Drop Reynolds Number Research Articles

Pendant drop motion and stability in vertical airflow

When exposed to an ascending flow, pendant drops oscillate at magnitudes determined by windspeed, drop diameter, and needle diameter. In this study, we investigate the retention stability and oscillations of pendant drops in a vertical wind tunnel. Oscillation is captured by a high-speed camera for a drop Reynolds number Re = 200–3000. Drops at Re ≲ 1000 oscillate up to 12 times the frequency of drops with high Re. Increasing windspeed enables larger volume drops to remain attached to the needles above Re = 500. We categorize drop dynamics into seven behavioral modes according to the plane of rotation and deformation of shape. Video frame aggregation permits the determination of a static, characteristic shape of our highly dynamic drops. Such a shape provides a hydraulic diameter and the evaluation of the volume swept by the oscillating drops with time. The maximum swept volume per unit drop volume occurs at Re = 600, corresponding to the peak in angular velocity.

A NOVEL EXPERIMENTAL APPROACH TO STUDY DROP-PARTICLE COLLISIONS

Free drop-particle collisions occurring in air are experimentally produced by combining a stream of drops and a stream of particles, which results from the selective and ultra-fast hardening of another regular drop stream. The set-up offers the possibility to vary accurately the drop and particle diameter, the collision eccentricity, and the relative drop-particle velocity. First observations obtained with drop Weber numbers ranging from 30 to 300, drop Reynolds number between 390 and 4600, and with typical equilibrium contact angle of 70° evidence the existence of full deposition, separation, indicating possible bouncing events. For off-center separation, a liquid ligament forms between the particle and the outlying drop cap that fragments due to excessive stretching, a phenomenon similar to drop-drop collisions. In contrast, for head-on collisions and intermediate inertia, a lamella first forms, whose constrained recoil leads to liquid protuberance(s) that eventually pinch(es)-off. These outcomes can be distinguished using a bi-dimensional regime map built on the impact parameter and the drop Weber number. Despite remarkable similarities with binary drop collisions, important differences are observed especially for low and moderate eccentricities.

Role of viscosity in turbulent drop break-up

We investigate drop break-up morphology, occurrence, time and size distribution, through large ensembles of high-fidelity direct-numerical simulations of drops in homogeneous isotropic turbulence, spanning a wide range of parameters in terms of the Weber number $We$ , viscosity ratio between the drop and the carrier flow $\mu _r=\mu _d/\mu _l$ , where d is the drop diameter, and Reynolds ( $Re$ ) number. For $\mu _r \leq 20$ , we find a nearly constant critical $We$ , while it increases with $\mu _r$ (and $Re$ ) when $\mu _r > 20$ , and the transition can be described in terms of a drop Reynolds number. The break-up time is delayed when $\mu _r$ increases and is a function of distance to criticality. The first break-up child-size distributions for $\mu _r \leq 20$ transition from M to U shape when the distance to criticality is increased. At high $\mu _r$ , the shape of the distribution is modified. The first break-up child-size distribution gives only limited information on the fragmentation dynamics, as the subsequent break-up sequence is controlled by the drop geometry and viscosity. At high $We$ , a $d^{-3/2}$ size distribution is observed for $\mu _r \leq 20$ , which can be explained by capillary-driven processes, while for $\mu _r > 20$ , almost all drops formed by the fragmentation process are at the smallest scale, controlled by the diameter of the very extended filament, which exhibits a snake-like shape prior to break-up.

Predictive modeling of drop impact force on concave targets

Impacting drops are ubiquitous and the corresponding impact force is their most studied dynamic quantity. However, impact forces arising from collisions with curved surfaces are understudied. In this study, we impact small cups with falling drops across drop Reynolds number 2975–12 800, isolating five dominant parameters influencing impact force: drop height and diameter, surface curvature and wettability, and impact eccentricity. These parameters are effectively continuous in their domain and have stochastic variability. The unpredictable dynamics of the system incentivize the implementation of tools that can unearth relationships between parameters and make predictions about impact force for parameter values for which there is not explicit experimental data. We predict force due to the impacting drop in a concave target using an ensemble learning algorithm comprised of four base algorithms: a random forest regressor, k-nearest neighbor, a gradient boosting regressor, and a multi-layer perceptron. We train and test our algorithm with original experimental data comprising 387 total trials using four cup radii with two wetting conditions each. Our approach permits the determination of relative importance of the input features in producing impact force and force predictions which can be compared to scaling relations modified from those for flat targets. Algorithmic predictions indicate that deformation of the drop and surface wettability, often neglected in scaling for impact force on flat surfaces, are important for concave targets. Finally, our approach provides another opportunity for the application of machine learning to characterize complex systems' fluid mechanics for which experimental variables are numerous and vary independently.

Hydrodynamic Studies during Gas‐Solid Conveying in a Vertically Upward Converging Riser Tube‡

AbstractExperimental and theoretical investigations on hydrodynamics for gas‐solid particles flow were carried out in a vertical upward converging pneumatic conveying system. One‐dimensional mathematical modeling and simulation were done using the FORTRAN‐95 program. The influence of convergence geometry on the hydrodynamic parameters like particle velocity, gas‐particle slip velocity, pressure drop, and particle Reynolds number (Rep) along the riser were studied. Experiments were conducted using the dilute phase mode with three types of granular cereal seeds of different sizes. Some significant differences in all hydrodynamic parameter profiles along the riser were observed between converging and uniform risers. Enhancement of Rep in the converging riser implies a higher gas‐solid transfer coefficient.

Transient surface temperatures upon the impact of a single droplet onto a heated surface in the film evaporation regime

Single droplet impingement on a heated surface is a fundamental problem of basic interest in understanding complex phenomena in spray cooling and other applications involving heat transfer to impinging droplets. The surface temperature experiences rapid temporal gradients upon droplet impact. These temperature transients are strongly dependent on the hydrodynamic and heat transfer regimes. Experimental results are presented for the transient surface temperature in the film evaporation heat transfer regime for water drop diameters of 2.1 and 3.5 mm at drop Reynolds numbers up to 34,000 and Weber number up to 5540 are reported for surface temperatures of 60 to 100 ∘C. High-speed video was used to capture the dynamics of the impact. Intrinsic thermocouples were manufactured to measure surface temperature with sufficient temporal resolution. It was found that the hydrodynamics of the impact were not significantly affected by the surface temperature. Heat removal was found to be more effective at lower impact velocities. The maximum temperature drop occurred at the maximum spreading diameter. An analytical model was developed to successfully predict the transient Nusslet number of the droplet motion on the surface for both free-falling and air-propelled droplets.

Formation of drops and rings in double-diffusive sedimentation

We conduct numerical simulations to investigate the formation and evolution of drops and vortex rings of particle-laden fingers in double-diffusive convection in stably stratified environments. We show that the temporal evolution can be divided into double diffusion, acceleration and deceleration phases. The acceleration phase is a result of the vanishing temperature perturbation in the drop during the descent in the layer of uniform temperature. The drop decelerates because it transforms into a vortex ring. A theoretical drag model is presented to predict the speed of the spherical drop with the low drop Reynolds number. By formulating the boundary condition based on the vorticity, our drag model gives a more general form of the drag coefficient for small spherical drops and shows good agreement in predicting the drag coefficient. Drops with five particle sizes are compared, and it is found that although the greater vertical settling enhances vertical transport, the final state differs little among the various sizes. Comparison of our drag model with the simulation results under various bulk conditions and previous experimental results shows good model predictability. Finally, a comparison with the salt-finger case shows that the diffusive nature of the dissolved scalar field, along with the wake effect, can result in an apparent loss of mass from the drop and a permanent presence of the connection between the drop and its parent finger. This makes the observed detachment of the particle-laden drop much less likely in the salt-finger case.

Pre-Darcy Flow and Klinkenberg effect in Dense, Consolidated Carbonate Formations

Experimental studies on pre-Darcy flow generally focus on unconsolidated porous media with high permeability. In this work, pre-Darcy flow is studied in consolidated carbonate rocks from different formations of Zagros basin. The core samples are calcite, dolomite and chalk-salt characterized by low-porosity (12.33–28.21%) and low permeability (0.011–18.53 md). Digital rock images were obtained using dental CT-scan with a resolution of 200 pixels per μm. A series of single-phase flooding experiments were conducted to evaluate the onset of pre-Darcy flow in different cores using N2 as gas phase. Superficial velocity versus pressure gradient was measured and different onset values were reported. Results indicate the presence of pre-Darcy flow in single phase gas experiments. The minimum observed Darcy velocity was 0.445 × 10−05 m/s, below which pre-Darcy flow prevails. In addition, different flow regimes such as pre-Darcy, Darcy and non-Darcy flow regimes were determined using reduced pressure drop analysis and Reynolds number analysis. The range of Reynolds number were reported for different flow regimes and different core permeabilities. The pre-Darcy regime was observed at velocities in the range of (0.445–5.88) × 10−05 m/s for all cores. For a carbonate core with k = 0.01 md, pre-Darcy flow was observed in the range of $$Re_{\sqrt k }$$ < 2.1 × 10−07, Red < 0.168 and Rep < 0.025. It was also found that pre-Darcy flow arises due to Klinkenberg effect at low gas pressure in different core samples which show different behavior depending on their permeability.

Heat or mass transport from drops in shearing flows. Part 2. Inertial effects on transport

We analyse the singular effects of weak inertia on the heat (or equivalently mass) transport problem from drops in linear shearing flows. For small spherical drops embedded in hyperbolic planar linear flows, which constitute a one-parameter family (the parameter being $\unicode[STIX]{x1D6FC}$ with $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 1$, and whose extremal members are simple shear ($\unicode[STIX]{x1D6FC}=0$) and planar extension ($\unicode[STIX]{x1D6FC}=1$)), there are two distinct regimes for scalar (heat or mass) transport at large Péclet numbers ($Pe$) depending on the exterior streamline topology (Krishnamurthy &amp; Subramanian, J. Fluid Mech., vol. 850, 2018, pp. 439–483). When the drop-to-medium viscosity ratio ($\unicode[STIX]{x1D706}$) is larger than a critical value, $\unicode[STIX]{x1D706}_{c}=2\unicode[STIX]{x1D6FC}/(1-\unicode[STIX]{x1D6FC})$, the drop is surrounded by a region of closed streamlines in the inertialess limit ($Re=0$, $Re$ being the drop Reynolds number). Convection is incapable of transporting heat away on account of the near-field closed streamline topology, and the transport remains diffusion limited even for $Pe\rightarrow \infty$. However, weak inertia breaks open the closed streamline region, giving way to finite-$Re$ spiralling streamlines and convectively enhanced transport. For $Re=0$ the closed streamlines on the drop surface, for $\unicode[STIX]{x1D706}&gt;\unicode[STIX]{x1D706}_{c}$, are Jeffery orbits, a terminology originally used to describe the trajectories of an axisymmetric rigid particle in a simple shear flow. Based on this identification, a novel boundary layer analysis that employs a surface-flow-aligned non-orthogonal coordinate system, is used to solve the transport problem in the dual asymptotic limit $Re\ll 1$, $RePe\gg 1$, corresponding to the regime where inertial convection balances diffusion in an $O(RePe)^{-1/2}$ boundary layer. Further, the separation of time scales in the aforementioned limit, between rapid convection due to the Stokesian velocity field and the slower convection by the $O(Re)$ inertial velocity field, allows one to average the convection–diffusion equation over the phase of the Stokesian surface streamlines (Jeffery orbits), allowing a simplification of the original three-dimensional non-axisymmetric transport problem to a form resembling a much simpler axisymmetric one. A self-similar ansatz then leads to the boundary layer temperature field, and the resulting Nusselt number is given by $Nu={\mathcal{H}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D706})(RePe)^{1/2}$ with ${\mathcal{H}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D706})$ given in terms of a one-dimensional integral; the prefactor ${\mathcal{H}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D706})$ diverges for $\unicode[STIX]{x1D706}\rightarrow \unicode[STIX]{x1D706}_{c}^{+}$ due to assumptions underlying the Jeffery-orbit-averaged analysis breaking down. Although the separation of time scales necessary for the validity of the analysis no longer exists in the transition regime ($\unicode[STIX]{x1D706}$ in the neighbourhood of $\unicode[STIX]{x1D706}_{c}$), scaling arguments nevertheless highlight the manner in which the Nusselt number function connects smoothly across the open and closed streamline regimes for any finite $Pe$.

Heat or mass transport from drops in shearing flows. Part 1. The open-streamline regime

We study the heat or mass transfer from a neutrally buoyant spherical drop embedded in an ambient Newtonian medium, undergoing a general shearing flow, in the strong convection limit. The latter limit corresponds to the drop Péclet number being large ($Pe\gg 1$). We consider two families of ambient linear flows: (i) planar linear flows with open streamlines (parametrized by $\unicode[STIX]{x1D6FC}$ with $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 1$, the extremal members being simple shear flow ($\unicode[STIX]{x1D6FC}=0$) and planar extension ($\unicode[STIX]{x1D6FC}=1$)) and (ii) three-dimensional extensional flows (parameterized by $\unicode[STIX]{x1D716}$, with $0\leqslant \unicode[STIX]{x1D716}\leqslant 1$, the extremal members being planar ($\unicode[STIX]{x1D716}=0$) and axisymmetric extension ($\unicode[STIX]{x1D716}=1$)). For the first family, an analysis of the exterior flow field in the inertialess limit (the drop Reynolds number, $Re$, being vanishingly small) shows that there exist two distinct streamline topologies separated by a critical drop-to-medium viscosity ratio ($\unicode[STIX]{x1D706}$) given by $\unicode[STIX]{x1D706}_{c}=2\unicode[STIX]{x1D6FC}/(1-\unicode[STIX]{x1D6FC})$. For $\unicode[STIX]{x1D706}&lt;\unicode[STIX]{x1D706}_{c}$ all streamlines are open, while the near-field streamlines are closed for $\unicode[STIX]{x1D706}&gt;\unicode[STIX]{x1D706}_{c}$. For the second family, the exterior streamlines remain open regardless of $\unicode[STIX]{x1D706}$. The two streamline topologies lead to qualitatively different mechanisms of transport for large $Pe$. The transport in the open streamline regime is enhanced in the usual manner via the formation of a boundary layer. In sharp contrast, the closed-streamline regime displays diffusion-limited transport, so there is only a finite enhancement even as $Pe\rightarrow \infty$. For $Re=0$, the drop surface streamlines in a planar linear flow may be regarded as generalized Jeffery orbits with a flow and viscosity dependent aspect ratio Jeffery orbits denote the aspect-ratio-dependent inertialess trajectories of a rigid axisymmetric particle in a simple shear flow; see Jeffery (Proc. R. Soc. Lond. A, vol. 102 (715), 1922, pp. 161–179). A Jeffery-orbit-based non-orthogonal coordinate system thus serves as a natural candidate to tackle the transport problem from a drop, in a planar linear flow, in the limit $Pe\gg 1$. Use of this system allows one to derive a closed-form expression for the dimensionless rate of transport (the Nusselt number $Nu$) from a drop in the open-streamline regime ($\unicode[STIX]{x1D706}&lt;\unicode[STIX]{x1D706}_{c}$). Symmetry arguments point to a Jeffery-orbit-based coordinate system for any linear flow, and a variant of this coordinate system is therefore used to derive the Nusselt number for the family of three-dimensional extensional flows. For both classes of flows considered, the boundary-layer-enhanced transport implies that the Nusselt number takes the form $Nu={\mathcal{F}}(P,\unicode[STIX]{x1D706})Pe^{1/2}$, with the parameter $P$ being $\unicode[STIX]{x1D6FC}$ or $\unicode[STIX]{x1D716}$, and ${\mathcal{F}}(P,\unicode[STIX]{x1D706})$ given as a one and two-dimensional integral, respectively, which is readily evaluated numerically.

Application of Computational Fluid Dynamics for Modeling of Hydrodynamics and Mass Transfer of Laboratory Scale Crude Palm Oil Degumming Process

In this research, computational fluid dynamics was applied to model a laboratory reactor for the degumming of crude palm oil (CPO) involving immiscible liquid-liquid mixing and being controlled by mass transfer. The fluid mixing of CPO and phosphoric acid in the reactor was simulated using multiphase mixture model and standard κ-ε turbulence model in steady state mode. The simulation predicts the distributions of the drop diameter, the dispersed-phase relative velocity, the drop Reynolds number and the interfacial area density. The mass transfer coefficient from experimental work is correlated using the model as Sherwood number Shd = 0.02576 Red0.673Sc0.431 with R2 being 0.91. Finally, the volumetric mass transfer coefficient was calculated and compared to the experiment result.

Interaction between two consecutive axisymmetric Taylor drops flowing in a heavier liquid in a vertical tube

A study regarding the interaction between two consecutive Taylor drops flowing in a heavier liquid in a vertical tube is reported. Under certain conditions, due to the wake of the leading drop, the trailing drop accelerates, leading to coalescence of the two drops. This study was developed using a numerical model based in the Volume of Fluid method in an axisymmetric geometry. The simulations reported in the present work had to fulfill two conditions: axisymmetry (due to the numerical model) and a high enough drop Reynolds number (which is related to the disturbances in the wake of an isolated drop, and thus to the tendency to drop interaction). Relevant dimensionless numbers are used to assess the effect of the acting forces. Detailed flow patterns and drop shapes are provided. Furthermore, the approaching velocity acquired by the trailing drop is analyzed and velocity profiles between the leading and the trailing drop are also reported. In general, the trailing drop shows an accelerating region, followed by a deceleration near the leading drop. The increase of Eotvos number promotes higher accelerations, while the increase in Morton number and viscosity ratio has the opposite effect. By comparison to literature gas-liquid studies, it was also found that interfacial forces promote the shape stability of the drops.

Aerosol particles scavenging by a droplet: Microphysical modeling in the Greenfield gap

Studying the scavenging of aerosol particle by drops has been a key topic of atmospheric science since the late seventies, given its relationships with atmospheric depollution, with the physics of clouds and precipitations and with global warming. However, the efficiency with which falling droplets capture aerosol particles is still imprecisely known for a wide range of drop Reynolds number, Weber numbers, aerosol particles inertia and Brownian Schmidt number. In this paper, microphysical modeling is used to compute precisely the drop collection efficiency for aerosol particles around the Greenfield gap which are submitted to both drag force and Brownian motion, for droplets falling in quiescent air at moderate Reynolds number (Red≤100). Depending on the impactional or diffusional parameters, the collection regions on the drop surface are highlighted. The results are then compressed by a correlation which extends the field of use of the theoretical model of Wang et al. (1978) by taking inertial capture into account. The proposed correlation is suitable to estimate the aerosol scavenging efficiency for a non-evaporating, non-deforming drop with Red≤100 and particle Stokes number Stp∈[0;+∞]. In case of evaporating or condensing droplets, the effect of thermophoresis and diffusiophoresis are also taken into account through an extension of the formulation proposed by Wang et al. (1978) and hence with similar accuracy.

A Taylor drop rising in a liquid co-current flow

The present work presents a numerical study on the behavior of isolated liquid Taylor drops rising in vertical tubes with co-current heavier continuous phase. Numerical simulations were performed with a previously validated model, implementing Volume of Fluid method in an axisymmetric geometry. Detailed flow patterns and drop shapes are provided and discussed for several conditions. The balance between gravity effect and velocity of the continuous phase flow was found to have a great influence in the flow patterns observed. The increase of inertial effects, due to the increase of Eo number and the co-current velocity, leads to the occurrence of closed recirculations below the drops. Furthermore, the continuous phase stabilization distance below the drop is a function of the drop Reynolds number. Drop and continuous phase velocities relationship was studied. A viscosity ratio related term was appended to a pre-existing correlation. The flow in the absence of gravity was also studied. Results demonstrate that micro-scale flow is a lower limit to the cases studied in the present work and suggest that the viscosity ratio affects mainly the inertial part of the drop velocity.

Experimental investigation of the pressure loss through a double skin facade by using perforated plates

The aim of this study is to analyze the effect of perforated elements on pressure drop in a double skin facade cavity. This cavity separates the exterior and interior space as thermally controllable. The temperatures of the surfaces facing cavity with exterior and interior spaces have been determined experimentally under different airflow conditions. Two distinct perforated plates having different circular hole dimensions are positioned in the double skin facade cavity in order to create a pressure drop in the cavity. Pressure drops and temperature distributions in the cavity have been examined based on experimental measurements. The results show the surface and air temperature distributions in the cavity, the pressure drops under three different air flow rates and two different perforated plates. The dependence of the dimensionless pressure drop coefficient, Euler versus Reynolds numbers is investigated experimentally for different geometric characteristic of the perforated plates. So, Eu numbers independency after 30,000 of the Re numbers approximately is shown graphically. Evaluating the pressure loss in the DSF’s cavity under usage of different type of pressure drop elements is essential for ventilating the cavity and choosing the fan capacity in the DSF applications.

Steady shear rheology of a viscous emulsion in the presence of finite inertia at moderate volume fractions: sign reversal of normal stress differences

The shear rheology of an emulsion of viscous drops in the presence of finite inertia is investigated using direct numerical simulation. In the absence of inertia, emulsions display a non-Newtonian rheology with positive first and negative second normal stress differences. However, recently it was discovered that a small amount of drop-level inertia alters their signs – the first normal stress difference becomes negative and the second one becomes positive, each in a small range of capillary numbers (Li &amp; Sarkar,J. Rheol., vol. 49, 2005, pp. 1377–1394). Sign reversal was shown numerically and analytically, but only in the limit of a dilute emulsion where drop–drop interactions were neglected. Here, we compute the rheology of a density- and viscosity-matched emulsion, accounting for the interactions in the volume fraction range of 5 %–27 % and Reynolds number range of 0.1–10. The computed rheological properties (effective shear viscosity and first and second normal stress differences) in the Stokes limit match well with previous theoretical (Choi–Schowalter in the dilute limit) and simulated results (for concentrated systems) using the boundary element method. The two distinct components of the rheology arising from the interfacial stresses at the drop surface and the perturbative Reynolds stresses are investigated as functions of the drop Reynolds number, capillary number and volume fraction. The sign change is caused by the increasing drop inclination in the presence of inertia, which in turn directly affects the interfacial stresses. Increase of the volume fraction or capillary number increases the critical Reynolds number for sign reversals due to enhanced alignment of the drops with the flow directions. The effect of increasing the volume fraction on the rheology is explained by relating it to interactions and specifically to the contact pair-distribution function computed from the simulation. The excess stresses are seen to show an approximately linear behaviour with the Reynolds number in the range of 0.1–5, while with the capillary number and volume fraction, the variation is weakly quadratic.

Parametric investigation of two aerosol scavenging models in the inertial regime

Models of drop scavenging of aerosols via inertial impaction proposed by Slinn and by Calvert are compared with published experimental measurements to determine which model is a better predictor of the data. Additionally, a parametric study was performed on the residual of the model predictions from the measurements to identify dimensionless groups not included in these models, which might increase model performance. The study found that the Calvert model predicts scavenging in the inertial regime with less error than the Slinn model. The study also found that two dimensionless groups, the relative Stokes number, Stkr, and the drop Reynolds number, ReD, are both well correlated with the residual of these models. They are included in modified versions of both of these models to provide better performance. That these two dimensionless groups improve model performance suggests that an inertial mechanism and an advective mechanism not accounted for in the existing models play some role in aerosol scavenging in the inertial regime.

Effect of drops on turbulence of kerosene–water two-phase flow in vertical pipe

The effect of introducing kerosene drops on turbulence of kerosene–water two-phase in a vertical pipe is investigated experimentally. A hot-film and dual optical probes are used to measure the water velocity, turbulence fluctuation, drop relative velocity, volume fraction and drop diameter. Experiments are performed in a 78.8mm diameter vertical pipe for four average water velocities of 0.11, 0.29, 0.44 and 0.77m/s. The measurements were carried out for two area average volume fraction 〈α〉 of 4.6% and 9.2% as well as for water single phase flow to investigate the effect of introducing kerosene drops on two-phase flow turbulence. The kerosene–water mixture was generated by adding the kerosene to constant flow rates of water. The results indicate that drops induced turbulence is a function of the ratio of the drop Reynolds number (UrdB/ν) to the turbulence Reynolds number (u′Lt/ν) which decreased with higher water velocities. The results show that the Kolmogorov–Richardson scaling in the range of −4.5/3 to −6/3 for single phase flow which is replaced by −6/3 to −7/3 for two-phase flow. These values are less than −8/3 for air–water flow.

Sub-cavity liquid volume beneath spray droplet impacts into static liquid layers, and initial estimates of the heat flux required to dry out this volume

The time variation of the sub-cavity liquid volume beneath individual droplet impact cavities was measured for ranges of drop Weber and Reynolds numbers that match those for a full cone spray nozzle of interest. Cavity lifetime was also measured. These results will be used in a Monte-Carlo model of the spray cooling process that is currently under development. Droplet Weber numbers were varied between 140 and 1000. Corresponding Reynolds numbers ranged between approximately 1200 and 3600. These ranges matched Phase Doppler results that were obtained for the water spray under study. Thickness of the static liquid layer into which the single droplets impacted was varied between 0.2 and 1.0 times the droplet diameter.The measured sub-cavity liquid volume generally was between 60% and 80% of the original droplet volume over much of the cavity lifetime. Increasing the static liquid layer thickness increased this plateau value of the sub-cavity liquid volume between these lower and upper bounds, for Weber numbers greater than around 400. Sub-cavity liquid volume also increased somewhat as Weber number was increased. The cavity lifetime increased significantly as Weber number increased.The sub-cavity liquid volume and cavity lifetime results were scaled to values for the corresponding spray droplets at equal (We, Re). These were then used in an energy balance between the energy transferred through a heated wall to the sub-cavity liquid and the sum of the sensible heating and latent heat required to dry out the spray drop sub-cavity liquid volume within the cavity lifetime. These computed heat fluxes to dry out the drop impact cavities were then used to estimate the overall average heat flux for a heated surface that would dry out these individual spray droplet impact cavities. The resulting average heat flux values were between 400W/cm2 and 800W/cm2. These predictions are similar to the range of CHF values reported in the literature for water, of 500W/cm2 to 1000W/cm2.

Effects of dispersed phase viscosity on drop deformation and breakup in inertial shear flow

The deformation and breakup of a single liquid drop subjected to simple shear flow is studied numerically using a diffuse interface free energy lattice Boltzmann method. The effect of dispersed phase viscosity on the behavior of the drop at a drop Reynolds number Re=10 is investigated over the range of viscosity ratios λ=0.1−2 (dispersed phase viscosity over continuous phase viscosity) with a focus on λ<1. For every λ the critical capillary number Cac for breakup is determined. For the range of λ considered, Cac decreases as λ increases. Both the extent of deformation and the breakup mechanism depend on the viscosity ratio and the capillary number. At the highest subcritical capillary number, the drop becomes less elongated and more inclined towards the vertical axis as the viscosity ratio increases. The changes in the drop breakup process are examined as the capillary number increases from the lowest supercritical Ca~Cac, to 1.2, 1.5 and 2Cac. Drops break by the end-pinching mechanism, except for λ=2 at Ca=2Cac where the drop undergoes capillary wave breakup.