超音速探测器-刚性盘-缝-带型降落伞系统的大涡模拟研究

研究了Mach数为2时,流场不同块结构自适应网格加密精度对探测器-刚性盘-缝-带型降落伞系统的气动减速性能以及流场结构特性的影响.对于非定常可压缩流体流动,采用了兼顾激波与湍流的WENO(weighted essentially non-oscillatory)和TCD(tuned center difference)混合计算格式以及拉伸涡亚格子模型的大涡模拟方法.结果表明:在较低的流场块结构自适应网格分辨率下,是难以准确模拟计算降落伞系统重要的气动阻力系数和捕捉流场流动特征细节的.随后验证了流场自适应网格的收敛性.     

大气制动期间探测器的气动特性和轨道计算

以NASA火星全球勘测（MGS）号探测器作为大气制动计算模型,应用DSMC方法模拟了探测器在大气制动期间的稀薄气体动力学特性,分析了不同来流密度情况下探测器的流场特性、气动特性的变化情况以及气体动力学系数的变化关系．并提出了气动力-气动热-轨道一体化计算模型,利用DSMC模拟技术以及经典动力学理论对大气制动轨道变化进行了计算和分析．研究结果表明:行星大气密度、探测器俯仰角、偏航角的变化对探测器的气动特性有重要影响,计算结果与文献中的结果表现出很好的一致性;气动力-气动热-轨道一体化计算可以模拟大气制动过程,模拟所得到的大气制动轨迹反映出较好的制动效果．     

黏性分层流中椭球体俯仰振荡研究

以黏性密度分层流下椭球体自由俯仰振荡衰减过程为研究内容,建立了密度连续分层流数值计算模型.通过对经典小球黏性绕流场的数值模拟和增阻系数的计算验证了数值模型的正确性.以初始45°攻角下的椭球体俯仰振荡过程为研究对象,采用基于Aitken亚松弛适应算法的双向流固耦合方法,数值模拟了不同内Froude(弗汝德)数Fri下椭球体俯仰衰减振荡的动态绕流场.数值研究结果表明,俯仰振荡将上下搅动周围流体,在椭球体上下两侧对称形成四个密度涡环,密度的垂向分层限制了涡环的垂向传播,也加速了涡环的消失,这种限制助长了水平运动的发展,远场尾涡流场将以水平波动的形式传播.在较高的内Froude数Fri和Reynolds(雷诺)数Re下,双向耦合抑制了数值震荡.研究还发现,随着来流速度的增加,阻力系数不增反降,这说明,对于自由俯仰振荡的椭球体,负阻尼现象仍然会出现.     

金融风险管理中VaR度量的光滑估计效率

本文研究了金融风险管理理论中风险价值(VaR)的非参数核光滑估计和经验估计的效率问题.对非独立的时间序列损失/收益样本,在均方误差(MSE)准则的意义下引入亏量的概念,亏量越大表明估计效率越低.并利用亏量对VaR模型的核光滑估计和基于样本分位数的经验估计进行了比较,在理论上证明了VaR模型的核光滑估计优于经验估计.同时,通过计算机模拟证实了理论获得的结论.本文还对国内沪深两市上的证券投资基金进行了实证分析,计算了样本基金的VaR风险度量的经验估计和核光滑估计,并计算了样本基金基于周收益率和VaR估计的风险调整收益(RAROC)值,以此对样本基金的业绩做出了有用的评价.     

喷灌模型

针对农业生产中的喷灌 ,本文详细研究了喷头的排布问题 .根据分析和计算 ,得到如下结论 :当喷头采用正方形排布 ,且喷头间距是喷水半径 (即射程 )的 1 .0 62 79倍时有最均匀的喷灌效果 ,喷灌均匀系数为0 .982 5 1 2 3 .本模型具有较好的实用价值 .     

三阶WENO-Z格式精度分析及其改进格式

首先通过理论推导给出了三阶WENO格式(WENO-JS3格式)满足收敛精度的充分条件.采用Taylor(泰勒)级数展开的方法,分析发现传统的三阶WENO-Z格式(WENO-Z3格式)在光滑流场极值点处精度降低.为了提高WENO-Z3格式在极值点处的计算精度,根据收敛精度的充分条件构造一种改进的三阶WENO-Z格式(WENO-NZ3格式),并综合权衡计算精度和计算稳定性确定所构造格式的参数.通过两个典型的精度测试,验证了WENO-NZ3格式在光滑流场极值点区域逼近三阶精度.选用Sod激波管、激波与熵波相互作用、Rayleigh-Taylor不稳定性、二维Riemann(黎曼)问题经典算例,进一步证实了本文提出的WENO-NZ3格式相较其他格式(WENO-JS3、WENOZ3、WENO-N3),不仅提高了计算精度,而且提高了对复杂流场结构的分辨率.     

一种高阶牛顿法求解投资组合优化模型

建立了均值方差投资组合优化模型.通过把凸二次规划转化为非光滑的非线性方程组,并对其光滑化处理,进而转化为光滑非线性方程组,再用高阶牛顿法进行求解.最后应用于投资组合优化模型,通过改变年收益率而得到不同的投资决策.该算法计算速度快,效率高,因此算法具有较广泛的应用空间.     

Simulation of Aerodynamic Performances of Flexible Flapping Wing Airfoils北大核心CSCD

与固定翼相比,在低速、小Reynolds数条件下,扑翼飞行具有显著的气动性能优势,受到越来越多的重视。然而,目前对扑翼翼型的研究以刚性翼型为主,对柔性翼型气动性能认识还不清楚。该文建立了柔性椭圆翼型的流固耦合仿真模型,分析了不同风速、迎角下柔性椭圆翼型的周围流场、变形以及气动性能。仿真结果表明,较刚性翼型,柔性翼型延缓了尾涡脱落时间,有效降低升力扰动振荡频率;柔性翼型显著抑制了尾流流场的扰动,降低升力扰动振荡幅值,合适的弹性模量翼型使得扰动振荡完全消除。研究结果可为软飞行器气动设计提供参考。     

基于交叉评价策略的DEA灰色关联排序模型北大核心

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

基于交叉评价策略的DEA灰色关联排序模型

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

Numerical bifurcation analysis of static stall of airfoil and dynamic stall under unsteady perturbation

By the finite element method combined with Arbitrary-Lagrangian-Eulerian (ALE) frame and explicit Characteristic Based Split Scheme (CBS), the complex flows around stationary and sinusoidal pitching airfoil are studied numerically. In particular, the static and dynamic stalls are analyzed in detail, and the natures of the static stall of NACA0012 airfoil are given from viewpoint of bifurcations. Following the bifurcation in Map, the static stall is proved to be the result from saddle-node bifurcation which involves both the hysteresis and jumping phenomena, by introducing a Map and its Floquet multiplier, which is constructed in the numerical simulation of flow field and related to the lift of the airfoil. Further, because the saddle-node bifurcation is sensitive to imperfection or perturbation, the airfoil is then subjected to a perturbation which is a kind of sinusoidal pitching oscillation, and the flow structure and aerodynamic performance are studied numerically. The results show that the large-scale flow separation at the static stall on the airfoil surface can be removed or delayed feasibly, and the ensuing lift could be enhanced significantly and also the stalling incidence could be delayed effectively. As a conclusion, it can be drawn that the proper external excitation can be considered as a powerful control strategy for the stall. As an unsteady aerodynamic behavior of high angle of attack, the dynamic stall can be investigated from viewpoint of nonlinear dynamics, and there exists a rich variety of nonlinear phenomena, which are related to the lift enhancement and drag reduction.     

Variation of friction drag via spanwise transversal surface waves

Introducing spanwise velocity components into the near-wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near-wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-Dimensional Bodies of Minimum Total Drag in Hypersonic Flow

The problem of constructing three-dimensional bodies of minimum total drag is studied within the framework of a local interaction model. Under certain assumptions, this model can be adopted to describe the distributions of both pressure and skin friction on the body during its high-speed motion through gases and dense media. Without any constraints on the possible drag law within the scope of the accepted model, the optimum shapes providing the minimum drag are found without any simplifying assumptions regarding their geometry. It is shown that, for a given base area and specified limitations on the body size, one can construct an infinite number of optimum forebody shapes. It is proved that the desired shapes are formed by combinations of surface parts whose normal makes a certain constant angle with the direction of motion. The optimum angle is determined by the velocity and medium characteristics in terms of the constants of the drag law. A method of optimum shape design is proposed; in particular, it allows one to construct optimum bodies like missiles with aft feather and optimum bodies with a circular base. All the bodies constructed have the same minimal total drag for the given base area. Even for asymmetrical bodies, the acting force has no component in a plane perpendicular to the direction of motion. Special attention is paid to the particular case of the minimum drag body design in hypersonic flow, when the pressure on the body is specified by the Newton formula. A comparative study of the results obtained for Newtonian flow shows that the proposed shapes are more effective in providing a drag reduction than bodies found to be optimum in earlier studies under special simplifying assumptions.     

Flow Past a Swept Wing with a Compliant Surface: Stabilizing the Attachment-Line Boundary Layer

Many aquatic species such as dolphins and whales have fins, which can be modeled as swept wings. Some of these fins, such as the dorsal fin of a dolphin, are semi-rigid and therefore can be modeled as a rigid swept wing with a compliant surface. An understanding of the hydrodynamics of the flow past swept compliant surfaces is of great interest for understanding potential drag reduction mechanisms, especially since swept wings are widely used in hydrodynamic and aerodynamic design. In this paper, the flow past a swept wing with a compliant surface is modeled by an attachment-line boundary layer flow, which is an exact similarity solution of the Navier–Stokes equations, flowing past a compliant surface modeled as an elastic plate. The hydrodynamic stability of the coupled problem is studied using a new numerical framework based on exterior algebra. The basic instability of the attachment line boundary layer on a rigid surface is a traveling wave instability that propagates along the attachment line, and numerical results show that the compliance results in a substantial reduction in the instability region. Moreover, the results show that, although the flow-field is three-dimensional, the qualitative nature of the instability suppression is very similar to the qualitative reduction of instability of the two-dimensional Tollmien–Schlichting modes in the classical boundary-layer flow past a compliant surface.     

Natural laminar flow shape optimization in transonic regime with competitive Nash game strategy

The Natural Laminar Flow (NLF) airfoil/wing design optimization is an efficient method which can reduce significantly turbulence skin friction by delaying transition location at high Reynolds numbers. However, the reduction of the friction drag is competitively balanced with the increase of shock wave induced drag in transonic regime. In this paper, a distributed Nash Evolutionary Algorithms (EAs) is presented and extended to multi-level parallel computing, namely multi-level parallel Nash EAs. The proposed improved methodology is used to solve NLF airfoil shape design optimization problem. It turns out that the optimization method developed in this paper can easily capture a Nash Equilibrium (NE) between transition delaying and wave drag increasing. Results of numerical experiments demonstrate that both wave drag and friction drag performances of a NE are greatly improved. Moreover, performance of the NE is equivalent to that of cooperative Pareto-optimum solutions, but it is more efficient in terms of CPU time. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.     

RBF Neural Network Based Prediction on Blade Surface Pressure Fields in Compressors北大核心CSCD

The airflow characteristics of the internal flow path of an aero-engine compressor are complex, and the vortex flow field around the blade is characterized by high pressure, high speed, rotation, and unsteadiness. Therefore, there is an urgent need to calculate and predict the aerodynamic characteristics of the complex flow field around the compressor blade efficiently and accurately. The computational fluid dynamics (CFD) method was used to generate the aerodynamic load distribution on the blade surface under different operating conditions for the study of the complex flow fields around aero-engine blades. The radial based function (RBF) neural network was applied to establish the pressure surface aerodynamic load prediction model, and the neural network modeling method was combined with the flow field calculation. The neural network method can learn and train the CFD-based data set to properly compensate the errors from the CFD, which provides a reference for the effective prediction of the complex flow fields around aero-engine compressor blades. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

MHD boundary-layer flow of a micropolar fluid past a wedge with constant wall heat flux

The steady laminar magnetohydrodynamic (MHD) boundary-layer flow past a wedge with constant surface heat flux immersed in an incompressible micropolar fluid in the presence of a variable magnetic field is investigated in this paper. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables, and then they are solved numerically by means of an implicit finite-difference scheme known as the Keller-box method. Numerical results show that micropolar fluids display drag reduction and consequently reduce the heat transfer rate at the surface, compared to the Newtonian fluids. The opposite trends are observed for the effects of the magnetic field on the fluid flow and heat transfer characteristics.     

On the flow resistance of wide surface structures

The possibility of skin-friction drag reduction in channel flows due to surface structures is investigated numerically. In this context, surface structures with a high width to height ratio compared to the typical dimensions of riblets are studied in the laminar as well as in the turbulent flow regime. In general, it is found that a reduction of the flow resistance is possible in both flow regimes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stall-delay modelling of wind turbine blades

Most aerodynamic design tools for horizontal-axial wind turbines are based on the blade-element momentum theory (BEM). Due to the nature of this theory, the design tools need 2-D steady sectional lift and drag curves as an input. In practice, flow over a wind turbine rotor blade is neither two-dimensional nor steady, and is affected by rotation. Pioneering experiments have identified a consequence: at inboard rotor blade sections stall is delayed. This so-called Himmelskamp effect [1] gives a larger lift than predicted and, as a result, a higher power and loading than expected. Consequently, an aerodynamic model is needed to explain and predict sectional lift and drag under rotating conditions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)