Turbulent Droplet Research Articles

On respiratory droplets and face masks.

Face mask filters—textile, surgical, or respiratory—are widely used in an effort to limit the spread of airborne viral infections. Our understanding of the droplet dynamics around a face mask filter, including the droplet containment and leakage from and passing through the cover, is incomplete. We present a fluid dynamics study of the transmission of respiratory droplets through and around a face mask filter. By employing multiphase computational fluid dynamics in a fully coupled Eulerian–Lagrangian framework, we investigate the droplet dynamics induced by a mild coughing incident and examine the fluid dynamics phenomena affecting the mask efficiency. The model takes into account turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. The model mimics real events by using data, which closely resemble cough experiments. The study shows that the criteria employed for assessing the face mask performance must be modified to take into account the penetration dynamics of airborne droplet transmission, the fluid dynamics leakage around the filter, and reduction of efficiency during cough cycles. A new criterion for calculating more accurately the mask efficiency by taking into account the penetration dynamics is proposed. We show that the use of masks will reduce the airborne droplet transmission and will also protect the wearer from the droplets expelled from other subjects. However, many droplets still spread around and away from the cover, cumulatively, during cough cycles. Therefore, the use of a mask does not provide complete protection, and social distancing remains important during a pandemic. The implications of the reduced mask efficiency and respiratory droplet transmission away from the mask are even more critical for healthcare workers. The results of this study provide evidence of droplet transmission prevention by face masks, which can guide their use and further improvement.

On coughing and airborne droplet transmission to humans.

Our understanding of the mechanisms of airborne transmission of viruses is incomplete. This paper employs computational multiphase fluid dynamics and heat transfer to investigate transport, dispersion, and evaporation of saliva particles arising from a human cough. An ejection process of saliva droplets in air was applied to mimic the real event of a human cough. We employ an advanced three-dimensional model based on fully coupled Eulerian–Lagrangian techniques that take into account the relative humidity, turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. We computationally investigate the effect of wind speed on social distancing. For a mild human cough in air at 20 °C and 50% relative humidity, we found that human saliva-disease-carrier droplets may travel up to unexpected considerable distances depending on the wind speed. When the wind speed was approximately zero, the saliva droplets did not travel 2 m, which is within the social distancing recommendations. However, at wind speeds varying from 4 km/h to 15 km/h, we found that the saliva droplets can travel up to 6 m with a decrease in the concentration and liquid droplet size in the wind direction. Our findings imply that considering the environmental conditions, the 2 m social distance may not be sufficient. Further research is required to quantify the influence of parameters such as the environment’s relative humidity and temperature among others.

Surface Density Function Evolution in Spherically Expanding Flames in Globally Stoichiometric Droplet-laden Mixtures

ABSTRACT The statistical behaviors of the magnitude of the reaction progress variable gradient (alternatively known as the Surface Density Function (SDF)) and the strain rates, which affect the SDF evolution, have been analyzed using three-dimensional Direct Numerical Simulations (DNS) of spherically expanding flames in globally stoichiometric initially mono-sized droplet-laden mixtures for different initial turbulence intensities and droplet diameters. It has been found that gaseous phase combustion predominantly takes place under fuel–lean mode and this tendency strengthens for large droplets and high turbulence intensities. The mean values of flame displacement speed, dilatation rate and normal strain rate decrease with increasing turbulence intensity and droplet diameter. By contrast, the mean tangential strain rate increases with increasing turbulence intensity for all droplet diameters. The mean normal strain rate induced by flame propagation remains negative but its magnitude decreases with increasing droplet size and turbulence intensity. The mean tangential strain rate induced by flame propagation (alternatively curvature stretch rate) assumes negative values except for the laminar flame with small droplets. The mean effective normal strain rate has been found to assume predominantly positive values and increases with increasing turbulence intensity for the droplet cases considered here. The mean effective tangential strain rate (alternatively stretch rate) is found to assume mostly negative values except for the laminar case with small droplets. The mean effective tangential strain rate decreases with increasing droplet size, which leads to a smaller extent of flame surface area generation for flames with larger droplets.

A robust virtual-camera 3D shape reconstruction of deforming bubbles/droplets with additional physical constraints

Bubbles and droplets in strong turbulence exhibit non-affine deformation, especially near a breakup event when the strong necking and interfacial instability begin to play roles. The virtual-camera (VC) method was designed and implemented to mitigate the limited-angle reconstruction problem for complex bubble/droplet geometries. The VC method incorporates the additional physical constraint of minimum surface curvature into reconstruction. This framework helps to reduce the reconstruction uncertainty for experiments studying multiphase flows that use a limited number of cameras, non-ideal camera positions, or the combination of both. The method was tested with three synthetic geometries– sphere, ellipsoid, and dumbbell–that represent the undeformed, gently-deformed, and severely-deformed bubbles. In addition, a DNS dataset of bubbles with a 2% void fraction in turbulent channel flow was also utilized to generate a synthetic dataset for tests, and the volume overestimation was found to decrease from over 20% to about 10% after implementing the VC method. Finally, the method was applied to the experimental dataset of bubble-turbulence interaction, and the result shows over 20% improvement in volume estimation. An indirect uncertainty quantification that relies on the bubble aspect ratio and orientation has also been developed to estimate the bubble reconstruction uncertainty in each frame. This allows a more selective postprocessing step to obtain the statistics of deformation and breakup based on the quality of reconstruction.

Large-Eddy Simulations of Oil Droplet Aerosol Transport in the Marine Atmospheric Boundary Layer

In this study, a hybrid large-eddy simulation (LES) model is developed and applied to simulate the transport of oil droplet aerosols in wind over progressive water waves. The LES model employs a hybrid spectral and finite difference method for simulating the wind turbulence and a bounded finite-volume method for modeling the oil aerosol transport. Using a wave-following coordinate system and computational grid, the LES model captures the turbulent flow and oil aerosol fields in the region adjacent to the unsteady wave surface. A flat-surface case with prescribed roughness (representing a pure wind-sea) and a wavy-surface case with regular plane progressive 100 m long waves (representing long-crest long-wavelength ocean swells) are considered to illustrate the capability of the LES model and study the effects of long progressive waves on the transport of oil droplet aerosols with four different droplet diameters. The simulation results and statistical analysis reveal enhanced suspension of oil droplets in wind turbulence due to strong disturbance from the long progressive waves. The spatial distribution of the aerosol concentration also exhibits considerable streamwise variations that correlate with the phase of the long progressive waves.

Collision of Particles and Droplets in Turbulent Two-Phase Flows

The problems and features of an accounting of the collisions of particles (droplets) in turbulent two-phase flows are considered. The developed approaches for the determination of collision nuclei of monodisperse and bidisperse particles (droplets) in uniform isotropic turbulence, as well as under the combined action of turbulence, averaged velocity gradient, and gravity, are described. The results of experimental and theoretical calculations of the effect of collisions on the characteristics of two-phase jet flows and flows in channels are presented and analyzed.

Understanding aerosol–cloud interactions through modeling the development of orographic cumulus congestus during IPHEx

Abstract. A new cloud parcel model (CPM) including activation, condensation, collision–coalescence, and lateral entrainment processes is used to investigate aerosol–cloud interactions (ACIs) in cumulus development prior to rainfall onset. The CPM was applied with surface aerosol measurements to predict the vertical structure of cloud development at early stages, and the model results were evaluated against airborne observations of cloud microphysics and thermodynamic conditions collected during the Integrated Precipitation and Hydrology Experiment (IPHEx) in the inner region of the southern Appalachian Mountains (SAM). Sensitivity analysis was conducted to examine the model response to variations in key ACI physiochemical parameters and initial conditions. The CPM sensitivities mirror those found in parcel models without entrainment and collision–coalescence, except for the evolution of the droplet spectrum and liquid water content with height. Simulated cloud droplet number concentrations (CDNCs) exhibit high sensitivity to variations in the initial aerosol concentration at cloud base, but weak sensitivity to bulk aerosol hygroscopicity. The condensation coefficient ac plays a governing role in determining the evolution of CDNC, liquid water content (LWC), and cloud droplet spectra (CDS) in time and with height. Lower values of ac lead to higher CDNCs and broader CDS above cloud base, and higher maximum supersaturation near cloud base. Analysis of model simulations reveals that competitive interference among turbulent dispersion, activation, and droplet growth processes modulates spectral width and explains the emergence of bimodal CDS and CDNC heterogeneity in aircraft measurements from different cloud regions and at different heights. Parameterization of nonlinear interactions among entrainment, condensational growth, and collision–coalescence processes is therefore necessary to simulate the vertical structures of CDNCs and CDSs in convective clouds. Comparisons of model predictions with data suggest that the representation of lateral entrainment remains challenging due to the spatial heterogeneity of the convective boundary layer and the intricate 3-D circulations in mountainous regions.

A Model for Fuel Spray Formation with Atomizing Air

The formation of a liquid spray emanating from a nozzle in the presence of atomizing air was studied using a computational model approach that accounted for the deformation and break up of droplets. Particular attention was given to the formation of sprays under non-swirling flow conditions. The instantaneous fluctuating fluid velocity and velocity gradient components were evaluated with the use of a probability density function (PDF)-based Langevin equation. Motions of atomized fuel droplets were analyzed, and ensemble and time averaging were used for evaluating the statistical properties of the spray. Effects of shape change of droplets, and their breakup, as well as evaporation, were included in the model. The simulation results showed that the mean-square fluctuation velocities of the droplets vary significantly with their size and shape. Furthermore, the mean-square fluctuation velocities of the evaporating droplet differed somewhat from non-evaporating droplets. Droplet turbulence diffusivities, however, were found to be close to the diffusivity of fluid point particles. The droplet velocity, concentration, and size of the simulated spray were compared with the experimental data and reasonable agreement was found.

The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave

The prediction of droplet sizes in emulsions is important for fields ranging from the chemical process industry to emergency planning in the event of an underwater oil release. Typically scale models have needed to be built and the results scaled up, but as computational resources have grown and turbulence models have matured it has become possible to use computational fluid dynamics (CFD) to simulate the behaviour of the fluid/s. While direct simulation of multiphase breakup at high Reynolds number is currently computationally impractical, this paper looks into the use of CFD along with a correlation function based on maximum turbulent kinetic energy dissipation rate to predict the Sauter mean diameter of droplets in a 1 in. baffle-and-vane type autoclave. The results show that using a RNG-k∊ turbulence model with a simplified 2D geometry gave droplet sizes within 26.2 μm of the Sauter mean diameter observed in experiments with no additional tuning of parameters. Correlating pipe and autoclave flows through the Reynolds number and the turbulent kinetic energy dissipation rate was also investigated. Using the traditional definitions of the Reynolds numbers the correlation is poor, the coefficient of determination of the linear fit to the log-log data is 0.64. The first modification replaced the diameter of the blade as characteristic length with the tip swept circumference which increased the coefficient of determination to 0.960. A further modification using data obtained from the turbulent fields of the simulation showed a significant improvement with the coefficient of determination increasing to 0.988.

Impact of spacer on inter sub-channel mixing of coolant in nuclear fuel bundle: a survey and future patterns of research and advances

Abstract Broad efforts have been ended in the last decade for the development of spacer and its effect on droplets that present in the vapour core. The spacers operate as droplet collectors and accumulate considerable amount of the droplet flux in an emblematic spacer section. This development paved the way for engineers and researchers to come up with spacer that exhibit better inter subchannel mixing in the reactor. The review is based on the correlation developed by different researchers for the spacer modelling, grey areas and challenges for further improvement in the prediction and some of the good models have been recommended. The effect of spacer on liquid films and droplet depositions before spacer and near spacer have been studied and finally based on this investigation a proposed LDV measurement techniques have been applied on 1/12th segment of Advanced Heavy Water Reactor for further analysis of spacer effect on annular flow. Efforts are made to uncover the investigated gaps from the precedent literatures, as an effect of which it is concluded that there is extremely inadequate work published in the field of thermal-hydraulics incorporating spacer effect such as turbulent mixing, droplet deposition and liquid film thickness in the case of AHWR.

Experimental investigation of atomization and droplet turbulence characteristics of a twin-fluid nozzle with different self-excited vibrating cavity structures

The spray atomization properties and droplet turbulence characteristics of a twin-fluid nozzle with and without a self-excited vibrating cavity are investigated and compared using a phase Doppler particle analyzer (PDPA). In the presence of a self-excited vibrating cavity, the spray cone angle and the droplet number concentration increase by nearly 50% and 55%, respectively, and the droplet Sauter mean diameter (SMD) and the mean axial velocity decrease by approximately 40% and 33.8%, respectively. However, the root mean squared (RMS) velocity fluctuation and the droplet turbulence simultaneously worsen. By combining the comparative analysis of the dimensionless parameters of the Reynolds number, Weber number and Ohnesorge number, the results indicate the significant role of the self-excited vibrating cavity in promoting twin-fluid atomization. Quantitative measurements using PDPA with the twin-fluid nozzle in the absence and presence of a self-excited vibrating cavity reveal the effects of the gas to liquid mass flow rate ratio (GLR) on the spray cone angle and the axial distribution of droplet SMD, mean axial velocity and number concentration. The fixed gas flow rate of 0.0003 kg·s−1 and the liquid flow rate of 0.0077 kg·s−1 are selected as representative, and the influence of the structural parameters of a self-excited vibrating cavity on the droplet turbulence characteristics are further investigated. The mean axial velocity along the radial direction first increases as a result of extrusion and diffusion and then decreases, possibly due to the drag effect caused by the surrounding air and droplets; it decreases along the axial direction due to the air resistance. The droplet mean velocity increases with an increase in orifice diameter or orifice depth, and a superior velocity characteristic is obtained when the orifice diameter is 2.5 mm or when the orifice depth is 2.5 mm. Meanwhile, the droplet mean velocity first increases and then decreases with the increase in the distance between the nozzle outlet and the self-excited vibrating cavity, and an appropriate distance value of 4.0 mm is obtained. The variation of RMS velocity fluctuation along the axial direction and radial direction is consistent with the change in mean axial velocity, whereas the droplet turbulence shows an opposite trend. There is a peak of RMS velocity fluctuation and a valley of droplet turbulence at approximately 50 mm from the z-axis. Furthermore, the RMS velocity fluctuation and droplet turbulence increase with the increase in orifice diameter or orifice depth whereas that first increase and then decrease with the increase in the distance between the nozzle outlet and the self-excited vibrating cavity. Thus, the self-excited vibrating cavity profoundly influences the droplet turbulence characteristics by affecting the variation of droplet oscillation.

Droplets in isotropic turbulence: deformation and breakup statistics

The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of a drop previously introduced by Olbricht et al. (J. Non-Newtonian Fluid Mech., vol. 10, 1982, pp. 291–318) is used to predict the behaviour of the above quantities analytically.

Evaporating droplets in turbulence studied with statistically stationary homogeneous direct numerical simulation

The present paper investigates droplet laden turbulent gas flows with point droplet direct numerical simulations. A novel flow configuration is presented, which allows us to simulate statistically stationary homogeneous isotropic regions of turbulent sprays. This configuration enables a physical analysis with small statistical errors under controllable conditions. The length scales of clusters are analyzed with spectra of the droplet number density and vapor mass fraction fluctuations. The local conditions in clusters and voids are analyzed with probability density functions of the local droplet number density, local vapor mass fraction, and evaporation rate. Effects of the mass loading and Stokes number on the clustering of droplets and the mixing of vapor are characterized, and the compositions of clusters and voids are examined. As the mass loading increases from 2.5% to 12.5%, the fluctuations in the vapor mass fraction and droplet number density increase almost equally at all length scales. Clusters contain more droplets that together release more vapor, but their characteristic size remains unchanged. As the mean Stokes number increases from 1 to 4, the fluctuations in the vapor mass fraction and droplet number density decrease predominantly at small length scales. Clusters contain fewer droplets that together release less vapor, and their characteristic size increases. At a mass loading of 7.5% and a mean Stokes number of 2, clusters contain considerably more droplets and vapor than voids. Droplets located in clusters therefore evaporate more slowly than droplets located in voids.

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.

Extreme Small-Scale Clustering of Droplets in Turbulence Driven by Hydrodynamic Interactions.

We perform three-dimensional particle tracking measurements on droplets in a turbulent airflow. The droplets display the well-known preferential concentration of inertial particles, with an additional extreme clustering at the smallest scales. We explain this additional clustering phenomenon theoretically based on a Stokes-flow description of two spheres including their mutual hydrodynamic interaction and a perturbative small-inertia expansion.

Bridging the condensation–collision size gap: a direct numerical simulation of continuous droplet growth in turbulent clouds

Abstract. In most previous direct numerical simulation (DNS) studies on droplet growth in turbulence, condensational growth and collisional growth were treated separately. Studies in recent decades have postulated that small-scale turbulence may accelerate droplet collisions when droplets are still small when condensational growth is effective. This implies that both processes should be considered simultaneously to unveil the full history of droplet growth and rain formation. This paper introduces the first direct numerical simulation approach to explicitly study the continuous droplet growth by condensation and collisions inside an adiabatic ascending cloud parcel. Results from the condensation-only, collision-only, and condensation–collision experiments are compared to examine the contribution to the broadening of droplet size distribution (DSD) by the individual process and by the combined processes. Simulations of different turbulent intensities are conducted to investigate the impact of turbulence on each process and on the condensation-induced collisions. The results show that the condensational process promotes the collisions in a turbulent environment and reduces the collisions when in still air, indicating a positive impact of condensation on turbulent collisions. This work suggests the necessity of including both processes simultaneously when studying droplet–turbulence interaction to quantify the turbulence effect on the evolution of cloud droplet spectrum and rain formation.

Interaction of droplet dispersion and evaporation in a polydispersed spray

The interaction between droplet dispersion and evaporation in an acetone spray evaporating under ambient conditions is experimentally studied with an aim to understand the physics behind the spatial correlation between the local vapour mass fraction and droplets. The influence of gas-phase turbulence and droplet–gas slip velocity of such correlations is examined, while the focus is on the consequence of droplet clustering on collective evaporation of droplet clouds. Simultaneous and planar measurements of droplet size, velocity and number density, and vapour mass fraction around the droplets, were obtained by combining the interferometric laser imaging for droplet sizing and planar laser induced fluorescence techniques (Sahu et al., Exp. Fluids, vol. 55, 1673, 2014b, pp. 1–21). Comparison with droplet measurements in a non-evaporating water spray under the same flow conditions showed that droplet evaporation leads to higher fluctuations of droplet number density and velocity relative to the respective mean values. While the mean droplet–gas slip velocity was found to be negligibly small, the vaporization Damköhler number ($Da_{v}$) was approximately ‘one’, which means the droplet evaporation time and the characteristic time scale of large eddies are of the same order. Thus, the influence of the convective effect on droplet evaporation is not expected to be significant in comparison to the instantaneous fluctuations of slip velocity, which refers to the direct effect of turbulence. An overall linearly increasing trend was observed in the scatter plot of the instantaneous values of droplet number density ($N$) and vapour mass fraction ($Y_{F}$). Accordingly, the correlation coefficient of fluctuations of vapour mass fraction and droplet number density ($R_{n\ast y}$) was relatively high (${\approx}0.5$) implying moderately high correlation. However, considerable spread of the $N$ versus $Y_{F}$ scatter plot along both coordinates demonstrated the influence on droplet evaporation due to turbulent droplet dispersion, which leads to droplet clustering. The presence of droplet clustering was confirmed by the measurement of spatial correlation coefficient of the fluctuations of droplet number density for different size classes ($R_{n\ast n}$) and the radial distribution function (RDF) of the droplets. Also, the tendency of the droplets to form clusters was higher for the acetone spray than the water spray, indicating that droplet evaporation promoted droplet grouping in the spray. The instantaneous group evaporation number ($G$) was evaluated from the measured length scale of droplet clusters (by the RDF) and the average droplet size and spacing in instantaneous clusters. The mean value of $G$ suggests an internal group evaporation mode of the droplet clouds near the spray centre, while single droplet evaporation prevails near the spray boundary. However, the large fluctuations in the magnitude of instantaneous values of $G$ at all measurement locations implied temporal variations in the mode of droplet cloud evaporation.

Characterising Dynamic Instability in High Water-Cut Oil-Water Flows Using High-Resolution Microwave Sensor Signals

Abstract In the present study, multi-scale entropy algorithm was used to characterise the complex flow phenomena of turbulent droplets in high water-cut oil-water two-phase flow. First, we compared multi-scale weighted permutation entropy (MWPE), multi-scale approximate entropy (MAE), multi-scale sample entropy (MSE) and multi-scale complexity measure (MCM) for typical nonlinear systems. The results show that MWPE presents satisfied variability with scale and anti-noise ability. Accordingly, we conducted an experiment of vertical upward oil-water two-phase flow with high water-cut and collected the signals of a high-resolution microwave resonant sensor, based on which two indexes, the entropy rate and mean value of MWPE, were extracted. Besides, the effects of total flow rate and water-cut on these two indexes were analysed. Our researches show that MWPE is an effective method to uncover the dynamic instability of oil-water two-phase flow with high water-cut.

Fuel vaporization: Effect of droplet size and turbulence at elevated temperature and pressure

This paper presents an extensive experimental study regarding the effect of turbulence and droplet size on the evaporation rate of suspended monocomponent alkane droplets at elevated temperature and pressure conditions of up to 100 °C and 10 bar, respectively. Individual droplets of n-heptane and n-decane were suspended at the intersection of two crossed micro-fibers in the center of a fan-stirred spherical vessel. The droplet size was varied in the range between 110 and 730 µm. Eight axial fans generated a controlled turbulent flow field with quasi-zero mean velocity and turbulence intensity up to 1.5 m/s. The results reveal a linear relationship between the initial droplet size and its turbulent steady-state evaporation rate, where larger droplets evaporate at a faster rate than their smaller counterparts at all elevated temperature and pressure conditions. The normalized turbulent evaporation rate increases with pressure, whereas elevated temperature produces the opposite effect. The ratio of the Kolmogorov length scale to initial droplet diameter is shown to be of paramount importance for interpreting the effect of turbulence, as the normalized evaporation rate increases dramatically at lower values of this ratio under all test conditions. However, the ability of turbulence to enhance the vaporization rate vanishes when this ratio approaches unity, suggesting that only droplets which are initially larger than the smallest turbulent eddies experience enhanced evaporation. In addition, the widespread belief that turbulence enhances less volatile fuels more than their high volatility counterparts also depends on the ambient pressure and initial droplet size. The ability of turbulence to generate small-scale structures and, subsequently, the interaction of these eddies with the available fuel concentration gradient at the surface of the droplet governs the relationship between fuel type, initial droplet size, and ambient temperature and pressure. A turbulent Reynolds number or a vaporization Damköhler number is used to correlate turbulent droplet evaporation rates at all explored test conditions.

A novel multiscale theoretical model for droplet coalescence induced by turbulence in the framework of entire energy spectrum

This work mainly focused on the droplet coalescence induced by turbulence. Two kinds of interaction mechanisms between turbulent eddies and droplets were proposed, and the corresponding coalescence model for each mechanism has also been proposed by counting the number of collisions that can lead to coalescence directly. Most of previous coalescence models only considered the contribution of the turbulent eddies of size equal to the size of droplets since the droplet velocity was assumed to be equal to the velocity of turbulent eddies of same size. In contrast, the contribution of multiscale turbulent eddies (i.e. turbulent eddies with various sizes, not just the turbulent eddies of size equal to the size of droplets) to the coalescence of droplets of given sizes was considered in the proposed model. This work also simulated the coalescence in the framework of entire energy spectrum. Simultaneously, the influences of the average collision free path between droplets and turbulent eddies as well as the lifetime of turbulent eddies on the coalescence were considered. Furthermore, this work proposed a novel second-order longitudinal structure function, which showed a good agreement with the results of direct numerical simulation. Finally, the predicted droplet size distributions of the proposed model were in agreement with experimental data.