Droplet Splashing Research Articles

An efficient multi-dimensional implementation of VSIAM3 and its applications to free surface flows

We propose an efficient multidimensional implementation of VSIAM3 (volume/surface integrated average-based multi-moment method). Although VSIAM3 is a highly capable fluid solver based on a multi-moment concept and has been used for a wide variety of fluid problems, VSIAM3 could not simulate some simple benchmark problems well (for instance, lid-driven cavity flows) due to relatively high numerical viscosity. In this paper, we resolve the issue by using the efficient multidimensional approach. The proposed VSIAM3 is shown to capture lid-driven cavity flows of the Reynolds number up to Re = 7500 with a Cartesian grid of 128 × 128, which was not capable for the original VSIAM3. We also tested the proposed framework in free surface flow problems (droplet collision and separation of We = 40 and droplet splashing on a superhydrophobic substrate). The numerical results by the proposed VSIAM3 showed reasonable agreements with these experiments. The proposed VSIAM3 could capture droplet collision and separation of We = 40 with a low numerical resolution (8 meshes for the initial diameter of droplets). We also simulated free surface flows including particles toward non-Newtonian flow applications. These numerical results have showed that the proposed VSIAM3 can robustly simulate interactions among air, particles (solid), and liquid.

An adaptive mesh refinement-multiphase lattice Boltzmann flux solver for simulation of complex binary fluid flows

This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.

Two mechanisms of droplet splashing on a solid substrate

We investigate droplet impact on a solid substrate in order to understand the influence of the gas in the splashing dynamics. We use numerical simulations where both the liquid and the gas phases are considered incompressible in order to focus on the gas inertial and viscous contributions. We first confirm that the dominant gas effect on the dynamics is due to its viscosity through the cushioning of the gas layer beneath the droplet. We then describe an additional inertial effect that is directly related to the gas density. The two different splashing mechanisms initially suggested theoretically are observed numerically, depending on whether a jet is created before or after the impacting droplet wets the substrate. Finally, we provide a phase diagram of the drop impact outputs as the gas viscosity and density vary, emphasizing the dominant effect of the gas viscosity with a small correction due to the gas density. Our results also suggest that gas inertia influences the splashing formation through a Kelvin–Helmholtz-like instability of the surface of the impacting droplet, in agreement with former theoretical works.

Visualization and mechanisms of splashing erosion of electrodes in a DC air arc

The splashing erosion of electrodes in a DC atmospheric-pressure air arc has been investigated by visualization of the electrode surface and the sputtered droplets, and tracking of the droplet trajectories, using image processing techniques. A particle tracking velocimetry algorithm has been introduced to measure the sputtering velocity distribution. Erosion of both tungsten–copper and tungsten–ceria electrodes is studied; in both cases electrode erosion is found to be dominated by droplet splashing rather than metal evaporation. Erosion is directly influenced by both melting and the formation of plasma jets, and can be reduced by the tuning of the plasma jet and electrode material. The results provide an understanding of the mechanisms that lead to the long lifetime of tungsten–copper electrodes, and may provide a path for the design of the electrode system subjected to electric arc to minimize erosion.

Dynamics of spreading of impinged droplets on the curved-grooved surface

Impact of droplets on rough surfaces has many industrial applications. Various types of splashing and spreading of liquid droplets result due to impingement of the droplets on the different surfaces incorporating formation of satellite droplets. Dynamics of splashing and spreading is different with respect to the point of impact—groove or hill—on the grooved surface. Physics of spreading of impacted droplets on the curved-grooved surfaces is not known so far. Impact of droplets on curved-grooved surface has been studied for a narrow range of Weber number to know the abrupt change in projected area of splashed droplets. Such abrupt change in the geometry of splashed droplets due to exaggerated elongation in the direction of groove was observed for narrow range of Weber numbers from 42 to 45. The present findings explore new direction for further fundamental research work to comprehend the physics of dynamics of impacted droplets for development of new theory helpful for spray painting, printing, and designing of shielding structures.

Boundary-layer effects in droplet splashing.

A drop falling onto a solid substrate will disintegrate into smaller parts when its impact velocity V exceeds the so-called critical velocity for splashing, i.e., when V>V^{*}. Under these circumstances, the very thin liquid sheet, which is ejected tangentially to the solid after the drop touches the substrate, lifts off as a consequence of the aerodynamic forces exerted on it. Subsequently, the growth of capillary instabilities breaks the toroidal rim bordering the ejecta into smaller droplets, violently ejected radially outward, provoking the splash [G. Riboux and J. M. Gordillo, Phys. Rev. Lett. 113, 024507 (2014)]PRLTAO0031-900710.1103/PhysRevLett.113.024507. In this contribution, the effect of the growth of the boundary layer is included in the splash model presented in Phys. Rev. Lett. 113, 024507 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.024507, obtaining very good agreement between the measured and the predicted values of V^{*} for wide ranges of liquid and gas material properties, atmospheric pressures, and substrate wettabilities. Our description also modifies the way at when the liquid sheet is first ejected, which can now be determined in a much more straightforward manner than that proposed in Phys. Rev. Lett. 113, 024507 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.024507.

Multiphase injector modelling for automotive SCR systems: A full factorial design of experiment and optimization

Advances in emission control technologies have seen the introduction of Selective Catalyst Reduction (SCR) systems as a method for NOx decontamination in light and heavy duty vehicles. SCR systems make use of a urea–water solution (UWS) injected directly into the exhaust gas stream for the reduction of NOx contaminants to Nitrogen (N2) over a monolith catalyst [2]. The effectiveness of an SCR system depends on many factors including the type of catalysts, the injection and mixing pattern of the UWS, temperature and more [1].Spray analysis involves multi-phase flow phenomena and requires the numerical solution of the conservation and transport equations for the gas and the liquid phase simultaneously. Spray/wall interaction mechanisms such as droplet splash, spread, rebound or stick are complex to model and directly affected by the injection parameters [4]. The accurate modelling of the UWS injector can help in the prediction of phenomena such as wall film formation, droplet evaporation and urea crystallization [7].This study presents a series of multi-phase numerical analyses, computed with the commercial software AVL Fire 2014 v, to measure the impact of injection velocity, spray angle and droplet size, in the overall performance of an SCR system. The analysis consisted of a completely mixed turbulent flow, solved using a two equations turbulence model (k−zeta−f). The interaction of the injected particles was solved with an Euler/Lagrange approach, the liquid phase calculation was based on the statistical Discrete Droplet Method interacting with the numerical solution of the conservation equations of the flow pattern.It was found that the injection parameters had an impact on the final results of the ammonia uniformity index (NH3UI) and wall film formation on the SCR system. The method applied in this work successfully predicted the performance of an SCR system. Moreover, a series of response surfaces were created based on a linear regression model which allowed for further design optimization outside of the initial experimental space.

The Statistical Analysis of Droplet Train Splashing After Impinging on a Superheated Surface

An orderly droplet splashing is established when a water droplet train impinges onto a superheated copper surface. The droplets continuously impinge onto the surface with a rate of 40,000 Hz, a diameter of 96 μm or 120 μm, and a velocity of 8.4 m/s or 14.5 m/s. The heat transfers under different wall temperatures are measured, and the corresponding droplet splashing is recorded and analyzed. The effects of wall temperature, droplet Weber number, and surface roughness on the transition of the droplet splashing are investigated. The results suggest that the transferred energy is kept a constant in the transition regime, but a sudden drop of around 25% is observed when it steps into post-transition regime, indicating that the Leidenfrost point is reached. A higher Weber number of droplet train results in a more stable splashing angle and a wider range of splashed droplet diameter. The surface roughness plays no significant role in influencing the splashing angle in the high Weber number case, but the rougher surface elevates the fluctuation of the splashing angle in the low Weber number case. On the rougher surface, the temporary accumulation of the impact droplets is observed, a “huge” secondary droplet can be formed and released. The continuous generation of the huge droplets is observed at a higher wall temperature. Based on the result of droplet tracking of the splashed secondary droplets, the diameter and velocity are correlated.

Efficient Implementation of Volume/Surface Integrated Average-Based Multi-Moment Method

We investigated discretization strategies of the conservation equation in volume/surface integrated average-based multi-moment method (VSIAM3) which is a numerical framework for incompressible and compressible flows based on a multi-moment concept. We investigated these strategies through the lid-driven cavity flow problem, shock tube problems, 2D explosion test and droplet splashing on a superhydrophobic substrate. We found that the use of the constrained interpolation profile-conservative semi-Lagrangian with rational function (CIP-CSLR) method as the conservation equation solver is critically important for the robustness of incompressible flow simulations using VSIAM3 and that numerical results are sensitive to discretization techniques of the divergence term in the conservation equation. Based on these results, we proposed efficient implementation techniques of VSIAM3.

Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact.

Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlying mechanism. An effective viscosity is defined accordingly to quantitatively explain the observations.

Scaling Relations of Lognormal Type Growth Process with an Extremal Principle of Entropy

The scale, inflexion point and maximum point are important scaling parameters for studying growth phenomena with a size following the lognormal function. The width of the size function and its entropy depend on the scale parameter (or the standard deviation) and measure the relative importance of production and dissipation involved in the growth process. The Shannon entropy increases monotonically with the scale parameter, but the slope has a minimum at p 6/6. This value has been used previously to study spreading of spray and epidemical cases. In this paper, this approach of minimizing this entropy slope is discussed in a broader sense and applied to obtain the relationship between the inflexion point and maximum point. It is shown that this relationship is determined by the base of natural logarithm e ' 2.718 and exhibits some geometrical similarity to the minimal surface energy principle. The known data from a number of problems, including the swirling rate of the bathtub vortex, more data of droplet splashing, population growth, distribution of strokes in Chinese language characters and velocity profile of a turbulent jet, are used to assess to what extent the approach of minimizing the entropy slope can be regarded as useful.

Benchmark computations for 3D two-phase flows: A coupled lattice Boltzmann-level set study

Following our previous work on the application of the diffuse interface coupled lattice Boltzmann-level set (LB-LS) approach to benchmark computations for 2D rising bubble simulations, this paper investigates the performance of the coupled scheme in 3D two-phase flows. In particular, the use of different lattice stencils, e.g., D3Q15, D3Q19 and D3Q27 is studied and the results for 3D rising bubble simulations are compared with regard to isotropy and accuracy against those obtained by finite element and finite difference solutions of the Navier–Stokes equations. It is shown that the method can eventually recover the benchmark solutions, provided that the interface region is aptly refined by the underlying lattice. Following the benchmark simulations, the application of the method in solving other numerically subtle problems, e.g., binary droplet collision and droplet splashing on wet surface under high Re and We numbers is presented. Moreover, implementations on general purpose GPUs are pursued, where the computations are adaptively refined around the critical parts of the flow.

Experimental Investigation of Droplet Impact on Metal Surfaces in Reduced Ambient Pressure

Impacting water droplets are capable of eroding steam turbine blades, high speed aircraft and even serve as a machining operation. In this latter process, high velocity (∼100m/s) water droplets impact a solid surface under conditions in which the ambient air pressure is sub-atmospheric. The physics of this erosion mechanism is not completely understood. To begin to unravel these physics, we present results pertaining to the effects of ambient air pressure on the impact force of low velocity (1m/s) droplets. It is well known that droplet splash is suppressed when the ambient air pressure is reduced. The effects on the associated impact force are, however, unknown. In this article we examine the impact force of 3.5mm diameter, low velocity droplets in a reduced pressure environment. A 38x38x50cm vacuum chamber fitted with a unidirectional piezoelectric force sensor to measure the transient force of impacting droplets. Preliminary results in atmospheric air pressure reveal that the impulse of the droplets depends linearly on impact velocity while the average impact force depends quadratically on impact velocity. The results under reduced pressures are compared and discussed relative to the underlying physics.

Effect of Ice and Blade Interaction Models on Compressor Stability

As air traffic continues to increase in the subtropical areas where high moisture laden air is present at subfreezing conditions, engine icing probability increases. It has been shown that compressor stages rematch under icing conditions—front stages are choked, while rear stages throttle due to ice melting and evaporation. Such an analysis uses various empirical models to represent ice-breakup and water-splash processes as ice/water particles interact with rotors/stators. This paper presents a compressor stall sensitivity analysis around different splash models. The effect of droplet splash at both rotor and stator blades, blade solidity effect, and trailing edge shed effect is modeled. A representative ten-stage high-speed compressor section operating near design point (100% Nc) is used for the study. Results show that the temperature drop at high-pressure compressor (HPC) exit and the overall compressor operability are functions of evaporating stages, and droplet–blade interaction models influence them. A comprehensive compressor stability envelope has been evaluated for different models. It is observed that the droplet–blade interaction behavior influences overall compressor stability and the stall-margin predictions can vary by as much as 25% with different models. Therefore, there is a need for better calibration and continual improvement of empirical models to capture compressor interstage dynamics and stage rematching accurately under ice/water ingestion.

Modeling of droplet/wall interaction based on SPH method

Fuel droplet impingement on different wall conditions have been studied using Smoothed Particle Hydrodynamics (SPH) method, and a new splashing sub-model is proposed based on numerical results to calculate the splashing mass fraction of the incident droplet and compared with experimental results. Temporal evolution of the droplet shape after impingement is studied with various initial and boundary conditions. It is found that few splashes take place when the drop hits a relatively smoothed dry surface. Wall film plays a great role on droplet splashing. On one hand, the film slows down the droplet spreading process and transmits the energy to the crown part, making it easier to splash; on the other hand, the incident energy is dissipated when the drop moves through the film. The result shows that when non-dimensional wall film (hnd) is less than 0.5, the splashing mass fraction is relatively high and secondary droplets are easier to form. Further increase hnd, the fraction goes down and more film part splashes. The splashing sub-model is fitted and modified using numerical data and experimental data in a wet wall case. The result shows that the splashing mass and secondary droplets can be predicted as a function of We using the proposed sub-model.

Droplet impinging behavior on surfaces Part I - Hydrogen Peroxide on Aluminium Surface

In the present work the droplet behavior of the hydrogen peroxide (6% by weight) on a aluminum surface is reported. The behavior of hydrogen peroxide droplet is compared with water droplet for the same temperature conditions. Visualization of the droplet falling on a aluminum surface is done using a high speed camera. A data acquisition system is used for measuring the real time temperature. The characterization of droplet dynamics with variation in temperatures is detailed. The results reveal that with increase in temperature, the droplet splashes in to the ambient like a jet which is unlike water behavior, which when subjected to the same temperature conditions. The behavior of water droplet and hydrogen peroxide droplet after impinging and spreading over the surface and evaporation phenomenon is studied and observed.

Identification of the impact regimes of a liquid droplet propelled by a gas stream impinging onto a dry surface at moderate to high Weber number

In “vapor assisted” spray cooling it is well known that the droplet spray is more effective in cooling when smaller droplets are formed and propelled by a vapor phase towards the target surface. In the ideal spray evaporative cooling regime, the droplet impacts, spreads into a thin film, and then evaporates. In the presence of a carrier vapor, the vapor phase may affect the droplet dynamics by accelerating the droplet and by imposing hydrodynamic forces on the free surface during spreading and receding. There is a lack of understanding of the complicated physics at play. In the present study, the impact of a water droplet propelled by an air stream onto a dry smooth unheated surface was experimentally investigated. It was observed that higher impact Weber numbers led to a larger diameter and thinner film thickness. It was found that the gas stream did not significantly influence the spreading phase. However, the propellant gas noticeably decreased the droplet receding phase, delayed the onset of droplet splashing, and increased the upper Weber number limit for the droplet spreading regime. An analytic model using an energy balance approach was developed to predict dynamic and instantaneous droplet diameter and the agreement with the experimental observations was within 5% in the spreading phase, with poorer agreement in the receding phase due to the assumption of constant receding contact angle.

Multiple-relaxation-time color-gradient lattice Boltzmann model for simulating two-phase flows with high density ratio.

In this paper we propose a color-gradient lattice Boltzmann (LB) model for simulating two-phase flows with high density ratio and high Reynolds number. The model applies a multirelaxation-time (MRT) collision operator to enhance the stability of the simulation. A source term, which is derived by the Chapman-Enskog analysis, is added into the MRT LB equation so that the Navier-Stokes equations can be exactly recovered. Also, a form of the equilibrium density distribution function is used to simplify the source term. To validate the proposed model, steady flows of a static droplet and the layered channel flow are first simulated with density ratios up to 1000. Small values of spurious velocities and interfacial tension errors are found in the static droplet test, and improved profiles of velocity are obtained by the present model in simulating channel flows. Then, two cases of unsteady flows, Rayleigh-Taylor instability and droplet splashing on a thin film, are simulated. In the former case, the density ratio of 3 and Reynolds numbers of 256 and 2048 are considered. The interface shapes and spike and bubble positions are in good agreement with the results of previous studies. In the latter case, the droplet spreading radius is found to obey the power law proposed in previous studies for the density ratio of 100 and Reynolds number up to 500.

Influence of surface structure and chemistry on water droplet splashing

Water droplet splashing and aerosolization play a role in human hygiene and health systems as well as in crop culturing. Prevention or reduction of splashing can prevent transmission of diseases between animals and plants and keep technical systems such as pipe or bottling systems free of contamination. This study demonstrates to what extent the surface chemistry and structures influence the water droplet splashing behaviour. Smooth surfaces and structured replicas of Calathea zebrina (Sims) Lindl. leaves were produced. Modification of their wettability was done by coating with hydrophobizing and hydrophilizing agents. Their wetting was characterized by contact angle measurement and splashing behaviour was observed with a high-speed video camera. Hydrophobic and superhydrophilic surfaces generally showed fewer tendencies to splash than hydrophobic ones. Structuring amplified the underlying behaviour of the surface chemistries, increasing hydrophobic surfaces' tendency to splash and decreasing splash on hydrophilic surfaces by quickly transporting water off the impact point by capillary forces. The non-porous surface structures found in C. zebrina could easily be applied to technical products such as plastic foils or mats and coated with hydrophilizing agents to suppress splash in areas of increased hygiene requirements or wherever pooling of liquids is not desirable.This article is part of the themed issue 'Bioinspired hierarchically structured surfaces for green science'.

From splashing to bouncing: The influence of viscosity on the impact of suspension droplets on a solid surface.

We experimentally investigated the splashing of dense suspension droplets impacting a solid surface, extending prior work to the regime where the viscosity of the suspending liquid becomes a significant parameter. The overall behavior can be described by a combination of two trends. The first one is that the splashing becomes favored when the kinetic energy of individual particles at the surface of a droplet overcomes the confinement produced by surface tension. This is expressed by a particle-based Weber number We_{p}. The second is that splashing is suppressed by increasing the viscosity of the solvent. This is expressed by the Stokes number St, which influences the effective coefficient of restitution of colliding particles. We developed a phase diagram where the splashing onset is delineated as a function of both We_{p} and St. A surprising result occurs at very small Stokes number, where not only splashing is suppressed but also plastic deformation of the droplet. This leads to a situation where droplets can bounce back after impact, an observation we are able to reproduce using discrete particle numerical simulations that take into account viscous interaction between particles and elastic energy.