时间准确自由尾迹方法建模及（倾转）旋翼气动特性分析
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摘要
本文建立了一个新的“时间准确”旋翼自由尾迹模型,利用该模型针对旋翼和倾转旋翼的尾迹和气动特性进行了计算和分析,同时开展了旋翼倾转状态的气动试验研究,主要工作如下:
作为前提和背景,本文首先阐述了论文的研究目的,以及旋翼自由尾迹方法研究、旋翼气动特性研究和倾转旋翼气动特性研究的国内外现状,指出了现有研究中存在的不足,提出了本文拟采用的研究方法和本文的研究内容。
在第二章,本文基于Vatistas公式给出了一个不同的粘性涡核模型,分析了涡模型中涡核半径的确定方法,并考虑了涡核实际的耗散影响。然后,以平面涡环和三维涡管为算例,计算了诱导速度分布,以表明涡模型对实际诱导速度计算的影响,并通过旋翼入流的计算验证了本文涡模型的有效性。
针对尾迹步进计算的多步差分格式,在第三章给出了一个通用推导方法,并利用该方法推导了一个新的二步二阶预测-校正差分算法——“D2PC”算法。然后,对“D2PC”差分格式的精度和稳定性进行了分析,并与典型的单步、三步差分格式作了对比。此外,还进行了自由尾迹涡线离散处理的误差分析,并对采用“D2PC”差分格式表示的涡线主控方程进行了修正,以提高尾迹求解精度。
第四章从刚体的扩展欧拉动力学模型出发,分别推导了旋翼在定常飞行时、有角运动时及作倾转运动时的桨叶挥舞动力学方程。同时,建立了桨叶Weissinger-L升力面气动模型,并给出了适用于旋翼气动力分析的桨叶环量求解方程以及桨尖涡强度和释放位置的确定方法。
在第五章,给出了一个适用于时间步进分析的旋翼配平模型,并结合第二、三和四章的模型,建立了一个能适合于旋翼在定常飞行、有角运动以及旋翼倾转运动时的尾迹和气动特性分析的“时间准确”自由尾迹方法。在第六章,首先通过旋翼尾迹、入流和气动力响应等多种算例计算,验证了本文建立的“时间准确”旋翼自由尾迹方法的有效性,然后,应用该方法分别对直升机旋翼的尾迹几何形状、桨盘入流、旋翼下洗流场等时均气动特性进行了计算与分析,并对旋翼在总距突增时的瞬时动态响应特性、旋翼在有角运动时的尾迹几何形状和桨盘入流特性进行了计算,得出一些新的结论。
第七章在南京航空航天大学研制的倾转旋翼实验台上进行了倾转旋翼的气动特性试验研究,首先测量了不同旋翼半径、不同总距角条件下,旋翼不倾转时的气动特性。然后,测量了不同旋翼转速及不同倾转时间条件下,旋翼倾转时的非定常气动力,并与计算结果进行了对比。
本文在第八章,应用建立的“时间准确”旋翼自由尾迹模型针对旋翼在不同倾转状态下的尾迹进行了计算和分析,并对旋翼倾转状态下的非定常气动力和挥舞响应特性进行了研究,在此基础上,得出了一些新的结果。
In this paper, a new time-accurate rotor free wake method has been developed, and using the method, vortical wake and aerodynamic characteristics of rotor and tilting rotor are calculated and analyzed. As the same time, the aerodynamic experiments for the tilting rotor are performed. The major contributions of the author’s research work are as follows:
As the background of the work, the research and development in the field of the rotor free wake method, the aerodynamic characteristics of rotor and tiltrotor are described in Chapter 1. The difficulties in the current rotor free wake method research are pointed out. And the importance of simulating aerodynamic characteristics of rotor and tiltrotor by the wake method is emphasized. Moreover, the present work is briefly introduced.
In Chapter 2, a different algebraic vortex model is developed based on the Vatistas formula, and the expression of vortex core radius is given under the consideration of vortex diffusion. As numerical examples, the induced velocity distributions of the vortex ring and vortex tube are calculated to indicate the effects of the vortex model on the calculated results of induced velocity. Then the calculated inflows for rotor are compared with the available experimental data to show the validity of the present vortex model.
A general method used to deduce multi-step differencing scheme is given in Chapter 3, and based upon the method, a new 2-step 2-order accurate predictor-corrector with backward difference algorithm—named“D2PC”is deduced. Both the stability and accuracy of the“D2PC”numerical wake solution algorithm are examined. By comparisons with the critical 1-step and 3-step difference algorithms, the validity of“D2PC”algorithm is demonstrated. Numerical errors associated with the wake discretization are analyzed. In order to increase the accuracy of the solution for rotor wake, the discrete approximations of vortex governing equations using“D2PC”algorithm are modified and improved.
In Chapter 4, based on the extended Euler dynamic equations, the rigid blade flap dynamic equations for rotor in steady flight, angular motion and tilting motion are deduced. The blade is simulated by the Weissinger-L lift-surfacing model, and the methods for determining the blade bound vorticity strength, tip vortex strength and release position are given.
In Chapter 5, a trimming model is modified for fitting the time-stepping wake calculation. Combined the trimming model with models of Chapter 2, 3 and 4, a new time-accurate free wake method is developed for the calculation on vortical wake and aerodynamic characteristic of rotor in steady flight, angular motion and tilting motion.
In Chapter 6, by the comparisons of calculated results with experimental results for some numerical examples on wake geometries, inflows, induced velocities, aerodynamic responses, the present time-accurate free wake method is validated. Using the method, time-average aerodynamic characteristics on the wake geometry, inflow and induced velocity of rotor are calculated and analyzed. Then the rotor aerodynamic responses with abrupt increase of collective pitch have been calculated. Additionally, the vortical wake geometry and inflow distribution with rotor angular motion have been analyzed. Some new conclusions are obtained.
Based on the tiltrotor test rig of Nanjing University of Aeronautics and Astronautics, experimental investigations for rotor and tilting rotor have been carried out in Chapter 7. The aerodynamic characteristics of fixed rotor are tested for different rotor radius and collective pitch. Then aerodynamic characteristic tests of tilting rotor for different rotor radius, collective pitch and tilting rate have been performed. And the comparisons between experimental results and calculated results by the present method are made.
In Chapter 8, the wake geometries of tilting rotor for different operating conditions are calculated and analyzed, and analysis on the aerodynamic forces and flapping responses for rotor during tilting motion has been performed. Some new conclusions are presented.
作为前提和背景,本文首先阐述了论文的研究目的,以及旋翼自由尾迹方法研究、旋翼气动特性研究和倾转旋翼气动特性研究的国内外现状,指出了现有研究中存在的不足,提出了本文拟采用的研究方法和本文的研究内容。
在第二章,本文基于Vatistas公式给出了一个不同的粘性涡核模型,分析了涡模型中涡核半径的确定方法,并考虑了涡核实际的耗散影响。然后,以平面涡环和三维涡管为算例,计算了诱导速度分布,以表明涡模型对实际诱导速度计算的影响,并通过旋翼入流的计算验证了本文涡模型的有效性。
针对尾迹步进计算的多步差分格式,在第三章给出了一个通用推导方法,并利用该方法推导了一个新的二步二阶预测-校正差分算法——“D2PC”算法。然后,对“D2PC”差分格式的精度和稳定性进行了分析,并与典型的单步、三步差分格式作了对比。此外,还进行了自由尾迹涡线离散处理的误差分析,并对采用“D2PC”差分格式表示的涡线主控方程进行了修正,以提高尾迹求解精度。
第四章从刚体的扩展欧拉动力学模型出发,分别推导了旋翼在定常飞行时、有角运动时及作倾转运动时的桨叶挥舞动力学方程。同时,建立了桨叶Weissinger-L升力面气动模型,并给出了适用于旋翼气动力分析的桨叶环量求解方程以及桨尖涡强度和释放位置的确定方法。
在第五章,给出了一个适用于时间步进分析的旋翼配平模型,并结合第二、三和四章的模型,建立了一个能适合于旋翼在定常飞行、有角运动以及旋翼倾转运动时的尾迹和气动特性分析的“时间准确”自由尾迹方法。在第六章,首先通过旋翼尾迹、入流和气动力响应等多种算例计算,验证了本文建立的“时间准确”旋翼自由尾迹方法的有效性,然后,应用该方法分别对直升机旋翼的尾迹几何形状、桨盘入流、旋翼下洗流场等时均气动特性进行了计算与分析,并对旋翼在总距突增时的瞬时动态响应特性、旋翼在有角运动时的尾迹几何形状和桨盘入流特性进行了计算,得出一些新的结论。
第七章在南京航空航天大学研制的倾转旋翼实验台上进行了倾转旋翼的气动特性试验研究,首先测量了不同旋翼半径、不同总距角条件下,旋翼不倾转时的气动特性。然后,测量了不同旋翼转速及不同倾转时间条件下,旋翼倾转时的非定常气动力,并与计算结果进行了对比。
本文在第八章,应用建立的“时间准确”旋翼自由尾迹模型针对旋翼在不同倾转状态下的尾迹进行了计算和分析,并对旋翼倾转状态下的非定常气动力和挥舞响应特性进行了研究,在此基础上,得出了一些新的结果。
In this paper, a new time-accurate rotor free wake method has been developed, and using the method, vortical wake and aerodynamic characteristics of rotor and tilting rotor are calculated and analyzed. As the same time, the aerodynamic experiments for the tilting rotor are performed. The major contributions of the author’s research work are as follows:
As the background of the work, the research and development in the field of the rotor free wake method, the aerodynamic characteristics of rotor and tiltrotor are described in Chapter 1. The difficulties in the current rotor free wake method research are pointed out. And the importance of simulating aerodynamic characteristics of rotor and tiltrotor by the wake method is emphasized. Moreover, the present work is briefly introduced.
In Chapter 2, a different algebraic vortex model is developed based on the Vatistas formula, and the expression of vortex core radius is given under the consideration of vortex diffusion. As numerical examples, the induced velocity distributions of the vortex ring and vortex tube are calculated to indicate the effects of the vortex model on the calculated results of induced velocity. Then the calculated inflows for rotor are compared with the available experimental data to show the validity of the present vortex model.
A general method used to deduce multi-step differencing scheme is given in Chapter 3, and based upon the method, a new 2-step 2-order accurate predictor-corrector with backward difference algorithm—named“D2PC”is deduced. Both the stability and accuracy of the“D2PC”numerical wake solution algorithm are examined. By comparisons with the critical 1-step and 3-step difference algorithms, the validity of“D2PC”algorithm is demonstrated. Numerical errors associated with the wake discretization are analyzed. In order to increase the accuracy of the solution for rotor wake, the discrete approximations of vortex governing equations using“D2PC”algorithm are modified and improved.
In Chapter 4, based on the extended Euler dynamic equations, the rigid blade flap dynamic equations for rotor in steady flight, angular motion and tilting motion are deduced. The blade is simulated by the Weissinger-L lift-surfacing model, and the methods for determining the blade bound vorticity strength, tip vortex strength and release position are given.
In Chapter 5, a trimming model is modified for fitting the time-stepping wake calculation. Combined the trimming model with models of Chapter 2, 3 and 4, a new time-accurate free wake method is developed for the calculation on vortical wake and aerodynamic characteristic of rotor in steady flight, angular motion and tilting motion.
In Chapter 6, by the comparisons of calculated results with experimental results for some numerical examples on wake geometries, inflows, induced velocities, aerodynamic responses, the present time-accurate free wake method is validated. Using the method, time-average aerodynamic characteristics on the wake geometry, inflow and induced velocity of rotor are calculated and analyzed. Then the rotor aerodynamic responses with abrupt increase of collective pitch have been calculated. Additionally, the vortical wake geometry and inflow distribution with rotor angular motion have been analyzed. Some new conclusions are obtained.
Based on the tiltrotor test rig of Nanjing University of Aeronautics and Astronautics, experimental investigations for rotor and tilting rotor have been carried out in Chapter 7. The aerodynamic characteristics of fixed rotor are tested for different rotor radius and collective pitch. Then aerodynamic characteristic tests of tilting rotor for different rotor radius, collective pitch and tilting rate have been performed. And the comparisons between experimental results and calculated results by the present method are made.
In Chapter 8, the wake geometries of tilting rotor for different operating conditions are calculated and analyzed, and analysis on the aerodynamic forces and flapping responses for rotor during tilting motion has been performed. Some new conclusions are presented.
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