由尾迹分析模型,该模型既能用于风力机定常气动性能分析,也能用于复杂来流时的非定常气动性能分析。
③风力机桨叶产生动态失速时,采用二维静态翼型数据进行载荷预测会低估风轮的动力产生,从而对风轮的结构设计产生严重的影响,因此在设计、校核过程中必须认真考虑动态失速的作用。本文将原本用于直升机旋翼分析的动态失速Beddoes-Leishman半经验模型进行相应的修改后,应用于S809翼型的正弦俯仰振荡计算,并与实验数据进行比较,结果表明:在平均攻角较小时计算值与实验数据吻合较好,随着平均攻角的增大,计算误差增大,但总体趋势是正确的,从而验证了模型的有效性。然后将失速模型耦合入②所建立的时间步进自由尾迹模型,以更准确地预测桨叶的气动载荷。
④对数值离散算法的精度和稳定性进行分析。采用根轨迹法对几种差分格式的线性稳定性进行分析,结果表明:Euler显式是不稳定的,PCC格式是中性稳定的,而PC2B及本文推导的PC3B格式均满足稳定性条件。由修正方程的推导对离散差分格式的精度及非线性稳定性的分析表明:本文推导的3阶PC3B格式能够减小尾迹时间步进计算时的误差累积,从而提高尾迹求解精度,且方程中包含与速度梯度无关的耗散项,离散格式是强稳定,具有明显的优势。
⑤应用时间步进自由尾迹分析模型对TUDelft风力机和NREL PhaseⅥ风力机在轴流和偏航时的尾迹形状和气动性能进行计算,并与文献实验数据进行比较,结果表明:当风力机处于来流风速较小的轴流工况时,尾迹涡不能被输运到下游较远的地方,使得涡-涡干扰较大,桨尖涡的位置及气动载荷的计算误差较大,随着风速的增大,涡的诱导影响减小,计算值与实验值吻合非常好;稳定偏航时,本文模型能够在不添加任何修正模型的情况下较好地预测偏航引起的尾迹结构的非对称性及周期载荷,从而验证了模型的有效性。
⑥对风力机处于变桨、稳态风剪切、极端动态来流等非定常风况时的气动性能计算表明:复杂来流时,转子尾迹会出现瞬时畸变,同时桨叶上的涡在脱落并向下游传输的过程中,需要一定的时间才能使尾迹从一个流态变成另一个流态,导致诱导速度的时间滞后响应,本文的自由尾迹模型能够较好的体现这种滞后响应对气动性能的影响,具有明显的优势。在此基础上,得到了一些有意义的结论,为风力机的优化设计及选型提供支持。
During Horizontal Axis Wind Turbine (HAWT)’s design and checking process, aerodynamic performance prediction is very important. Calculation of blades’aerodynamic performance after the design of aerodynamic shape is an evaluation for design results; conversely, aerodynamic performance results can be used as feedback for the amendment of aerodynamic shape of blades. But the load prediction is very difficult, because HAWT operates in complex natural environment, such as wind shear, variation of wind speed and direction, tower influence and so on. Currently, wind turbine designers rely on safety factors to compensate for the effect of unknown loads acting on the turbine, which results in components that are overdesigned because precise load level and load paths are unknown. In order to advance wind turbine technology, the forces acting on the turbine structure must by accurately characterized.
When HAWT is rotating, wake vortices are released from blades’trailing edge, form an inboard vortex sheet and rolled up to strong tip vortex. The strength of the vortex is determined by the geometry and motion parameters of airfoils, also the aerodynamic loads on blades, conversely; the induced effect of the vortex changes the velocity field around the rotor, consequently effect the strength of vortex, which means that blades and vortex interference each other. The calculation of the vortex wake is the key factor to wind turbine’s aerodynamic load analysis, and also carry out wind turbine’s aerodynamics research. It also has important scientific and practical significance when in-depth research of vortices wakes. In this paper, a time-marching free wake method was developed to analyze aerodynamic load of HAWT, the major contributions of the author’s word are as follows:
①The widely used method in aerodynamic airload prediction of HAWT is blade element theory (BEM theory), but which cannot account for yaw inflow’s influence. Aiming at this shortcoming, vortex cylinder theory is used to replace momentum theory in BEM. Aerodynamic performance of TUDelft based on the modified BEM model is put forward, which shows large error even turbine works at low wind speed and steady yaw condition. So develop a new method for aerodynamic performance prediction of HAWT is urgent needed.
②An integrated HAWT rotor wake model is developed by combination of free vortex wake model and blade aerodynamic model. Free vortex wake model is used to represent the wake behind the rotor, and Vatistas turbulence vortex core model, which is suitable for the turbulent effects of tip vortex, is introduced to eliminate numerical singularity of Biot-Savart law. Then a general method used to deduce multi-step differencing scheme is given, and base upon this method, a new 3-step 3-order accurate predictor-corrector with backward difference algorithm—named PC3B is deduced to improve the accuracy of wake solution. On the other hand, blade aerodynamic model is based on Weissinger-L lifting surface model, which can be used to deduce blades bound circulation distribution, tip vortices strength and release point. The integrated rotor wake model is not only suitable for turbine’s aerodynamic performance analysis during steady inflow conditions, but also complex inflow, which is absolutely unsteady.
③Using 2-D static airfoil data to calculate airloads on HAWT’s blades will underestimate turbine’s power generation seriously when blades experiencing dynamic stall, so dynamic stall phenomena’s influence must be considered seriously during design and checking process. The Beddoes-Leishman dynamic stall model, which is used for helicopter rotor’s dynamic stall analysis originally, is introduced to HAWT’s dynamic stall model after some modification. Good agreement is obtained between the predictions and the experimental results for pitch oscillations of S809 at several mean angles of attack and reduced frequencies.
④The linear stability, accuracy, nonlinear stability and convergence are analyzed by deduced modified equations, which provide key insight into the nonlinear behavior of the numerical solution. Results shows that 3-step 3-order difference algorithm is stable for all values of time discretization, and which introduces extra implicit dissipation that is independent of the velocity gradients. Finally, numerical experiments were performed for a wind turbine to better understand the concept of the nonlinear stability and wake convergence of the time-marching method.
⑤The time-marching free wake model is comprehensively validated against experimental measurements for rotor wake geometry and aerodynamic performance of TUDelft and NREL PhaseⅥ, with which operate under axial and yaw inflow condition. The results shows that: when the wind turbine suffers small axial inflow wind, the wake vortex can not be transported to distant places downstream, vortex-vortex interferences are significant, resulting in the blade tip vortex location and aerodynamic loads calculation error, but with wind speed increases, the vortex induced effects on the blade reduce, and the calculated values are good agreement with experimental data; when turbine suffers steady yaw, the present model needn’t any amendments to predict asymmetric wake structure and cyclic loading caused by yaw error, which verify the validity of the free wake model.
⑥When wind turbine suffers pitch operation, steady wind shear or extreme dynamic inflow conditions, the aerodynamic performance predicted by the free wake model shows that: there will be instantaneous rotor wake distortion, and the vortex shedding and transmitting to the downstream will take some time to make the wake from one flow pattern into another, resulting in induced velocity response lag, and the free wake model is able to reflect the lagged response of the aerodynamic performance. In additional, wind shear and dynamic inflow will create substantial asymmetries and non-periodicities in the structure of the wake. Conclusions reached by the calculation could support the optimized design and selection of HAWTs.
引文
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