Droplet Radius Research Articles

Roles of Drop Size Distribution and Turbulence in Autoconversion Based on Lagrangian Cloud Model Simulations

AbstractThe roles of the drop size distribution (DSD) and turbulence in the autoconversion rate A are investigated by analyzing Lagrangian cloud model (LCM) data for shallow cumulus clouds. The correlations of DSD and turbulence with other cloud parameters are estimated, and they are applied to parameterize their effects on A. A new parameterization of A based on this analysis is proposed: with , where is the cloud water mixing ratio, and are the number concentration and the volume mean radius of cloud droplets, is the dissipation rate, is the threshold value of , H is the Heaviside step function, and X, , and b are constants. Here, represents the effect of DSD via its correlation with and , while represents the effect of gravitational collisional growth for a given DSD and turbulence. The correlation between turbulence and DSD makes b larger than expected from turbulence‐induced collision enhancement only. The effects of DSD and turbulence and their correlations with and explain a wide range of exponent values of and in many existing parameterizations of A. The new parameterization is compared with the LCM data and applied to a bulk cloud model (BCM) while clarifying the difference between the cloud droplet mixing processes in the LCM and BCM. The importance of DSD and turbulence in raindrop formation in shallow cumulus clouds is shown by comparing the A results with and without these effects.

Condensation Heat Transfer Correlation for Micro/Nanostructure Properties of Surfaces.

Condensation, which can be observed in nature as a phase change heat transfer phenomenon, is a critical phenomenon in industrial fields such as power generation, water desalination, and environmental control. Many existing studies have applied surfaces with different wettability by controlling the surface topology to enhance condensation heat transfer. However, the industrial applicability is close to zero due to the limited size and shape of surfaces and low supersaturation conditions. Here, we regulate the surface topology of large-area copper tubes, which are representative industrial metals. We fabricated four copper tubes with different surface structures. We analyzed the condensation phenomenon of the modified tube under specific supersaturation conditions by measuring the overall heat transfer coefficient. We analyzed the condensation phenomenon by measuring the condensation heat transfer coefficient. We have recognized that there is a difference between the maximum droplet radius and the droplet detaching frequency depending on the size and shape of the structure. We measured the contact angle and contact angle hysteresis to accurately analyze the droplet behavior on each surface. As a result, we show that there is a correlation between contact angle hysteresis (CAH) and the total heat transfer coefficient, indicating heat transfer performance. These findings can be applied when evaluating surfaces with excellent condensation heat transfer performance for use in real industrial environments, which can dramatically reduce time and cost.

Growth of a fluid-infused patch from droplet drainage into a thin porous layer

Growth of a fluid-infused patch on a thin porous layer, e.g. on a piece of paper or cloth, is related to the transmission of virus particles through exhaled droplets and aerosols. We present a theoretical model to describe how a wet patch develops gradually through imbibition, once a sessile droplet attaches at a permeable surface and drains gradually into a thin porous layer. Two limiting cases are considered based on different assumptions on the motion of the contact line during the coupled process of drop drainage and patch growth: (i) the apparent contact angle remains unchanged, so the radius of a sessile droplet decreases with time; and (ii) the location of the contact line remains pinned, so the contact angle decreases as time progresses. The model leads to evolution pathways for both the droplet and the fluid film within the porous layer, without introducing arbitrary fitting parameters. Potential implications of the model and its solutions are also discussed briefly in the context of the outspread of COVID-19, employing physical parameters for exhaled droplets, paper and cloth.

Carbon capture in laval nozzles with different bicubic parametric curves and translation of witoszynski curves

This work investigates the influence of convergent curve of supersonic nozzle on the carbon separation process. The CFD model based on nucleation and growth theory, second-order upwind scheme and density-based solution method are employed to predict the CO2 supersonic separation process in the nozzle. The effects of bicubic parametric curve and translation of Witoszynski curve on flow characteristics and spontaneous condensation characteristics are illustrated. The results show that the mixed gas accelerates and deviates from the equilibrium state in the Laval nozzle, and nucleation occurs when the supersaturation is greater than 1.81. After nucleation, gas enters the droplet growth stage, during which mass and heat transfer are carried out between gas and liquid phase, and the droplet radius increases continuously. With the increase of the parameter xm in the bicubic parametric curve equation and the axis shift quantity yh in the translation of Witoszynski curve equation, the flow parameters in the nozzle change more violently, the nucleation location moves to the nozzle exit, and the interphase mass transfer rate and liquid fraction decrease in varying degrees.

Numerical investigation on the coupling effect of sessile ethanol droplet evaporation and the induced thermal flow in its pure vapor environment at low pressure

In order to reveal the coupling characteristics of sessile ethanol droplet evaporation and induced thermal flow in its pure vapor system at low pressure, a series of three-dimensional numerical simulations were carried out on the ethanol droplet evaporation on a copper substrate. The droplet radius is 2.5 mm. The droplet height ranges from 2.2 to 0.4 mm. To investigate the effect of vapor pressure, two pressure ratios (η) of 0.9 and 0.6 are chosen. The results show that, when η = 0.9, regardless of the droplet height, the surface temperature distribution in most areas is always uniform. However, when η = 0.6, several surface thermal patterns appear. Because of the evaporation, the substrate temperature distribution always has the lowest value near the contact line. The thermal pattern evolution will affect the evaporation rate and the substrate temperature distribution dynamically. When η = 0.6, the evaporation rate shows a non-monotonic variation trend with the decrease of the height. Although the droplet size is larger than the capillary length, buoyancy has little effect on the thermal pattern evolution and evaporation rate.

Asymmetric Condensation Characteristics during Dropwise Condensation in the Presence of Non-condensable Gas: A Lattice Boltzmann Study.

In this work, the condensation characteristics of droplets considering the non-condensable gas with different interaction effects are numerically studied utilizing a multicomponent multiphase thermal lattice Boltzmann (LB) model, with a special focus on the asymmetric nature induced by the interaction effect. The results demonstrate that for isolated-like growth with negligible interactions, the condensation characteristics, that is, the concentration profile, the temperature distribution, and the flow pattern, are typically symmetric in nature. For the growth regime in a pattern, the droplet has to compete with its neighbors for catching vapor, which leads to an overlapping concentration profile (namely the interaction effect). The distribution of the condensation flux on the droplet surface is consequently modified, which contributes to the asymmetric flow pattern and temperature profile. The condensation characteristics for droplet growth in a pattern present an asymmetric nature. Significantly, the asymmetric condensation flux resulting from the interaction effect can induce droplet motion. The results further demonstrate that the interaction strongly depends on the droplet's spatial and size distribution, including two crucial parameters, namely the inter-distance and relative size of droplets. The asymmetric condensation characteristics are consequently dependent on the difference in the interaction intensities on both sides of the droplet. Finally, we demonstrate numerically and theoretically that the evolution of the droplet radius versus time can be suitably described by a power law; the corresponding exponent is kept at a constant of 0.50 for isolated-like growth and is strongly sensitive to the interaction effect for the growth in a pattern.

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

A model of droplet evaporation: New mathematical developments

A previously developed model for mono-component droplet evaporation is revisited using new mathematical tools for its analysis. The analysis is based on steady-state mass, momentum, and energy balance equations for the vapor and air mixture surrounding a droplet. The previously obtained solution to these equations was based on the assumption that the parameter ε (proportional to the squared ratio of the diffusion coefficient and droplet radius) is equal to zero. The analysis presented in the paper is based on the method of integral manifolds, and it allowed us to present the droplet evaporation rate as the sum of the evaporation rate predicted by the model based on the assumption that ε=0 and the correction proportional to ε. The correction is shown to be particularly important in the case of small water and methanol droplets (diameters less than 5 μm) evaporating in air at low pressure (0.1 atm.). In this case, this correction could reach 35% of the original evaporation rate. In the case of evaporation of relatively large droplets (with radii more than 10 μm) in air at atmospheric and higher pressures, these corrections are shown to be small (less than 10−3 of the evaporation rate predicted by the model based on the assumption that ε=0).

Simulation of coalescence dynamics of droplets on surfaces with different wettabilities

The head-on-collision coalescence dynamics for droplets on surfaces with different wettabilities was numerically investigated by using the method of coupled level set and volume of fluid, and a high-speed video experiment was used to validate the simulation results. The simulated coalescence behavior of droplets is consistent with the experiment results. We compared droplets with different Weber numbers (3.67 ≤ We ≤ 50) coalescing on solid surfaces of different wettabilities and contact angles (80° ≤ α ≤ 160°). The result is a regional division diagram that relates Weber number and contact angle based on different coalescence phenomena. The factors causing droplet deposition, air entrapment, bounce, and partial bounce during collision coalescence are described based on an analysis of interactions involving inertial forces, surface tension, and wall adhesion forces. Furthermore, the effect of Weber number and contact angle on droplet coalescence behavior is elaborated by analyzing the relationship between coalescence time and wettability radius under different Weber numbers and contact angles. Finally, through an energy analysis, we explain the maximum spreading radius and oscillation of droplets with different Weber numbers on solid surfaces with different wettabilities and in the process of head-on-collision coalescence.

Molecular Dynamics Simulation of Spreading of Mixture Droplets on Chemically Heterogeneous Surfaces.

The dynamic spreading process of mixed droplets on chemically heterogeneous surfaces has attracted significant attention owing to its extensive industrial applications. The spreading of mixture droplets on a chemically heterogeneous surface is more complex than that for pure fluid droplets and needs to be understood further. In this study, molecular dynamic simulations were performed to investigate the dynamic spreading process of R32/R1234yf mixture droplets and water/ethanol mixture droplets of radius 4.7-6.5 nm with different compositions, on chemically heterogeneous surfaces. The variation in the relative spreading radius with time was analyzed and compared with the molecular kinetic theory. It was observed that for the R32/R1234yf mixture, the actual component mole fraction did not deviate from the nominal one in the triple contact region, and the dynamic spreading behavior was identical to that for the pure fluids. Meanwhile, the converse was true for the ethanol/water mixture. The molecular kinetic theory could accurately predict the spreading of droplets for R32/R1234yf mixtures when the mixture properties were used. However, this was not feasible for ethanol/water mixtures. It was observed that the local physical properties in the triple contact line (including the mole fraction and the lyophilic and lyophobic area ratio) play key roles in the spreading of the ethanol/water mixture droplets. The prediction of the dynamic spreading of water/ethanol mixture droplets on chemically heterogeneous surfaces can be improved significantly by using local properties to modify the molecular kinetic theory.

Optimization of the pitch to chord ratio for a cascade turbine blade in wet steam flow

• Optimization by GA is used to gain the suitable pitch to chord ratio for a blade. • WF, ADR, MO, PL, and IE at the exit of the cascade turbine blade are the objectives. • A pitch to chord ratio of Pi/AC = 0.76 is suggested. • The modified Zweifel coefficient for wet steam flow in the cascade is proposed C Z F = 0.62 . • The wetness and radius decrease 3.59% and 1.94%, and the momentum increases 7.28%. This study has used shape optimization by the genetic algorithm to gain the suitable pitch to axial chord ratio for a cascade turbine blade. The innovation of the present paper is the modification of the Zweifel coefficient for the wet steam flow passing through the steam turbine cascade. Wetness fraction (WF), average droplet radius (ADR), momentum (MO), pressure loss (PL), and isentropic efficiency (IE) at the exit of the cascade turbine blade in wet steam flow are selected as the objective functions. The ultimate goal was to minimize the wetness fraction, average droplet radius at the outlet of the blade, and pressure losses of the passage and maximize the efficiency and momentum at the outlet together. The Navier-Stokes equations, S S T k - ω turbulence model, and the Eulerian-Eulerian approach are applied for modeling the condensing flow. The agreement gained between the numerical results and the experimental results is satisfactory. A pitch to axial chord ratio of Pi/AC = 0.76 is suggested, and the modified Zweifel coefficient for wet steam flow in the cascade is proposed C Z F = 0.62 . In the optimal case, the wetness fraction and the average droplet radius at the outlet decrease 3.59% and 1.94%, respectively, and the momentum increases 7.28%. In addition, the optimal case compares with original case, the isentropic efficiency decreases 2.48% and the pressure losses increases 2.15%.

Numerical simulation of real gas one-component two-phase flow using a Roe-based scheme

The objective of this paper is to derive and test a set of algebraic equations describing the fluid flow based on the Euler equations. The derivation is based on the finite volume approach and the benefits of Roe’s approach are preserved. A further objective is that the set of algebraic equations can be solved by incorporating an equation of state as complex as for example the EOS for CO2 given by Span and Wager albeit this equation of state is not used during the derivation. The particular innovation stems from the assumption made during the derivation. Only small changes of fluid properties are assumed at first. This allows to use the equation of state of a thermally perfect gas (specific heat capacity constant) to derive Roe’s matrix. Effectively this leads to the set of equations already derived by Roe. But the determination of any state variables and in particular the Roe-averaged speed of sound is done by means of the previously chosen EOS. Thereafter, the obtained set of equations is utilised to calculate flows with small to large gradients. It turns out that the derived scheme gives results in good agreement even for Sod’s problem and flows in Laval nozzles with the compressibility factor changing from 1.5 to 0.5 across the shock. Subsequently, the solver is used for predicting condensing steam flows. Besides the calculation of thermodynamic properties also the radii of droplets are derived. The results obtained could be used for optimising the numerical stability of flow prediction in steam turbines. The integration of the EOS for CO2 given by Span and Wager in the Roe-based solver could also be applied to the investigation of Joule cycles operated with Carbon Dioxide in a supercritical state, thus increasing the accuracy. Due to the novel way of integrating an arbitrary equation of state into a numerical scheme, it also represents a contribution to current developments in the field of computational fluid dynamics.

Theoretical analysis on condensation heat transfer on the hydrophobic–hydrophilic hybrid surfaces with the impact of the Marangoni convection

Condensation occurs in the forms of filmwise condensation and dropwise condensation. Over the past decade, hybrid hydrophobic–hydrophilic surfaces have received significant attention due to their potential to enhance the heat transfer rate compared to complete dropwise condensation. The maximum condensed droplet radius in the hydrophobic region has a considerable impact on the heat transfer characteristics. This paper discusses the effect of the maximum droplet radius on hybrid surface heat transfer characteristics. On top of that, Marangoni convection effects originated due to the temperature gradient as a heat transfer resistance on the heat transfer rate is considered, modelled and investigated. Three models were investigated in this paper. The results indicate that there is an optimum maximum droplet radius for each model that can improve the heat transfer rate. When the filmwise region width increases from 0.5 mm to 1.0 mm, the optimum maximum droplet radius increases from 0.25 mm to 0.3 mm. For a fixated droplet contact angle and filmwise and dropwise region widths, the hybrid heat flux of the smooth dropwise model can be up to 1.55 times higher than that of the Cassie–Baxter model, and the hybrid heat flux of the smooth dropwise model can be up to 1.38 time higher than that of the Wenzel state. Finally, considering Marangoni convection showed up to a 30% increase in the heat transfer coefficient in some cases.

NaCl Salts in Finite Aqueous Environments at the Fine Particle Marine Aerosol Scale

We investigated isolated sodium/chloride aqueous droplets at the microscopic level, which comprise from about 5k to 1M water molecules and whose salt concentrations are 0.2$m$ (brackish water) and 0.6$m$ (sea water), by means of molecular dynamics simulations based on an \emph{ab initio}-based polarizable force field. The size of our largest droplets is at the submicron particle marine aerosol scale. From our simulations, we investigated ion spatial distributions, ion aggregates (size, composition, lifetime and distribution), droplet surface potentials and the densities of the water vapor surrounding the droplets. Regarding ions, they form a weak electrostatic double layer extending from the droplet boundary to 2~nm within the droplet interior. Free $\mathrm{Na^+}$ and ion aggregates are more repelled from the boundary than free $\mathrm{Cl^-}$. Most of the droplet properties depend on the droplet radius $R$ according to the standard formula $A=A_\infty(1 - 2 \delta/R) $, where $A_\infty$ is the bulk magnitude of the quantity $A$ and $\delta$ is a length at most at the~nm scale. Regarding the water vapor densities they obey a Kelvin relation corresponding to a surface tension whose Tolman length is negative and at the 1~nm scale. That length is about one order of magnitude larger than for pure water droplets, however it is weak enough to support the reliability of a standard Kelvin term (based on planar interface surface tensions and water densities) and of the related K{\"o}lher equation to model sub-micron salty aerosols.

The mechanisms of underwater wet flux-cored arc welding assisted by ultrasonic frequency pulse high-current

An ultrasonic frequency pulse high-current (UFPHC) was utilized to improve the stability of underwater wet flux-cored arc welding on Q235 steel. Based on the studies of the bubble evolution, arc behavior, droplet geometry, weld formation, and mechanical properties of the joint, the arc extinguishing phenomenon was suppressed effectively by the additional UFPHC, which decreased the amount of spatter on the workpiece and improved the appearance of the weld. The additional UFPHC reduced the average droplet radius by 40% and increased the average transition frequency by 99%, compared with the same value of additional welding current. The UFPHC enabled to decrease the hardness of the heat-affected zone by 15% due to the production of less martensite compared to results obtained by simply increasing the welding current. The vibration effect of the UFPHC in the welding pool was indirectly confirmed by the significantly decreased porosities in the final joint. The morphology of the impact fracture of different welding cases showed that the UFPHC was helpful to decrease the brittle fracture area in the weld joint and increase the value of the impact toughness for the weld joint.

Estimation radius regression in PLIC-VOF method for droplet evaporation

Heat & fluid flow conservation equations of carburant liquid droplet are solved by a semi-implicit method of the Volume Of Fluid ( VOF ) scheme. A new technique of the droplet radius regression estimation based on the Piece-wise Linear Interface Calculation ( PLIC ) is developed. Numerical computation is performed for stagnant carburant droplets in evaporation in natural convection (which takes into consideration the buoyancy forces) and in an air atmosphere at a pressure of 1 bar. The results are presented in the form of radius, area and mass regressions, volumetric mass flow, liquid temperature, surface temperature, and vapor temperature evolutions by taking into account the influence of the ambient temperature, the initial radius, and the component variations. Using the time evolution of the color function, our radius regression estimation technique is related to the instant detection of the liquid volume fraction. This regression is not affected by the changing of the droplet’s shape nor the temperature collecting and synchronization with the method for the evaporation analysis.

Contact time of a droplet impacting hydrophobic surfaces

A droplet impacting hydrophobic surfaces is explored via lattice Boltzmann method simulations. Dynamics of the spreading and retraction processes of the impacting droplet with different surface wettability (θ = 106°–145°) at various Weber numbers (We = 15–35) and Reynolds numbers (Re = 235–359) are investigated. It indicates that the spreading time, the time interval from a droplet just touching the surface to reaching the maximum spreading diameter, is a fixed value that is not related to the above factors. The retraction time, the time interval from a droplet reaching the maximum spreading diameter to rebounding the surface, is just closely dependent on the surface wettability. Therefore, the contact time, the sum of the spreading time and the retraction time, is mainly related to the retraction process and dependent on the surface wettability. The time is commonly normalized as the non-dimensional time, τ = t/(ρR03/σ)1/2, where R0 is the initial droplet radius and σ is the surface tension. The emphasis of this work is placed on establishing a relationship of the contact time with the surface wettability. Based on simulation research and theoretical modeling, the surface wettability is incorporated into the scaling law of contact time, and a modified scaling law, tc ∼ (R0/V0)We1/2(1 − cosθ)−1/2, where V0 denotes the initial impact velocity, is established for a droplet impacting hydrophobic surfaces of θ = 106°–145°and We = 15–35. It is demonstrated that the scale relationship can be well applied to calculate the contact time of a droplet impacting hydrophobic surfaces for moderate Weber numbers.

Measurement of mechanical properties of liquid by observing droplet oscillation on substrates

In this paper, we introduce a method to measure the surface tension of a droplet on a solid substrate by observing the resonance oscillation excited by applying Maxwell stress using electric field tweezers in a noncontact manner. Additionally, we measured the frequency spectrum of the oscillation amplitude using a stroboscopic imaging technique. The resonance frequency of the droplet was inversely proportional to the 3/2th power of the droplet radius, with a contact angle of approximately π/2 rad. The acquired result is in good agreement with the theory derived by extending the established formula for a free-sphere droplet. Furthermore, the contact angle dependence of the resonance frequency can be qualitatively explained based on the behavior of waves on a confined liquid surface.

Effects of cloud condensation nuclei concentration on the evolution of severe convective storms

Idealized three-dimensional storm simulations were created to investigate the effects of varying initial cloud condensation nuclei (CCN) concentrations (CCNCs) ahead of the severe convective storm using the Weather Research and Forecasting (WRF) model with the National Severe Storms Laboratory (NSSL) double-moment microphysics scheme. The simulations showed that increased initial CCNC ahead of the storm (CCN mainly entrains from the boundary layer) increased the rain- and hailfall intensities. Multiple strong centers of rain- and hailfall appeared at the surface along the moving direction of the convective storm. The increased initial CCNC ahead of the storm played an important role in the warm cloud processes. As the CCNC increased, a large amount of CCN enter the cloud and was activated, which decreased the equivalent sphere radius of the cloud droplets and increased the content of cloud droplets. Thus, the equivalent sphere radius of the raindrops increased due to the enhanced collection process of cloud droplets by raindrops. Furthermore, the collection processes of supercooled cloud droplets and raindrops by hail were also enhanced as the CCNC increased, resulting in an increase in the content of hail. These processes further influenced the cold cloud processes. The increase in CCNC ahead of the storm accelerated the downdraft by the cloud microphysical processes and formed a stronger cold pool and front outflow. These thermodynamic and dynamic processes were favorable for increasing the updraft and thus enhancing the cloud microphysical processes. Therefore, the increase in the CCNC ahead of the storm created a positive feedback mechanism to the thermodynamic and dynamic processes by the cloud microphysical processes, which promoted the development and maintenance of the storm and increased rain- and hailfall intensities at the surface.

Compressible gas-droplet flow and heat transfer behind a condensation shock in an expanding channel

A two-fluid mathematical model of a supersonic gas-droplet mixture flow with account of droplet growth due to vapor condensation behind a condensation shock in a plane expanding channel is constructed. The flow structure in both the inviscid core and the two-phase boundary layer assumed to be laminar is studied numerically. The range of flow parameters is considered in which the spontaneous condensation zone (“condensation shock”) is fairly narrow, and just behind this shock thermal parameters of the phases almost reach thermodynamic equilibrium. Downstream, the droplet radius continues to grow due to the flow expansion and further vapor condensation. Of primary concern is the flow region where the droplets become sufficiently inertial to travel with a velocity slip, and hence to model adequately the velocity and temperature fields in both phases a two-fluid model is required. In addition to the Stokes drag, the Saffman lifting force exerted on the droplets in the boundary layer is taken into account. The Saffman force results in droplet deposition and the formation of a thin liquid film on the channel walls. A parametric numerical analysis of the two-phase flow structure in the inviscid flow region and in the near-wall boundary layer is performed, and the effects of phase transitions (droplet condensation and evaporation, as well as the film formation) on the reduction of the adiabatic channel wall temperature are analyzed.