可压缩流气动声场的数值模拟

气动声学是一门流动力学和声学之间的交叉学科，主要研究流动及其与物体相互作用产生噪声的机理。动用计算技术研究气动声学问题的手段称为计算气动声学。本文的目的是，基于高精度数值算法的研究，分别运用Lighthill比拟理论、Kirchhoff积分和直接数值模拟等方法，针对翼型绕流、激波-涡干扰和轴对称射流，研究了物面非定常脉动压力、涡脱落、激波-涡干扰以及涡对并等产生噪声的机理。首先针对声场与主流场在能级和特征尺度等方面的差异，从空间离散角度分析了几种差分格式，表明迎风紧致格式/对称紧致格式有较小的数值色散、耗散和各向异性误差，因而适用于气动噪声的计算。以Runge-Kutta格式为例，对时间离散带来的误差进行了分析。指出对声波计算来说，仅考虑格式稳定性是不够的，时间步长还受到允许色散误差和耗散误差的限制。基于保色戎关系的思想，构造了优化Runge-Kutta格式。处例显示优化Runge-Kutta格式相对于经典格式有更高的计算效率。采用3阶迎风紧致格式和3阶Runge-Kutta格式数值模拟了NACA0012翼型的可压缩非定常绕流流场，并将此流场作为近场声源，运用声学比拟理论对偶极子声和四极子声进行研究。结果指出，主流速度对远场声压有决定性影响，在来流马赫数较大时，四极子噪声和偶极子噪声具有相同量级，不能被忽略，表明了可压缩效应对声场的影响。采用5阶迎风紧致格式和4阶Runge-Kutta格式求解非定常可压缩Navier-Stokes方程，对激波-单涡/双涡干扰导致的声场进行了直接数值模拟。详细研究了激波-涡干扰产生噪声的机理，指出噪声的产生及其性质和激波变形密切相关。研究了近场噪声衰减和传播距离r的关系，发现噪声衰减大致和r~(4/5)而不是r~(1/2)成反比关系，提出这种差异是由流场的非线性效应引起的。构造了Kirchhoff积分和非定常流动计算相结合的算法。采用5阶迎风紧致格式和3阶Runge-Kutta格式对亚声速轴对称射流进行直接数值模拟。将射流流场作为近场声源，结合Kirchhoff方法求解远场 气动噪声。数值结果表明远场噪声具有方向性，噪声声压在离开对称轴20°处达到最大值。随着传播距离增大，噪声方向性逐渐减弱。

垂直激励圆柱形容器中的非线性表面波及其不稳定性研究

本文分别在理想流体和弱粘性流体中，利用奇异摄动理论的两时间变量展开法，研究了垂直强迫激励圆柱形容器中的单一表面驻波模式的形成、结构特，点及其随时间的演化规律。首先假设流体是无粘、不可压且运动是无旋的，在忽略了表面张力的影响下，得到了描述表面波运动的非线性振幅方程及二阶自由面位移的解析表达式。通过数值计算，在不同驱动频率下，从理论上得到了非常丰富且只有少数在鄂学全等（19％，1998）的实验中报道过的表面波流谱模式。尽管所建立的数学模型和鄂学全等（19％。1998）的实验显示有所差别，但计算的结果可以用来解释他们实验中所观察到的表面波模态。进而研究了特定模式的空间结构（如节点的个数及分布规律）及其随时间三维演化规律，从理论上验证了此类表面波具有驻波的特点，丰富了前人的研究成果。液体表面张力的影响在所研究问题的尺度（如容器的半径为几个厘米，驱动的振幅只有微米量级）范围内对表面波的模式选择也不可忽视。故本文通过边界条件引入了表面张力的影响，研究了表面波模式的性质，并和无表面张力时的情况进行了比较。结果表明，当外激励频率较小时，表面张力对表面波模式选择的影响较小；但当驱动频率较大时，表面张力对表面波的模式选择影响很大，反映出表面张力具有使得自由面回到平衡位置的作用，更加逼近问题的真实情况。由于实际的物理系统中会产生阻尼，而阻尼系数的确定对研究表面波的模式特点及其发展规律有非常重要的意义。本文在弱粘性流体中，把Navier-Stokes方程线性化，研究了圆柱形容器受垂直强迫激励的表面驻波运动。将整个流场分为外部势流区和内部的边界层流动，求得了粘性阻尼系数的解析表达式，并研究了阻尼系数随某些参数，如粘度、驱动振幅、液体的深度等的变化规律。将在弱粘性流体情况下得到的粘性阻尼系数加到无粘流体中所得的色散关系和非线性振幅方程中对其进行修正，修正的结果使得所研究的问题更进一步接近实验的真实情况。粘性阻尼和表面张力二者对模式选择的影响中，当波数较小，即表面波的模式较简单时，粘性阻尼的影响起主要作用；相反，当波数较大，即表面波的模式较复杂时，表面张力的影响起主要作用。最后将阻尼项加到理想流体中得到的非线性振幅方程中，对其进行修正。对新的修正方程进行了稳定性分析。结合相平面特点研究了解的性质，得到形成稳定表面波模式的必要条件，给出了不稳定区域。。研究结果表明对已形成的稳态模式来说，它对小的扰动是不会失稳的。

再入尾迹电磁特性的湍流效应研究

本文旨意在于通过探讨高超声速再入尾迹中的湍流等离子体与电磁波相互作用的机理，以及建立能反映此机理的应用性理论模型，从而提供一套可进行目标特性分析的方法，以便为工程部门的突防技术服务。本题目在再入气动物理现象研究中具有重要意义。综合分析指出，地面雷达观测到的非相干散射信号主要来源于再入尾迹的亚密湍流区产生的体积散射。因此，电磁散射特性分析主要针对尾迹亚密湍流等离子体。并且，这里所有的分析都是根据在工程应用中最成熟的一阶畸变波Born近似理论模型。再入尾迹电磁特性的湍流效应研究，着眼点就在于湍流等离子体场的研究。对湍流等离子体场理论模型，本文试图通过模式理论来表达，即求解平均化的全Navier-Stokes方程及其封闭方程k-ε-g模型，从而准确获得流动平均场和脉动场信息。这种表达方式较以前有了较大改进。注意到高超声速流动具有强烈可压缩性的特点，故使用的N-S平均方程由质量加权平均过程产生，湍流模型方程也经过可压缩性修正。方程的离散求解方法，都是运用带矢通量分裂的二阶TVD格式的有限体积法。再入尾迹湍流场的初始条件由近尾迹（底部）流动经N-S方程求解给定，初始值更加准确可靠。尾迹从层流到湍流的转捩过程采用相对成熟的半经验公式确定。飞行器的高超声速再入过程必然导致它周围的空气温度升高，使得流动表现出真实气体效应。对重点考察的湍流流动而言，真实气体效应主要表现为气体处于热化学平衡状态。就工程部门面临的实际问题，把一阶畸变波Born近似的解算方法做些改进，使其能够处理的范围从轴对称尾迹扩展到三维湍流等离子体场是必要的。这为深入的理论分析提供了有力的保障。在能够准确模拟湍流流动的刻划雷达散射截面的基础上，考察亚密湍流等离子体对电磁散射的影响。通过选择的几个有代表性的因素进行讨论，初步结果表明：湍流转捩方式、湍流尺度对尾迹雷达散射截面值计算影响不大，而电子组份脉动能初始值影响较明显，且在特定条件下湍流模型的影响亦不大。但由于湍流模型涉及脉动初始值，其影响需进一步确定。同时，一些今后开展继续此项研究工作的有益建议也提了出来。

均匀来流绕旋转及旋转振荡圆柱绕流研究

该文通过数值方法求解二维不可压Navier-Stokes方程，对均匀来流中静止、旋转和旋转振荡圆柱绕流进行了系统的数值模拟.该文采用有限体积法对控制方程进行离散，选用元结构化四边形网格剖分计算区域，关于速度-压力耦合的处理使用了SIMPLEC方法.经过了大量的数值模拟，分盺166L鸬玫搅苏饧钢秩屏鞯氖的Ｄ饨峁?该文重点是用快速傅里叶变换（FFT）方法对旋转振荡圆柱绕流中的频率耦合现象进行研究，并分析在不同频率耦合作用下涡形成、发展和脱落的规律.

An Atomistic-Continuum Hybrid Simulation Of Fluid Flows Over Superhydrophobic Surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper, an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces, in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths, which cannot be obtained by molecular dynamics simulation alone.

Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence

A scale-similarity model for Lagrangian two-point, two-time velocity correlations LVCs in isotropic turbulence is developed from the Kolmogorov similarity hypothesis. It is a second approximation to the isocontours of LVCs, while the Smith-Hay model is only a first approximation. This model expresses the LVC by its space correlation and a dispersion velocity. We derive the analytical expression for the dispersion velocity from the Navier-Stokes equations using the quasinormality assumption. The dispersion velocity is dependent on enstrophy spectra and shown to be smaller than the sweeping velocity for the Eulerian velocity correlation. Therefore, the Lagrangian decorrelation process is slower than the Eulerian decorrelation process. The data from direct numerical simulation of isotropic turbulence support the scale-similarity model: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

Space-time correlations of fluctuating velocities in turbulent shear flows

Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation DNS of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shearinduced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the spacetime correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

SPT方法在纳米粒子布朗运动观测中的应用

纳米粒子布朗运动特性对Micro-/Nano-PIV的使用和与粒子相关的物理现象的研究有重要意义.观测了200nm荧光粒子的布朗运动,利用单粒子追踪(SPT)算法和自编程序处理图像,获得粒子的均方位移,计算了实验扩散系数D_(exp)为2.09×10~(-12) m~2/s.与Stokes-Einstein公式估计的理论扩散系数D_(th)相比,二者量阶一致,但实验扩散系数的数值偏小约5%.对相关的实验误差进行了分析.

Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Solute transport in nanochannels with roughness-like structures

Newfound attention has been given to solute transport in nanochannels. Because the electric double layer (EDL) thickness is comparable to characteristic channel dimensions, nanochannels have been used to separate ionic species with a constant charge-to-size ratio (i.e., electrophoretic mobility) that otherwise cannot be separated in electroosmotic or pressure- driven flow along microchannels. In nanochannels, the electrical fields within the EDL cause transverse ion distributions and thus yield charge-dependent mean ion speeds in the flow. Surface roughness is usually inevitable during microfabrication of microchannels or nanochannels. Surface roughness is usually inevitable during the fabrication of nanochannels. In the present study, we develop a numerical model to investigate the transport of charged solutes in nanochannels with hundreds of roughness-like structures. The model is based on continuum theory that couples Navier-Stokes equations for flows, Poisson-Boltzmann equation for electrical fields, and Nernst-Planck equation for solute transports. Different operating conditions are considered and the solute transport patterns in rough channels are compared with those in smooth channels. Results indicate that solutes move slower in rough nanochannels than in smooth ones for both pressure- driven and electroosmotic flows. Moreover, solute separation can be significantly improved by surface roughness under certain circumstances.

El tiempo como observable en mecánica cuántica

121 p.

Numerical Investigation On The Flowfield Of "Swallowtail" Cavity For Supersonic Mixing Enhancement

A "swallowtail" cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the "swallowtail" cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-epsilon turbulence model in a multi-block mesh. Turbulence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the "swallowtail" cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the "swallowtail" cavity structure.