信天翁近海面飞行时的气动力研究

针对信天翁近海面的飞行条件,研究信天翁能在大风浪中高效飞行的力学机理．将信天翁简化为二维机翼,采用势流理论的面元方法,重点研究了波浪的有益干扰．给出了信天翁在匀速固定高度飞行和自由飞行两种状态下的波浪扰动力．计算结果表明:信天翁的飞行效率不仅取决于飞行的高度和速度,而且取决于浪高和波长;在大风浪下信天翁可以从波浪有益干扰中获得推力来抵消部分飞行阻力,提高飞行效能．     

翼涡干扰前缘开孔被动控制数值研究

开孔方法是一种简单的流动被动控制方法.为找到一种有效降低桨涡干扰效应的被动控制方法,以NACA 0012翼型作为研究对象,建立了4种前缘开孔的模型.在不同来流速度、涡的强度和干扰距离条件下,对4种前缘开孔模型和无孔的基准翼型进行了二维平行桨涡干扰（翼涡干扰）数值模拟,对比了升力系数的变化.结果表明:前缘开孔可以降低翼涡干扰效应,但对翼型升力系数有一定的影响;宽度为2.5%弦长的直孔能在翼型升力系数损失较小的情况下有效地降低翼涡干扰效应,且适用范围较广.     

昆虫拍动翅的非定常变形对其气动力的影响

通过在动态变形网格上求解N-S方程的方法,研究了昆虫拍动翅的非定常变形对其气动力的影响．其中,拍动翅的扭转变形对气动力影响很小,拱形变形则会产生显著的影响,扭转和拱形组合变形的效果与拱形变形单独的效果基本相同．在6%拱形和20度扭转组合变形的情况下（此为对大量昆虫观察所得到的典型值）,相对于无变形平板翅,升力增加了10～20%,升阻比增加了约10%．翅膀的变形可增大最大升力系数;同时,可减小飞行的能耗,例如,对于做悬停飞行的熊蜂,其翅膀的动态变形（6%拱形和20度扭转组合变形）使其飞行中的能耗比无变形情况降低了约16%．     

非线性自由表面波问题的差分解法

本文提出计算二维非定常位势流动的有限差分法,流动是因自由表面任意瞬间扰动所产生的.自由表面上同时满足动力和运动的非线性条件.本方法的基本特征是利用坐标变换将时间相关的物理计算域变换为固定域;建立迭代格式解Poisson方程以求速度势;通过快速富氏变换化为三对角型代数方程组计算未知量,因而大量节省计算机时.为解非定常自由表面波浪问题提供了一个有效的方法.引用了两个例题验证方法的可行性.     

非定常二维Navier-Stokes方程流函数-涡度形式的特征-混合有限元数值模拟

本文针对非定常的二维Navier-Stokes方程提出了一种基于流函数一涡度形式的数值模拟方法——特征一混合有限元方法，得到了流函数、涡度函数和流场速度的最优阶的L^2误差估计．     

昆虫振翅飞行的数值模拟

在非惯性参考系下对昆虫振翅扰动的二维非定常流场进行了数值模拟,避免了计算中的移动边界困难,从而缩短了计算时间,模型具有3个自由度,可以模拟任意已知的翅的平面运动．通过模拟相对复杂的自然界昆虫的振翅运动,研究昆虫是如何控制飞行．计算结果表明,有2个参数可能被昆虫用来控制飞行:翅平动和转动间的相位差以及垂直于平均振翅平面方向的横向振幅．     

翼型绕流干涉噪声的实验与数值研究

来流湍流干扰噪声在风力机叶片气动总噪声级中占有重要地位．选取圆柱/翼型干涉模型从实验和数值两方面研究此类干涉发声现象．实验中通过对翼型表面非定常载荷的测量,重点研究了圆柱位置和翼型攻角的影响,选取的翼型包括两个NACA系列翼型（NACA0012和NACA0018）和两个风力机翼型（s809和s825）,同时利用PIV（particle image velocimetry）技术对低攻角状态下翼型的前缘流场进行了研究．实验结果表明翼型表面非定常压力与圆柱涡脱落存在一定相关性．与此同时采用非定常Reynolds平均(URANS)方法对圆柱/NACA0012翼型的干涉流场进行了非定常数值模拟,并将得到的翼型表面压力频谱与实验结果进行了对比．     

昆虫翼拍动中受载变形的粘弹性本构模型

昆虫翼拍动受载时发生被动变形,被看作为有助于改善飞行性能的机制之一．决定这种被动变形大小的一个关键因素是昆虫翼的材料本构关系,至今缺乏研究．基于蜻蜓翼(离体)的应力松弛实验和模型翼拍动时受载变形的有限元数值分析,揭示了粘弹性本构关系是昆虫翼材料性能的合理描述,并研究了粘弹性参数对被动变形的影响．     

气波增压器转子中气体的二维非定常运动

本文研究了相对旋转坐标系中气波增压器转子子午面上气体的二维非定常运动。使用二阶精度的MacCormack差分格式求解了子午面上的非定常Euler微分方程,给出了一个对中小型气波增压器有代表意义的数值解,还与实验及一维数值计算结果进行了比较。计算表明采用二维模型更全面地揭示了气波增压器转子中气体非定常运动的规律。     

非定常 N-S 方程的非线性 Galerkin 算法及其误差估计

本文给出了二维非定常N-S方程的三种数值格式,其中空间变量用谱非线性Galerkin算法进行离散,时间变量用有限差分离散,并研究了这些格式数值解的逼近精度．最后,给出了部分数值计算结果．     

Finite element method to fluid–solid interaction problems with unbounded periodic interfaces

Consider a time‐harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid fluid of constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by its Lamé constants. This article is concerned with a variational approach to the fluid–solid interaction problems with unbounded biperiodic Lipschitz interfaces between the domains of the acoustic and elastic waves. The existence of quasiperiodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. A finite element scheme coupled with Dirichlet‐to‐Neumann mappings is proposed and the convergence analysis is performed. The Dirichlet‐to‐Neumann mappings are approximated by truncated Rayleigh series expansions. Finally, numerical tests in 2D are presented to confirm the convergence of solutions and the energy balance formula. In particular, the frequency spectrum of normally reflected signals is plotted for water–brass and water–brass–water interfaces. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 5–35, 2016     

Quasi-2D model for computation of supercritical free surface flow in sudden expansion

This work deals with the mathematical modeling of a supercritical flow at an abrupt channel expansion. A simplified approach for the study of the characteristics and features of the flow in the presence of the cross shock waves is then proposed. Based on the two-dimensional Saint-Venant equations and using certain simplifying assumptions in practice, this 2D shallow water model is reconverted to an equivalent 1D flow problem by inverting space time variables. The numerical solution of the 1D equation then makes it possible to reconstitute the solution of the 2D flow field according to translating planes. The results obtained show a satisfactory agreement with the experiments carried out for this problem. The profiles of the waterline along the wall and the flow axis are accurately reconstituted thus allowing the good design of the channel walls and the positioning of the oblique shock waves.     

BIFURCATIONS OF THE TRAVELLING WAVE SOLUTIONS TO A GENERALIZED CAMASSA-HOLM EQUATION

In this paper, we study some generalized Camassa-Holm equation. Through the analysis of the phase-portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave and compactons were discussed. In some certain parametric conditions, many exact solutions to the above travelling waves were given. Further-more, the 3D and 2D pictures of the above travelling wave solutions are drawn using Maple software.     

Existence and qualitative theory for stratified solitary water waves

This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water and vacuum is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity field and density function, there exists a continuous curve of such solutions that includes large-amplitude surface waves. Furthermore, following this solution curve, one encounters waves that come arbitrarily close to possessing points of horizontal stagnation.We also provide a number of results characterizing the qualitative features of solitary stratified waves. In part, these include bounds on the wave speed from above and below, some of which are new even for constant density flow; an a priori bound on the velocity field and lower bound on the pressure; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical solitary waves of elevation have an axis of even symmetry.     

Global Infinite Energy Solutions for the 2D Gravity Water Waves System

We prove global existence and a modified scattering property for the solutions of the 2D gravity water waves system in the infinite depth setting for a class of initial data, which is only required to be small above the level . No assumption is made below this level. Therefore, the nonlinear solution can have infinite energy. As a direct consequence, the momentum condition assumed on the physical velocity in all previous small energy results by Ionescu‐Pusateri, Alazard‐Delort, and Ifrim‐Tataru is removed.© 2017 Wiley Periodicals, Inc.     

Modeling the capacity of a novel flow-energy harvester

The performance of a new type of flow energy harvester based on oscillating foils is investigated through numerical modeling by using two methods, a 2D thin-plate model and a 3D nonlinear boundary-element model. The fluid–structure interaction problem involved in the dynamics of a heaving/pitching foil coupled with an actuation/energy harvesting system in this device is examined. The 2D analysis allows us to simulate dynamics of the flapping-foil system over a large range of parameters and to identify areas of special interests (e.g., high energy output or high efficiency). In the vicinity of these areas the 3D model can accurately predict the performance of the system. By examining the power extraction capacity and efficiency of the system at various geometric, mechanical, and kinematic parameters, the optimal performance of the system is determined. In addition, the performance is found to be enhanced by the presence of a solid ground, as well as the thickness of the foil (at certain frequencies).     

自由来流湍流与三维壁面局部粗糙诱导平板边界层不稳定T-S波的数值研究

采用直接数值模拟（DNS）方法,研究了在自由来流湍流与三维壁面局部粗糙作用下平板边界层内诱导产生不稳定T-S波的物理问题.数值结果可知,在平板边界层内发现了二维和三维T-S波组成的波包空间序列以及求得了波包向前传播的群速度大小,从而证明了自由来流湍流与三维壁面局部粗糙作用是激励平板边界层内诱导产生不稳定T-S波的一种机制.随后,建立了平板边界层内被激发的二维和三维T S波的初始幅值与自由来流湍流度,三维壁面局部粗糙的流向长度、展向宽度及法向高度之间的关系.这一问题的深入研究,进一步完善了流动稳定性与湍流理论.     

A Quasi‐Planar Model for Gravity‐Capillary Interfacial Waves in Deep Water

A dynamical model equation for interfacial gravity‐capillary (GC) waves between two semi‐infinite fluid layers, with a lighter fluid lying above a heavier one, is derived. The model proposed is based on the fourth‐order truncation of the kinetic energy in the Hamiltonian of the full problem, and on weak transverse variations, in the spirit of the Kadomtsev‐Petviashvilli equation. It is well known that for the interfacial GC waves in deep water, there is a critical density ratio where the associated cubic nonlinear Schrödinger equations changes type. Our numerical results reveal that, when the density ratio is below the critical value, the bifurcation diagram of plane solitary waves behaves in a way similar to that of the free‐surface GC waves on deep water. However, the bifurcation mechanism in the vicinity of the minimum of the phase speed is essentially similar to that of free‐surface gravity‐flexural waves on deep water, when the density ratio is in the supercritical regime. Different types of lump solitary waves, which are fully localized in both transverse and longitudinal directions, are also computed using our model equation. Some dynamical experiments are carried out via a marching‐in‐time algorithm.     

The mathematics of scattering by unbounded,rough, inhomogeneous layers

In this paper we study, via variational methods, a boundary value problem for the Helmholtz equation modelling scattering of time harmonic waves by a layer of spatially varying refractive index above an unbounded rough surface on which the field vanishes. In particular, in the 2D case with TE polarization, the boundary value problem models the scattering of time harmonic electromagnetic waves by an inhomogeneous conducting or dielectric layer above a perfectly conducting unbounded rough surface, with the magnetic permeability a fixed positive constant in the medium. Via analysis of an equivalent variational formulation, we show that this problem is well-posed in two important cases: when the frequency is small enough; and when the medium in the layer has some energy absorption. In this latter case we also establish exponential decay of the solution with depth in the layer. An attractive feature is that all constants in our estimates are bounded by explicit functions of the index of refraction and the geometry of the scatterer.