Original Research PaperNumerical investigations of acoustic agglomeration of liquid droplet using a coupled CFD-DEM model
Graphical abstract
Introduction
It is important to investigate the effects of acoustic waves on the agglomeration and dispersion of suspended aerosols, as this technology has been applied to industrial dust removal and airport defogging [1], [2], [3]. In recent years, acoustic agglomeration technology has been applied to enhance artificial precipitation [4], [5], [6]. As a potentially effective technology for artificial defogging and precipitation, acoustic agglomeration has received wide attention due to its low operating cost and lack of pollution. The main principle of acoustic agglomeration technology is to emit directional low-frequency acoustic waves to the target area with high-concentration aerosol, causing the collision of liquid droplet or droplet aerosol and agglomeration of these droplets into large-sized droplets, eventually leading to a decrease in the droplet concentration (Fig. 1). Therefore, the key requirement for application of this technology is to understand the mechanism of acoustic agglomeration of liquid droplets and increase acoustic precipitation.
The phenomenon of acoustic agglomeration was first observed by Patterson and Cawood [7], which led to several experimental and theoretical investigations [8], [9], [10]. Acoustic agglomeration is a spatially uneven and temporally unstable process involving a variety of mechanisms such as orthokinetic interaction [8], [11], hydrodynamic interaction [12], [13], [14], acoustically generated turbulence [15], [16], [17], and Brownian agglomeration [18], [19]. Of these, orthokinetic and hydrodynamic interactions are widely considered the main agglomeration mechanisms. Orthokinetic interaction refers to agglomeration behavior caused by different amplitudes of particles with different sizes under the entrainment of air flow. This theory successfully explains the collision and agglomeration behavior of discrete particles in a multi-dispersed system, but it fails to explain monodisperse particle groups lacking relative oscillation motion [13], [20]. Instead, hydrodynamic interactions that originate from the viscous interaction between aerosol particles and the ambient asymmetry flow are generally considered to be the dominant agglomeration mechanism of monodisperse aerosols in the acoustic field. Typical hydrodynamic interactions include the acoustic wake effect [11], [21], [22] and mutual radiation pressure effect [10], [12], [20], [23]. The acoustic wake effect refers to the influence of the wake of aerosol particles on the motion responses of sheltered particles. A particle in the wake of another particle, also known as a sheltered particle, has a tendency to accelerate toward the front particle due to the decrease of fluid resistance (Fig. 2). In another arrangement, two particles attract each other when their center line is perpendicular to the direction of sound propagation. This is due to a decrease in the gas pressure in the narrow area between the two particles due to the shrinkage of the overflow area according to Bernoulli's hydrodynamic principle. The mutual radiation pressure effect is caused by the scattering of acoustic waves on the particles, which can be considered as a refill mechanism of orthokinetic agglomeration [24]. However, this analytical theory has not been fully verified by experimental observation [13], [14].
In general, although above mechanisms reveal dynamic processes of acoustic agglomeration, understanding of these processes remains insufficient or even contradictory [22]. Most studies have focused on the motion patterns of individual and binary particles under the action of acoustic waves, while ignoring the macroscopic agglomeration behavior of particle clusters. The complex dynamic behaviors of particle clusters in the fields of acoustic wave and jet flow, such as collision, agglomeration, and fragmentation, have not been fully considered. Until now, most studies on acoustic agglomeration have concentrated on parameter optimization of the macroscopic removal effect of solid particles [3], [25], [26], [27], but related research for liquid particles is quite limited [28]. Unlike solid agglomerates, liquid agglomerates lack multiple contact structures, and several small liquid aerosols can merge into a new larger droplet after agglomeration [29]. Overall, in-depth research is required to better describe the dynamics and agglomeration performance of liquid droplets in the acoustic field.
Most studies on the acoustic agglomeration effect of aerosol particles have been theoretical analysis or semi-deterministic experimental research. However, laboratory and field tests are limited because (i) the physical parameters of droplet aerosols are difficult to monitor finely, (ii) the experimental boundary conditions are difficult to control, and (iii) the high cost of experimental research makes it difficult to comprehensively optimize acoustic agglomeration of droplet aerosols based on theoretical analysis and physical experiments. Instead, the mechanism of acoustic agglomeration of droplet can be studied by numerical methods. Numerical simulation is widely applied in the field of multiphase flow, and use of a numerical model allows analysis of discrete particle dynamics and acoustic agglomeration process with a wide operating parameter range [30], [31], [32], [33], [34], which largely compensates for the lack of theoretical analysis and experimental research. In general, numerical models in this field fall into two categories. Population balance modeling (PBM) uses statistical methods to describe discrete phase dynamic events and obtains the dynamic evolution process of the internal variables of the particle group by solving the particle internal function distribution transfer equation [35]. Because the agglomeration mechanisms of discrete system are insufficiently understood, present acoustic agglomeration models are usually simplified in terms of agglomeration kernels. Examples of these simplifications include (i) only considering orthokinetic interaction while neglecting hydrodynamic interaction [9], [36], [37], or (ii) only considering the mutual radiation pressure effect while ignoring the acoustic wake effect [10], [38]. Of course, these simplifications directly affect the accuracy of the numerical model. In addition, PBM approaches usually assume that the particle field is uniform and isotropic, which is to some extent contrary to what occurs in real agglomeration events [39]. The second main type of numerical model is the Lagrangian-based Discrete Element Method (DEM) model [40]. The DEM model can characterize the evolutionary dynamics through the detailed information of a discrete system and is widely applied in the field of particle flow [41], [42], [43]. DEM strategy directly solves the motion of discrete particles in the flow field according to Newton's second law, allowing good resolution of time-varying dynamic processes of discrete particles. Recently, some researchers applied a DEM model to investigate the agglomeration behavior of aerosol particles in acoustic waves [30], [32], [34], [44], [45], [46]. The main agglomeration mechanisms such as orthokinetic interaction [8] and hydrodynamic interaction [13], [14] are implicitly included in the DEM simulation by introduction of drag force and mutual radiation pressure force into the motion equations of individual particles, without the requirement for an agglomeration kernel function [32]. The acoustic agglomeration performance of micron-sized solid particles in the acoustic field has been fully investigated in two-dimensional [32], [46] and three-dimensional [30], [34], [45] particle systems. These studies demonstrate the advantages of using the DEM model to simulate the acoustic agglomeration process, allowing characterization of the motion response of aerosol particles. However, effects of turbulent airflow and droplet fragmentation on acoustic agglomeration have not yet been studied. The motion of the air flow under acoustic waves is often reduced to a type of sinusoidal wave, which may differ from reality.
Therefore, this work presents a three-dimensional CFD-DEM model to investigate the dynamic characteristics of liquid droplets in the field of acoustic wave and turbulent flow with consideration of droplet fragmentation. A four-way coupling strategy is utilized, allowing simulation that considers the drag effect of the fluid on the droplet, the disturbance of droplets on the fluid, movements of the air flow and droplet, and the interactions between the droplets. The airflow process is obtained by solving the Reynolds-averaged Navier-Stokes (RANS) and fluid turbulence characteristics are taken into account. The velocity and trajectory of liquid droplet are solved using Newton's second law with consideration of the drag force, gravitational force, and acoustophoretic force. The agglomeration performances of liquid droplets under high-intensity acoustic waves can then be numerically investigated in terms of the effects of the acoustic characteristics of acoustic frequency, acoustic intensity, and operating period as well as the droplet size and distribution.
The paper is organized as follows. After the introductory section, the methodology of numerical model is presented, which includes the governing equations of the CFD-DEM model, the boundary treatment method, and the time stepping technique. In Section 3, the numerical model is validated against the acoustic field structure data and liquid particle distribution. In Section 4, influences of acoustic and droplet parameters on aerosol agglomeration are discussed. Additionally, relationships between agglomeration performance and operating parameters are described. In Section 5, conclusions are summarized.
Section snippets
Governing equations for air flow
Continuous airflow is solved by the Reynolds-averaged Navier-Stokes (RANS) equations as follows [47]where ρ denotes fluid density, u denotes time-averaged fluid velocity, Fpl denotes the volume force induced by liquid droplets, g denotes the gravity force, and σ denotes the stress tensor, which can be expressed aswhere p denotes the fluid pressure and μ denotes the total fluid viscosity, which is the sum of the molecular and dynamic viscosities.
To
Experimental setup
The experimental device includes an agglomeration chamber, an industrial atomizing nozzle, an acoustic generator and its measuring device, and a laser particle size analyzer. The measuring range of the acoustimeter (Model 308 from BSWA Tech, Inc.) is 22-154 dB and its precision is 0.1 dB. A laser particle size analyzer (Model 319 from Winner Particle, Inc.) is used to observe the size and distribution of micro-droplets in the agglomeration chamber in real time, with a range of 1-500 μm and
Influence of droplet fragmentation
Fig. 13(a) shows that the flow field in the agglomeration chamber is obviously uneven in space, which is different from what was reported in previous studies [22], [32], [45]. There is a conical high-speed airflow area above the atomizing nozzle, and the liquid droplets inside this region are carried by the ambient air-flow and thereby have a relatively higher velocity. Liquid droplets with higher velocities also tend to have more kinetic energy and move more violently. It can be seen from
Conclusions
This paper investigated the acoustic agglomeration of liquid droplets using a three-dimensional CFD‐DEM coupled model. The numerical model solves the flow field based on the Reynolds-averaged Navier-Stokes equations coupled with a k–ε turbulence model, and describes the acoustic field by Linearized Navier-Stokes Equations (LNSEs) in the time domain. The motion of the liquid droplet follows Newton’s second law with consideration of complex aerosol dynamics process such as collision,
CRediT authorship contribution statement
Yang Shi: Formal analysis, Methodology, Writing - original draft. Jiahua Wei: Methodology, Data curation, Writing - review & editing, Supervision. Wenwen Bai: Formal analysis. Guangqian Wang: Supervision.
Acknowledgements
This research is supported by National Key Research and Development project, grant number 2017YFC0403600, 2016YFE0201900; the China Postdoctoral Science Foundation, grant number 2018M641372; State Key Laboratory of Hydroscience and Engineering of China, grant number 2017-KY-04.
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2022, Atmospheric ResearchCitation Excerpt :Previous studies have shown that the SPL value of the air-modulated speaker decays exponentially with the traveling distance (L, in m) of sound waves following the expression of SPL = 148.6 L-0.06339. Since air-suspended droplets can agglomerate in the sound field of 80– 90 dB (Shi et al., 2020a), thus the effective range of a single speaker for acoustic precipitation is in the range of 5– 8 km (Cao et al., 2019), which exceeded the precipitating cloud base height in the Darlag region, at ~2 km (Shi et al., 2021a). Note that the acoustic interference in clouds may cause potential risk on local precipitation balance and ecological environment.