Investigating charged water sprays through simulation and experiments
Antoni Brentjes is a PhD student in the department Energy Technology. Supervisors are prof.dr.ir. G. Brem and dr.ir. A.K. Pozarlik from the faculty of Engineering Technology.
A commonly used method to improve the efficiency of industrial spraying processes is electrostatic charging of the spray droplets. Charges of equal polarity repel each other, resulting in improved spray dispersion. Furthermore, charged droplets are attracted to grounded or oppositely charged objects, allowing the deposition of the spray droplets to be controlled to a degree. This technology was initially developed in the field of spray painting, but has spread to various applications. In a novel development, electrostatic spraying systems are being introduced in food chilling warehouses, to improve the rate of cooling while reducing the moisture loss that would otherwise occur.
A challenging aspect of designing effective spraying systems is the difficulty of measuring the behaviour of the spray. Most methods for tracking the motion of droplets through space rely on high quality cameras and laser lighting, making them expensive and impractical in industrial settings. Measurement techniques that can determine droplet diameters can only do so inside a small investigated area. Furthermore, setting up experiments in general is expensive and time consuming.
Numerical simulations have over the past decades become a popular tool for rapidly evaluating system designs, replacing experimental tests. At present, models to simulate the flow of gases and liquids are well understood, as is the motion of particles suspended in a liquid or gas stream. Less well documented are the phenomena that occur near the sprayer nozzle. Spray formation in pneumatic sprayers is a highly dynamic process, as is the electric charging of the resulting droplets. The objective of this thesis is to investigate these phenomena, and develop a comprehensive modelling approach for charged sprays in the context of food chilling.
The work needed to achieve this objective is split into two lines; one of numerical simulations, and one of experimental measurement. The first line starts with the construction of a simulation framework. Models to simulate fluid flow, heat transfer, droplet motion and electrostatic fields are selected based on existing literature, and implemented in the Fluent Computational Fluid Dynamics solver. The resulting Eulerian-Lagrangian model is validated against experimental data, and found to match previously obtained results. A model case is simulated, and it is found that using a charged spray significantly improves the fraction of liquid transferred to the target. Furthermore, the self-dispersing properties of the charged spray increase the fraction of evaporated liquid, and thereby the rate of cooling.
The second part of the numerical research line is the development of a model to predict the charge imparted on spray droplets. In previous works, the droplet charge is typically derived from experimental results, and assumed constant for a given sprayer nozzle. The need for experimental testing undercuts the benefits of numerical simulations, and moreover, neglects the fact that the droplet charge depends not only on the nozzle, but also on the surroundings. A model that takes these effects into account is developed from two main physical principles. First, the charge induced on a droplet depends on the electric field strength at the nozzle. Second, the presence of charged droplets between the nozzle and electric ground effectively “pushes back” against charge accumulating on subsequent droplets. The former effect is calculated using an analytical derivation based on the sprayer nozzle geometry, while an algorithm computing the latter effect is implemented in the numerical simulation. The implemented model is validated by simulating several cases for which experimental data is available, and is found to predict the droplet charge with an error below 20% for all cases. This is significant in particular because the model does not need to be tuned for any sprayer or geometry in particular, instead working on purely physical principles.
The models developed thus far can predict droplet motion and droplet charging, leaving the remaining aspect of droplet formation. Present models that predict the size and velocity distribution of sprays use empirical relationships, with the fitting constants varying for different models of sprayer. Thus, to model the pneumatic electrostatic sprayer that is to be used to assist food chilling, an experimental parametric study is carried out using a droplet shadowgraphy method. Pulsed laser illumination and a high-speed camera with a long-distance microscopic lens are used to record images of the shadows of the spray droplets. The diameters of the recorded droplets are extracted from the images, and successive images are correlated to find the droplet velocities. It is found that the investigated sprayer is capable of producing a fine spray of water, with a Sauter Mean Diameter of 40 μm, with water and air supplied at two bar gauge pressure. The droplet size distribution follows a Rosin-Rammler curve, and is relatively wide with a spread factor of 2. Increasing the air supply pressure increases the energy available for atomisation, and results in finer droplets being produced. An empirical relation between the Sauter Mean Diameter of the spray and the air- and water supply rates is calculated, based on conservation of energy. A surprising finding is that the electric potential applied to the sprayer nozzle does not influence the droplet size distribution or the droplet velocity. This is not generally the case for electrostatic sprayers, but may be explained by the fact that pneumatic sprayers supply far more energy to the spray formation region in the form of high pressure air than in the form of electrical energy.
The final work discussed in this thesis is an effort to use numerical simulation to resolve the spray formation process, in the same type of sprayer previously investigated experimentally. This is made possible by a combination of recently developed methods and algorithms. The Volume of Fluid method that can be used to simulate the interaction of water and air in the sprayer nozzle cannot resolve droplets that are smaller than several times the grid resolution. Filling a volume the size of the sprayer nozzle with grid cells small enough to model droplets as small as ten micrometres would exceed the capability of the most powerful computational hardware available. However, using a coarse grid resolution, and only refining the cells near the water-air interface reduces the number of grid cells dramatically. An algorithm that recognises stable droplets and converts those into Lagrangian point-particles is applied, avoiding the need for fine grid cells to exist anywhere except in the spray formation region. Simulating spray formation with this approach is successful, and the resulting spray has physically plausible properties. There are notable differences with the experimentally obtained data however, as the simulated spray contains far fewer large droplets, and the Sauter Mean Diameter is off by 30%. The results suggest that using a finer grid resolution and smaller time steps would improve the results. Doing so would come with a substantial computational cost, as even the present simulation took over a month to compute.
In conclusion, the methods described and developed in this thesis can be used to numerically simulate the use of electrically charged sprays in industrial contexts. The presented method for determining the charge of spray droplets in particular is novel and useful for simulating sprayers in systems with changing or moving geometry. The performance of a pneumatic electrostatic sprayer is analysed, and an empirical model for the spray properties is presented. Advances are made toward a numerical simulation of the spray formation in said sprayer, showing the capabilities of recent developments in computational fluid dynamics. The use of these modelling methods is recommended for future research into the fundamentals of spray formation.
