Acceleration correlations and pressure structure functions in high-reynolds number turbulence

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian particle tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation of fluid particle acceleration at Taylor microscale Reynolds numbers between 200 and 690. We also obtained indirect, nonintrusive measurements of the Eulerian pressure structure functions by integrating the acceleration correlations. Our measurements are in good agreement with the theoretical predictions of the acceleration correlations and the pressure structure function in isotropic high-Reynolds number turbulence by Obukhov and Yaglom in 1951 [Prikl. Mat. Mekh. 15, 3 (1951)]. The measured pressure structure functions display K41 scaling in the inertial range.     

Granular avalanches in fluids

Three regimes of granular avalanches in fluids are put in light depending on the Stokes number St which prescribes the relative importance of grain inertia and fluid viscous effects and on the grain/fluid density ratio r. In gas (r>1 and St>1, e.g., the dry case), the amplitude and time duration of avalanches do not depend on any fluid effect. In liquids (r approximately 1), for decreasing St, the amplitude decreases and the time duration increases, exploring an inertial regime and a viscous regime. These three regimes are described by the analysis of the elementary motion of one grain.     

Sweep-stick mechanism of heavy particle clustering in fluid turbulence

It is proposed that the inertial range clustering of small heavy particles in fluid turbulence occurs as a result of the sweep-stick mechanism which causes inertial particles to cluster so as to mimic the clusters of points where the fluid acceleration is perpendicular to the direction of highest contraction between neighboring particles. Direct numerical simulations of inertial particles subjected to linear Stokes drag and suspended in homogeneous isotropic turbulence support the validity of the sweep and stick properties on which the sweep-stick mechanism is based, and also support the clustering consequences of this mechanism. It also explains the observed Stokes-number dependence of inertial particle clustering.     

Inertial clustering of particles in high-Reynolds-number turbulence

We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.     

Critical role of gravity in filters

The efficiency of filters depends crucially on the mass of the particles one wants to capture. Using analytical and numerical calculations we reveal a very rich scenario of scaling laws relating this efficiency to particle size and density and the velocity and viscosity of the carrying fluid. These are combined in the dimensionless, so-called Stokes number St. In the case of horizontal flow or neutrally buoyant particles, we find a critical number St{c} below which no particles are trapped; i.e., the filter does not work. Above St{c} the capture efficiency increases like the square root of (St-St{c}). Under the action of gravity, the threshold abruptly vanishes and capture occurs at any Stokes number increasing linearly in St. We discovered further scaling laws in the penetration profile and as function of the porosity of the filter.     

直接模拟离散颗粒对湍流射流的影响

发展了一种基于双向耦合的直接数值模拟方法,研究了两相湍流射流中离散颗粒对气相射流的影响。流场采用高分辨率的算法直接耦合求解,颗粒相采用拉格朗日方法跟踪。结果表明不同Stokes数的颗粒对射流的影响不同。所有的颗粒都降低了射流速度半宽,但对流向平均速度剖面的影响比较复杂.Stokes数为0.01和50的颗粒降低了横向平均速度,使得湍流强度剖面变的更宽更低;而Stokes数为1的颗粒则增加了横向平均速度,降低了湍流强度。     

转捩射流中涡结构与颗粒扩散的直接模拟

为考察转捩射流中拟序结构的空间演化过程及其对不同Stokes颗粒扩散的影响,采用有限容积方法和分步投影算法对三维气固两相射流进行了直接模拟。其中流体控制方程组的时间积分采用低存储三阶精度的Runge-Kutta格式; 颗粒的跟踪在拉格朗日框架下进行。模拟结果发现,在流场拟序结构由大尺度转化为小尺度的过程中,中、小Stokes数的颗粒能自发地调整它们的扩散方式,分别由非均匀状态向均匀状态以及由均匀状态向非均匀状态转变。     

Measurement of the electric fluctuation spectrum of magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) turbulence in the solar wind is observed to show the spectral behavior of classical Kolmogorov fluid turbulence over an inertial subrange and departures from this at short wavelengths, where energy should be dissipated. Here we present the first measurements of the electric field fluctuation spectrum over the inertial and dissipative wave number ranges in a Beta > or approximately = 1 plasma. The k(-5/3) inertial subrange is observed and agrees strikingly with the magnetic fluctuation spectrum; the wave phase speed in this regime is shown to be consistent with the Alfvén speed. At smaller wavelengths krho(i) > or = 1 the electric spectrum is enhanced and is consistent with the expected dispersion relation of short-wavelength kinetic Alfvén waves. Kinetic Alfvén waves damp on the solar wind ions and electrons and may act to isotropize them. This effect may explain the fluidlike nature of the solar wind.     

Variable-range projection model for turbulence-driven collisions

We discuss the relative speeds DeltaV of inertial particles suspended in a highly turbulent gas when the Stokes number, a dimensionless measure of their inertia, is large. We identify a mechanism giving rise to the distribution P(DeltaV) approximately exp(-C|DeltaV|(4/3)) (for some constant C). Our conclusions are supported by numerical simulations, and by the analytical solution of a model equation of motion. The results determine the rate of collisions between suspended particles. They are relevant to the hypothesized mechanism for formation of planets by aggregation of dust particles in circumstellar nebula.     

气固轴对称射流中固粒扩散的研究

由三维离散涡丝方法对气固轴对称射流场数值模拟的结果表明,当固粒 Ｓｔ数＜＜１时,固粒明显受到流场运动的影响; Ｓｔ＝ １时,固粒均匀分布在涡结构周围;当 Ｓｔ ＞＞１时,固粒受流场影响较弱。对涡环沿周向施以五个波长扰动时,固粒扩散范围较宽。     

Non-equilibrium Wall Deposition of Inertial Particles in Turbulent Flow

Non-equilibrium effects resulting from the slow relaxation of inertial particles to statistical equilibrium with flow fluctuations in turbulence are known to have important consequences, but they are not readily incorporated into models. Here, a simple analysis of these effects predicts −2/3 power-law dependence of the particle deposition rate on Stokes number (normalized particle inertia) in the far field of a confined turbulent flow, and a weaker near-field dependence. Near-field measurements and numerical simulations exhibit this weaker dependence, as do models that are generally viewed as validated by this result, but the models fail to capture the newly identified far-field behavior due to their equilibrium assumptions. Quantification of these qualitative observations is obtained by incorporating particle response to fluid motion into ‘one-dimensional turbulence’ (ODT), a stochastic computational model of turbulence.     

强梯度复杂流场中的粒子动力学响应试验研究

示踪粒子在(高)超声速流场中的动力学响应是粒子成像测速等粒子示踪测量技术的关键问题之一.现有文献对粒子动力学响应的试验测量往往是通过单个斜激波响应的测量方法.然而,当示踪粒子用于测量高速飞行器发动机内部复杂的激波串流场时,粒子将经历由多道激波导致的速度、压力、黏性等剧烈变化.本文结合目前(高)超声速飞行器的研究热潮,重点关注示踪粒子在应用于发动机内部具有连续激波的复杂流场测量中存在的跟随性评估方面,开展了一系列的相关试验研究.包括测量超声速风洞的喷管出口速度分布以验证测试系统的性能,在马赫4.2和3.0流场中测量了粒子对二维10°和15°单斜劈绕流中的斜激波动力响应,并测量了模拟发动机内部连续梯度的双斜劈粒子斜激波动力响应.结合粒子动力学的理论模型,得到了各状态的粒子弛豫时间、弛豫距离、Stokes数.基于图像方法、统计学规律分析了激波非定常抖动对测量结果的影响,并对测量结果进行了修正.结果显示,相同斜劈角度下,马赫数越高,粒子的弛豫时间、弛豫距离就越大.但是在相同的来流马赫数下,斜劈角度越大,粒子的弛豫时间、弛豫距离反而减小.在强梯度之后由于流场的雷诺数和黏性系数变化剧烈,粒子的跟随性降低了大约5.7%,stokes数增加了约1%.虽然在本文条件下Stokes数仍满足超声速流场对粒子跟随性的要求,但粒子响应的降低无疑是值得关注的,尤其是当其被应用于具有更多连续梯度的复杂流场测量中.     

High order Lagrangian velocity statistics in turbulence

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to R(lambda) = 815 ) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.     

Turbulent transport of material particles: an experimental study of finite size effects

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle's diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle's acceleration probability density functions is not found to depend significantly on its size while the particle's acceleration variance decreases as it becomes larger in quantitative agreement with the classical k(-7/3) scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.     

Structure-based interpretation of the Strouhal-Reynolds number relationship

The wake in the flow past a circular cylinder has posed a long-standing challenge to scientists since the late 19th century. Many aspects of this seemingly simple phenomenon remain unexplained. Of particular interest is the relationship between the dimensionless vortex shedding frequency (the Strouhal number St) and the ratio of inertial to viscous forces in the fluid (the Reynolds number Re). We propose a new St-Re relation based on the observations of the structure of a vortex street in flowing soap films. The measurements suggest a simple two-parameter form St=1/(A+B/Re) that describes laminar vortex shedding remarkably well for bulk fluids as well as for two-dimensional flowing soap films.     

气固两相圆柱绕流的直接数值模拟

本文运用谱元方法对气固两相圆柱绕流进行了直接数值模拟。在获得高精度计算流场信息基础上,进行颗粒扩散运动的研究。通过研究颗粒大小对颗粒扩散运动的影响来刻画气固两相圆柱绕流的物理特征。研究时发现,由于圆柱尾流独特的涡结构特征,颗粒在流场中心轴线附近区域的扩散机理主要是决定于吸力作用,该作用会驱使小颗粒卷吸进入圆柱尾部近壁区,甚至与圆柱后壁发生碰撞,这种扩散机理与混合层中颗粒扩散机理明显不同。     

Interaction of solid particles with a tangle of vortex filaments in a viscous fluid

Homogeneous isotropic turbulence consists of coherent filamentary vortex structures superimposed to a more incoherent background. The question which we address is the effect of these structures on the dynamics of small, neutrally buoyant solid particles. Rather than generating the turbulence by direct numerical simulation (DNS) of the Navier-Stokes equations, we use a model of turbulence based entirely on viscous vortex filaments which interact via inertial forces and reconnect with each other. Using this model, we show that solid particles can become trapped around vortex filaments, something difficult to achieve with DNS. Unlike most studies, we have not neglected inviscid inertial effects. By comparing the Stokes, local, and convective components of the particle's acceleration, we also show that the convective part clearly identifies the trapping.     

考虑双向耦合效应的格子Boltzmann气固两相湍流模型

在流体粒子概率密度函数输运方程中考虑颗粒对流体的反作用力,发展了考虑双向耦合效应的LB气固两相流模型,引入Smagorinsky亚格子模型模拟高雷诺数气相流场.对经典后台阶气固两相流动进行模拟,气相和颗粒相速度分布与实验结果进行比较,发现考虑双向耦合效应的LB气固两相流模型结果明显优于单向耦合结果.进一步研究不同惯性颗粒在流场中的弥散特性,小颗粒(St~O(0.1))对流体的跟随性较好,在流场中分布较为均匀;而St~O(1)的颗粒难被流场涡卷吸进入涡内,呈现倾向性弥散现象;大颗粒(St~O(10))由于自身惯性进入流场涡,在流场中分布较为均匀.     

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries

We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains.