Droplet Collision Research Articles

Experimental estimation of the probabilities of collision of water droplets in the environment of heated gases

Experimental estimation of the probabilities of collision of water droplets in the environment of heated gases

Характеристики "отскока" взаимодействующих капель воды

AbstractWe report on the results of experiments devoted to analysis of conditions and characteristics of “bounce” (approach and interaction through a gaseous buffer envelope) of water droplets moving in a gaseous media with different parameters: velocity and direction of motion, temperature, and composition. Experiments were performed in flows of air, water vapor, and combustion products. Peculiarities of bounce of droplets with different initial temperatures are considered, and the results obtained at 18–20 and 60–80°C are compared. More than 1000 collisions of droplets recorded by high-speed photography are divided into groups of bounce, coalescence, separation, and disruption. The results of criterion processing using the Weber numbers are obtained.

Two touching/self-assembly droplets in uniform Stokes flow: Viscous energy dissipation of the flow in droplets

Viscous energy dissipation of the flow in two touching or self-assembly droplets in uniform Stokes flow is investigated in this paper. Based on the Stokes solution, the energy dissipation per unit time of the two droplets is calculated and validated by comparing with the result of one droplet Stokes flow, and then a theoretical model to calculate the energy dissipation is established. The investigation reveals that the energy dissipation per unit time of either droplet increases with the increasing droplet viscosity at constant continuous fluid viscosity and reaches a peak value when the two viscosities are equal. Moreover, the energy dissipation per unit time of either droplet changes with the sizes of both droplets. The total energy dissipation per unit time of the two droplets is less than the sum of the energy dissipation per unit time of the two droplets before their contact or self-assembly, and in particular, it reaches the minimum value which is about 1/6 of the result of one droplet flow when the two droplets’ sizes are equal. Two droplets’ contact or self-assembly will minimize the energy dissipation of droplets, so it can save energy for the flow system. This study proposes a new perspective for droplet self-assembly study and can promote droplet collision and coalescence studies and then bring benefits to relevant applications.

Detection of Droplet Collisions Using Spatial Frequency Analysis of Hologram

Detection of Droplet Collisions Using Spatial Frequency Analysis of Hologram

Mesoscopic assessment of water droplet collision with a single stainless steel fiber in oil

Mesoscopic assessment of water droplet collision with a single stainless steel fiber in oil

A coupled discrete droplet and SPH model for predicting spray impingement onto surfaces and into fluid pools

• A combined DEM-SPH model is developed for spray impingement into a pool of liquid. • Momentum and mass are transferred from the discrete spray into the fluid phase. • The model is evaluated using experimental pressure measurements for 1–3 sprays. • Comparison of pressure predictions with experiment shows very good agreement. • Collisions of droplets from different sprays have a small but noticeable effect. In this paper we detail the development of a combined DEM-SPH model for spray impingement into a pool of water or onto a flat surface on which a pool of water can build up. The spray is represented by discrete particles which can collide with solid objects, each other and also merge with liquid surfaces. The liquid pool dynamics are solved for using the SPH method. The proposed coupling allows momentum to be transferred from the discrete spray phase into the fluid phase in the pool. The performance of this coupled DEM-SPH method is evaluated by comparing to experiments performed for simple spray arrangements in which the pressure in the pool just above the solid surface is carefully measured by a probe that is moved systematically across the surface. A comparison of the simulated pressure distribution with those from the experiments shows very good agreement for the size of the high pressure region, the average pressure the pressure distribution within this region generated by the spray impingement for cases with one, two and three overlapping sprays. Collisions between spray droplets in the case of multiple sprays are found to have a small but noticeable effect on the details of the high pressures in the regions of overlap of the sprays.

Accreted ice mass ratio (k‐factor) for rotating wind turbine blade profile and circular cylinder

AbstractThis paper describes a study to investigate the relation between ice accretion on a rotating wind turbine blade profile (airfoil) and a reference collector (circular cylinder). This relation, known as “k‐factor,” describes the ratio of accreted ice mass on a reference collector and wind turbine blade profile. Analyses are carried out by performing a series of multiphase numerical simulations and ISO 12494‐based analytical calculations. The results show that k‐factor is not equal to constant 20, contrary to currently postulated assumption by VTT and can vary to a significant degree depending on a number of different operating and geometric parameters. These factors include the effects of blade geometry on ice accretion, droplet collision efficiency, droplet distribution spectrum, and median volume diameter under different ambient conditions pertaining to wind speed and tip speed ratios experienced by both the reference collector and wind turbine blade. The results presented in this paper provide a simplistic explanation about k‐factor variance; however, further validation is necessary, in particular when it comes to the ice accretions on different wind turbine blade profiles under different operating and geometric conditions.

Icing Degree Characterization of Insulators Based on the Equivalent Collision Coefficient of Standard Rotating Conductors

Due to the complex structure of insulators, it is difficult to use parameters such as icicle length or ice thickness of an insulator to directly characterize the degree of icing of an insulator. Rotating conductors are widely used in monitoring icing degree on insulators, but the relationship between ice degree on the insulator and the rotating conductor has not been verified. In this paper, the water droplets collision coefficient α1 was put forward to characterize icing degree, and a new numerical calculation model where α1 on different regions of an insulator is calculated was proposed. Combining the freezing fraction α3 of the insulator and rotating conductor, the equivalent relationship of ice weight between insulator and rotating conductor can be established, which was afterwards verified through the icing tests. The test results indicate that ice weight on an insulator increases linearly with the increase of ice weight on the rotating conductor, and the model proposed in this paper can reflect actual results more accurately than previous models. In such cases, the method of using ice weight on a rotating conductor to predict that on an insulator based on the model proposed in this paper could be widely adopted.

A model for surface tension in the meshless finite volume particle method without spurious velocity

A surface tension model has been developed in the finite volume particle method (FVPM). FVPM is a conservative, consistent, meshless particle method that incorporates properties of both smoothed particle hydrodynamics and the mesh-based finite volume method. Surface tension force is applied only on free-surface particles, which are inexpensively and robustly detected using the FVPM definition of interparticle area, analogous to cell face area in the finite volume method. We present a model in which the direction of the pairwise surface tension force is approximated by the common tangent of free-surface particle supports. The new surface tension model is implemented in 2D. The method is validated for formation of an equilibrium viscous drop from square and elliptical initial states, drops on hydrophobic and hydrophilic walls, droplet collision, and impact of a small cylinder on a liquid surface. Results are practically free from parasitic current associated with inaccurate curvature determination in some methods.

The electric field effect on the droplet collision with a heated surface in the Leidenfrost regime

In this study, the impingement of a conductive droplet on a hot wall under an electric field in the Leidenfrost regime is simulated. Apart from electrostatic equations, the governing equations are conservation equations of mass, momentum, and energy in the incompressible case. The level set method is used for interface tracking. For the appropriate application of discontinuities at the interface, the ghost fluid method is adopted. First, a sessile droplet on a superheated surface under an electric field is simulated. Simulation results are validated against the experiments. Under an electric field, an increase in the heat flux dissipated from the surface is observed for a sessile droplet. In the next step, droplet impact on a hot surface in the range of low Weber numbers $$({We}\le 30)$$ in the presence of an electric field is simulated. According to the results, the droplet spreading radius and contact time increase with electric field strength. In addition, applying an electric field increases the heat transfer rate and total heat removal from the surface. If the potential difference between the droplet and the surface exceeds a specific value, the Leidenfrost state is suppressed. The threshold potential difference for Leidenfrost suppression decreases with Weber number and increases with surface superheat.

Toward the predictive simulation of bouncing versus coalescence in binary droplet collisions

Multi-scale simulations have been conducted in order to predict the collision outcome bouncing versus coalescence in numerical simulations. The flow on the macroscopic scale is solved by the Volume of Fluid code FS3D. On the microscopic scale, the flow in the gas film between the colliding droplets before possible coalescence is solved by a Sub-grid-scale (SGS) model, which is derived based on the classical lubrication theory and accounts for rarefaction effects. The SGS model has been implemented in FS3D and validated by means of comparing the obtained pressure field to that computed analytically and by means of direct numerical simulations. For the coupling of the SGS model with FS3D, the pressure field obtained from the SGS model applies as a pressure boundary condition on the collision plane. Employing the intersection of the PLIC surfaces with the collision plane as a coalescence criterion, the simulation has been able to yield both coalescence and bouncing. The predicted critical Weber number so far depends on the grid resolution; hence, further developments of the multi-scale approach are still required.

One-step electrodeposition of ligand-free PdPt alloy nanoparticles from water droplets: Controlling size, coverage, and elemental stoichiometry

We present a robust and facile method to produce metal nanoparticle (NP) alloys in a one-step synthesis using direct electrodeposition onto highly oriented pyrolytic graphite (HOPG). Precursor salts, H2PtCl6 and Pd(NO3)2, were dissolved in a 1 mM sodium dodecylsulfate (SDS) water droplet with 1× phosphate buffered saline solution and suspended in a dichloroethane (DCE) continuous phase. Tetrabutylammonium perchlorate was added to the DCE continuous phase to maintain charge balance during electrodeposition. NP fabrication via electrodeposition was driven by droplet collisions onto HOPG, which was biased at a potential where the metal precursor salts would reduce to their respective zero-valent atoms. Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDX) were used to study the size, coverage, and morphology of the NPs as well as the atomic stoichiometry. EDX mapping indicated homogeneous distribution of Pd and Pt at the single NP level. Homogeneously alloyed PdPt NPs were realized from this study with demonstrated control over metal composition, surface coverage, and NP size.

Numerical simulation for fluid droplet impact on discrete particles with coupled SPH-DEM method

PurposeA new coupled model is developed to simulate the interaction between fluid droplet collisions on discrete particles (DPs) by using mathematic function.Design/methodology/approachIn this model, the smoothed particle hydrodynamics (SPH) is used based on the kernel function and the time step which takes into consideration to the fluid domain in accordance with the discrete element method (DEM) with resistance function. The interaction between fluid and DPs consists of three parts, which are repulsive force, viscous shear force and attractive force caused by the capillary action. The numerical simulation of droplet collision on DPs presents the whole process of droplet motion. Otherwise, an experimental data were conducted to record the realistic process for verification.FindingsThe comparison result indicated that the numerical simulation is capable of capturing the entire process for droplet collision on DPs.Research limitations/implicationsHowever, based on the difference of experimental environment, type of the DP and setups, the maximum spreading dimeters of could not fit the experimental data exactly.Originality/valueIn sum, the coupled SPH-DEM method simulation shows that the coupled model of SPH-DEM developed an entire effectiveness process for fluid–solid interaction problem.

Numerical simulation of micron and submicron droplets in jet impinging

Micron droplet deposition onto a wall in an impinging jet is important for various applications like spray cooling, coating, fuel injection, and erosion. The impinging process is featured by abrupt velocity changes and thus complicated behaviors of the droplets. Either modeling or experiment for the droplet behaviors is still challenging. This study conducted numerical modeling and compared with an existing experiment in which concentric dual-ring deposition patterns of micron droplets were observed on the impinging plate. The modeling fully took into account of the droplet motion in the turbulent flow, the collision between the droplets and the plate, as well as the collision, that is, agglomeration among droplets. Different turbulence models, that is, the v2− f model, standard k–ε model, and Reynolds stress model, were compared. The results show that the k–ε model failed to capture the turbulent flow structures and overpredicted the turbulent fluctuations near the wall. Reynolds stress model had a good performance in flow field simulation but still failed to reproduce the dual-ring deposition pattern. Only the v2− f model reproduced the dual-ring pattern when coupled with droplet collision models. The results echoed the excellent performance of the v2− f model in the heat transfer calculation for the impinging problems. The agglomeration among droplets has insignificant influence on the deposition.

VOF simulation studies on binary seawater droplets collision

VOF simulation studies on binary seawater droplets collision

Effects of Dissolved CO2 on the Crude Oil/Water Interfacial Viscoelasticity and the Macroscopic Stability of Water-in-Crude Oil Emulsion

In CO2 flooding, the dissolution of CO2 in produced fluid may change the stability of crude oil emulsion, thereby affecting the design/operation of the gathering pipeline and oil–water separation. The purpose of this study is to investigate the stability change of crude oil emulsion and its mechanisms after the dissolution of CO2. The stability of the CO2-dissolved crude oil emulsions is determined with a self-made apparatus. The mechanisms of the stability change are uncovered from interfacial properties and bulk viscosity. It is found that the stability of the crude oil emulsions is visibly reduced with an increasing dissolved quantity of CO2. This is partly attributed to the fact that dissolved-state CO2 can lessen the interfacial dilational modulus and increase the loss angle markedly, thus lowering the structural strength and elasticity of the interface. Meanwhile, the dissolution of CO2 in crude oil can reduce its viscosity, resulting in easier collision of droplets. In view of these experimental re...

Towards a deterministic composite collision outcome model for surface-tension dominated droplets

The focus of the present study is on the modeling and simulation of coalescence of surface-tension dominated liquid droplets in a gaseous environment. In the framework of a four-way coupled Euler-Lagrange approach using the large-eddy simulation technique, an improved composite collision outcome model identifying the four regimes of binary collisions of such droplets (bouncing, fast coalescence, reflexive and stretching separation) is assembled based on well-known correlations. A specific feature is that a hard-sphere model in combination with a deterministic collision detection is applied and hence the stochastic parcel approach often used for spray simulations is obsolete. In this composite model the bounding curves between the regimes mentioned before are taken from available experiments and described by well-known analytic correlations. The main objective is to provide a compilation of the different modeling assumptions resulting in a consistent model for the entire regime. Furthermore, the composite model is improved by introducing an additional condition to consider the overlapping region of the stretching and reflexive separation regimes at high Weber numbers. The outcome of a binary collision is identified based on the collision Weber number, the dimensionless impact parameter and the droplet size ratio. The results of each collision is treated separately with regard to the collision regime found, whereas the formation of satellite droplets during stretching and reflexive separation is currently not taken into account. Additionally, a droplet injection model for spray systems is introduced to specify the injected mass, the position, the velocity and the diameters of the released droplets. In this model the initial droplet diameters mimicking the primary break-up (atomization process) of the jet are modeled by means of a number distribution function. The implementation of the composite collision outcome model is verified using the test case of an inter-impingement spray system consisting of two crossing conical water sprays. Besides correctly reproducing the experimental correlations the composite model predicts a coalescence rate which is within the experimental range found in the literature. Then, the composite collision outcome model is applied to simulate the injection process of a solid-cone non-evaporating diesel spray into a quiescent nitrogen environment and validated against experimental data. The validation study is carried out in terms of the spray tip penetration, since it is one of the most important characteristics of sprays. A detailed comparative study is carried out to investigate the effect of different simulation parameters on the spray tip penetration. The results clearly show that a four-way coupled simulation using the enhanced composite model leads to the best agreement with the experiment.

Cross-impingement and combustion of sprays in high-pressure chamber and opposed-piston compression ignition engine

Spray cross-impingement in a high-pressure chamber (10–30 atm) was studied experimentally, the results being compared to the spray opposed-impingement. The comparison was subsequently extended to the spray combustion in a model opposed-piston compression ignition engine. To account for the ambient pressure effects in collision outcomes, a recently proposed pressure-dependent droplet collision model was implemented in the KIVA-3V computer program for simulating the experiments. Compared with the widely used Estrade et al.’s and O’Rourke’s models, the pressure-dependent model produces satisfactory predictions to spray characteristics. The uncertainty of the kinetic energy recovery coefficient, which affects the post-collision characteristics of bouncing droplets, was found to cause insignificant difference in model predictions. In the high-pressure chamber, droplet collisions in cross-impingement occur earlier than those in the opposed-impingement and result in more coalescence, consequently producing larger droplet sizes. With increasing the ambient pressure, the increasing tendency of droplet bouncing diminishes the difference of these two spray impingements. In the model OPCI, the presence of strong swirling flow deflects sprays from impingement and therefore the opposed-impingement shows slightly better combustion performance by producing more spatially uniform droplet distribution. However, the spray cross-impingement enhances droplet collision hence promotes atomization in the absence of swirling flow.

Analytical parametrizations of droplet collision efficiency on cylinders – A review study

Within the scope of this work several major ice accretion parameterizations have been investigated, staring from the original Langmuir and Blodgett work 1946) on the water droplet trajectories, up to and including the Finstad et al. model (1988a) of overall collision efficiency, which is part of the current governing ISO 12494 standard (2001), thus covering a timeframe of several decades of investigations in icing modeling. This paper provides a general and mathematical review of those parameterizations, includes necessary formulae for calculations of the droplet overall collision efficiency, starting with the trajectory evaluation, and discuses underlying assumptions and approximations made by respective authors. This discussion might be of interest to icing modelers who wish to obtain more general understanding of icing modeling. As an application example, two experimental datasets have also been used for the droplet overall collision efficiency calculations and comparison. These experiments span large amount of operating conditions, thus covering significant range of the droplet inertia parameter range, K, and the overall collision efficiency, E, values which should cover majority of possible icing conditions. The results show that for higher values of the droplet inertia parameter (K), the monodisperse distribution yields good agreement with the experimental values, however, with gradual decrease in values of droplet's inertia parameter, the MVD approximation tends to underestimate the overall collision efficiency when compared with the experimental and spectrum-averaged values. Moreover, for very low values of K and E, roughly corresponding to the limits provided in ISO 12494, the MVD approximation tends to underestimate the overall collision efficiency significantly. For those cases the recalculation of droplet trajectories using full spectrum is recommended. If actual droplet distribution spectrum is not available, it is recommended to carry out the analysis using the Langmuir distributions, such as widely used ‘Langmuir D' distribution (Wright, 2008), (Bidwell, 2012), (Papadakis et al., 2007).

An Economical Model for Simulating Turbulence Enhancement of Droplet Collisions and Coalescence

AbstractClusColl, an economical simulation method for droplet motions and collisions in turbulent flows, has been developed, implemented, tested, and applied. In the Linear Eddy Model, permutations called triplet maps representing individual turbulent eddies implement turbulent advection of fluid in 1‐D. This captures flow processes down to the smallest turbulent eddy (Kolmogorov microscale), but the inertial response of small Stokes number droplets to turbulence has important features at scales down to the droplet radius, notably sub‐Kolmogorov‐scale clustering of finite‐inertia droplets that can increase collision rates significantly. Additionally, shear due to the smallest scales of turbulence increases collision rates of zero‐inertia droplets. In ClusColl, a 3‐D triplet map for droplets captures both effects. We implemented collision detection, enabling simulation of droplet collisions and coalescence, and a sedimentation treatment in ClusColl. Published direct numerical simulations (DNSs) of monodispersions were used to tune parameters. For sedimenting droplets in turbulence, ClusColl's turbulent enhancement of bidisperse collision kernels agrees reasonably well with published DNS results. We compared ClusColl and DNS coalescence growth results. For weak turbulence (ε≤100 cm2/s3), ClusColl's turbulent enhancement of coalescence growth closely matches that of the DNS. For ε≥200 cm2/s3, lack of accurate collision efficiencies precludes definitive quantitative evaluation of ClusColl's coalescence growth. In a comparison of coalescence growth dependence on the droplet size distribution width and on turbulent enhancement, ClusColl indicates that the latter dramatically accelerates cloud droplet conversion into raindrops, while the former has significantly less impact.