Multi-step spray modelling of a flat fan atomizer

doi:10.1016/j.compag.2017.11.005

Computers and Electronics in Agriculture

Volume 144, January 2018, Pages 58-70

https://doi.org/10.1016/j.compag.2017.11.005 Get rights and content

Highlights

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A multi-step model is proposed to simulate primary spray atomization.
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Model can characterize the flat spray nozzles used in the agricultural industry.
•
Model combines numerical and analytical approaches to find the spray droplet size.
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Output of each sub-model is used in subsequent sub-models as input.
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The paper shows this systematic study of the nozzles can reduce prototyping costs.

Abstract

The present study combines Eulerian CFD modeling of the liquid flow inside an atomizer, instability analysis of liquid sheet, statistical spray analysis, and Lagrangian modeling for spray transport of a flat fan atomizer widely used in agricultural spraying. High-speed spray imaging and spray size measurements carried out for validation of numerical models and the experimental results agreed reasonably with the modeling results. Although the subject of the study is a flat fan atomizer, the methodology presented could be employed to other types of spray nozzles that rely on liquid sheet disintegration mechanism. The systematic modeling of spray systems with the methodology explained in the paper not only reduces the design and prototyping time and costs but also gives engineers a better understanding of the design parameters for improved spray system performance.

Introduction

There are many kinds of spray atomizers for different applications. However, they all essentially convert an external energy source to liquid surface energy for increasing the rate of heat and mass transfer by forming multiplicity of droplets.

Although a spray may contains droplets with widely varying range of sizes and velocities, many applications have specific or sometimes very strict spray requirements or need to control spray dynamics to work efficiently. For instance, in nasal drug administration to ensure successful deposition within the nasal cavities, droplet sizes between 30 and 120 µm are desired, for example see Copley and Kippax (2012). While droplets larger than 120 µm deposit at the front of the nose, the finer ones are inhaled and reaches the lungs that may cause safety issues and should be avoided, see Kulkarni and Shaw (2012) and Sangolkar et al. (2012). In mass spectrometry applications with inductively coupled plasma (ICP-MS) droplets larger than 10 µm do not undergo complete vaporization in the plasma torch and may not contribute into signal, see Montaser and Golightly (1992). In addition to this size restriction, droplets must fall below a certain velocity to have enough residence time in the plasma torch for total consumption. Therefore, to control spray flow to the plasma torch and achieve reasonable efficiency in ICP-MS, spray chambers are used to filter large and fast moving droplets.

In agricultural applications, spray droplet size also plays a crucial role in aerial or ground spraying of crop protection products and fertilizers. Undesired pesticide or fertilizer deposition is likely to occur if spray is not within a certain size range, see Liu (2000). Production of very small droplets is undesirable as they drift and result in environmental contamination and waste of pesticide. While pesticide particles carried by air currents may injure people, the most frequent claim for damages is drift from an herbicide that is carried onto nontarget agricultural crops, see Cetner (2014). Accuracy of spraying is also a very important issue in controlling the drifting of sprayed pesticides. Herbicides such as dicamba and 2,4-D should not reach non-GMO varieties of soybeans or cotton which from past experience are known to be highly sensitive to low-dose exposures of these agents, Egan et al. (2014).

The above examples show the importance of spray characteristics for different applications. Atomizing nozzles must therefore be designed with great care to fulfill the design criteria for their intended application. Since the manufacturing process is often very lengthy and prototyping cost in designing a nozzle could be substantial, it would be very helpful to employ numerical tools to help speed up the process. There have been many attempts to model the atomization and spray in the past and the mechanism of the breakup has been studied in details, for example see Liu (2000). For instance in a recent study, Xue et al. (2014) used volume of fluid (VOF) method to integrate the internal nozzle flow and the developing fuel spray. Zhou et al. (1996) employed CFD to relate the spray angle of a flat fan atomizer to its internal geometry. As another example, Altimira et al. (2009) studied influence of the nozzle geometry on the flow as well as formation and development of liquid sheet by numerical modeling. Their model was able to predict the discharge coefficient and the liquid sheet thickness of a fan spray atomizer and validated by experimental measurements.

However, despite great advances in the computational fluid dynamics, simulating atomization still remains a challenging task. One reason is that in primary spray atomization, there are different dimensions involved. A nozzle with dimensions in the order of few millimeters could generate a sheet with thickness as low as few micrometers disintegrating into many droplets which could travel some decimeters downstream of the nozzle. Obviously modeling a system with such a wide range of length scales is numerically challenging.

In this paper, we present an approach for the prediction of spray characteristics that combines several sub-models to accurately predict spray dynamics for an actual application. First, we employ an Eulerian based model to simulate the liquid flow inside the atomizing nozzle, its evolution and spreading as it exits the tip of the nozzle to form a thin liquid sheet before the primary breakup occurs. The data gathered such as sheet spreading angle, surface area, thickness and velocity from the Eulerian sub-model is then fed into an analytical model to find average quantities such as mass mean diameter. The results of Eulerian and analytical sub-models are then used as input for the statistical sub model to predict joint size and velocity distributions which in turn are used as input in a Lagrangian sub-model to simulate spray transport.

We modeled a flat-fan spray nozzle that is used for spraying herbicide, fungicide and insecticide. This class of atomizers produces a wide spray angle and is well suited for field sprayers equipped with sprayer controllers.

Section snippets

Experiments

An experimental setup was prepared to characterize the flat nozzle. This spray nozzle falls into the category of flat-fan atomizers which are capable of producing wide spray angles (typically over 100 degrees) and provide a good spray distribution over the pressure range of 15–60 psig (1–4 bar).

The setup was used for spray imaging to extract experimental data such as spray angle and liquid sheet breakup length. The spray size measurement was also performed using D₃₀ Spray Sizer by Coraltec Inc.

Eulerian Sub-model

For the Eulerian sub-model, we employed the SimSpray software suite by Simulent Inc. SimSpray flow solver has been used to study a wide range of industrial spray nozzles, e.g. pressure swirl and splash-plate atomizers, see Fard et al., 2002, Fard et al., 2007 and Levesque et al. (2005).

SimSpray employs a two-step projection, Eulerian fixed-grid method to solve the Navier-Stokes equations. The interface is resolved by the volume-of-fluid (VOF) method (Bussman, 2000). The flow is assumed to be

Analytical sub-model

To spray liquids, many atomizers transform the bulk of liquid into a sheet which undergoes series of oscillations before disintegrating into liquid ligaments. These ligaments are in turn broken into droplets.

The liquid sheet breakup has been extensively studied by many researchers. Most researchers such as Taylor (1940) and Dombrowski and Johns (1963) employed temporal and spatial instability analysis and postulated that the droplet sizes are correlated with the wavelength that grows on the

Statistical sub-model

The stochastic nature of sprays has severely limited the development of mathematical and numerical modeling of sprays. For instance, deterministic methods such as instability analysis (described in previous section) are not advanced enough and incapable of including all the mechanisms involved in a simple atomization process. Therefore, one can hope to predict a single characteristic droplet size under controlled conditions from these models. In the absence of such comprehensive models,

Lagrangian Sub-model

Once the complete map of spray size and velocity is obtained from the maximum entropy principle (MEP), this information could be used as input to a Lagrangian sub-model to track individual class of droplets with particular size and velocity.

For instance, Eq. (38) can be integrated over time to find the local velocity and the new location of droplets in the space. Here F_d and F_b are drag force acting on the droplet and buoyancy force, respectively. These are in fact the only external forces

Conclusion

A combination of Eulerian VOF modeling, Instability and statistical analyses and Lagrangian modeling were used to study liquid sheet formation, evolution and its disintegration to droplets as well as spray delivery by drifting forces in the case of an agricultural flat spray nozzle. The primary break up model in this work, that employed the results of the Eulerian VOF modeling, showed reasonable agreement with spray imaging and measurements. The methodology presented in this work could be used

Acknowledgment

The authors would like to thank Dr. Mehrdad Taheri for conducting the experimental part of this task. We are also deeply grateful to Dr. S. Chandra from Centre of Advanced Coating Technologies at the University of Toronto for his support and lending us his lab facilities and also his Ph.D. Candidate, Dwight Bouchard, for setting up the photographic experiments and spray measurements.

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View full text

Multi-step spray modelling of a flat fan atomizer

Highlights

Abstract

Introduction

Section snippets

Experiments

Eulerian Sub-model

Analytical sub-model

Statistical sub-model

Lagrangian Sub-model

Conclusion

Acknowledgment

Int. J. Heat Fluid FL

Chem. Eng. Sci.

Chem. Eng. Sci.

Combust. Flame.

Int. J. Multiphas. Flow.

J. Agr. Eng. Res.

Comparative study of some probability distributions applied on liquid sprays

Part. Part. Syst. Char.

A Three dimensional model of an impacting droplet

Damages from pesticide spray drift under Trespass Law

Ecol. L. Currents

Aerodynamic instability and disintegration of inviscid liquid sheets

Proc. R. Soc. Lond. A.

From actuation to deposition: Particle sizing techniques for characterizing nasal drug delivery systems

Inhalation

A meta-analysis on the effects of 2, 4-D and dicamba drift on soybean and cotton

Weed Sci.

Characterization of splash-plate atomizers using numerical simulations

Atomization Sprays

A Balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework

J. Comput. Phys.

Information theory and statistical mechanics

Phys. Rev.

Formulation and characterization of nasal sprays: an examination of nasal spray formulation parameters and excipients and their influence on key in vitro tests

Inhalation

BLSpray: understanding the effects of black liquor properties and splash-plate nozzle configuration on spray characteristics

Pulp Pap-Canada

Droplet size distribution: a derivation of a Nukiyama-Tanasawa type distribution function

Combust. Sci. Technol.

Derivation of droplet size distribution in sprays by using information theory

Combust. Sci. Technol.