声场中PM2.5相互作用机理

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摘要

声凝并作为一种 PM2.5 预处理技术，在颗粒物污染控制方面富有应用潜力。

在含有大量 PM2.5 的烟气进入除尘器前，应用高强度声场对颗粒进行预处理。由

于声波作用，颗粒之间迅速发生相对运动，进而碰撞、凝并，促使颗粒粒径增大，

数目减少。该方法能够提高后续除尘器的除尘效率，从而达到控制 PM2.5 排放的

目的。相比其他 PM2.5 排放控制技术，声凝并具有适应性强、经济性好的优点。

本文针对声凝并技术中所涉及的颗粒相互作用机理和凝并动态过程问题，通

过理论推导建立相关数学模型，利用数值模拟方法研究单颗粒在声场中的运动特

性、颗粒对的相互作用过程，以及大量颗粒在声场中的凝并规律和动态过程。

在考虑粘性阻力、压力梯度力、虚拟质量力、漂移力的情况下，建立单颗粒

在声场中的动力学模型，研究颗粒的振动和漂移特性，结果表明，粘性阻力对颗

粒在声波传播方向的运动起主导作用，压力梯度力、虚拟质量力与阻力相比可以

忽略不计；漂移力虽然相对阻力而言也很小，但由于它是以时间平均力的方式作

用在颗粒上，在较长时间内，漂移力的作用效果变得显著；声波频率低于 10 kHz

时，亚微米颗粒处于零惯性区，具有几乎相同的运动规律；微米尺度颗粒处于有

限惯性区，受颗粒粒径和声波频率的影响，其行为规律有较大差别；在声强级为

150 dB、频率为 2000 Hz 条件下，微米尺度颗粒在声波方向的运动表现出显著的

漂移特性，颗粒所受漂移力主要由非对称漂移力决定。

模拟了颗粒对在声场中的相互作用过程，分析了互辐射压力与声尾流对颗粒

运动产生的不同作用，研究了颗粒间距、颗粒中心连线与声波传播方向的夹角、

颗粒位置、粒径和声波频率、声强对颗粒相互作用过程的影响。研究发现，颗粒

相互作用受到互辐射压力与声尾流作用的共同影响，互辐射压力主要在近距离发

挥作用，声尾流在较远距离也能发挥作用，近距离时互辐射压力作用强于声尾流

作用，两种作用相互耦合有效地促进了颗粒的相互靠近，并导致颗粒发生碰撞。

结果还表明，颗粒距离和夹角越小，颗粒相互作用越强烈，颗粒的碰撞时间越短；

靠近波腹位置的颗粒相互作用较为强烈，靠近波节位置的颗粒，相互作用较为微

弱；较大粒径颗粒间相互作用较强，增加频率和声强，能够促进颗粒间的相互作

用，使颗粒在更短时间内发生碰撞。

基于多重蒙特卡罗方法，构建了颗粒声凝并模型及相应的数值模拟平台。对

不同情况下颗粒的声凝并效果以及声凝并动态过程进行了数值模拟。研究发现，

与同向与重力作用、声尾流作用、互辐射压力作用相比，布朗运动对颗粒的声凝

并效果影响较小；颗粒粒径分布主要集中在亚微米区域时，声尾流作用与互辐射

压力作用效果也较差；增加频率、提高声强能有效促进颗粒的声凝并；对于对数

正态分布的颗粒，中位径越大，声凝并效果越好；随声波作用时间的延长，声凝

并效果增强，但增幅减小，声波作用时间以在 3～5秒内为宜；颗粒凝并的动态

过程模拟有助于分析颗粒声凝并的机理。

关键词：细颗粒物（PM2.5）声凝并声波颗粒动力学

颗粒间相互作用多重蒙特卡罗方法

ABSTRACT

Acoustic agglomeration as a preconditioning technology of PM2.5, has great

potential in the field of particulate emission control. A high-intensity sound field is

used to treat the gas-particle suspensions, before the flue gas enters the particulate

removal devices. Due to the effect of sound wave, the relative motion, collsion and

agglometation of the particles occur rapidly. As a result, the average particle size is

enlarged and the number of the particles is greatly reduced. Hence the particles can be

efficiently removed by the dust removal devices. Compared to other PM2.5

preconditioning and removal technologies, acoustic agglomeration has advantages in

its good adaptability and cost-efficiency.

This thesis aims at exploring the interaction mechanisms and dynamic processes

of the particles subjected to the sound field. The relavant mathamatical models were

established based on the theoretical derivation and the numerical simulation method

was applied to investigate the motion of a single particle, to examine the interaction of

two particles, and to discuss the agglomeration effect and the dynamic processes of a

large number of particles in the sound field.

Taking into account of the viscous force, pressure gradient force, virtual mass

force and the drift force, the dynamical model of single particle in the sound field was

established. Based on this, the oscillatory motion and the drift of PM2.5 were studied.

The results show that the viscous force dominates the particle motion in the wave

propagation direction, whereas the pressure gradient force and the virtual mass force

are negligible compared with the viscous force. Although the drift force is much less

than the viscous force, it becomes obvious in a relatively long period of time because

of its time-averaged nature. When the frequency is below 10 kHz, the submicron

particles are in the zero inertial range, thus they almost exhibit the same behavior and

the micron-sized particles are in the limited inertial range, their motion differs greatly,

depending on the particle diameter and the sound frequency. In cases with a sound

field with intensity level of 150 dB and frequency of 2000 Hz, the micron-sized

particles dirft dramatically in the wave propagation direction and the particle dirft is

mainly determined by the asymmetric drift force.

The interaction of the particles in the sound field was simulated. The influences

of the mutual radiation pressure effect and the acoustic wake effect on particle motion

were analysed. The effects of the separation distance between the particles, the

orientation, positions, diameters of the particle, the sound frequency and intensity on

the interaction process were examined. It is found that the particle interaction is

affected by the combination effect of the mutual radiation pressure and the acoustic

wake. The mutual radiation pressure effect is important when the two particles are

very close to each other, whereas the acoustic wake effect is also important when the

separation distance is relatively large. The combination of the two effects effectively

promotes the particle approaching and leads to inter-particle collision. The results also

show that the smaller the separation distance and the orientational angle are, the more

intensive the particle interaction is and the shorter the collision time is. The particles

with initial positions close to the wave antinodes interact quite strongly, and those

close to the wave nodes interact relatively weak. The interaction is more intensive for

the larger particles. Increasing the sound frequency and intensity can promote the

particle interaction, so that the particles are able to collide within a shorter period of

time.

Based on the multi-Monte Carlo method, the model of acoustic agglomeration

and the relavant numerical simulation platform were established. The effects and the

dynamic processes of acoustic agglomeration under different conditions were

numerically simulated. It is found that the effect of Brownian motion on the acoustic

agglomeration is very weak compared with the effects of the orthokinetic interaction

gravity, the acoustic wake, and the mutual radiation pressure. When the particle size

distribution is mainly concentrated in the submicron size range, the acoustic wake

effect and the mutual radiation pressure effect are also very weak. Increasing the

sound frequency and intensity can effectively promote acoustic agglomeration. For

particles of lognormal distribution, the agglomeration efficiency is higher when the

medium diameter of the particles is larger. As the effect time of the sound wave on the

particles increases, the agglomeration efficiency increases, but the increase rate is

decreases greatly. The effect time of 3 to 5 s is recommended. The dynamic simulation

can help analyze the mechanisms of acoucstic agglomeration.

Key Words：Fine particles (PM2.5), Acoustic agglomeration, Sound

wave, Particle dynamics, Particle interaction, Multi-Monte Carlo

(MMC) method

中文摘要

ABSTRACT

第一章绪论 .....................................................1

1.1 研究背景 ...................................................1

1.1.1 PM2.5 的危害 ...........................................2

1.1.2 各国空气质量标准中关于 PM2.5 的限值 .....................3

1.2 颗粒物控制技术 .............................................4

1.2.1 传统除尘器发展现状 .....................................4

1.2.2 PM2.5 脱除新技术 ........................................5

1.3 声凝并技术研究进展 .........................................6

1.3.1 实验研究进展 ...........................................6

1.3.2 理论研究进展 ...........................................8

1.4 颗粒物声凝并的数值模拟 .....................................9

1.4.1 区域算法 ...............................................9

1.4.2 矩量法 ................................................10

1.4.3 蒙特卡罗方法 ..........................................10

1.5 本文研究内容与实施方案 ....................................11

1.6 本章小结 ..................................................12

第二章声场中单颗粒动力学 .......................................13

2.1 引言 ......................................................13

2.2 声场基本原理 ..............................................14

2.2.1 声压 ..................................................14

2.2.2 声速 ..................................................14

2.2.3 声强及声强级 ..........................................15

2.3 声场中颗粒运动模型 ........................................15

2.3.1 声场颗粒动力学模型假设 ................................15

2.3.2 颗粒受力分析 ..........................................15

2.3.3 声场颗粒漂移现象 ......................................17

2.3.4 声场中单颗粒运动模型及方程 ............................20

2.4 数值模拟 ..................................................21

2.4.1 数值模拟平台 ..........................................21

2.4.2 数学模型和计算方法的验证 ..............................22

2.4.3 频率对颗粒运动学的影响 ................................23

2.4.4 颗粒的漂移特性 ........................................26

2.5 结论 ......................................................29

第三章声场中颗粒对的相互作用过程 ...............................30

3.1 引言 ......................................................30

3.2 颗粒相互作用模型 ..........................................30

3.2.1 互辐射压力模型 ........................................32

3.2.2 声尾流作用模型 ........................................35

3.2.3 颗粒运动模型 ..........................................37

3.3 颗粒相互作用数值模拟平台的构建 ............................39

3.3.1 数值计算方法和条件 ....................................39

3.3.2 程序流程图 ............................................41

3.4 结果分析 ..................................................42

3.4.1 与 González 的实验结果对比验证 ..........................42

3.4.2 互辐射压力作用与声尾流作用效果对比 ....................43

3.4.3 参数改变时颗粒相互作用结果分析 ........................52

3.5 结论 ......................................................61

第四章颗粒声凝并模型及动态过程模拟 .............................63

4.1 引言 ......................................................63

4.2 运动系统模型 ..............................................64

4.2.1 物理模型 ..............................................64

4.2.2 颗粒运动模型 ..........................................64

4.2.3 流体运动模型 ..........................................65

4.2.4 凝并核函数 ............................................65

4.2.5 描述颗粒凝并的多重蒙特卡罗方法 ........................68

4.3 数值模拟条件和步骤 ........................................72

4.3.1 模拟条件设置 ..........................................72

4.3.2 数值计算流程 ..........................................74

4.4 实验结果对比验证 ..........................................74

4.5 数值计算结果与分析 ........................................76

4.5.1 不同声凝并机理的作用效果对比 ...........................76

4.5.2 不同频率下颗粒的声凝并效果 .............................77

4.5.3 不同声强下颗粒的声凝并效果 .............................78

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摘要：

摘要声凝并作为一种PM2.5预处理技术，在颗粒物污染控制方面富有应用潜力。在含有大量PM2.5的烟气进入除尘器前，应用高强度声场对颗粒进行预处理。由于声波作用，颗粒之间迅速发生相对运动，进而碰撞、凝并，促使颗粒粒径增大，数目减少。该方法能够提高后续除尘器的除尘效率，从而达到控制PM2.5排放的目的。相比其他PM2.5排放控制技术，声凝并具有适应性强、经济性好的优点。本文针对声凝并技术中所涉及的颗粒相互作用机理和凝并动态过程问题，通过理论推导建立相关数学模型，利用数值模拟方法研究单颗粒在声场中的运动特性、颗粒对的相互作用过程，以及大量颗粒在声场中的凝并规律和动态过程。在考虑粘性阻力、压力梯度力、...

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