Aerodynamic design optimization of helicopter rotor blades including airfoil shape for hover performance

This study proposes a process to obtain an optimal helicopter rotor blade shape for aerodynamic performance in hover flight. A new geometry representation algorithm which uses the class function/shape function transformation (CST) is employed to generate airfoil coordinates. With this approach, airfoil shape is considered in terms of design variables. The optimization process is constructed by integrating several programs developed by author. The design variables include twist, taper ratio, point of taper initiation, blade root chord, and coefficients of the airfoil distribution function. Aerodynamic constraints consist of limits on power available in hover and forward flight. The trim condition must be attainable. This paper considers rotor blade configuration for the hover flight condition only, so that the required power in hover is chosen as the objective function of the optimization problem. Sensitivity analysis of each design variable shows that airfoil shape has an important role in rotor performance. The optimum rotor blade reduces the required hover power by 7.4% and increases the figure of merit by 6.5%, which is a good improvement for rotor blade design.     

A fully automated framework for helicopter rotor blades design and analysis including aerodynamics,structure, and manufacturing

This study describes an integrated framework in which basic aerospace engineering aspects (performance, aerodynamics, and structure) and practical aspects (configuration visualiza-tion and manufacturing) are coupled and considered in one fully automated design optimization of rotor blades. A number of codes are developed to robustly perform estimation of helicopter config-uration from sizing, performance analysis, trim analysis, to rotor blades configuration representa-tion. These codes are then integrated with a two-dimensional airfoil analysis tool to fully design rotor blades configuration including rotor planform and airfoil shape for optimal aerodynamics in both hover and forward flights. A modular structure design methodology is developed for real-istic composite rotor blades with a sophisticated cross-sectional geometry. A D-spar cross-sectional structure is chosen as a baseline. The framework is able to analyze all realistic inner configurations including thicknesses of D-spar, skin, web, number and ply angles of layers of each composite part, and materials. A number of codes and commercial software (ANSYS, Gridgen, VABS, PreVABS, etc.) are implemented to automate the structural analysis from aerodynamic data processing to sec-tional properties and stress analysis. An integrated model for manufacturing cost estimation of composite rotor blades developed at the Aerodynamic Analysis and Design Laboratory (AADL), Aerospace Information Engineering Department, Konkuk University is integrated into the framework to provide a rapid and dynamic feedback to configuration design. The integration of three modules has constructed a framework where the size of a helicopter, aerodynamic performance analysis, structure analysis, and manufacturing cost estimation could be quickly investigated. All aspects of a rotor blade including planform, airfoil shape, and inner structure are considered in a multidisciplinary design optimization without an exception of critical configuration.     

Research of low boom and low drag supersonic aircraft design

Sonic boom reduction will be an issue of utmost importance in future supersonic transport, due to strong regulations on acoustic nuisance. The paper describes a new multi-objective optimization method for supersonic aircraft design. The method is developed by coupling Seebass–George–Darden(SGD) inverse design method and multi-objective genetic algorithm.Based on the method, different codes are developed. Using a computational architecture, a conceptual supersonic aircraft design environment(CSADE) is constructed. The architecture of CSADE includes inner optimization level and out optimization level. The low boom configuration is generated in inner optimization level by matching the target equivalent area distribution and actual equivalent area distribution. And low boom/low drag configuration is generated in outer optimization level by using NSGA-II multi-objective genetic algorithm to optimize the control parameters of SGD method and aircraft shape. Two objective functions, low sonic boom and low wave drag, are considered in CSADE. Physically reasonable Pareto solutions are obtained from the present optimization. Some supersonic aircraft configurations are selected from Pareto front and the optimization results indicate that the swept forward wing configuration has benefits in both sonic boom reduction and wave drag reduction. The results are validated by using computational fluid dynamics(CFD) analysis.     

An innovative study on low surface energy micronano coatings with multilevel structures for laminar flow design

Laminar flow design is one of the most effective ways to reduce the drag of a commercial aircraft by expanding the laminar flow region on the surface of the aircraft. As material science develops, the emergence of new materials such as low surface energy materials has offered new choices for laminar flow design of commercial aircraft. Different types of low surface energy micro-nano coatings are prepared to verify the effects on the boundary layer transition position and the drag of the airfoil through wind tunnel tests. The infrared thermal imaging technology is adopted for measuring the boundary layer transition, while the momentum integral approach is employed to measure the drag coefficient through a wake rake. Infrared thermal imaging results indicate that the coatings are capable of moving backward the boundary layer transition position at both a low velocity of Mach number 0.15 and a high velocity of Mach number 0.785. Results of the momentum integral approach demonstrate that the drag coefficients are reduced obviously within the cruising angle of attack range from 1° and 5° by introducing the low surface energy micro-nano coating technology.     

An efficient aerodynamic shape optimization of blended wing body UAV using multi-fidelity models

This paper presents a novel optimization technique for an efficient multi-fidelity model building approach to reduce computational costs for handling aerodynamic shape optimization based on high-fidelity simulation models. The wing aerodynamic shape optimization problem is solved by dividing optimization into three steps—modeling 3D(high-fidelity) and 2D(lowfidelity) models, building global meta-models from prominent instead of all variables, and determining robust optimizing shape associated with tuning local meta-models. The adaptive robust design optimization aims to modify the shape optimization process. The sufficient infilling strategy—known as adaptive uniform infilling strategy—determines search space dimensions based on the last optimization results or initial point. Following this, 3D model simulations are used to tune local meta-models. Finally, the global optimization gradient-based method—Adaptive Filter Sequential Quadratic Programing(AFSQP) is utilized to search the neighborhood for a probable optimum point. The effectiveness of the proposed method is investigated by applying it, along with conventional optimization approach-based meta-models, to a Blended Wing Body(BWB) Unmanned Aerial Vehicle(UAV). The drag coefficient is defined as the objective function, which is subjected to minimum lift coefficient bounds and stability constraints. The simulation results indicate improvement in meta-model accuracy and reduction in computational time of the method introduced in this paper.     

An optimization method for metamorphic mechanisms based on multidisciplinary design optimization

The optimization of metamorphic mechanisms is different from that of the conventional mechanisms for its characteristics of multi-configuration. There exist complex coupled design variables and constraints in its multiple different configuration optimization models. To achieve the compatible optimized results of these coupled design variables, an optimization method for metamorphic mechanisms is developed in the paper based on the principle of multidisciplinary design optimization（MDO）. Firstly, the optimization characteristics of the metamorphic mechanism are summarized distinctly by proposing the classification of design variables and constraints as well as coupling interactions among its different configuration optimization models. Further, collaborative optimization technique which is used in MDO is adopted for achieving the overall optimization performance. The whole optimization process is then proposed by constructing a two-level hierarchical scheme with global optimizer and configuration optimizer loops. The method is demonstrated by optimizing a planar five-bar metamorphic mechanism which has two configurations,and results show that it can achieve coordinated optimization results for the same parameters in different configuration optimization models.     

Applications of numerical optimization techniques to design of axial compressor blades

This paper describes the shape optimization of NASA rotor 37 and rotor and stator blades in a single-stage transonic axial compressor.Shape optimization of the blades operating at the design flow condition has been performed using the response surface method and three-dimensional Navier-Stokes analysis.Thin-layer approximation is introduced to the Navier-Stokes equations,and an explicit Runge-Kutta scheme is used to solve the governing equations.The three design variables,blade sweep,lean and skew,are introduced to optimize the three-dimensional stacking line of the blades.The objective function of the shape optimization is an adiabatic efficiency.Throughout the optimization of rotor and stator blades, optimal blade shape can be obtained.It is noted the increase of adiabatic efficiency by optimization of the blade shape with the stacking line in the single-stage transonic axial compressor is more effective in a rotor blade rather than a stator blade because of the large deformation of blade shape in the stator blade.      

Robust design and analysis of a conformal expansion nozzle with inverse-design idea

This paper examines robust optimization design and analysis of a conformal expansion nozzle of flying wing Unmanned Aerial Vehicle(UAV) with the inverse-design idea.In view of flow features and stealth constraints, the inverse-design idea is described and the uncertainty-based robust design model is presented.A robust design system employs this model to combine deterministic optimization and robust optimization and is applied into design of a conformal expansion nozzle.The results indicate that design optimization can conform to the anticipation of the inversedesign idea and significantly improve the aerodynamic performance that meet the requirement of 6σ.The present method is a feasible nozzle design strategy that integrates robust optimization and inverse-design.     

Variable-fidelity optimization with design space reduction

Advanced engineering systems, like aircraft, are defined by tens or even hundreds of design variables. Building an accurate surrogate model for use in such high-dimensional optimization problems is a difficult task owing to the curse of dimensionality. This paper presents a new algorithm to reduce the size of a design space to a smaller region of interest allowing a more accurate surrogate model to be generated. The framework requires a set of models of different physical or numerical fidelities. The low-fidelity (LF) model provides physics-based approximation of the high-fidelity (HF) model at a fraction of the computational cost. It is also instrumental in identifying the small region of interest in the design space that encloses the high-fidelity optimum. A surrogate model is then constructed to match the low-fidelity model to the high-fidelity model in the identified region of interest. The optimization process is managed by an update strategy to prevent convergence to false optima. The algorithm is applied on mathematical problems and a two-dimen-sional aerodynamic shape optimization problem in a variable-fidelity context. Results obtained are in excellent agreement with high-fidelity results, even with lower-fidelity flow solvers, while showing up to 39% time savings.     

Effect of Variable Selection on Multidisciplinary Design Optimization： a Flight Vehicle Example

Different multidisciplinary design optimization (MDO) problems are formulated and compared. Two MDO formulations are applied to a sounding rocket in order to optimize the performance of the rocket. In the MDO of the referred vehicle, three disciplines have been considered,which are trajectory, propulsion and aerodynamics. A special design structure matrix is developed to assist data exchange between disciplines. This design process uses response surface method (RSM) for multidisciplinary optimization of the rocket. The RSM is applied to the design in two categories: the propulsion model and the system level. In the propulsion model, RSM deter-mines an approximate mathematical model of the engine output parameters as a function of design variables. In the system level, RSM fits a surface of objective function versus design variables. In the first MDO problem formulation, two design variables are selected to form propulsion discipline. In the second one, three new design variables from geometry are added and finally, an optimization method is applied to the response surface in the system level in order to find the best result. Application of the first developed multidisciplinary design optimization procedure increased accessible altitude (performance index) of the referred sounding rocket by twenty five percents and the second one twenty nine.     

基于响应面的翼型稳健设计研究

翼型的稳健设计就是要考虑环境中不确定因素的影响,提高翼型的性能,同时保证翼型性能对环境因素的变化不敏感的设计方法。本文应用响应面模型,通过减小翼型在不确定因素变化范围内阻力系数的均值和方差,构建了一个有效的翼型稳健设计的方法。应用本文的方法,选择马赫数作为不确定因素,假设马赫数在0.7~0.8间均匀分布,在满足升力约束条件下最小化阻力系数,结果证明本文的方法进行翼型的稳健设计是可行,高效的。     

现代超临界翼型设计及其风洞试验

开展了现代超临界翼型的设计研究,对现役飞机的压力分布形态进行了分析,针对现役飞机在巡航状态和阻力发散点的压力分布进行对比,提取了现役飞机超临界剖面设计的要点。采用类函数/型函数变换(CST)参数化方法、基于二阶震荡及自然选择的随机权重混合粒子群算法(RwSecSelPSO)、雷诺平均Navier-Stokes(RANS)方程、Kriging代理模型结合定期望值型的目标函数建立了优化设计系统。针对提高阻力发散马赫数和降低巡航低头力矩的设计指标,利用优化设计系统通过调整目标期望值设计了一系列满足设计指标但阻力发散马赫数不同的超临界翼型,并选择了其中具有典型特性的翼型进行了对比分析,验证了提高阻力发散马赫数和低速失速特性的设计方法,指出了在阻力发散点形成平顶形压力分布的超临界翼型具有较好的综合性能。对设计的超临界翼型进行了高、低速风洞试验验证,试验结果表明:设计结果达到了设计指标要求,提出的低速改进方案有效,层流对超临界翼型失速特性影响较大。     

Robust design of NLF airfoils

 A robust optimization design approach of natural laminar airfoils is developed in this paper. First, the non-uniform rational B-splines (NURBS) free form deformation method based on NURBS basis function is introduced to the airfoil parameterization. Second, aerodynamic characteristics are evaluated by solving Navier-Stokes equations, and the γ-Re_θt transition model coupling with shear-stress transport (SST) turbulent model is introduced to simulate boundary layer transition. A numerical simulation of transition flow around NLF0416 airfoil is conducted to test the code. The comparison between numerical simulation results and wind tunnel test data approves the validity and applicability of the present transition model. Third, the optimization system is set up, which uses the separated particle swarm optimization (SPSO) as search algorithm and combines the Kriging models as surrogate model during optimization. The system is applied to carry out robust design about the uncertainty of lift coefficient and Mach number for NASA NLF-0115 airfoil. The data of optimized airfoil aerodynamic characteristics indicates that the optimized airfoil can maintain laminar flow stably in an uncertain range and has a wider range of low drag.     

超临界翼型稳健型优化设计研究

基于标准遗传算法、RBF神经网络以及类函数/型函数变形技术建立了翼型气动优化设计系统,在选取3次CST方法即分别对翼型上下表面采用4个设计变量进行参数化,对某型客机基本翼型在给定设计指标下进行优化设计,分别研究了巡航状态下的气动优化,以及结合蒙特卡洛分析方法马赫数随机平均分布下的翼型稳健型优化设计。结果显示,优化后的翼型的气动特性有着显著提高。     

旋翼翼型多目标多约束气动优化设计

为了克服传统旋翼翼型优化设计方法的不足,发展了一种基于Kriging模型与遗传算法的旋翼翼型多目标多约束气动优化设计方法。采用基于雷诺平均Navier-Stokes方程的数值模拟获得样本翼型气动性能,并建立目标函数和状态函数的Kriging模型,采用遗传算法搜索Kriging模型最小值和相应的EI(Expected Improvement)函数最大值,更新Kriging 模型直至找到满足约束的最优翼型。运用加权目标函数法进行了旋翼翼型的多设计点优化设计。优化结果表明,优化后旋翼翼型在满足约束的同时,与基准旋翼翼型OA209相比:在悬停状态下,阻力系数下降了2.1%;在机动状态下,最大升力系数提高了4.2%;在前飞状态下,阻力系数在不同马赫数下均有所减小。     

高空长航时无人机翼型设计方法研究

使用解析形状函数法表示翼型,将求解绕翼型流场的N-S方程解与遗传算法相结合,可用于高空长航时无人机翼型的设计.设计实践表明,设计的新翼型满足设计要求,且获得比原始翼型高得多的升阻比,采用的翼型设计方法是正确和有效的.     

自适应翼型的气动外形优化设计

 二维翼型自适应的研究是设计自适应机翼的基础。提出了在不同 Ma数、迎角下,用 Powell法优化二维翼型前、后缘襟翼的偏转角,以获得比常规翼型在亚声速时升阻比大而在超声速时阻力系数小的自适应翼型的研究方案。并与原始翼型以及气动双目标 (亚声速时,大升阻比;超声速时,小阻力系数 )的优化翼型进行了比较,证明了自适应翼型比气动双目标的优化翼型气动效率更高。初步探讨了二维翼型前、后缘襟翼的偏转位置对气动效率的影响。     

基于CST参数化方法气动优化设计研究

翼型及机翼优化设计中,设计变量的个数对优化算法的收敛速度及代理模型的精度有很大的影响.因此,在精确描述翼型的同时,发展较少设计变量的翼型参数化方法对翼型优化设计有着重要的意义.本文基于CST(class function/shape function transformation)翼型参数化方法对Kriging模型的预测精度进行研究,并采用改进的粒子群优化算法构建气动优化设计系统.某亚声速机翼单点减阻设计及超临界翼型的稳健性设计表明该系统具有较高的设计质量,方法可靠,有较高的工程应用前景.     

后缘连续变弯度对跨声速翼型气动特性的影响

针对后缘连续变弯度对跨声速翼型气动特性的影响进行了研究。首先不考虑翼型后缘连续变弯度,基于搭建的优化设计系统对跨声速翼型进行气动减阻优化设计,通过添加不同的约束优化得到两种跨声速翼型:无激波翼型和超临界翼型。然后在这两种翼型的基础上,以后缘偏转角度为设计变量、以阻力系数最小为目标,针对不同的升力系数分别进行优化设计,并根据优化结果深入分析后缘连续变弯度对这两种翼型极曲线特性的影响机理。优化结果表明:无激波翼型与超临界翼型相比,其设计点处的气动特性较好,但鲁棒性较差;升力系数小于设计升力系数时,应用后缘连续变弯度后,无激波翼型的极曲线特性明显提高,减阻最高达到3.9%,而超临界翼型的极曲线特性提高不明显;升力系数大于设计升力系数时,应用后缘连续变弯度后,无激波翼型和超临界翼型的极曲线特性都明显提高,减阻分别达到2.4%~18.1%和1.7%~13.2%。     

基于遗传算法的翼型气动优化设计

采用遗传算法进行跨声速翼型的反设计与阻力和升阻比的优化设计。翼型的反设计达到了设计要求,优化设计后的翼型其气动特性也有显著的改善,这表明了遗传算法应用于翼型气动优化设计的可行性。在优化设计的过程中,翼型由解析函数线形叠加法表示,目标函数和个体的适应值由二维欧拉方程的流场解来提供。