The peculiarities of sprayed liquid’s thermal state change,as droplets are heated by conduction

The change of thermal state and phase transformation intensity of sprayed water, n-hexane, n-heptane and n-decane is numerically modelled in the case, as droplets are heated by conduction; the influence of the Knudsen layer is neglected; warming and evaporation of the droplets has no influence on the state of the carrying air flow. The research results prove that a peculiar change of the thermal state of sprayed liquid, irrespective of droplet’s dispersivity, exists in the time scale, expressed by Fourier number. The above-mentioned change can be conveniently defined by the characteristic curves, representing the change of a droplet surface, centre, and mean mass temperatures, which are sensibly influenced by temperature of gas mixture and partial pressure of liquid vapour in it. As these characteristic curves were expressed in regards to the initial and equilibrium evaporation temperatures of liquid, the universal curves, representing the change of thermal states of the examined liquids, were obtained in the time scale, expressed by Fourier number. It is shown that liquid evaporation rate and the change of a droplet dimension can also be described by characteristic curves.     

Evaporation and condensing augmentation of water droplets in flue gas

The unsteady heat and mass transfer of sprayed water in the flue gas is modelled according to the iterative method of numerical research. The complex “droplet problem” covers the analysis of combined energy transfer in a semitransparent droplet, also combined heating and evaporation of the droplet. The surface temperature of the evaporating droplet is determined, at which the balance of energy fluxes taken to the surface and taken from the surface is reached. The thermal state mode of an evaporating droplet depends on the way of droplet heating as well. The change of thermal state and phase transformations parameters of water droplets warming in flue gas is analysed in the universal time scale. The initial evaluation of heat energy accumulated in exhaust flue gas utilization by water injection is presented.     

Interaction of the transfer processes in semitransparent liquid droplets

The study presents the mathematical model of unsteady heat transfer in evaporating semitransparent droplets of non-isothermal initial state and the numerical research method, evaluating selective radiation absorption and its influence on the interaction of transfer processes. The relation of the transfer processes inside droplets and in their surroundings and the necessity of thorough research of these processes are substantiated. When modeling the combined energy transfer in water droplets, the evaluation of thermoconvective stability in evaporating semitransparent liquid droplets is presented; the influence of the droplet initial state on its heating and evaporation process is investigated. The influence of heat transfer peculiarities on the change of the evaporating droplet state is indicated. Main parameters, which decide the peculiarities of the interaction of unsteady transfer processes in droplets and their surroundings, are discussed. The results of the numerical research are compared to the known results of the experimental studies of water droplet temperature and evaporation rate.     

Interaction of transfer processes during unsteady evaporation of water droplets

The change of water droplets state is modelled numerically under various heat and mass transfer conditions during their unsteady evaporation. The modelling is performed using the method of combined analytic–numeric research of heat and mass transfer in a two-phase “droplets–gas” flow. The algorithm of an iterative research is constructed for the analytically obtained system of integral equations. Regularities of heat transfer process interaction are examined. The dependence of the droplet state change on its heating manner is determined. Unsteadiness and interaction of transfer processes, as well as selectivity of radiant absorption in water droplets are evaluated. It is indicated that cognition of the droplet state change regularities in the case of conductive heating is very important in determination of two-phase flow and in construction of an engineering research method.     

Prediction of micro-explosion delay of emulsified fuel droplets

Burning a water-in-oil emulsion enables reduction in solid and gaseous pollutants in comparison with neat oil. In the emulsion, Heavy Fuel-Oil and water lie in distinct phases, having a high difference in boiling point (up to 200 K). In an emulsion droplet injected and subsequently heated inside a flame, the internal water droplets are enclosed inside the emulsion and do not systematically vaporise at boiling point. They are known to reach a metastable state, breaking up at a temperature below the spinodal limit of water. From this moment, the surrounding Fuel-Oil is fragmented into numerous faster and smaller droplets by the suddenly expanding steam. This physical phenomenon is called “micro-explosion”. This work demonstrates a numerical modelisation of unsteady heat and mass transfer at the surface and inside of the emulsion droplet, and provides a prediction of its micro-explosion delay, using homogeneous nucleation hypothesis. This assumption of homogeneous nucleation for internal water droplets matches the use of a “drop tower” experimental facility. Finally, comparisons between predicted ranges for micro-explosion delays and experimental delays from literature are discussed, along with combustion parameters (ambient temperature, relative velocity) and combustible emulsion parameters. As a result, the experimental and numerical micro-explosion delays decrease with liquid or ambient temperature and relative velocity, and increase with water content and radius of emulsion droplet. Their low average deviation reveals the accuracy of the assumption of homogeneous nucleation in the considered situations.     

Interphase heat transfer during bulk condensation in the flow of vapor–gas mixture

The investigation of heat transfer between a single droplet and a vapor–gas mixture at different Knudsen numbers of growing droplet is presented. The influence of the interphase heat transfer on the behavior of macroparameters and the distribution function of droplets was studied using the results obtained for bulk condensation of vapor–gas mixture flow in a nozzle. A comparison of results obtained within the frames of general formulation and ones following from the certain simplifying assumptions on the droplets temperature was carried out for the free molecular regime of droplets growth.     

A coupled level set and volume-of-fluid simulation for heat transfer of the double droplet impact on a spherical liquid film

A coupled level set and volume-of-fluid method is applied to investigate the double droplet impact on a spherical liquid film. The method focuses on the analysis of surface curvature, droplet diameter, impact velocity, double droplets vertical spacing, the thickness of the liquid film of two liquid droplets after the impact on a spherical liquid film, and the influence of flow and heat transfer characteristics. The results indicate that the average wall heat flux density of the double liquid droplet impact on a spherical liquid film is greater than that of a flat liquid film. Average wall heat transfer coefficient increases with the increase in the liquid film’s spherical curvature. When the liquid film thickness is smaller, the average wall heat flux density of the liquid film is significantly reduced by the secondary droplets generated from the liquid film. When the liquid film thickness is larger, the influence of liquid film thickness on the average wall heat flux density gradually decreases. The average wall heat flux density increases with the increase in impact velocity and the droplet diameter; it also decreases with the increase in double droplets vertical spacing.     

A model for the ignition and extinction of liquid fuel droplets

The model of the ignition and extinction of liquid fuel droplets presented in this paper is an application of stability theory, and specifically of Liapunov's first (indirect) method, which is well developed for lumped parameter autonomous systems. Since the behavior of liquid droplets is usually represented by a distributed nonautonomous system, an important part of the paper deals with the method by which the equations governing droplet combustion are reduced to the form appropriate to this analysis.The model consists of two unsteady autonomous coupled ordinary differential equations in temperature and oxygen mass fraction. Far field assumptions have made it necessary to treat the fuel mass fraction as a parameter. The results include the familiar S curves of temperature versus Damköhler number, as well as a great deal of detailed information about the static and the dynamic stability of the transitions between steady state evaporation and steady state combustion.     

A thermal immiscible multiphase flow simulation by lattice Boltzmann method

The lattice Boltzmann (LB) method, as a mesoscopic approach based on the kinetic theory, has been significantly developed and applied in a variety of fields in the recent decades. Among all the LB community members, the pseudopotential LB plays an increasingly important role in multiphase flow and phase change problems simulation. The thermal immiscible multiphase flow simulation using pseudopotential LB method is studied in this work. The results show that it is difficult to achieve multi-bubble/droplet coexistence due to the unphysical mass transfer phenomenon of “the big eat the small” – the small bubbles/droplets disappear and the big ones getting bigger before a physical coalescence when using an internal energy based temperature equation for single-component multiphase (SCMP) pseudopotential models. In addition, this unphysical effect can be effectively impeded by coupling an entropy-based temperature field, and the influence on density fields with different energy equations are discussed. The findings are identified and reported in this paper for the first time. This work gives a significant inspiration for solving the unphysical mass transfer problem, which determines whether the SCMP LB model can be used for multi-bubble/droplet systems.     

Characterization of the heat transfer accompanying electrowetting or gravity-induced droplet motion

Electrowetting (EW) involves the actuation of liquid droplets using electric fields and has been demonstrated as a powerful tool for initiating and controlling droplet-based microfluidic operations such as droplet transport, generation, splitting, merging and mixing. The heat transfer resulting from EW-induced droplet actuation has, however, remained largely unexplored owing to several challenges underlying even simple thermal analyses and experiments. In the present work, the heat dissipation capacity of actuated droplets is quantified through detailed modeling and experimental efforts. The modeling involves three-dimensional transient numerical simulations of a droplet moving under the action of gravity or EW on a single heated plate and between two parallel plates. Temperature profiles and heat transfer coefficients associated with the droplet motion are determined. The influence of droplet velocity and geometry on the heat transfer coefficients is parametrically analyzed. Convection patterns in the fluid are found to strongly influence thermal transport and the heat dissipation capacity of droplet-based systems. The numerical model is validated against experimental measurements of the heat dissipation capacity of a droplet sliding on an inclined hot surface. Infrared thermography is employed to measure the transient temperature distribution on the surface during droplet motion. The results provide the first in-depth analysis of the heat dissipation capacity of electrowetting-based cooling systems and form the basis for the design of novel microelectronics cooling and other heat transfer applications.     

Numerical investigation on the evaporation of droplets depositing on heated surfaces at low Weber numbers

The evaporation of water droplets, impinging with low Weber number and gently depositing on heated surfaces of stainless steel is studied numerically using a combination of fluid flow and heat transfer models. The coupled problem of heat transfer between the surrounding air, the droplet and the wall together with the liquid vaporisation from the droplet’s free surface is predicted using a modified VOF methodology accounting for phase-change and variable liquid properties. The surface cooling during droplet’s evaporation is predicted by solving simultaneously with the fluid flow and heat transfer equations, the heat conduction equation within the solid wall. The droplet’s evaporation rate is predicted using a model from the kinetic theory of gases coupled with the Spalding mass transfer model, for different initial contact angles and substrate’s temperatures, which have been varied between 20–90° and 60–100 °C, respectively. Additionally, results from a simplified and computationally less demanding simulation methodology, accounting only for the heat transfer and vaporisation processes using a time-dependent but pre-described droplet shape while neglecting fluid flow are compared with those from the full solution. The numerical results are compared against experiments for the droplet volume regression, life time and droplet shape change, showing a good agreement.     

Modeling gas oil spray coalescence and vaporization in gas solid riser reactor

The sprayed feed droplet behavior, including coalescence and vaporization into gas–solid flow, is complex especially near the atomizer region in fluid catalytic cracking (FCC) riser reactor. A three dimensional CFD model of the riser reactor has been developed, which takes into the account three phase hydrodynamics, heat transfer and evaporation of the liquid droplets into a gas–solid flow as well as phase interactions. A hybrid Eulerian–Lagrangian approach was applied to numerically simulate the collision and vaporization of gas oil droplets in the gas–solid fluidized bed. This numerical simulation accounts the possibility of coalescence of feed spray droplets in computing the trajectories and its impact on droplet penetration in the reactor. The modeling result shows that droplet coalescence mainly occurs at the initial part of the atomizing region and where three phase flow hits the reactor wall and bounces back. The model has the ability of inspecting the effects of feed injector geometry on the overall reactor hydrodynamic and heat transfer. The CFD simulation results showed that the evaporated droplet gas caused higher local velocities of the gas and solid particles and gas–solid flow temperature reduction.     

Numerical investigation of the cooling effectiveness of a droplet impinging on a heated surface

Computational fluid dynamics numerical simulations for 2.0 mm water droplets impinging normal onto a flat heated surface under atmospheric conditions are presented and validated against experimental data. The coupled problem of liquid and air flow, heat transfer with the solid wall together with the liquid vaporization process from the droplet’s free surface is predicted using a VOF-based methodology accounting for phase-change. The cooling of the solid wall surface, initially at 120 °C, is predicted by solving simultaneously with the fluid flow and evaporation processes, the heat conduction equation within the solid wall. The range of impact velocities examined was between 1.3 and 3.0 m/s while focus is given to the process during the transitional period of the initial stages of impact prior to liquid deposition. The droplet’s evaporation rate is predicted using a model based on Fick’s law and considers variable physical properties which are a function of the local temperature and composition. Additionally, a kinetic theory model was used to evaluate the importance of thermal non-equilibrium conditions at the liquid–gas interface and which have been found to be negligible for the test cases investigated. The numerical results are compared against experimental data, showing satisfactory agreement. Model predictions for the droplet shape, temperature, flow distribution and vaporised liquid distribution reveal the detailed flow mechanisms that cannot be easily obtained from the experimental observations.     

Investigation of wetting states and wetting transition of droplets on the microstructured surface using the lattice Boltzmann model

Abstract

In this study, the wetting states and wetting transition of droplets on the microstructured surfaces are investigated using the multiphase lattice Boltzmann method. The Cassie-Baxter (Cassie) and Wenzel wetting states on the rough surfaces are captured through the simulations, and the stability of Cassie state and the wetting transition are then studied and discussed by simulating the evaporation of droplets on several specified microstructured surfaces. The simulated apparent contact angles of the droplet on various rough surfaces fit the theoretical predictions very well. The results also present the coexistence of the Wenzel and Cassie states when the substrate is moderately hydrophobic with its Young’s angle smaller than the critical angle. In addition, the “De-pinning” wetting transition from Cassie to Wenzel state is observed for the moderately hydrophobic substrate once the droplet reduces to its critical radius, while the stable Cassie state is obtained when the substrate’s Young’s angle larger than the critical angle. The simulated critical radii for wetting transition are in quantitative agreements with the analytical values for different surface geometries and Young’s angles. This work provides mesoscopic information necessary for understanding the wetting phenomena on microstructured rough surfaces.     

Evaporative cooling of water in a mechanical draft cooling tower

A new mathematical model of a mechanical draft cooling tower performance has been developed. The model represents a boundary-value problem for a system of ordinary differential equations, describing a change in the droplets velocity, its radii and temperature, and also a change in the temperature and density of the water vapor in a mist air in a cooling tower. The model describes available experimental data with an accuracy of about 3%. For the first time, our mathematical model takes into account the radii distribution function of water droplets.Simulation based on our model allows one to calculate contributions of various physical parameters on the processes of heat and mass transfer between water droplets and damp air, to take into account the cooling tower design parameters and the influence of atmospheric conditions on the thermal efficiency of the tower. The explanation of the influence of atmospheric pressure on the cooling tower performance has been obtained for the first time.It was shown that the average cube of the droplet radius practically determines thermal efficiency. The relative accuracy of well-defined monodisperse approximation is about several percent of heat efficiency of the cooling tower. A mathematical model of a control system of the mechanical draft cooling tower is suggested and numerically investigated. This control system permits one to optimize the performance of the mechanical draft cooling tower under changing atmospheric conditions.     

Heat and mass transfer from a supercritical lox spray

The injection, evaporation and diffusion of liquid oxygen in a high pressure airstream in a parallel wall mixing channel is analyzed and computationally solved. The droplet evaporation in the supercritical environment is treated by a non-isothermal droplet heat transfer model which accounts for the finite thermal conductivity of oxygen droplets and the gas film. The non-ideal gas effects in the gas phase are modeled by the Redlich-Kwong equation of state. The mixture density and enthalpy are determined by applying the ideal-solution limit which is shown to be valid for the prevailing conditions. The coupled dynamics of droplet and gas phases is calculated by solving numerically the Navier-Stokes equations in two dimensions. The turbulence effects are modeled by a two equation (k-ε) model. The results show that the non-ideal gas behavior prevails over a large portion of the mixing channel. Furthermore, the injected liquid oxygen droplets achieve critical temperature very quickly, and as a result they evaporate in the vicinity of the injection point. The effects of injection angle on oxygen mixing characteristics is also investigated.     

Interfacial temperature measurements,high-speed visualization and finite-element simulations of droplet impact and evaporation on a solid surface

The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid–liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid–gas boundary. For cases involving evaporation, the diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. High-speed visualizations are performed to provide matching parameters for the wetting model used in the simulations. Numerical and experimental results are compared for the transient heat transfer and the fluid dynamics involved during the droplet deposition. Our results describe and explain temperature oscillations at the drop–substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.     

The effect of Weber number on the central binary collision outcome between unequal-sized droplets

The central binary collision of two unequal sized droplets is numerically investigated using the volume of fluid (V.O.F.) methodology. The numerical method based on the solution of the continuity and momentum equations in axi-symmetric formulation is coupled with a recently developed adaptive local grid refinement technique, thus allowing an accurate representation of the interface between the liquid and gas phase. Mass transfer mechanisms are reproduced by solving a transport equation for a colour function representing the mass of one of the colliding droplets before and after collision and mixing. The investigation is performed assuming either constant relative velocity of the colliding droplets or constant total energy of the system, thus creating a combination of the standard non-dimensional parameters affecting the collision process, i.e. Weber (We) and Ohnesorge (Oh) numbers as also droplet diameter ratio (Δ). The reliability of the procedure is first established by comparing predictions with available experimental data. The effect of the above mentioned parameters on ligament’s formation, maximum deformation of the two droplets, the penetration of one droplet into the other and satellite droplet formation is quantified.     

Vaporization of polydisperse fuel sprays in a laminar boundary layer flow: A sectional approach

The effect of the presence of a cold wall on the downstream changes in size distribution of a spray of fuel droplets undergoing vaporization and combustion is theoretically analyzed. The fuel is considered to be in the form of discrete liquid droplets which have an arbitrary range of sizes and differ in their rates of vaporization. In fact, the total number of discrete droplet sizes needed to simulate actual fuel sprays can be immense. To avoid the dimensionality problem associated with the discrete form of population balance equations of an ensemble of individual burning or evaporating particles, “sectional conservation equations” are used. The method, based on dividing the droplet size domain into sections and dealing only with one integral quantity in each section (e.g., number, surface area of droplets, or volume), has the advantage that the integral quantity is conserved within the computational domain and the number of conservation equations required is simply equal to the number of sections. Employing known solutions for the boundary layer flow field, the “sectional size conservation equations” are solved assuming that droplets follow streamlines. New solutions for the changes in size distributon of droplets as a function of temperature and distance from the wall are presented. Since the present analysis uses an arbitrary droplet size distribution as an initial condition, it may be used to evaluate the performance of various atomizers, as demonstrated in the present study.     

The behavior of water droplets on the heated surface

The effect of the volume of distillate droplets and temperature of the heated wall on evaporation process was investigated. The strong influence of thermal-physical and geometrical parameters of the wall on droplet evaporation is shown. A change in the ratio of droplet diameter to the wall thickness can lead to a change in evaporation regimes. Distribution of interface temperature along the droplet length is measured. At evaporation the wall temperature under the droplet changes significantly. A new method for measurement of the droplet mass on the heated wall is presented. The regimes of droplet boiling differ significantly from pool boiling. The droplet mass is directly changed in time; evaporation is separated into several stages.