Investigation of heat and mass transfer between the two phases of an evaporating droplet stream using laser-induced fluorescence techniques: Comparison with modeling

Heat and mass exchanges between the two phases of a spray is a key point for the understanding of physical phenomena occurring during spray evaporation in a combustion chamber. Development and validation of physical models and computational tools dealing with spray evaporation requires experimental databases on both liquid and gas phases. This paper reports an experimental study of evaporating acetone droplets streaming linearly at moderate ambient temperatures up to 75 °C. Two-color laser-induced fluorescence is used to characterize the temporal evolution of droplet mean temperature. Simultaneously, fuel vapor distribution in the gas phase surrounding the droplet stream is investigated using acetone planar laser-induced fluorescence.Temperature measurements are compared to simplified heat and mass transfer model taking into account variable physical properties, droplet-to-droplet interactions and internal fluid circulation within the droplets. The droplet surface temperature, calculated with the model, is used to initiate the numerical simulation of fuel vapor diffusion and transport in the gas phase, assuming thermodynamic equilibrium at the droplet surface. Influence of droplet diameter and droplet spacing on the fuel vapor concentration field is investigated and numerical results are compared with experiments.     

The effect of gas and liquid properties and droplet size ratio on the central collision between two unequal-size droplets in the reflexive regime

A numerical investigation of various parameters affecting the collision process of two unequal sized droplets in a gaseous environment in the reflexive regime is presented. The investigation is based on the finite volume numerical solution of the Navier–Stokes equations, in their axial-symmetric formulation, expressing the flow field of the two phases, liquid and gas, coupled with the volume of fluid method (VOF) for tracking the liquid–gas interfaces; a recently developed adaptive local grid refinement technique is used in order to track more accurately the liquid–gas interface with reduced computational cost. A colour function is used in order to follow the mixing process of the two droplets after collision. The reliability of the procedure is first established by comparing predictions with available experimental data and important details as regards the time evolution of the deformed shapes, the ligament formation, the maximum deformation of the droplets and the penetration of one droplet into the other are presented. The collision process and its outcome are investigated having the liquid properties (Ohnesorge number based on the liquid properties), the gas phase properties (Reynolds number based on gas properties) and droplet size ratio as the controlling parameters.     

Transport processes and associated irreversibilities in droplet combustion in a convective medium

A mathematical model of the combustion of a droplet surrounded by hot gas with a uniform free stream motion is made from the numerical solution of conservation equations of heat, mass and momentum in both the carrier and the droplet phases. The gas-phase chemical reaction between the fuel vapour and the oxidizer is assumed to be single-step and irreversible. The phenomenon of ignition is recognised by the sudden rise of temperature in the temperature/time histories at different locations in the carrier phase. To ascertain the process irreversibilities, the instantaneous rate of entropy production and its variation with time have been determined from the simultaneous numerical solution of the entropy conservation equations for both the gas and liquid phases. The relative influences of pertinent input parameters, namely the initial Reynolds number Re_i, the ratio of the free stream to initial temperature T_∞ and the ambient pressure on (i) the local and average Nusselt numbers, (ii) the life histories of burning fuel drops, and (iii) the entropy generation rate in the process of droplet combustion have been established.     

Evaporation of multicomponent liquid fuel droplets

A theoretical investigation on evaporation of a two-component liquid fuel droplet in high-temperature quiescent gaseous surroundings has been made from the numerical solution of conservation equations of heat, mass and momentum transports in the carrier and droplet phases. Liquid fuel droplets containing (i) components of widely varying volatilities, namely, n-hexane and n-hexadecane and (ii) components of closely spaced volatilities, namely, n-hexane and benzene, have been considered for the studies. The evaporation characteristics, namely mass depletion, droplet temperature and droplet composition histories with time, have been evaluated in terms of the pertinent input parameters, namely the initial composition of the drop constituents and the free stream temperature. The present studies have been made on the basis of both (i) the interdiffusion (finite diffusion in the droplet phase) model, and (ii) the rapid mixing (infinite diffusion in the droplet phase) model. The results from both the models have been compared to ascertain the accuracy of the rapid mixing model.     

Numerical simulation of closed wet cooling towers for chilled ceiling systems

A numerical technique for evaluating the performance of a closed wet cooling tower for chilled ceiling systems is presented. The technique is based on computational flow dynamics (CFD) for the two-phase flow of gas and water droplets. The eulerian approach is used for the gas phase flow and the lagrangian approach for the water droplet phase flow, with two-way coupling between two phases. Numerical simulation indicates that CFD can be used to predict the performance of a closed wet cooling tower, given the appropriate rate of heat generation from the heat exchanger. The technique is suitable for optimization of the design and operation of the cooling tower for chilled ceilings.     

Simulating low temperature diesel combustion with improved spray models

Current spray models based on the Lagrangian-droplet and Eulerian-fluid (LDEF) method in the KIVA-3V code are strongly mesh dependent due to errors in predicting the droplet–gas relative velocity and errors in describing droplet–droplet collision and coalescence processes. To reduce the mesh dependence, gas-jet theory is introduced to predict the droplet–gas relative velocity, and a radius of influence (ROI) of collision methodology is established for each gas phase cell to estimate the collision probability for each parcel in the cell. Spray and combustion processes in a low temperature combustion diesel engine under early and late injection strategies with a fine mesh were predicted using the conventional LDEF model and compared with the measurements of soot, OH, fuel liquid and vapor distributions obtained by laser based diagnostics including, PLIF, LII, and Mie scattering. Then, the KIVA-3V code implemented with the improved spray model based on the gas-jet model and modifications of the spray models was utilized to simulate the processes on a relatively coarse numerical mesh. Comparison of the simulations between the fine and coarse meshes shows that the improved spray model can greatly reduce the mesh dependence for low temperature combustion diesel engine CFD simulations.     

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.     

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.     

A three-fluid model of two-phase dispersed-annular flow

A three-fluid model of the dispersed-annular regime of two-phase flow is suggested. The model is based on the conservation equations of mass, momentum, and energy for the gas phase, the dispersed phase (droplets), and the film. Additionally, this model includes the equation for the number density of particles of the dispersed phase, which is used to determine the mean particle size. Calculations are compared with experimental data on the entrainment coefficient, film and droplet flow rates, film thickness, pressure drop, and droplet size.     

Numerical model of evaporative cooling processes in a new type of cooling tower

A numerical model for studying the evaporative cooling processes that take place in a new type of cooling tower has been developed. In contrast to conventional cooling towers, this new device called Hydrosolar Roof presents lower droplet fall and uses renewable energy instead of fans to generate the air mass flow within the tower. The numerical model developed to analyse its performance is based on computational flow dynamics for the two-phase flow of humid air and water droplets. The Eulerian approach is used for the gas flow phase and the Lagrangian approach for the water droplet flow phase, with two-way coupling between both phases. Experimental results from a full-scale prototype in real conditions have been used for validation. The main results of this study show the strong influence of the average water drop size on efficiency of the system and reveal the effect of other variables like wet bulb temperature, water mass flow to air mass flow ratio and temperature gap between water inlet temperature and wet bulb temperature. Nondimensional numerical correlation of efficiency as a function of these significant parameters has been calculated.     

Numerical simulation of fuel sprays at high ambient pressure: the influence of real gas effects and gas solubility on droplet vaporisation

This paper deals with the numerical simulation of the vaporisation of an unsteady fuel spray at high ambient temperature and pressure solving the appropriate conservation equations. The extended droplet vaporisation model accounts for the effects of non-ideal droplet evaporation and gas solubility including the diffusion of heat and species within fuel droplets. To account for high-temperature and high-pressure conditions, the fuel properties and the phase boundary conditions are calculated by an equation of state and the liquid/vapour equilibrium is estimated from fugacities. Calculations for an unsteady diesel-like spray were performed for a gas temperature of 800 K and a pressure of 5 MPa and compared to experimental results for droplet velocities and diameter distribution. The spray model is based on an Eulerian/Lagrangian approach. The comparison shows that the differences between the various spray models are pronounced for single droplets. For droplet sprays the droplet diameter distribution is more influenced by secondary break-up and droplet coagulation.     

Analysis of evaporating mist flow for enhanced convective heat transfer

Enhancement of forced convective heat transport through the use of evaporating mist flow is investigated analytically and by numerical simulation. A two-phase mist, consisting of finely dispersed water droplets in an airstream, is introduced at the inlet of a longitudinally-finned heat sink. The latent heat absorbed by the evaporating droplets significantly reduces the sensible heating of the air inside the heat sink which translates into higher heat-dissipation capacities. The flow and heat transfer characteristics of mist flows are studied through a detailed numerical analysis of the mass, momentum and energy transport equations for the mist droplets and the airstream, which are treated as two separate phases. The coupling between the two phases is modeled through interaction terms in the transport equations. The effects of inlet mist droplet size and concentration on the thermal performance of the heat sink are analyzed parametrically. The results provide insight into the complex transport processes associated with mist flows. The simulations indicate that significantly higher heat transfer coefficients are obtained with mist flows as compared to air flows, highlighting the potential for the use of mist flows for enhanced thermal management applications.     

Influences of spray and operating parameters on penetration of vaporizing fuel droplets in a gas turbine combustor

The effects of inlet spray and operating parameters on penetration and vaporization histories of fuel droplets of a liquid fuel spray injected into a turbulent swirling flow of air through a typical can type gas turbine combustor, have been evaluated from numerical solutions of the conservation equations in gas and droplet phases. The computational scheme is based on the typical stochastic separated flow model of the gas-droplet flow within the combustor. A κ–ε model with wall function treatment for near wall region has been adopted for the solution of conservative equations in gas phase. The initial spray parameters are specified by a suitable PDF size distribution and a given spray cone angle. It has been recognized that the penetration of vaporizing droplets is reduced with an increase in inlet air swirl and spray cone angle. An increase in inlet air pressure or a decrease in inlet air temperature also results in a reduction in droplet penetration. The inlet air pressure and spray cone angle are found to be the most influencing parameters in this regard.     

Investigation of catalyst particle hydrodynamic and heat transfer in three phase flow circulating fluidized bed

Vaporization of gas oil droplets has significant effects on the gas-solid flow hydrodynamic and heat transfer characteristic. A three dimensional CFD model of the riser section of a CFB have been developed considering three phase flow hydrodynamic, heat transfer and evaporation of the feed droplets. Several experiments were performed in order to obtain the data needed to evaluate the model using a pilot scale CFB unit. The Eulerian approach was used to model both gas and catalyst particle phases comprising of continuity, momentum, heat transfer and species equations as well as an equation for solid phase granular temperature. The flow field and evaporating liquid droplet characteristics were modeled using the Lagrangian approach. The catalyst particle velocity and volume fraction were measured using a fiber optic probe. The comparison between model predictions of catalyst particle velocity and volume fraction with the experimental data indicated that they were in good agreements and the Syamlal-O'Brien was the most accurate drag equation. The CFD model was capable of predicting the main characteristic of the complex gas-solids flow hydrodynamic and heat transfer, including the cluster formation of the catalyst particles near the reactor wall. In addition, the simulation results showed droplet vaporization caused reduction of catalyst particle residence time. Moreover, the higher ratios of the feed to catalyst flow rates led to the lower values of the catalyst temperature profile minimum.     

Droplet evaporation in a turbulent high-pressure freestream – A numerical study

This paper presents a 3D numerical model for predicting the evaporation of a droplet exposed to a turbulent, high-pressure and high-temperature gaseous nitrogen freestream. The governing complete set of time-dependent conservation equations of mass, momentum, energy, and species concentration for both gas- and liquid-phase are solved numerically. The turbulence term in the conservation equations of the gas-phase is modeled by using the shear-stress transport (SST) closure model. In addition, variable thermophysical properties, unsteadiness of the gas and liquid phases, radiation, non-ideal gas behavior, and solubility of gas into the droplet are all accounted for in the numerical model. A wide range of freestream conditions is explored. The present numerical predictions revealed that the freestream turbulence intensity still has an effect on the droplet vaporization even at significantly high-pressure and high-temperature conditions, although this effect weakens with an increase in both ambient pressure and temperature. More importantly, new correlations are proposed to account for the effects of freestream ambient conditions on the droplet vaporization process.     

MODELING OF TRANSPORT PHENOMENA IN A GAS METAL ARC WELDING PROCESS

A numerical study of three-dimensional heat transfer and fluid flow in a moving gas metal arc welding (GMAW) process is performed by considering various driving forces of fluid flow such as buoyancy, Lorentz force, and surface tension. The computation of the current density distribution and the resulting Lorentz force field is performed by solving the Maxwell equations numerically in the domain of the workpiece. The phase change process during melting and solidification is modeled using the enthalpy-porosity technique. Mass and energy transports by droplet transfer are also considered through a thermal analysis of the electrode. The droplet heat addition to the molten pool is considered to be a volumetric heat source distributed in an imaginary cylindrical cavity within the weld pool ("cavity" model). This nature of the heat source distributed due to the falling droplets takes into account the momentum and thermal energy of the droplets. The numerical model is able to capture the well-known "finger" penetration commonly observed in the GMAW process. Numerical prediction regarding the weld pool shape and size is compared with the corresponding experimental results, showing good qualitative agreement between the two. The weld pool geometry is also found to be dependant on some key parameters of welding, such as the torch speed and power input to the workpiece.     

A numerical investigation of the evaporation process of a liquid droplet impinging onto a hot substrate

A numerical investigation of the evaporation process of n-heptane and water liquid droplets impinging onto a hot substrate is presented. Three different temperatures are investigated, covering flow regimes below and above Leidenfrost temperature. The Navier–Stokes equations expressing the flow distribution of the liquid and gas phases, coupled with the Volume of Fluid Method (VOF) for tracking the liquid–gas interface, are solved numerically using the finite volume methodology. Both two-dimensional axisymmetric and fully three-dimensional domains are utilized. An evaporation model coupled with the VOF methodology predicts the vapor blanket height between the evaporating droplet and the substrate, for cases with substrate temperature above the Leidenfrost point, and the formation of vapor bubbles in the region of nucleate boiling regime. The results are compared with available experimental data indicating the outcome of the impingement and the droplet shape during the impingement process, while additional information for the droplet evaporation rate and the temperature and vapor concentration fields is provided by the computational model.     

Evaporation of acoustically levitated multi-component liquid droplets

A theoretical model for the evaporation of multi-component liquid droplets based on the model by Abramzon and Sirignano is presented and applied to the evaporation of acoustically levitated droplets. The liquid phase is treated as a thermodynamically real fluid, using the UNIFAC method for calculating the component activities, and the gas phase as ideal. Computational results, which consist in the droplet surface and volume, temperature and composition as functions of time, are verified by experiments carried out with single droplets evaporating in an acoustic levitator. The results are in excellent agreement, suggesting that the model correctly captures the physico-chemical phenomena in multi-component liquid droplet evaporation.     

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.