Rotary Bell Research Articles

Investigating atomization characteristics in an electrostatic rotary bell atomizer

Electrostatic rotary bell atomizers are commonly used in several engineering applications, including the automobile industry. A high-speed rotating nozzle operating in a strong background electric field atomizes paint into charged droplets that range from a few micrometers to tens of micrometers in diameter. The atomization process directly determines the droplet size and droplet charge distributions which subsequently control the transfer efficiency and the surface finish quality. We have previously developed a tool to perform high fidelity simulations of near-bell atomization with electrohydrodynamic effects. In this work, we perform simulations employed with a droplet ancestry extraction tool to analyze previously inaccessible information and understand the physical processes driving atomization. We find that the electric field accelerates breakup processes and enhances secondary atomization. The total number of droplets, the ratio of secondary to primary droplets, and the ratio of coalescence to breakup activity are all much higher when operating in an electric field. We analyze the droplet velocity, local Weber number and charge density statistics to understand the complex physics in electrically assisted breakup. The results of the study have helped us gain insights into the physics of atomization in electrostatic rotary sprays.

High-fidelity simulations of a rotary bell atomizer with electrohydrodynamic effects

Electrostatic rotary bell atomizers are extensively used as paint applicators in the automobile industry. Paint undergoes atomization after exiting the edge of a high-speed rotating bell. In most setups, the paint is electrically charged and a background electric field is applied between the nozzle and the target surface to increase the transfer efficiency (TE). The atomization process directly determines the droplet size and droplet charge distributions which subsequently control TE and surface finish quality. Optimal spray parameters used in industry are often obtained from expensive trial-and-error methods. In this work, three-dimensional near-bell atomization is computationally simulated using a high-fidelity volume-of-fluid transport scheme that includes electrohydrodynamic (EHD) effects. We find that electrifying the setup results in the production of smaller droplets. Additionally, the electric field has a minor effect on primary atomization but a negligible effect on the size and stability of atomized droplets after secondary breakup. This cost-effective method of simulating EHD-assisted atomization allows for the understanding of the effect of the electric field and the extraction of droplet charge characteristics which is otherwise challenging to obtain experimentally.

Insights from high-fidelity modeling of industrial rotary bell atomization

The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.

Thin liquid films on a rotary bell atomizer in surface-following coordinates

This article analyzes a published formulation of the Navier–Stokes equations cast into surface-following coordinates and provides some additional mathematical background to follow the article. Ubiquitous in the paint shops of automotive plants around the world, a high-speed rotary bell is succinctly described as a rapidly spinning concave axisymmetric surface with liquid paint supplied from a port coinciding with the center of rotation. The spinning surface transfers momentum to the paint film causing it to flow outward. Upon reaching the bell periphery, it is flung off, subsequently forming an atomized spray transferred to an automotive body through advection and electrostatics. Common analytical frameworks of rotating films were spherical or cylindrical coordinate systems where the wetted surface profile of the bell was constrained to follow a coordinate axis. This led to solutions for films modeled with conical, disk-like, or partial hemispherical profiles. An alternative was a more general case using a surface-following orthogonal curvilinear coordinate system along with its derived vector operators. In the unique case of a thin film, these results validated a simpler pattern found in common coordinate systems.

Generating prediction model of fan width by optimizing paint application process for Electrostatic Rotary Bell atomizer

Fan Width plays a critical role in the paint spray application process, so much so that it can be represented as the backbone of the process. In this process, a high voltage Rotary atomizer along with shaping air discharge paint particles to create a spray pattern which defines the basic fan width. Many painting industries practice a "trial and error" method to determine the fan width of their coating process which can be inconsistent and lead to poor quality results. A predictive model for this dynamic fan width pattern, based on the application inputs, can make a significant efficiency improvement in the spray application technique to deliver a uniform paint distribution across the painted object. This research presents a fan width prediction model for a specific rotary bell atomizer and a waterborne automotive OEM paint color. A full factorial Design of Experiement has been performed to analyze factors that influence the dynamic spray pattern. From this a linear regression model has been derived to calculate the fan width which varies within 2.5 cm to maintain manufacturing tolerance. The model has been verified statistically and experimentally, so that it can eliminate the trial-and-error method to save time and cost.

High-fidelity simulation of a rotary bell atomizer with electrohydrodynamic effects

High-fidelity simulation of a rotary bell atomizer with electrohydrodynamic effects

Numerical Simulation of the Electrostatic Coating Process: the Effect of Applied Voltage, Droplet Charge and Size on the Coating Efficiency

<div class="section abstract"><div class="htmlview paragraph">Electrostatic Rotary Bell Sprayers (ERBSs) have been widely used in the painting industry, especially in the automotive and aerospace industries, due to their superior performance. The effects of the applied voltage and paint droplet charge values on the spraying pattern and coating Transfer Efficiency (TE) in the ERBS, including a high-voltage ring for spray cloud control, have been studied numerically in a wide range of droplet size distribution. A 3D Eulerian-Lagrangian numerical analysis is implemented under the framework of the OpenFOAM package. The fluid dynamics of turbulence, primary and secondary breakup procedures are modeled using a large eddy simulation (LES) model, Rosin-Rammler distribution, and modified TAB approach, respectively. Compared to the conventional ERBSs, in the current work an exhaustive exhibition of the airflow dynamic and spray pattern characteristics around the ERBS with outer high-voltage control-ring field pattern, i.e., velocity, vorticity, electric potential field, overspray, film thickness are reported. Our findings indicate that the control-ring around the rotary bell rim improves the coating procedure TE and produces a more harmonized and narrower spray plume. Our in-depth investigation clearly shows the importance of the droplet charge values, voltage quantity, and considered droplet size range on the film thickness and its corresponding quality that is obtained from the workpiece.</div></div>

Numerical analysis of charged droplets size distribution in the electrostatic coating process: Effect of different operational conditions

This paper presents a numerical performance evaluation of the electrostatic rotary bell sprayer (ERBS) with a particular focus on droplet charge, electric field, and ambient conditions through the implementation of a high-voltage control-ring field pattern effect into the fully turbulent airflow and by including the atomized droplets discrete phase. The simulation shows that the inclusion of droplet charging and electric field coupling, with different parametric values, significantly impacts the atomized droplet distribution over the spray plume and the deposition rate. This analysis was conducted using a three-dimensional (3D) Eulerian–Lagrangian model to describe the two-phase spraying flow by extending the base OpenFOAM package. The procedure includes an unsteady compressible Navier–Stokes solver combined with a large Eddy simulation approach to model turbulence effects on the air flowfield. This is coupled to the spray dynamics by including droplet trajectory tracking, wall film dynamics, and electric field charge. The approach is further extended to include the evaporation phenomenon and the transport of its products. Compared to a conventional ERBS, herein, we provide an in-depth analysis of the fluid dynamic characteristics around the ERBS with a control-ring field pattern for vorticity, velocity, and electrical fields. The results indicate that the control-ring operation improves the performance and transfer efficiency of the ERBS, and it also helps to harmonize the direction of the charged paint droplets. For the first time, finding a balance between the effect of the inside bell cup surface and control-ring voltage and charged droplet has been conducted.

Dimensional analysis of droplet size and ligament length during high-speed rotary bell atomization

Modern spray-coating processes are based on high-volume, low-pressure, airless atomization or high-speed rotary bell atomization, often assisted by electrostatic charging to increase the transfer efficiency. The process from the liquid film flow beneath the bell, through ligament formation and consecutive disintegration to droplet deposition, has been constantly explored during the evolution of automotive spray coating. This work proposes a set of dimensionless groups that fully describe the process from film flow to ligament disintegration, including shear and elongational flow effects during atomization of particle laden, shear thinning, viscoelastic fluids.

Atomization and spray characteristics around an ERBS using various operational models and conditions: numerical investigation

The impetus of the current paper is to conduct numerical evaluations about the fundamental behaviors of the flow in an electrostatic rotary bell sprayer (ERBS) during the formation of the droplets and depositing on a target. The effect of operational parameters like bell rotational speed, shaping air and paint flow rate, electrical charge values and droplet distributions are considered precisely. Here, an Eulerian-Lagrangian algorithm that contains a model for airflow field, spray dynamics, electric charge field, droplet trajectory tracking and wall film dynamics has been extended by using the OpenFOAM package. The fluid dynamics is computed by using a large eddy simulation (LES) turbulence model. The mechanism of atomization is facilitated by the action of the centrifugal force that conducted the disintegrated droplets to the cup edge. Following that, the high-velocity droplets affected by the shaping airflow and electric force are transported towards the workpiece. The effect of the bell rotational speed in comparison with other parameters is dominant. The measured size of the droplets is controlled by increasing the bell rotational speed or decreasing the paint flow rate, in this case, promoting a reduction in droplet size. The droplet size near the bell cup was increased noticeably, however, their radius becomes more uniform at a longer lateral distance. Investigation of the various breakup models is one of the main goals of this work to predict the droplet size more precisely. The Reitz-KHRT, Reitz-Diwakar, Pilch-Erdman and the newly modified TAB model are examined in order to predict the breakup process in the ERBS. As the paint droplets are a viscous fluid a modification of the Taylor Analogy Breakup (TAB) approach taking non-linear influences for large viscosity into account is recommended. The use of the breakup models creates a smaller droplet size and this means they are more sensitive to recirculation regions flow pattern. The implemented wall film function was able to predict the transport in the boundary layer over the target. The numerical results describe exact values for the size, distribution, velocity and trajectory of the particles in ERBS, and these results are important for coating industries, in order to optimize their working conditions.

Initial droplet conditions in numerical spray painting by electrostatic rotary bell sprayers

In computational fluid dynamics, the modeling of paint application processes by electrostatic rotary bell sprayer is mostly performed using an Euler–Lagrange approach. The initial conditions of the discrete phase—position, velocity, size, and charge—have an essential influence on the resulting film thickness distribution and the total charge transferred to the object. Typically, so-called injection models are used to specify these initial conditions, whereby the determination of the injection model coefficients is crucial. In this paper, a framework is proposed that combines experimental input data, an injection model, and a metamodel-based optimization. The painting tests for the generation of input and validation data were carried out in a technical center in the industrial standard. The simulations were performed using ANSYSFluent. Initial droplet conditions could efficiently be determined via the framework so that the painting-specific objectives were achieved with reasonable accuracy. In addition to the framework, a turbulence study of the strongly swirled shaping air of this atomizer was carried out, whereby a substantial underestimation of the axial air velocity was found in the turbulence models being investigated. The initial droplet conditions were also used in this study to draw conclusions about the accuracy of the airflow simulation. The proposed framework can be adapted to other solvers and efficiently finds injection model coefficients for other paint applicators.

Numerical modeling of electrostatic spray painting transfer processes in rotary bell cup for automotive painting

Here we implemented a 3D comprehensive Eulerian-Lagrangian model in order to investigate the electrostatic spray transfer processes in the high-speed rotary bell sprayer. This efficient algorithm contains spray dynamics, airflow, paint droplets tracking and an electrostatic effect to simulate atomization. The algorithm is implemented using the OpenFOAM package. A solver for the particle trajectory was used to illustrate the process of spray transport and also the interaction of the airflow and the particle that is solved by momentum coupling. Creating an initial condition of the particle approach has been proposed that is matched with practical applications. The fluid-dynamics is simulated by solving the unsteady 3D compressible Navier-Stokes equations. Unsteady flow is computed by using a Large eddy simulation (LES) turbulence approach, while the motion of the particles is simulated by tracking the droplet size distribution approach. The model correctly predicts that the bell cup spin forces the paint particles to fall off from the bell surface towards the high-velocity airflow. The present work illustrates a tentative benchmark and contains a systematic analysis of the recirculation zone length, the toroidal vortex, the overspray phenomena and the flowfield characteristics like mean velocity, pressure, turbulent kinetic energy and velocity fluctuation. The results indicate as dominant operating parameter the air-paint flow rate with voltage level deeply affecting the spray shape. A more uniform distribution of the coating is obtained by growing this high-velocity shaping airflow, although the values of the transfer efficiency (TE) are reduced. The distribution of the particle size is very sensitive to changes in the rotational speed. Experimental results obtained in this study put forward a clear link between the shaping air flow rate and the rotation frequency on the aerodynamics and also provide valuable insights to design modern ERBS. The paint spray distribution obtained in the present work is validated against coating experimental results with suitable accuracy.

What controls filament thinning in uniaxial extension?

Breakup of fluid threads is omnipresent in nature and highly relevant for technical processes such as atomization, printing, coating, or spinning. We discuss how to control the filament lifetime of shear-thinning, viscoelastic fluids during uniaxial extension without affecting their shear viscosity. Two commercial acrylic thickeners differing with respect to the co-polymerized hydrophobic monomers, and hence different hydrophobic intra- and intermolecular association, are mixed to obtain aqueous solutions with similar shear viscosity. The elongational relaxation time as determined by capillary breakup extensional rheometry, however, varies by almost two orders of magnitude. Filament lifetime of these solutions can be varied upon adding non-Brownian, plate-shaped particles, again without affecting shear viscosity. A trace amount of particles increases elongational relaxation time by about a factor of four. Car bodies are usually coated using high-speed rotary bell atomizers guaranteeing high transfer efficiency and high-quality appearance. We use the solutions and suspensions described above to investigate the effect of extensional viscosity on ligament formation at the bell edge as a decisive intermediate step prior to droplet formation. High-speed imaging reveals a logarithmic scaling of ligament length with extensional relaxation time for pure thickener solutions. In contrast, ligament length monotonically decreases with increasing particle concentration, i.e. extensional viscosity. Plate-shaped particles obviously act as defects promoting ligament breakup. Extended filament lifetimes are commonly observed during atomization and spraying as a consequence of fluid viscoelasticity. On the other hand, low viscosity fluid threads rupture quickly. Here, we demonstrate that a unique banding instability during extension of a low viscosity surfactant solution with no measurable elasticity leads to extremely long filament lifetimes and to the formation of remarkably long threads. Combining filament stretching and particle image velocimetry we found an unexpected heterogeneous, banded flow in opposing directions. This phenomenon is not limited to surfactant solutions but can also occur in biopolymer solutions, thus broadening the view on instabilities in complex elongational flows.

Analysis of Paint Flow Pulsations during High-Speed Rotary Bell Atomization

High-speed rotary bell atomization is the preeminent coating technique in the automotive industry. It is widely accepted that a narrow droplet size distribution and constant spray are necessary in order to guarantee uniform film thickness and high-quality appearance. This may be deteriorated by paint flow pulsations. So far, however, no studies exist regarding such fluctuations quantitatively for this type of atomizers. We fill this gap using image analysis of high-speed recordings close to the bell edge. We could show that the fundamental pulsation frequency increases linearly with rotational speed. A ratio of pulsation frequency and true rotational speed of about 3 was found, indicating that pulsations were initiated mainly by the three struts of the distributor disc. The coefficient of variation, i.e., the amplitude of fluctuation increased with decreasing liquid volume rate and rotational speed. Beyond that, we could show that the formation of droplets larger than 100 μm, which are assumed to cause paint defects, is promoted by the degree of fluctuation. These findings may stimulate development of bell cups showing less paint flow pulsations.

Numerical Investigation of Electrostatic Spray Painting Transfer Processes for Vehicle Coating

<div class="section abstract"><div class="htmlview paragraph">In this study we examined numerically the electrostatic spray transfer processes in the rotary bell spray applicator, which is this case implemented in a full 3D representation. Instead of an experimental approach [Stevenin et al., 2015, Fluids Eng., 137 (11)], here an algorithm implemented and developed for this simulation includes airflow, spray dynamics, tracking of paint droplets and an electrostatic modularized solver to present atomization and in-flight spray phenomena for the spray forming procedure. The algorithm is implemented using the OpenFOAM package. The shaping airflow is simulated via an unsteady 3D compressible Navier-Stokes method. Solver for particle trajectory was developed to illustrate the process of spray transport and also the interaction of airflow and particle that is solved by momentum coupling. As the numerical results in this paper indicates dominant operating parameter voltage setting, further the charge to mass ratio and air-paint flow rate deeply effect the spray shape and the transfer efficiency (TE). The spin of the bell forced the paint to fall off from the bell edge into the high-velocity airflow. By increasing the shaping airflow more uniform distribution of mass of paint is produced but the TE decreases. The size distribution is highly sensitive to the bell rotational speed. Our results demonstrate the validity of the numerical procedure and also the applicability of it in reducing the production costs for painting. Unsteady and dynamic treatment of the flow is described using Large eddy simulation (LES) turbulence models, whereas the movement of the paint particles is modeled by the approach of tracking droplet size distribution, also the electrical potential effect on its size and form can be predicted. Using this advanced numerical simulation the efficiency and quality of the program can be evaluated precisely for industrial robots of paint over Off-Line Programming (OLP). Further, the paint spraym structure obtained from the numerical simulations is compared with the experimental data at the same working condition with appropriate quantitative accuracy.</div></div>

Spatial Positioning and Operating Parameters of a Rotary Bell Sprayer: 3D Mapping of Droplet Size Distributions

In this study, we evaluated the fundamental physical behavior during droplet formation and flow from a rotary bell spray in the absence of an electrostatic field. The impact of a wide range of operating parameters of the rotary bell sprayer, such as flow rates, rotational speeds, and spatial positioning, on droplet sizes and size distributions using a three-dimensional (3-D) mapping was studied. The results showed that increasing the rotational speed caused the Sauter mean diameter of the droplets to decrease while increasing flow rate increased the droplet sizes. The rotational speed effect, however, was dominant compared to the effect of flow rate. An increase in droplet size radially away from the cup was noted in the vicinity of the cup, nevertheless, as the lateral distances from the cup and rotational speed were increased, the droplet sizes within the flow field became more uniform. This result is of importance for painting industries, which are looking for optimal target distances for uniform painting appearance. Furthermore, the theoretical formulation was validated with experimental data, which provides a wider range of applicability in terms of environment and parameters that could be tested. This work also provides an abundance of measurements, which can serve as a database for the validation of future droplet disintegration simulations.

Reduction of Order: Analytical Solution of Film Formation in the Electrostatic Rotary Bell Sprayer

This brief paper explains the slight differences in governing equations for a fluid film in a spinning cone, and the mechanism that reduces the order of a solution. Spinning cones with a centrally supplied fluid that spreads over its inner surface as a thin film have been the subject of interest for many years. Though often cast as a mathematical analysis, understanding this process is important, especially in the application of automotive painting. The analysis consists of a system of equations obtained from the Navier–Stokes equations along with simple boundary conditions that describe radial and tangential momentum conservation. Solutions to this system of equations are shown using several techniques. The connection between these techniques is slightly subtle. However, the conditions that enable reduction of order are clear once they are exposed. Directional velocity profiles in the film can be a combination of four roots in the complex plane. This system of roots also contains two diagonal axes of symmetry that are offset by 90 degrees. Alternatively, if the radial and tangential velocity profiles are expressed as a single complex function, a reduced order solution that is a combination of one set of diagonal set of roots can be found.

Primary breakup of a non-Newtonian liquid using a high-speed rotary bell atomizer for spray-painting processes

The present contribution deals with numerical and experimental studies of the primary liquid breakup process using a high-speed rotary bell atomizer. The first part of the investigations focuses on the film formation on the distributor disk and the inner surface of the rotary bell. Numerical simulations using the volume-of-fluid approach were carried out. A non-Newtonian liquid that has shear-thinning behavior is used to investigate the effect of the viscosity on the initial wetting, the film formation process, and the film thickness distribution on the bell. A nonhomogeneous film structure is found on the inner surface of the rotary bell. This is also observed in experimental investigations using a high-speed camera. The second part focuses on the disintegration process of the paint liquid in the near bell region. As inlet conditions for the breakup simulations, the properties of the liquid film at the bell edge, i.e., film thickness, velocities, and apparent viscosity, resulting from the film formation simulations were applied. Two different liquid disintegrations in the near-field were found, which were also observed in experimental investigations using a high-speed camera. Furthermore, user-defined functions were compiled in ANSYS Fluent to uniquely identify and characterize droplets formed through the breakup process. In this way, droplet properties such as diameter, velocity, and position can be determined.

Characteristics of Spray Atomization for Liquid Droplets Formed Using a Rotary Bell Atomizer

In automotive engineering, paint evaporation is considered one of the major sources of volatile organic compound emission. The rotary bell atomizer (RBA) is a special atomizer used for improved automotive painting. A model to predict the droplet size was developed by combining two already-reported models. Further, the calculated values of evaporation rate constant, K, and the RBA nozzle parameter, K1, for water and clearcoat at room temperature (24 °C) are presented here. K1 was dependent on the flow rate and bell speed, but its variance for clearcoat was less than the measurement uncertainty. The Sauter mean diameter of the particle leaving the RBA at different flow rates and bell speeds can be predicted using K1. The values of K were 1.3 × 10−5 to 2.0 × 10−5 cm2/s for clearcoat and 8.6 × 10−6 to 1.53 × 10 −5 cm2/s for water. A generic model which can anticipate the evaporation rate of droplets with time length was also introduced.

Schlieren Visualization of Shaping Air during Operation of an Electrostatic Rotary Bell Sprayer: Impact of Shaping Air on Droplet Atomization and Transport

Electrostatic rotary bell sprayers (ERBSs) are widely used in the automotive industry. In ERBS, atomization is facilitated using centrifugal forces which disintegrate the paint film inside the cup into droplets at the cup edge. The droplets are then transported by the flow of a shaping air (SA) and electrostatic forces to a target surface; the characteristics of these droplets dramatically influence the quality of a painted surface and the painting transfer efficiency. In the current paper, a novel Schlieren-based visualization of the shaping air in the absence of paint droplets was performed during a qualitative investigation to delineate shaping air flow behavior and its interaction with droplets and droplet transport. An infrared thermographic flow visualization (IRFV) method and droplet size measurement were used to complement the Schlieren data for providing insight into shaping air-droplet interactions. The results demonstrated the impact of different operating conditions on the SA flow pattern, and the influence SA has on the secondary atomization and transport of droplets. Hence, these experimental methods combine with a useful tool for optimizing SA configurations that improve spray quality, droplet transport, and the efficiency of ERBS operations.