Effects Of Droplet Interactions Research Articles

Eulerian-lagrangian investigation of de-oiling hydrocyclones: The effects of droplet interaction and size distribution

The widespread use of de-oiling hydrocyclones to separate oil and water from wastewater has attracted the interest of many researchers. The close density of oil and water, and their breakup and coalescence, make research in this area quite challenging. In the present research, a numerical Eulerian-Lagrangian (E-L) framework was developed to investigate the effects of droplet interaction, inlet size distribution, and phase-coupling schemes on hydrocyclone efficiency. The results show that droplet interaction, including the breakup and coalescence phenomena and the inlet size distribution, should be considered to obtain accurate numerical results in the E-L framework. Using the E-L approach, the efficiency of de-oiling hydrocyclones was estimated with a minimum error of 7%. Also, the phase-coupling schemes affected the velocity field of the continuous phase (water) and the separation efficiency. The coalescence and breakup-dominated regions were investigated in different designs of de-oiling hydrocyclone using the E-L approach. Examining different designs shows that large changes in cone angle create a region of high turbulence and enhance droplet breakup. It can be concluded that the Sauter mean diameter of droplets and, consequently, the separation efficiency decrease in designs with the sharp cone angle.

Successive droplet impingement onto heated surfaces of different wettabilities

New high-performance electronic components generate a massive amount of heat per unit of area, and spray cooling is a field of interest for this application. Spray cooling achieves higher heat transfer coefficients than commonly used forced air convection cooling systems. In this study, we performed multiple droplet impingement experiments over heated surfaces in the non-boiling regime, a scenario that is closer to the phenomena of spray cooling than individual droplet impact. This paper focuses on the effects of droplet interactions with surfaces exhibiting distinct wettabilities. A surface thermocouple was used concomitantly as the impact surface and the temperature sensor. The surface thermocouple was originally hydrophilic (uncoated), which later we treated with a low cost commercial superhydrophobic coating (coated). High-speed imaging showed the droplet motion during impact. We proposed a one-dimensional inverse heat conduction semi-analytical solution, adopting a time-dependent droplet heat flux as one of the boundary conditions to represent the droplet cooling effect. We compared the heat transfer performances of both uncoated and coated surfaces for different droplet velocities but same initial temperature. The results showed higher heat transfer rates on uncoated surface relative to the coated one. Also, higher droplet velocities showed higher heat transfer mainly due to the increase in the droplet spreading diameter in contact with the solid. Successive droplets showed lower heat flow for the uncoated surface because of the low thermal effusivity and thickness of the heated solid, where most of the heat is removed by the first droplet. The first droplet thermal resistance and damping effects for the subsequent droplets, reduced the overall cooling performance. On the other hand, for the coated surface we found that the consecutive droplets continued to transfer heat with a similar rate as the previous one, which is desirable for spray cooling. However, the reduced overall heat transfer performance for the coated surface can be explained by the air pockets within the coating structure.

A CFD study of the transport and fate of airborne droplets in a ventilated office: The role of droplet-droplet interactions.

Previous studies reported that specially designed ventilation systems provide good air quality and safe environment by removing airborne droplets that contain viruses expelled by infected people. These water droplets can be stable in the environment and remain suspended in air for prolonged periods. Encounters between droplets may occur and droplet interactions should be considered. However, the previous studies focused on other physical phenomena (air flow, drag force, evaporation) for droplet transport and neglected droplet interactions. In this work, we used computational fluid dynamics (CFD) to simulate the transport and fate of airborne droplets expelled by an asymptomatic person and considered droplet interactions. Droplet drag with turbulence for prediction of transport and fate of droplets indicated that the turbulence increased the transport of 1 µm droplets, whereas it decreased the transport of 50 µm droplets. In contrast to only considering drag and turbulence, consideration of droplet interactions tended to increase both the transport and fate. Although the length scale of the office is much larger than the droplet sizes, the droplet interactions, which occurred at the initial stages of release when droplet separation distances were shorter, had a significant effect in droplet fate by considerably manipulating the final locations on surfaces where droplets adhered. Therefore, it is proposed that when an exact prediction of transport and fate is required, especially for high droplet concentrations, the effects of droplet interactions should not be ignored.Electronic Supplementary MaterialSupplementary material is available in the online version of this article at 10.1007/s11783-021-1465-8 and is accessible for authorized users.

Effect of spray characteristics influences combustion in DI diesel engine – A review

In a DI Diesel Engine performance, emission and combustion characteristics, spraying behaviour plays a vital role. Emerging research in new fuels is increasing day by day, to find the best fuel in light of the combustion characteristics. It is mandatory to study about effects of spray behavior, droplet growth and the formation of new droplets. The aim of this review is to compare the spray characteristics of diesel engines under various ambient conditions. It can be inferred that if the incident primary sprays developed have a generalized kind of size distribution, then the resulting spray after injection breeds part of the same class of distributions. A spray combustion model is being researched to include more standard size distributions including the effects of droplet interactions and the relative movement of droplets and air, which can affect the engine’s combustion characteristics. Numerical investigation of spray structure gives the immense knowledge on spray behaviors inside the combustion chamber.

A point sink superposition method for predicting droplet interaction effects during vapor-diffusion-driven dropwise condensation in humid air

During dropwise condensation from the ambient environment, water vapor present in air must diffuse to the surface of each droplet. The spatial distribution of water vapor in the local surroundings of each individual droplet determines the total condensation rate. However, available models for dropwise condensation in humid air assume that such systems of droplets grow either as an equivalent film or that the growth of each droplet is completely isolated; the interactions between droplets are poorly described and, consequently, predictions of total condensation rates may mismatch experimental observations. This paper presents a reduced-order analytical method to calculate the condensation rate of each individual droplet within a group of droplets on a surface by resolving the vapor concentration field in the surrounding air. A point sink superposition method is used to account for the interaction between droplets without requiring solution of the diffusion equation for a full three-dimensional domain containing all of the droplets. For a simplified scenario containing two neighboring condensing droplets, the rates of growth are studied as a function of the inter-droplet distance and the relative droplet size. For representative systems of condensing droplets on a surface, the total condensation rates predicted by the reduced-order model match numerical simulations to within 15%. The results show that assuming droplets grow as an equivalent film or in a completely isolated manner can severely overpredict condensation rates.

Evaporation of closely-spaced interacting droplets arranged in a single row

Predictive models of heating and evaporation of fuel droplets in the dense region of sprays are essential to optimize the design of combustion chambers in internal combustion engines. This topic is addressed here, based on an experimental study using lines of equally-spaced droplets evaporating in a high temperature chamber (540°C). The experimental set-up allows controlling several key parameters including the droplet size, velocity and the inter-droplet distance. The volume-averaged temperature of the droplets is measured using two-color laser-induced fluorescence, while the droplet size and velocity are deduced from a double-pulse shadowgraphy method. The combination of these measurement techniques allows evaluating the heating and evaporation rates of single-component droplets made of ethanol, n-dodecane, n-decane and isohexane. Nusselt and Sherwood numbers are estimated from the experiments and compared with the existing correlation concerning the isolated droplet, which allows quantifying the effects of droplet interactions on the heat and mass transfers. The droplet spacing appears to have a strong influence on the size and temperature evolutions. However, it also seems necessary to consider the development of a boundary layer around the chain of droplets. As the thickness of the boundary layer increases with the distance from the injector, forced convection has a more and more limited influence on the heat and mass transport. Inside the boundary layer, the transfers are mainly governed by diffusion and convection by the Stefan flow. In a first approach, these effects are partially incorporated in a reduced parameter using the concept of volume of influence. Then, a more detailed study based on numerical simulation is carried out. The Navier–Stokes equations and the vapor transport equation are solved for various periodical arrangements of droplets. A parametric study of the influence of the main characteristic numbers involved allows to infer a correlation for Nusselt and Sherwood numbers which is finally validated against the measurements.

Effects of droplet interaction on spontaneous ignition of an n-decane droplet pair

As a fundamental study on the droplet-interaction effect in the fuel-spray ignition, spontaneous ignition of an n-decane droplet pair rapidly inserted into hot air was experimentally studied in the ambient temperature range where the low-temperature oxidation reactions are active. Two droplets suspended on 14μm SiC fibers initially at room temperature were inserted into a hot furnace. Droplet diameter was 1mm. Three hot junctions of K-type thermocouples with a diameter of 25μm were located near the droplet pair, and cool-flame and hot-flame appearances were detected. The experiments were performed in microgravity to exclude the effect of buoyancy. First, at atmospheric pressure, where only cool flame appears, cool-flame ignition delay and cool-flame temperature increased with decreasing inter-droplet distance. The former is supposed to be mainly caused by the mutual cooling effect, and the latter is by the enhanced fuel supply through duplicated fuel sources. Next, at 0.3MPa, where two-stage ignition occurs, cool-flame ignition delay increased with decreasing inter-droplet distance in the same way as at atmospheric pressure. On the other hand, the duration between cool-flame appearance and hot-flame appearance (second induction time) decreased with decreasing inter-droplet distance. This is supposedly caused by higher cool-flame temperature through higher fuel concentration in the reaction zone at the moment of cool-flame appearance. Thus the mutual cooling effect was dominant before cool-flame appearance, while the effect of duplicated fuel sources was dominant after cool-flame appearance.

Modeling fluid behavior and droplet interactions during liquid–liquid separation in hydrocyclones

A mechanical separation process in a hydrocyclone is described in which disperse water droplets are separated from a continuous diesel fuel phase. This separation process is influenced by droplet–droplet interaction effects like droplet breakup and coalescence resulting in a change of droplet size distribution. A simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics with population balances. The droplet size distribution is discretized and each discrete droplet size fraction is assumed to be an individual phase within a multiphase-mixture model. The droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases by the aid of user-defined functions. All model equations are solved with the CFD software package FLUENT™. The investigations show the impact of the cyclone geometry on the coupled population and separation dynamics. Cyclone separators with an optimized geometry show less steep velocity gradients increasing the coalescence rates and improving the separation efficiency. The calculated droplet size distributions at the cyclone overflow and at the underflow show good accordance with experimental data. The basic modeling approach can be extended and adapted to other disperse multiphase flow systems.

Vaporization and combustion in three-dimensional droplet arrays

The quasi-steady vaporization and combustion of multiple-droplet arrays is studied numerically. Utilizing the Shvab–Zeldovich formulation, a transformation of the governing equations to a three-dimensional Laplace’s equation is performed, and the solution to Laplace’s equation is obtained numerically to find the effects of droplet interactions in symmetric, multiple-droplet arrays. Vaporization rates, flame surface shapes, and flame locations are found for different droplet array configurations and fuels. The number of droplets, the droplet arrangement within the arrays, and the droplet spacing within the arrays are varied to determine the effects of these parameters. Computations are performed for uniformly spaced three-dimensional arrays of up to 216 droplets, with center-to-center spacing ranging from 3 to 25 droplet radii. As a result of the droplet interactions, the number of droplets and relative droplet spacing significantly affect the vaporization rate of individual droplets within the array, and consequently the flame shape and location. For small droplet spacing, the individual droplet vaporization rate decreases below that obtained for an isolated droplet by several orders of magnitude. A similarity parameter which correlates vaporization rates with array size and spacing is identified. Individual droplet flames, internal group combustion, and external group combustion can be observed depending on the droplet geometry and boundary conditions.

The extinction behavior of small interacting droplets in cross-flow

Experiments were conducted on monodisperse streams of small (<100 μm) methanol and ethanol droplets, injected perpendicularly to the axis of an axisymmetric methane diffusion flame. After crossing the methane flame, the droplets ignited and continued to burn outside of the “domain of influence” of the gaseous flame till they eventually extinguished. The extinction behavior was studied as a function of droplet spacing, oxidizer concentration and velocity, and droplet velocity by measuring droplet size and velocity at the time of extinction using a commercial Phase Doppler Anemometer. The onset of droplet interaction effects on extinction was found at interdroplet distances well above the limits reported in the literature. The interaction is attributed to the vitiated atmosphere left behind by the leading droplet that affects the extinction conditions of the trailing one. The ratio between interdroplet time and convection time normal to the droplet direction of travel was found to be the controlling parameter. Results were correlated in terms of a critical Damköhler number that was found to scale as dY o,∞ n o / v, where d is the droplet diameter, Y o,∞ is the oxidizer mass fraction, v is the droplet velocity, and n o is 0.5 and 0.75 for methanol and ethanol, respectively.

Droplet Spacing on Drag Measurement and Burning Rate for Isothermal and Reacting Conditions

To understand the effects of droplet interaction on the drag coefficient and vaporization process, our experiment investigated the nonreacting and combustion history of a single stream of monosized droplets. Continuous monosized streams of fuel droplets were injected into quiescent surrounding air. An electronic device designed to modulate the droplet spacing C (ratio of interdroplet spacing to droplet diameter) was used. Measurements of droplet diameter, droplet velocity, and droplet temperature were performed using nonintrusive laser interoferometry. Ethanol was used as the simulation fluid throughout the experiment. The droplet stream was investigated in cold conditions to study the influence of droplet spacing on the drag coefficient. The data compiled for an extensive range of parameters (Re, droplet spacing) were compared with previous correlations from the literature. We propose a new correlation that improves the prediction of the drag coefficient for a large range of spacing parameter 2 2 law does not apply rigorously for interacting droplets, and so a corrective factor for burning rate was determined.

Hysteresis effects of two interactive droplets burning in convective flows

The hysteresis characteristics of two equal-sized droplets in tandem burning in hot convective flows are investigated numerically. Similar to the results of convective single-droplet burning of Jiang et al. (1995), the present study shows that at certain flow conditions, dual solutions are also exhibited for the flame structure around the two droplets, depending upon the initial conditions assumed. For the lower-branch solution where the droplets are initially merged in a chemically frozen flow, four combustion modes, including pure vaporization, wake flame, transition flame, and envelope flame, are obtained sequentially as the ambient flow temperature varies from a low 600 K to a high 1400 K at Re=10. The upper-branch solution, where the droplets are initially enclosed by an envelope flame, however, possesses only two modes of wake and envelope flame under the equivalent conditions. The vaporization rates of both the leading and trailing droplets are hence found to be multi-valued at certain flow conditions where multiple flame configurations exist. The effects of droplet interaction are more profound on the trailing droplet so that its vaporization rate is generally lower than that of the leading droplet. However, as a transition flame occurs, the inverse exhibition in contrast to the foregoing result is observed, while the double reaction zones are excited. When the droplet spacing becomes large enough, the leading droplet behaves just like a single droplet in an equivalent flow condition, although it is not true for the trailing one.

97/03049 Flame and droplet interaction effects during droplet-stream combustion at zero Reynolds number

In the presence of Friedel–Crafts acids, residual pyrolysis oil (RPO) [Ullmann's encyclopedia of industrial chemistry, 4th ed. 1993: A23; p. 89; Kirk-Othmer encyclopedia of chemical technology, 3rd ed. 1990: 13; p. 717] is easily converted to a petroleum aromatic resin (PAR) [Jeremic K, Jovanovic JA. Erdoel and Kohle, erdgas petrochemie, 1993: 46; 430–434]. By using HPLC chromatography, GC-MS, HPLC-MS and APCI-MS/MS techniques and the reaction of indene and naphthalene in the presence of boron trifluoride for comparison, it was proved that the PAR sample investigated in this work represented a mixture of the components that remained from RPO, an oligomer with dimers, trimers and tetramers in, respectively, decreasing quantities, an alkylate with naphthalene being the main substrate and a polymer in which products with 7–32 monomer moieties prevailed. The monomers and alkylation agents present in the RPO were identified, as were the components that do not polymerize and could be alkylated. By taking into account all the possible oligomerization products including dimers, trimers and tetramers, both in the form of homopolymers and heteropolymers, and all the possible alkylation products, the molecular weights of compounds expected in the oligomer and the alkylate part of the PAR were calculated. All of them were detected in the PAR by using direct sample insertion APCI-MS/MS analysis. GC-MS and HPLC analysis of the PAR and GC-MS, HPLC and HPLC-MS analysis of a product mixture of the reaction of indene in naphthalene in the presence of boron trifluoride, were accomplished. By using the described analytical procedure, it has become possible to control and manage the reaction of the conversion of RPO to PAR, and to characterize this complex system in a very precise manner.

Flame and droplet interaction effects during droplet-stream combustion at zero reynolds number

This work presents a numerical analysis of the quasi-steady combustion of an infinite stream of droplets in the limit of infinite Damköhler number and stagnant ambient conditions. The small and large length-scale phenomena associated with the process are addressed by splitting the physical domain into near- and far-field subdomains. Within the inner subdomain, validated expressions are used during the grid generation procedure, allowing the development of appropriate finite-difference expressions and control of the distribution of points. Analytical transformations are developed and applied to the outer subdomain coordinate system in order to match the inner and outer grids along the domain interface and to properly address the outflow boundary conditions using a regularly spaced grid. A system of transformed governing equations is obtained and discretized into a coupled system of algebraic equations, which are solved by standard scientific subroutines, incorporating automatic control of error. The developed transformations are inverted and the solutions within the physical domain are obtained. Interdroplet interaction effects are presented in terms of droplet mass vaporization rate, droplet lifetime, and flame-sheet shape and position for different droplet spacings and fuels. The results indicate interaction effects present over a broad range of interdroplet spacings and are compared with theoretical and experimental ones available in the literature.

Multi-droplet interaction effects in dense sprays

A new approach for dense-spray modeling is employed to develop a model for multi-droplet interaction effects. A statistical description of droplets in a cloud and correlation functions for the effects of interactions between neighboring droplets are used to extract correction factors for various parameters that are affected by droplet interactions (e.g. drag cofficient, Nusselt number and Sherwood number). The correction factors enable the calculation of the drag coefficient, evaporation rate and heat transfer of a droplet in a cloud based on models for a single droplet. The model is employed to study the effects of droplet interactions on the evaporation and motion of a dense spray in a hot gaseous environment. It is shown that interaction effects are important during a larger fraction of the droplet lifetime as the droplet size decreases. The multi-droplet interactions cause the drag coefficient of a droplet in a dense spray to be lower—and hence its velocity higher—than that for an isolated droplet. For 100 μm droplets, as expected, the evaporation rate decreases and the droplet lifetime increases due to multi-droplet interactions. For 40 μm droplets, however, the evaporation rate increases and the droplet lifetime decreases. Although heat transfer to an interacting droplet is slower than to an isolated droplet, at the same gas-phase conditions and relative velocity of the droplets, the higher relative velocity of a 40 μm interacting droplet more than compensates for this effect to result in a shorter droplet lifetime.

Experimental studies on the dynamics and evaporation of tandem liquid droplets in a hot gas flow

Dynamics and evaporation of tandem droplets moving upward in a free convective thermal boundary layer were experimentally investigated. The free convective boundary layer was formed from a hot isothermal vertical plate which has a high wall-to-ambient temperature difference. The gas velocity and temperature profiles were numerically obtained using the variable gas property model, and the results were used to analyze the droplet dynamic behavior and vaporization process. The effects of droplet interaction in the streamwise direction and mass transfer on the drag coefficient were studied. In addition, the effects of droplet dynamics on droplet evaporation were investigated. The experimental parameters tested in this study were the initial droplet size, spacing between droplets, and liquid properties. New drag coefficients for various liquids and droplet spacings were obtained and applied to the vaporization process.

Droplet interactions in axisymmetric thermocapillary motion

A combined analytical—numerical study is presented for the axisymmetric thermocapillary motion of a finite chain of spherical droplets along their line of centers. The droplets may be formed from different fluids and have arbitrary radii, and they are allowed to be unequally spaced. Using a boundary-collocation method, the appropriate equations of conservation of energy and momentum are solved in the quasisteady limit and the droplet interaction effects are calculated for various cases. The numerical solutions can be obtained to the satisfactory degree of accuracy by the increase of the collocation points on each droplet interface. For the thermocapillary motion of two-droplet systems, our results for the droplet velocities agree very well with the exact calculations using spherical bipolar coordinates. For the cases of two or three droplets touching one another, the numerical calculations for the particle interaction parameters compare quite favorably with the formulas derived analytically. All of our data for the special case of multiple gas bubbles demonstrate the fact that the thermocapillary migration velocity of each bubble is unaffected by the presence of the others if all the bubbles have identical radii.

Numerical study of the interactions between droplets at intermediateReynolds numbers

Effects of droplet interactions on drag, evaporation, and combustion of a planar droplet array oriented perpendicular to the approaching flow are studied numerically. The three-dimensional Navier-Stokes equations, with variable thermophysical properties, are solved using finite-difference techniques. Parameters investigated include the droplet spacing, droplet Reynolds number, approaching stream oxygen concentration, and fuel type. Results are obtained for a Reynolds number range of 5 to 100, droplet spacings from 2 to 24 diameters, oxygen concentrations of 0.1 and 0.2, and methanol and n-butanol fuels. The calculations show that gasification rates of interacting droplets decrease as droplet spacings decrease. The reduction in gasification rates is significant only at small spacings and low Reynolds numbers. The effects of adjacent droplets on drag are shown to be small for the present array orientation.

Burning times of linear fuel droplet arrays: A comparison of experiment and theory

To understand better the effects of droplet interaction on the burning of fuel droplet sprays, the combustion history of single streams of monosized droplets was investigated by both experimental and theoretical methods. Continuous monodispersed streams of fuel droplets were injected into a hot environment where the droplet combustion histories were recorded photographically for spacings ranging from a few droplet diameters to about 30 diameters. Theoretical predictions from a model which describes the quasisteady (QS) combustion of fuel droplet arrays in a quiescent ambience were compared with experimental observations to examine the nature and extent of droplet interaction. Both measured and predicted results show a gradual, but substantial, monotonic increase in burning time with decreasing droplet spacing. For droplet spacing of the order of 2 droplet diameters, extremely strong droplet interaction is indicated by a twofold increase in burning time. Consistent with theoretical predictions, a compilation of data for an extensive range of experimental parameters (2 alcohols, 2 pure hydrocarbons, 3 binary hydrocarbon mixtures, No. 2 fuel oil, 100–300-μm droplets, and 4 ambient conditions) demonstrate that the increase in droplet lifetime due to droplet interaction depends universally on droplet spacing and not on fuel type, droplet size, or ambient conditions. These results also show that the classical “D 2-law,” which states that the surface area of an isolated droplet decreases linearly with time, does not apply rigorously for interacting droplets. Using an ad hoc quasi-steady (QS) “Halo model,” in an attempt to represent the transient nature of droplet interaction, the effect of interaction on droplet lifetime is shown to be mildly dependent on ambient oxygen content.

A model for the effect of droplet interactions on vaporization

Effects of droplet interactions on vaporization were simulated by evaporation of a droplet inside a “bubble”. Initially the droplet-in-bubble vaporization rate exceeded that of a single droplet. Subsequently vaporization was retarded by cooling and vapor addition. If the bubble was not much larger than the droplet, saturation occurred before complete vaporization. With increasing bubble size the droplet radius at saturation was diminished until complete vaporization ensued. This saturation-complete vaporization transition was sensitive to pressure and initial gaseous temperature and insensitive to volatility and vapor content. A correlation was developed to incorporate interactions into spray vaporization models.