Numerical analysis of the interactions between evaporating droplets in a monodisperse stream

A numerical simulation of evaporation in a monodisperse droplet stream is proposed, taking into account the transient state of the evaporation, and the non-uniform mass and heat transfer coefficients on the droplet surface. These investigations emphasize the strong interaction effects between closely spaced droplets in a dense spray, reducing significantly the transfer coefficients. Moreover, the Marangoni force becomes more significant than the viscous force, driving the internal motion of the droplet and affecting the temperature fields. Otherwise, a better understanding of the evaporation phenomenon around closely spaced droplets will help to refine the existing models used in dense sprays.     

Heat and mass transfer in evaporating droplets in interaction: Influence of the fuel

The prediction of heat and mass transfer in fuel sprays is a key issue in the design of combustors where the fuel is injected in a liquid form. The development and validation of new physical models requires reliable experimental data. This paper reports on an experimental study to characterize the Nusselt and Sherwood numbers of monodisperse droplets made of fuels having different volatilities and evaporating into flowing hot air. Simultaneous measurements of the droplet size and mean temperature allowed evaluating the heat fluxes that take part in the evaporation. The experimental Nusselt and Sherwood numbers are then compared to the case of an isolated droplet. It appears that these numbers are particularly dependent on the interactions between the droplets in a way that depends on the fuel nature.     

Surface tension of evaporating nanofluid droplets

Measurements of nanofluid surface tension were made using the pendant droplet method. Three different types of nanoparticles were used – laponite, silver and Fe₂O₃ – with de-ionized water (DW) as the base fluid. The reported results focus on the following categories: (1) because some nanoparticles require surfactants to form stable colloids, the individual effects of the surfactant and the particles were investigated; (2) due to evaporation of the pendant droplet, the particle concentration increases, affecting the apparent surface tension; (3) because of the evaporation process, a hysteresis was found where the evaporating droplet can only achieve lower values of surface tension than that of nanofluids at the same prepared concentrations; and (4) the Stefan equation relating the apparent surface tension and heat of evaporation was found to be inapplicable for nanofluids investigated. Comparisons with findings for sessile droplets are also discussed, pointing to additional effects of nanoparticles other than the non-equilibrium evaporation process.     

Natural convection in evaporating sessile drops with crystal growth

Laser shadowgraphy is employed to study interfacial instability and natural convection inside a minute drop evaporating on a plate with internal crystal growth. Both pure and binary liquids are considered. Two methods of crystal growth are developed, one by the bulk-supercooling method and the other by the point-supercooling method. Interfacial instability is determined by the characteristics of periphery shape of the shadowgraph, while the shadowgraphic image describes the nature of flow behavior inside the drop. While internal crystallization plays no role in interfacial instability, it exerts a profound found influence on natural convection.     

Radiation effect on thermal explosion in a gas containing evaporating fuel droplets

The dynamics of thermal explosion in a fuel droplets/hot air mixture is investigated using the geometrical version of the method of integral manifolds. The results are applied to the modelling of the ignition process in diesel engines. Effects of the thermal radiation, semi-transparency of droplets and oxidizer are taken into account. In contrast to the previous studies, the difference between gas temperature (responsible for convective heating of droplets) and external temperature (responsible for radiative heating of droplets) is taken into account. The dynamics of the explosion is presented in terms of the dynamics of a multi-scale, singularly perturbed system. The relevant parametric regions of this system are analyzed. Explicit analytical formulae for the ignition delay in the presence of thermal radiation are derived. It is shown that the effect of thermal radiation can lead to considerable reduction (up to about 30%) of the total ignition delay time.     

Heat transfer in evaporating black liquor falling film

Black liquor is a fluid with high viscosity, implying high Pr numbers. Most of the previously developed correlations for falling film evaporation heat transfer were developed for fluids with relatively low Pr numbers, and therefore are not valid for most black liquor evaporation conditions. Experimental heat transfer data from black liquor evaporation are presented here. They show that the Nu number, as expected, increases in the turbulent region. However, at a specific Re number for each Pr number level, the Nu number ceases to increase with increasing Re number. A new correlation, taking this observation into account, has been developed on the basis of experimental data in the region of 4.7 < Pr < 170 and 47 < Re < 6740, and is presented in this paper. A dry solid content dependence is included in the new correlation and improves its predictions for black liquor.     

High-pressure combustion of submillimeter-sized nonane droplets in a low convection environment

An experimental study of droplet combustion of nonane (C₉H₂₀) at elevated pressures burning in air is reported using low gravity and small droplets to promote spherical gas-phase symmetry at pressures up to 30 atm (absolute). The initial droplet diameters range from 0.57 to 0.63 mm and they were ignited by two electrically heated hot wires positioned horizontally on opposite sides of the droplet. The droplet and flame characteristics were recorded by a 16-mm high-speed movie and a high-resolution video camera, respectively. A photodiode is used to measure broadband gray-body emission from the droplet flames and to track its dependence on pressure. Increasing the pressure significantly influences the ability to make quantitative measurements of droplet, soot cloud, and luminous zone diameters. At pressures as low as 2 atm, soot aggregates surrounding the droplet show significant coagulation and agglomeration and at higher pressures the soot cloud completely obscures the droplet, with the result being that the droplet could not be measured. Above 10 atm radiant emissions from hot soot particles are extensive and the resulting flame luminosity further obscures the droplet. Photographs of the luminous zone in subcritical pressures show qualitatively that increasing pressure produces more soot, and the mean photodiode voltage output increases monotonically with pressure. The maximum flame and soot shell diameters shift to later times as pressure increases and the soot shell is located closer to the flame at higher pressure. The soot shell and flame diameter data are correlated by a functional relationship of reduced pressure derived from scaling the drag and thermophoretic forces on aggregates that consolidates all of the data onto a single curve.     

Heat transfer characteristics and pressure variation in a nanoscale evaporating meniscus

A nanoscale evaporating meniscus is simulated in this work using molecular dynamics. The heat and mass transfer characteristics and pressure variation in the non-evaporating and interline regions are studied. Very high heat and evaporation flux rates of the order of 100 MW/m² and 1000 kg/m² s, respectively, are achieved. The disjoining pressure increased significantly after the formation of the non-evaporating film. High negative liquid pressure induced due to capillary and disjoining pressures are obtained. Cavitation cannot occur as the film thickness is smaller than the critical cavitation radius, and the meniscus can exist in metastable state. A curve-fitted meniscus boundary condition is developed; a force function of the form F_n = An^?3 ? Cn^?2 can be applied at the boundaries of a liquid film to create curvature and form a meniscus.     

Interaction of Marangoni convection with mass transfer effects at droplets

For the system water–acetone–toluene the mass transfer is measured up to a pressure of 200 bar at a constant temperature of 20 °C for two different concentrations at quiescent pendant droplets. The measurements are compared to empirical predictions. The influence of a surfactant is investigated.A three-mode magnetic suspension balance is used to measure the transfer. Additionally, a Schlieren optic is applied to visualise the convection.Only in case of the transfer direction from the droplet into the continuous phase Marangoni convection is detected. A good agreement of measurement and evaluation is achieved. The surfactant damps the interfacial convection.     

Heat convection length for boundary-layer flows

In analyses of heat convection problems, it is traditional to introduce the heat transfer coefficient, h, such that the average heat flux at the solid surface can be conveniently calculated. To find h, one has to simultaneously solve governing equations for conservations of mass, momentum, and energy. This task may prove too challenging for contemporary undergraduate students. In the present study, we propose a heat convection length, Δs, which can greatly simplify the analysis, yet allow the convection characteristics to be retained. Classical examples for laminar boundary-layer air flows driven by forced convection or free convection over flat plates with length L are presented. For forced convection, Δs/L is found to be 2.026 for a wide range of Re; for free convection, Δs/L is found to be 2.511 for various Gr values.     

Effect of multiple particle interactions on burning droplets

The interactions between burning droplets are analyzed on the basis of the quasi-steady assumption. A generalized treatment for burning rates of droplets in an array has been developed using a modified Laplace equation with point sources. This treatment is applied to two droplets of different sizes, as well as finite arrays containing up to eight symmetrically arranged monodisperse droplets. Particle interactions are shown to be a function of particle size, number density, and geometry of the array. Results are presented in terms of correction factors from which multiple particle burning rates can be calculated from single particle burning rates. The correction factors are shown to be in close agreement with results available in the literature.     

Heat flux dispersion in natural convection in porous media

Analytical solutions derived in this paper confirm the experimental and numerical results revealing a widespread dispersion of heat flux data in natural convection in porous media. The weak non-linear method of solution is used to evaluate the heat flux in a porous layer heated from below and subject to weak boundary and domain imperfections. Little attention has been paid so far to the effect that the lower branch of the imperfect bifurcation has on the average heat flux. The results presented in this paper demonstrate the latter effect and explain the reason behind the dispersion of data. The comparison of the results with existing experimental and numerical data confirms the findings. In addition the latter effect is shown to be essential in ones ability to control heat transfer enhancement via natural convection in porous metal foams, for example.     

Solutocapillary convection in the float-zone process with a strong magnetic field

This paper treats the steady axisymmetric flow and mass transport in a cylindrical liquid bridge between the melting end of a feed rod and the solidifying end of an alloyed semiconductor crystal. There is a strong, uniform, steady, axial magnetic field. The surface tension depends on the temperature and the concentration of the species, while variations of the concentration occur because one species is rejected into the liquid during solidification. The thermocapillary and solutocapillary convections tend to cancel over part of the liquid bridge. For certain parameter ranges, there are two different stable solutions: one where the concentration gradient along the free surface leads to dominance by the solutocapillary convection and one where the mass transport due to the thermocapillary convection makes the concentration gradient along the free surface small, so that the thermocapillary convection is dominant.     

Transient buoyant convection of air in an enclosure under strong magnetic effect

A numerical study is made of transient convective cool-down of air in a cylindrical container when both gravity and magnetizing force act. The magnetizing force is generated in an inhomogeneous magnetic field for an electrically non-conducting fluid with high magnetic susceptibility. Cooling of air is accomplished by abruptly lowering the temperature of the cylindrical sidewall under a strong vertical magnetic field. Comprehensive numerical computations are obtained for ranges of pertinent external parameters. The behavior of flow and temperature fields are delineated as the radius and axial position of the electrical coil are varied. When the magnetizing force is parallel to gravity, the flow is invigorated and cool-down process is facilitated. When the magnetizing force opposes the gravity, the overall cool-down process is least effective when the strength of magnetizing force is comparable to gravity.     

Heat transfers from pin-fin arrays experiencing forced convection

Steady-state heat-transfers from pin-fin arrays have been investigated experimentally for staggered and in-line arrangements of the pin fins, which were orthogonal to the mean air-flow. For the applied conditions, the optimal spacings of the fins in the span-wise and stream-wise directions have been determined. The dependences of the Nusselt number upon the Reynolds number and pin-fin pitch (in both directions) have been deduced.