Droplet Impingement Dynamics Research Articles

Spatio-temporal reconstruction of droplet impingement dynamics by means of color-coded glare points and deep learning

Abstract The present work introduces a deep learning approach for the three-dimensional reconstruction of the spatio-temporal dynamics of the gas–liquid interface on the basis of monocular images obtained via optical measurement techniques. The method is tested and evaluated at the example of liquid droplets impacting on structured solid substrates. The droplet dynamics are captured through high-speed imaging in an extended shadowgraphy setup with additional glare points from lateral light sources that encode further three-dimensional information of the gas–liquid interface in the images. A neural network is trained for the physically correct reconstruction of the droplet dynamics on a labeled dataset generated by synthetic image rendering on the basis of gas–liquid interface shapes obtained from direct numerical simulation. The employment of synthetic image rendering allows for the efficient generation of training data and circumvents the introduction of errors resulting from the inherent discrepancy of the droplet shapes between experiment and simulation. The accurate reconstruction of the three-dimensional shape of the gas–liquid interface during droplet impingement on the basis of images obtained in the experiment demonstrates the practicality of the presented approach based on neural networks and synthetic training data generation. The introduction of glare points from lateral light sources in the experiments is shown to improve the reconstruction accuracy, which indicates that the neural network learns to leverage the additional three-dimensional information encoded in the images for a more accurate depth estimation. By the successful reconstruction of obscured areas in the input images, it is demonstrated that the neural network has the capability to learn a physically correct interpolation of missing data from the numerical simulation. Furthermore, the physically reasonable reconstruction of unknown gas–liquid interface shapes for drop impact regimes that were not contained in the training dataset indicates that the neural network learned a versatile model of the involved two-phase flow phenomena during droplet impingement.

Lattice Boltzmann study of droplet dynamic behaviors impinging on textured surfaces under an external electric field

Textured surfaces contribute to enhancing the cooling effectiveness of electrostatic spray, while the droplet impacting dynamics on such substrates under the influence of electric field are crucial for cooling efficiency. This study utilized a multiphase lattice Boltzmann method combined with the leaky dielectric model to systematically examine the dynamics of droplet impingement on textured surfaces when exposed to electric field. The impact of Weber number, microstructural surface parameters, and electric field strength on droplet impact behavior was discussed in detail. Simulation outcomes reveal that, without the presence of an electric field, the impingement of droplets on textured surfaces results in three distinct deposition states: the Cassie state, partial penetration state, and Wenzel state, primarily contingent upon the surface solid fraction and the droplet impingement velocity. In the Cassie impact regime influenced by an applied electric field, the droplet spreading behaviors exhibit minimal sensitivity to the electric field, with surface tension and inertia primarily governing the spreading dynamics. Throughout the retraction stage, the droplet elongated the direction of the electric field as a result of electric field forces, and eventually, as the electric field strength grows, it bounces off the surface. In the Wenzel impact regime, as the strength of the electric field escalates, the droplet undergoes upward stretching and splits into satellite droplets during the retraction phase, attributed to the dynamic pressure and electrostatic pressure at the apex exceeding the capillary pressure and gravity. These findings could aid in advancing electrostatic spray cooling technology.

An analytical model for ice accretion on the engine strut surface

To predict flight icing more widely and practically, an ice accretion numerical framework that incorporates both the water droplet splash and the ice crystal sticking is developed. By proposing a deformation hypothesis, we deduce the modified energy conservation expression and the force balance relation for water droplet impingement. Subsequently, a new threshold determination and the probabilities for the droplet splash and ice crystal sticking are obtained, which are applicative across a wide range of Weber number after the validation. Through the interface tracking for a single droplet with the volume of fluid method, the droplet impingement dynamics are further explored, and the results of interaction with the wall serve the boundary treatments of droplet impingement in the discrete phase model. Additionally, the probability statistics method is employed to determine the parameters of the secondary droplets. Through the dynamic mesh technique, the retentive water droplets and the collected ice crystals are transformed into the accumulated ice in real time to update the ice accretion on the strut surface. Results demonstrate that the diameter, velocity, and content of droplets or crystals play significant roles in the impingement and the icing phenomena. Based on our numerical model, the predictions show that the ice accretion on the engine strut is influenced by flight parameters and environmental conditions, providing crucial guidance for the icing protection processes.

Numerical assessment of the drag force and Nusselt number during droplet impingement onto a particle

The dynamics of droplet impingement onto solid particles play a crucial role in various engineering applications, yet a fundamental understanding of the intricate momentum and heat transfer characteristics within the processes remains unclear. In this work, we numerically investigate and quantify the drag force and Nusselt (Nu) number during the process using a volume of fraction model. After model validations, it is employed to simulate the processes of molten iron ore spreading over a coke particle for demonstration. The results show that the drag force exhibits rapid initial growth, followed by significant fluctuations marked by two peaks, ultimately decreasing to a low value. The Nu number undergoes a sharp ascent to an immediate peak, followed by a two-stage decline with varying rates. Furthermore, the effect of three key operating parameters is quantified. The comparative analysis unveils that a larger droplet size significantly contributes to an augmented drag force, especially during the first peak. The Nu numbers under various droplet sizes follow a similar trajectory, rising and then decreasing until the wetter surface reaches the maximum. The larger droplets show a slower Nu number decrease. A higher initial droplet position can remarkably increase the drag force and Nu number with more rapid fluctuations. Conversely, the effect of gas velocity under the symmetrical and steady flow field is limited and can be practically disregarded. The present work reveals the fundamental characteristics of momentum and heat transfer process during droplets impact particles.

The effect of vibration on droplet dynamics and heat transfer of spray cooling

The heat transfer mechanism of spray cooling under vibration has yet to be revealed, so it is crucial to deeply analyze the droplet impingement dynamics and heat transfer mechanism under vibration. However, there is still a gap in analyzing how vibration quantitatively affects droplet impingement dynamics and heat transfer performance. To fill this research gap, this paper will employ high-speed cameras to quantitatively analyze droplets' dynamics and heat transfer properties under various vibrational conditions. The results demonstrate that droplet spreading is enhanced at high-frequency conditions, but the enhancement decreases with the reduction in amplitude. Under high amplitude conditions, droplets gain additional inertial forces to overcome adhesive forces, causing oscillation in the three-phase contact line of the droplets, which significantly consumes the kinetic energy of droplet spreading, thereby suppressing droplet spreading. Vibration overall suppresses droplet spreading; at an amplitude of 0.2 mm and frequency of 80 Hz, the spreading enhancement factor is merely 4 %. Moreover, the droplet's heat transfer rate, heat flux, heat transfer coefficient, and cooling efficiency all increase with the rise in vibrational frequency but are all subdued by the amplitude. Compared to a static surface, vibration suppresses droplet heat transfer but can facilitate droplet heat transfer under low amplitude and high-frequency conditions. At an amplitude of 0.2 mm, the maximum heat transfer enhancement factor (HTEF) is 16 %. At an amplitude of 0.8 mm and frequency of 10 Hz, the minimum HTEF is −44 %. This research undoubtedly brings innovative insights into spray droplet impact dynamics and heat transfer and can provide valuable guidance for related industrial applications.

Developing a novel ultrasonic atomization-based cutting fluid spray system and evaluating its performance during milling processes

Cutting fluid has been widespread in the metal cutting industry due to its cooling and lubrication properties. However, the excessive application of cutting fluids can lead to significant environmental issues and raise machining costs. Recently, the ultrasonic atomization-based cutting fluid (UACF) spray using minimum quantity has shown superior cooling and lubrication performance during machining processes, while the precise management of UACF spray and its influence on machining performance requires further comprehension. In this case, this paper developed a novel ultrasonic atomization-based cutting fluid (UACF) spray system, featuring a specialized nozzle unit that included an internal droplet nozzle and an external gas nozzle. Subsequently, the dynamics of droplet impingement on a rotated surface were analyzed, and the spray characteristic parameters were investigated. Then, comparative milling experiments were conducted under different cooling conditions, including dry cutting, flood cooling, high-pressure air cooling, and UACF. The influence of these cooling conditions on machining performance was investigated, in terms of cutting force, temperature, surface roughness, and chip morphology. The results obtained indicate that the critical velocity of droplet spreading was dependent on the cutting fluid properties, ultrasonic frequency, and velocity of the rotated surface. The droplets generated by ultrasonic atomization follow a Gaussian distribution. Flood cooling and UACF exhibit similar effects in reducing cutting force, temperature, and surface roughness due to the efficient penetration of liquid film into tool-workpiece interfaces. Additionally, UACF can significantly reduce the consumption of cutting fluid by up to 98.5 % compared to flood cooling. The effective cooling and lubrication in UACF can improve the surface quality and suppress machining vibration. Moreover, the appropriate droplet velocity can ensure the formation of a thin film on the tool surface, thereby enhancing cooling and lubrication performance in the UACF process.

Water-film thickness imaging based on time-multiplexed near-infrared absorption with up to 500 Hz repetition rate.

We demonstrate high-repetition-rate imaging of the liquid-film thickness in the 50-1000µm range resulting from impinging water droplets on a glass surface. The pixel-by-pixel ratio of line-of-sight absorption at two time-multiplexed near-infrared wavelengths at 1440 and 1353nm was detected with a high-frame-rate InGaAs focal-plane array camera. Frame rates of 1kHz and thus measurement rates of 500Hz could be achieved, well suited to capture the fast dynamics of droplet impingement and film formation. The droplets were sprayed onto the glass surface using an atomizer. Suitable absorption wavelength bands for water droplet/film imaging were determined from Fourier-transform infrared (FTIR) spectra of pure water between 298 and 338K. At 1440nm, the water absorption is nearly temperature-independent, making the measurements robust against temperature fluctuations. Time-resolved imaging measurements capturing the dynamics of the water droplet impingement and evolution were successfully demonstrated.

Synergistic Effect of the Fuel Microemulsion Characteristics on Drop Interaction with a Hot Wall

The utilization of fuel microemulsions helps in reducing harmful emissions, enhancing combustion efficiency, and preserving conventional fuels. This study is focused on the effect of the properties and phase behavior of water-in-diesel and water-in-biodiesel microemulsions that can be used as an alternative fuel on the droplet impingement dynamics of such fluids on a heated wall in the film boiling regime. The microemulsions represent complex fluids consisting of diesel fuel–rapeseed oil blends and distilled water with different mixture volume ratios. The emulsification is carried out using a mixture of a surfactant [isononylphenol poly(ethylene glycol) ether, PEG-6] and a co-surfactant (2-ethylhexanol) with a volume ratio of 9/1. The study considers the efficiency of the fuel samples in terms of the temperature-dependent viscosity and aggregate thermal stability as well as the quantitative characteristics of the spreading drop breakup, namely, mean diameter and number of ejected droplets. The fuel efficiency factor is derived to reveal the optimal samples. We test the phase behavior of the water–diesel fuel/rapeseed oil–PEG-6/2-ethylhexanol system in a wide temperature range. Comprehensive viscosity tests are carried out within the temperature ranges of stability to check the viscosity values of the developed microemulsions against the viscosity of the conventional diesel fuels.

An experimental study on the effect of nanoparticle shape on the dynamics of Leidenfrost droplet impingement

Extensive investigations have been carried out on the thermo-hydrodynamics of nanofluid droplet interaction with heated and non-heated flat surfaces. However, the influence of shape of nanoparticles on the dynamics of droplet impingement on heated flat surfaces is yet to be explored in detail. In this study, hydrodynamics of nanofluid droplet impingement process on heated and mechanically polished aluminum substrate was studied using dissolved Al2O3 nanoparticles having spherical as well as cylindrical shapes. Nanofluids of 0.3% volume fractions were prepared from spherical Al2O3 particles of mean size less than 50 nm and from cylindrical Al2O3 particles of 2–6 nm in diameter and 200–400 nm in length. It was observed that, the impact dynamics is different from that of base pure fluid owing to the presence of nanoparticles. Leidenfrost temperatures of both nanofluids were dropped drastically in comparison with pure liquid. Further, the residence time, spread factor as well as retraction height also exhibit a different behavior against the base fluid. Detailed investigations were carried out for different Weber numbers (We = 18–159) and surface superheat and resul ts obtained were compared with de-ionized (DI) water.

Dynamics of droplet impingement on bioinspired surface: insights into spreading, anomalous stickiness and break-up.

Inspired by the self-cleaning ability of lotus leaves and stickiness (towards water) of rose petals, we investigate the droplet impact dynamics on such bioinspired substrates. Impact studies are carried out with water droplets for a range of impact velocities on glass, PDMS and soft lithographically fabricated replicas of the lotus leaf and rose petals, which exhibit near identical wetting properties as that of the original biological entities. In this work, we investigate the spreading, dewetting and droplet break-up mechanisms subsequent to impact. Surprisingly, the rose petal and lotus leaf replicas manifest similar impact dynamics. The observation is extremely intriguing and counterintuitive, as rose petal and its replicas are sticky in contrast to lotus leaves. However, these observations are based on experiments performed with sessile water droplets. By contrast, in the current study, we find that rose petal replicas exhibit non-sticky behaviour at the short time scale s similar to that exhibited by lotus leaf replicas. Air entrapment in the micrometre features of bioinspired surfaces prevent frictional dissipation of droplet kinetic energy, leading to contact edge recession. We have also unveiled interesting universal physics that govern the spreading, recession of the contact edge and subsequent break-up modes (ligament or bulb-ligament) of the droplet.

Normal and oblique droplet impingement dynamics on moving dry walls.

Industrial applications that depend on jetting-based technology, such as painting or additive layered manufacturing, involve sequential deposition of droplets onto a moving surface. Spreading and receding dynamics of these impinging drops depend on the momentum transferred by the moving wall to the droplet liquid, which in turn governs the geometric precision and surface finish of the printed outcome. In this work, the impingement dynamics of microdroplets on a flat, smooth, and moving solid surface is computed using a phase-field-based lattice Boltzmann method. Moreover, the motion of the three-phase moving contact line is captured using a geometry-based contact angle formulation. First, we investigate the influence of various process and materials parameters such as wall velocity, droplet viscosity, surface tension, and wettability on the impact behavior of drops. The surface wettability significantly affects the droplet morphology; an elongated tail like structure forms on the rear end of the droplet which becomes sharper as the moving surface becomes more hydrophobic. Furthermore, we examine the underlying flow physics of the symmetry breaking during the spreading and recoiling phases. For a given contact angle, an increase in wall velocity is found to expedite droplet spreading. In addition, for the first time we explore the oblique droplet impingement dynamics on moving dry walls in this work. It is observed that wall momentum affects the structure of the leading edge during the inline impact situations, whereas the moving surface controls the delay in flow reversal inside the droplet for opposing impact scenarios.

Micrometer-sized droplet impingement dynamics on flat and micro-structured surfaces

An 85 μm diameter droplet impinging on a flat surface and on micro-structured surfaces with groove/stud characteristic sizes of 25–50 μm was simulated using the VOF method with dynamic contact angles calculated by Blake’s model to study the impingement dynamics and wetting behavior for spray cooling system in nuclear plants and other high heat flux applications. The simulations of the droplet impinging on the flat surface agreed well with experimental results (van Dam and Le Clerc, 2004). The results show that the droplet was successively dominated by the inertia force, viscous force and surface tension as it impinged on the surface. The total wetted area on the grooved surfaces at steady state was slightly larger than that on the studded surfaces with the same characteristic structure size, followed by that on the flat surface. The larger wetted area led to decreased droplet oscillations up to steady state for the micro-structures which increased the contact area between the droplet and the surface and the viscous dissipation. The increased viscous dissipation restricted the free movement and caused the droplet to reach steady state earlier. The studded surfaces were more conducive to enhancing the bottom surface wetting than the grooved surfaces.

A numerical study of spray/wall impingement based on droplet impact phenomenon

A new spray/wall impingement model is purposed based on droplet impact experiments and droplet morphology dynamics. Various splashing modes are summarized and analyzed based upon earlier research on droplet impact and conservation laws. Corona splash and prompt splash are distinguished in the new spray/wall impingement model taking the incident and wall conditions into consideration. Morphology dynamics of droplet impingement is analyzed and coupled into the conservation equations, which helps to obtain more accurate dynamic results of splashing droplets. The new wall impact model is validated in a constant volume combustion system under different conditions. Two different fuels, including n-tridecane and diesel, are adopted for spray impingement validations. It is found that this new model shows good performance in predicting impinging spray properties, including radius penetration and splashing height, in wide jet conditions.

Numerical Investigation of the Flow Dynamics and Evaporative Cooling of Water Droplets Impinging onto Heated Surfaces: An Effective Approach To Identify Spray Cooling Mechanisms.

Numerical investigations of the dynamics and evaporative cooling of water droplets impinging onto heated surfaces can be used to identify spray cooling mechanisms. Droplet impingement dynamics and evaporation are simulated using the presented numerical model. Volume-of-fluid method is used in the model to track the free surface. The contact line dynamics was predicted from a dynamic contact angle model with the evaporation rate predicted by a kinetic theory model. A species transport equation was solved in the gas phase to describe the vapor convection and diffusion. The numerical model was validated by experimental data. The physical effects including the contact angle hysteresis and the thermocapillary effect are analyzed to offer guidance for future numerical models of droplet impingement cooling. The effects of various parameters including surface wettability, surface temperature, droplet velocity, droplet size, and droplet temperature were numerically studied from the standpoint of spray cooling. The numerical simulations offer profound analysis and deep insight into the spray cooling heat transfer mechanisms.

Modelling on the dynamics of droplet impingement and bubble boiling in spray cooling

A spray cooling model incorporating a spray characteristics submodel and a heat transfer submodel to simulate the dynamics of spray characteristics, droplet impingement, and bubble boiling is presented. The spray characteristics submodel based on a Monte Carlo algorithm simulates the droplet diameter, velocity and spatial droplet flux distributions in actual spray conditions. The heat transfer submodel considers the spray cooling process as film flow boiling to include the processes of droplet impingement forced convection and thin film bubble boiling. Phase Doppler anemometry measurements are used as validation in the spray characteristics submodel, and as boundary conditions in the heat transfer submodel. Reasonable comparison is observed between the experiments and simulations. Parametric effects on the heat transfer performance and bubble dynamics are investigated. The simulation shows that increasing heat flux tends to increase the bubble growing frequency thereby causes the higher bubble collapsing flux and bubble puncturing flux. By fixing the droplet impinging velocity and flow rate, the surface temperature non-uniformity is found to be influenced by droplet diameter. A smaller impinging droplet diameter with a higher impinging droplet flux is favourable to bubble boiling due to more secondary nuclei and larger fractions of bubbles punctured at bigger diameters.

Lattice Boltzmann simulations of multiple-droplet interaction dynamics.

A lattice Boltzmann (LB) formulation, which is consistent with the phase-field model for two-phase incompressible fluid, is proposed to model the interface dynamics of droplet impingement. The interparticle force is derived by comparing the macroscopic transport equations recovered from LB equations with the governing equations of the continuous phase-field model. The inconsistency between the existing LB implementations and the phase-field model in calculating the relaxation time at the phase interface is identified and an approximation is proposed to ensure the consistency with the phase-field model. It is also shown that the commonly used equilibrium velocity boundary for the binary fluid LB scheme does not conserve momentum at the wall boundary and a modified scheme is developed to ensure the momentum conservation at the boundary. In addition, a geometric formulation of the wetting boundary condition is proposed to replace the popular surface energy formulation and results show that the geometric approach enforces the prescribed contact angle better than the surface energy formulation in both static and dynamic wetting. The proposed LB formulation is applied to simulating droplet impingement dynamics in three dimensions and results are compared to those obtained with the continuous phase-field model, the LB simulations reported in the literature, and experimental data from the literature. The results show that the proposed LB simulation approach yields not only a significant speed improvement over the phase-field model in simulating droplet impingement dynamics on a submillimeter length scale, but also better accuracy than both the phase-field model and the previously reported LB techniques when compared to experimental data. Upon validation, the proposed LB modeling methodology is applied to the study of multiple-droplet impingement and interactions in three dimensions, which demonstrates its powerful capability of simulating extremely complex interface phenomena.

Droplet impingement dynamics: effect of surface temperature during boiling andnon-boiling conditions

This study investigates the hydrodynamic characteristics of droplet impingement on heatedsurfaces and compares the effect of surface temperature when using water and ananofluid on a polished and nanostructured surface. Results are obtained foran impact Reynolds number and Weber number of approximately 1700 and 25,respectively. Three discs are used: polished silicon, nanostructured porous silicon andgold-coated polished silicon. Seven surface temperatures, including single-phase(non-boiling) and two-phase (boiling) conditions, are included. Droplet impact velocity,transient spreading diameter and dynamic contact angle are measured. Results ofwater and a water-based single-wall carbon-nanotube nanofluid impinging on apolished silicon surface are compared to determine the effects of nanoparticles onimpinging dynamics. The nanofluid results in larger spreading velocities, largerspreading diameters and an increase in early-stage dynamic contact angle. Results ofwater impinging on both polished silicon and nanostructured silicon show that thenanostructured surface enhances the heat transfer for evaporative cooling at lower surfacetemperatures, which is indicated by a shorter evaporation time. Using a nanofluid or ananostructured surface can reduce the total evaporation time up to 20% and 37%,respectively. Experimental data are compared with models that predict dynamic contactangle and non-dimensional maximum spreading diameter. Results show that themolecular-kinetic theory’s dynamic contact angle model agrees well with currentexperimental data for later times, but over-predicts at early times. Predictions of maximumspreading diameter based on surface energy analyses indicate that these modelsover-predict unless empirical coefficients are adjusted to fit the test conditions. This is aconsequence of underestimates of the dissipative energy for the conditions studied.

Simultaneous droplet impingement dynamics and heat transfer on nano-structured surfaces

This study examines the hydrodynamics and temperature characteristics of distilled deionized water droplets impinging on smooth and nano-structured surfaces using high speed (HS) and infrared (IR) imaging at We = 23.6 and Re = 1593, both based on initial drop impingement parameters. Results for a smooth and nano-structured surface for a range of surface temperatures are compared. Droplet impact velocity, transient spreading diameter and dynamic contact angle are measured. The near surface average droplet fluid temperatures are evaluated for conditions of evaporative cooling and boiling. Also included are surface temperature results using a gold layered IR opaque surface on silicon. Four stages of the impingement process are identified: impact, boiling, near constant surface diameter evaporation, and final dry-out. For the boiling conditions there is initial nucleation followed by severe boiling, then near constant diameter evaporation resulting in shrinking of the droplet height. When a critical contact angle is reached during evaporation the droplet rapidly retracts to a smaller diameter reducing the contact area with the surface. This continues as a sequence of retractions until final dry out. The basic trends are the same for all surfaces, but the nano-structured surface has a lower dissipated energy during impact and enhances the heat transfer for evaporative cooling with a 20% shorter time to achieve final dry out.

An Experimental Evaluation of an Atomization-Based Cutting Fluid Application System for Micromachining

An atomization-based cutting fluid application system is developed for micro-end milling. The system was designed to ensure spreading of the droplets on the workpiece surface based on the analysis of the atomized droplet impingement dynamics. The results of the initial experiments conducted to examine the viability of the system show that the cutting forces are lower and tool life is significantly improved with the atomized cutting fluids when compared to dry and flood cooling methods. Also, application of atomized cutting fluid is found to result in good chip evacuation and lower cutting temperature. Experiments were also conducted to study the effect of fluid properties on cutting performance, and the results show that cutting fluids with lower surface tension and higher viscosity perform better in terms of cutting forces.

Validation of Ink Media Interaction Mechanisms for Dye and Pigment-based Aqueous and Solvent Inks

In this article, the dynamics of droplet impingement, spreading, absorption, penetration, and evaporation are discussed for different ink jet ink classes. Both dye and pigment based aqueous inks are included, as well as solvent or eco-solvent inks. The fundamental physicochemical rules determining the dynamics can be very dependent from ink to ink, and are compared. After impact there is a fast spreading phase that takes into account the evolution of the kinetic energy of the droplet to forced spreading on the receiver. Later on, diffusion or capillary wicking is possible, and is depending upon the nature of the substrate. The speed of these processes can be influenced by the presence of dyes or pigments in the inks. After absorption / penetration, the carrier liquid can evaporate leading to the final equilibrium condition. For (eco)-solvent inks the evaporation is much more important compared to the other penetration/absorption processes, so that it cannot be easily separated into different independent time scales. In situ visualization of the dynamics for real size ink jet droplets is not easy, especially for the droplets of only a few pl volume. Comparison of large droplet impact dynamic studies with theory and extrapolation of the behavior to small droplet cases has some risks. Test experiments have been setup in order to simulate transient absorption phases on different receivers. Traditional microscopic evaluations have been done in order to verify whether the proposed models for describing the transient behavior are in agreement with the experimental observations for real small sized droplets.