论文题目：应用自由尾迹分析的新型桨尖旋翼气动特性研究

作者简介：徐国华，男，1963年生，1992年师从南京航空航天大学王适存教授，于1996年获博士学位。

摘 要

直升机之所以能垂直起降、空中悬停、飞行方向自由，全靠它的旋翼。旋翼的空气动力特性决定着直升机的性能和飞行品质，也是直升机的振动和噪声的主要根源。对旋翼空气动力学特性的了解，在于旋翼尾迹的分析，而对旋翼空气动力特性的改善，在于桨尖形状的研究。

因此，旋翼尾迹分析和桨尖形状研究是直升机空气动力学的两个重要研究方面。把先进的基于升力面理论的自由尾迹分析和各种不同的、特别是新型的下反的桨尖形状研究结合起来，建立一个新的分析方法(NRFWC)是本文的主要目的。

作为前提和背景，本文第一章首先对旋翼尾迹分析和桨尖形状研究的现状进行了评述。依据桨尖形状的发展及其对旋翼气动特性的改善，将现有的桨尖形状归纳为三个不同的层次。第一层次的桨尖形状为直线后掠或尖削，第二层次包括桨尖平面的曲线变化，而第三层次进入到下反桨尖这种三维变化。然后指出了目前的研究所存在的问题，提出了应用自由尾迹分析进行先进的复式桨尖形状研究的重要性。

涡元技术是尾迹分析的基础，本文第二章改进了先前的曲涡元模型。其中关键是用两个有限的级数展开式以代替Legendre 的不完全椭圆积分式，推导出圆弧涡元(CVEC)计算的解析公式，从而使曲涡元更为有效地应用于旋翼的自由尾迹分析。

在第三章，本文分析了悬停尾迹的特点，利用圆弧涡元建立了一个悬停状态旋翼自由尾迹计算的松弛迭代方法和程序——NRFWC－1。通过与已有尾迹形状和桨叶环量分布的试验结果对比，检验了计算方法的可靠性。于是，应用NRFWC－1对桨叶与尾迹之间的干扰进行了参数分析，分别讨论了不同叶尖马赫数、桨距角和桨叶片数对悬停尾迹形状的变化，表明了旋翼参数不同的影响。

在本文的第四章，应用时间步进法和改进的曲涡元模型，建立了一个前飞旋翼自由尾迹的分析方法和程序——NRFWC－2。在NRFWC－2中，利用了依据近尾迹的信息以确定远尾迹的手段，从而使远尾迹更接近实际。此外，为恰当地确定尾迹的长度，文中推导了一近似公式，可用于确定尾迹周数与前飞速度的关系。应用NRFWC－2对不同速度时的前飞尾迹形状和气动载荷进行了算例计算，展示出小速度时尾迹畸变和叶尖涡卷绕的重要特征，并分析了尾迹畸变对改进载荷计算的作用。

在桨叶的气动模型方面，本文第五章指出了一阶升力线理论对后掠桨尖的桨叶应用的不适宜性，并基于二阶升力线理论和上述的自由尾迹分析，建立了一个适用于后掠、尖削桨尖旋翼气动特性计算的新的模型及其分析方法——NRFWC/L。通过与“黑鹰”后掠桨尖旋翼试验结果的对比，验证了方法的正确性。对于尖削桨尖，应用该模型对桨叶环量和载荷分布进行了计算，并与矩形桨尖作了对比，表明了尖削对旋翼气动特性的影响。

在第六章，建立了一个适用于桨尖三维变化的旋翼气动特性计算的升力面/涡格法模型的先进分析方法——NRFWC/S，该模型可广泛地用于后掠、尖削、下反的各种组合形状，具有很强的实用性。应用NRFWC/S，对不同桨尖旋翼气动特性进行了计算和对比，着重分析了下反桨尖对桨叶环量、诱导速度、载荷和叶尖涡位置的改变，表明了这种新型桨尖对旋翼气动特性的改善。

最后，本文对三种不同的桨尖(矩形桨尖，尖削桨尖和尖削下反桨尖)在南京航空航天大学直升机旋翼动力学国防科技重点实验室的两米模型旋翼试验台上进行了初步试验研究，验证了不同桨尖形状对旋翼气动特性的影响。

旋翼空气动力学，气动特性，直升机，桨尖形状，尾流

附记：本文是航空科学基金项目“旋翼二维桨尖和三维桨尖的对比研究”和国家八五航空预研课题“旋翼气动载荷研究”的主要组成部分。这项成果在我国某陆军型直升机的新型旋翼上得到了成功应用，并以“直升机旋翼自由尾迹分析和气动特性研究”为题，获1998年航空工业总公司(部级)科技进步一等奖及1999年国防科工委(国家级)科技进步三等奖。

The capabilities of the helicopter for vertical taking—off and landing、 hovering as well as free to fly in any direction, all depend on its rotor. The aerodynamic characteristics of the rotor not only determines the performance and flight qualities of the helicopter, but also is the primary source of the helicopter’s vibration and noise. The key of understanding the rotor’s aerodynamic characteristics is to analyze its wake and the way of improving the rotor’s aerodynamic characteristics is to study its blade tip shape.

Therefore, the rotor wake analysis and the study of blade tip shapes are two very important aspects in the research field of helicopter aerodynamics. In this thesis, a new analytical method (NRFWC) based on the advanced free wake analysis of the lifting surface theory is established for evaluating aerodynamic characteristics of the rotor with different blade tip shapes. The major contributions of the author’s research work are as follows:

(1) As the background of the work, the evolution of rotor wake techniques and investigations on various blade tips are reviewed briefly, with emphasis on the free wake code and the anhedral tip. According to the development of blade tips’ geometry and their improvement on rotor performance, the existing studies on new blade tips are divided into three phases. The Phase I tip has simple straight swept or tapered shape, the curve change of the platform is included during Phase Ⅱ, and the geometry of the Phase Ⅲ tip is extended to anhedral modification. Afterwards the shortcomings of current studies are pointed out and the importance of investigation on complex blade tip shapes by the free wake analysis is described.

(2) An improved model of curved vortex element on the circular arc (CVEC) for rotor free wake analysis is presented. As the key of the improvement, two approximate formulas are derived by the series of limited terms to replace the Legendre incomplete elliptical integrals from the Biot-Savart integration, and an analytical solution of the induced velocity for the CVEC is obtained, which is more efficient than previous models in the complex rotor free wake calculation.

(3) A free wake model (NRFWC—1) of a hovering rotor, using an iterative procedure and the curved vortex element, is established and is checked by the comparisons with experimental data on the tip vortex path and blade bound circulation. Thus based on the NRFWC-1, the interaction between the tip vortex and the following blade is analyzed, and the influence of rotor parameters, such as the tip March number, the blade pitch and the number of blades, on the radial and axial geometry of tip vortex are calculated and discussed.

(4) A forward flight full-span free wake model (NRFWC—2), applying a time stepping approach and the improved curved vortex element, is established. A new far wake model is also developed which utilizes the near wake information to form the far wake shape more close to reality. In order to choose the wake length properly, an approximate expression is derived to obtain the relation between number of wake revolutions and forward flight velocity. Sample calculations on rotor free wake shapes and blade aerodynamic loads are performed for different advance ratios and rotors. The features of highly distorted free wake shapes and strong tendency toward rapid roll-up of the tip vortices immediately downstream of the rotor for low speed case are exhibited, and discussion on the effect of wake distortion on blade aerodynamic loads calculation is made.

Rotor aerodynamics; aerodynamic characteristics; helicopter; blade tip shape; wakes

Note: The content of this thesis is the major part of the Aeronautical Science Fund Program “Comparative Study of 2-Dimensional and 3-Dimensional Blade Tip Shapes” and the National 85 Aeronautical Pre-research Program “Study of the Rotor Aerodynamic Loads”. This work has been successfully used on the new rotor design of one our army helicopter and was awarded the first science and technology prize (ministerial) of AVIC and the third science and technology prize (National) of NDSTC.