Stochastic Vortex Structure Model for Adhesive Particles in Turbulent Flows

湍流中颗粒的输运是由于湍流涡间流体交换引起的大范围扩散过程和小尺度反扩散过程引起的。后者(我们将称为颗粒弥散)与重颗粒被抛出湍涡的趋势有关，在湍涡之间的间隙区域形成高浓度的粒子片。众所周知，这种小规模的非均质性会引起几个数量级的颗粒浓度波动，进而对涉及颗粒碰撞和团聚的过程产生巨大影响。虽然随机拉格朗日模型(SLM)已经被证明能够准确地模拟大尺度的粒子扩散，但这些方法缺乏必要的空间相关性来解释小尺度的浓度不均匀。本文提出的工作将用空间相关的随机强迫代替随机拉格朗日模型中使用的随机强迫，这种随机强迫是基于一组随机涡旋结构来近似湍流涡旋。SVS模式将在包含能量的湍流积分尺度和与涡度Stokes数等于1的长度尺度相关的最小尺度之间的长度尺度间隔上产生具有正确空间相关性的湍流速度场。所提出的随机模型将通过与均匀湍流和湍流剪切流中颗粒团聚形成的直接数值模拟的比较来验证。模拟将使用用于粘性颗粒的离散元方法、用于求解涡量诱导的速度场的快速多极子方法和用于湍流的直接数值模拟的伪谱方法。更广泛的影响：粘性颗粒主导着各种关键问题，从生物工程系统(血液流动、胃肠道流动、微生物悬浮)、制造过程(电喷雾、电涂层、降尘)、能源生产(煤粉燃烧、生物质燃烧、减少灰烬)、环境过程(沉积物输送、火山过程、过滤过程)，以及纳米和微尺度技术(纳米颗粒分散、纳米管排列、自组装)。这项拟议的研究将开发和验证一种新的基于结构的随机模型，该模型将为涉及粘性颗粒的广泛问题提供一种全新的模拟方法。该研究将通过佛蒙特大学和纽约城市大学之间的现有安排与一家为少数群体服务的机构共享。

Marshall, Jeffrey 1332472Particles present in turbulent flows are transported because of a large-scale diffusive process caused by exchange of fluid between turbulent eddies and by a small-scale anti-diffusive process. The latter (which we will refer to as particle dispersion) is associated with the tendency of heavy particles to be thrown out of turbulent eddies, forming high-concentration particle sheets in the interstitial region between the turbulent eddies. This small-scale heterogeneity is known to cause fluctuations in the particle concentration of several orders of magnitude, which in turn have a dramatic effect on processes that involve particle collision and agglomeration. While stochastic Lagrangian models (SLMs) have been shown to accurately simulate large-scale particle diffusion, these methods lack the spatial correlation necessary to account for small-scale concentration heterogeneity. The work proposed here will replace random forcing used in stochastic Lagrangian models with a spatially-correlated stochastic forcing based on approximating the turbulent eddies by a set of random vortex structures.Intellectual Merit :The proposed research will develop a stochastic vortex structure (SVS) model for simulating collision and agglomeration of adhesive particles in turbulent flows. The SVS model will generate a turbulent velocity field with correct spatial correlation over a length scale interval ranging between the energy-containing turbulence integral scale and a minimum scale that is associated with the length scale at which the eddy Stokes number is equal to unity. The proposed stochastic model will be validated by comparison to direct numerical simulations of particle agglomerate formation in homogeneous turbulence and turbulent shear flows. Simulations will be performed using a discrete element method for adhesive particles, a fast multipole method for solution of the vorticity-induced velocity field, and a pseudospectral method for direct numerical simulation (DNS) of turbulence. Broader Impacts :Adhesive particles dominate critical problems ranging from bioengineering systems (blood flow, GI flows, microorganism suspensions), manufacturing processes (electrospray, electrocoating, dust mitigation), energy generation (pulverized coal combustion, biomass combustion, ash mitigation), environmental processes (sediment transport, volcanic processes, filtration processes), and nano- and microscale technology (nanoparticle dispersion, nanotube alignment, self-assembly). The proposed research will develop and validate a novel structurally-based stochastic model that will enable an entirely new simulation approach for a wide range of problems involving adhesive particles.The research will be shared with a minority-serving institution via an existing arrangement between University of Vermont and City University of New York.