Droplet clouds in a box of turbulence

与预期相反，悬浮在湍流流动的气体或液体中的小颗粒不会混合，而是分离成高浓度和低浓度的区域。这些分离或聚集的模式是由于颗粒与气体中湍流的涡旋运动相互作用的方式而产生的。在任何时刻的湍流都可以被认为是由涡流/漩涡和它们之间的高应变率区域组成的。涡流中的颗粒将被离心远离涡流的中心，而在应变区域中，它将被聚焦朝向应变的中心。因此，颗粒将总是试图绕过它们之间的高应变区域中的涡旋边缘，并且颗粒将倾向于在那里积聚。与涡流的尺度和持久性相比，分离的程度取决于颗粒响应时间，并且由于湍流由许多尺度组成，因此通常会有一个特定的尺度发生分离。这种分离可以对许多工业和环境过程产生深远的影响（从粉末生产和燃烧到纳米尺寸颗粒的形成和生长，再到大气中的雨滴）。在分离足够高的情况下，它可以影响湍流产生和消散方式的实际动力学，因此在减阻现象中非常重要。这种分离过程的模拟和测量揭示了一些有趣的性质：奇异性发生在颗粒浓度，这是高度间歇性的空间和时间，在这种情况下的颗粒运动包含一个随机不相关的组件（RUM）或组件的准布朗运动。这个RUM的起源还没有很好的理解，但可能与流中奇点的出现以及粒子轨迹可以在流中任何给定点交叉的事实有关。本提案中描述的工作的目的是双重的：理解和量化这些功能，并建立其起源;获得第一次的统计描述，将这些功能的单粒子和双粒子分散。我们将使用的方法称为PDF方法，它与气体动力学理论相似，我们将为一个和两个粒子的弥散建立一个PDF方程，其中包括粒子速度及其位置。在此过程中，我们将使用实验和模拟来验证我们的模型方程。实验部分将开发一种新的设施，模拟雨在一个盒子的湍流，通过产生一个'盒子'的各向同性湍流，没有平均流，使用声致动器。实验将量化，第一次，粒子对分离和速度，粒子和流体速度之间的相关性和相关的统计数据的流动拓扑结构的粒子附近的PDF。所提出的研究的一个重要成果将是由于颗粒团聚的液滴尺寸分布的演变的量化，以及其与湍流结构的持久性和尺度的相关性。

Contrary to expectation, small particles suspended in a turbulent flowing gas or liquid, do not mix but segregate into regions of high and low concentrations. These patterns of segregation or clustering arise because of the way particles interact with the eddying motion of the turbulence in the gas. A turbulent flow at any instant of time may be considered as composed of eddies /vortices and regions of high straining rate between them. A particle in an eddy will be centrifuged away from the centre of the eddy whilst in a straining region it will be focused towards the centre of the strain. Particles will thus always try to skirt round the edges of vortices in the high straining regions between them and it is there that the particles will tend to accumulate. The degree of segregation depends up the particle response time compared to the scale and persistence of the eddy and since turbulence is composed of many scales there will usually be one particular scale where segregation will occur. This segregation can have a profound effect on many industrial and environmental processes (from powder production and combustion to formation and growth of nano-size particles to rain droplets in the atmosphere). In cases where the segregation is high enough, it can influence the actual dynamics of the way the turbulence is produced and dissipated and is therefore very important in the phenomenon of drag reduction. Simulation and measurement of this segregation process have revealed some interesting properties: singularities occur in the particle concentration which is highly intermittent both in space and time; particle motion in such circumstances contains a random uncorrelated component (RUM) or component of quasi Brownian motion. The origin of this RUM is not well understood but may be linked to the occurrence of singularities in the flow and the fact that particle trajectories can cross at any given point in the flow. The purpose of the work described in this proposal is two-fold: to understand and quantify these features and to establish their origin; to obtain for the first time a statistical description incorporating these features for single and two-particle dispersion. The approach we will use is called the PDF approach and is similar to the kinetic theory of gases in that we shall develop a pdf equation for one and two particle dispersion that includes the particle velocity as well as its position. In so doing we will use both experiment, and simulation to underwrite and validate our model equations. The experimental part will develop a novel facility to simulate rain in a box of turbulence , by generating a 'box' of isotropic turbulence, without mean flow, using acoustic actuators. The experiments will quantify, for the first time, pdfs of particle pair separations and velocities, correlations between particle and fluid velocities and associated statistics of the flow topology in the neighbourhood of particles. One important outcome of the proposed research will be the quantification of the evolution of the droplet size distributions due to particle agglomeration, and its correlation with the persistence and scales of the turbulent structures.