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Simple approximate formulae describing temporal evolution of diesel fuel droplet radii and temperatures predicted by the kinetic model are suggested. These formulae are valid in the range of gas temperatures relevant to diesel engine-like... more
Simple approximate formulae describing temporal evolution of diesel fuel droplet radii and temperatures predicted by the kinetic model are suggested. These formulae are valid in the range of gas temperatures relevant to diesel engine-like conditions and fixed values of initial droplet radii, or in the range of initial droplet radii relevant to diesel engine-like conditions and fixed values of gas temperature. During the time period before the hydrodynamic model predicts complete droplet evaporation, these approximations are based on the calculation of the correction to the prediction of the hydrodynamic model. At longer times, the approximations at the earlier times are extrapolated up until the total evaporation of the droplet, using quadratic fittings. The new approximations are shown to be reasonably accurate for predicting the temporal evolution of droplet radii and droplet evaporation times. The predictions of droplet temperature turned out to be less accurate than those of droplet radii, but this accuracy is believed to be sufficient for many practical applications.
A phenomenological study of vortex ring-like structures in gasoline fuel sprays is presented for two types of production fuel injectors: a low-pressure, port fuel injector (PFI) and a high-pressure atomizer that injects fuel directly into... more
A phenomenological study of vortex ring-like structures in gasoline fuel sprays is presented for two types of production fuel injectors: a low-pressure, port fuel injector (PFI) and a high-pressure atomizer that injects fuel directly into an engine combustion chamber (G-DI). High-speed photography and phase Doppler anemometry (PDA) were used to study the fuel sprays. In general, each spray was seen to comprise three distinct periods: an initial, unsteady phase; a quasi-steady injection phase; and an exponential trailing phase. For both injectors, vortex ring-like structures could be clearly traced in the tail of the sprays. The location of the region of maximal vorticity of the droplet and gas mixture was used to calculate the temporal evolution of the radial and axial components of the translational velocity of the vortex ring-like structures. The radial components of this velocity remained close to zero in both cases. The experimental results were used to evaluate the robustness o...
The results of modeling fluid dynamics, heat/mass transfer, and combustion processes in diesel engine-like conditions are presented with a view to establishing the effects of droplet heating and evaporation models on the prediction of... more
The results of modeling fluid dynamics, heat/mass transfer, and combustion processes in diesel engine-like conditions are presented with a view to establishing the effects of droplet heating and evaporation models on the prediction of spray penetration, in-cylinder gas pressure, and the amount of fuel vapor, O2, CO2, CO, and NO. The following models have been studied: the infinite thermal conductivity (ITC) and effective thermal conductivity (ETC) liquid phase models, the basic gas phase model, and the gas phase model suggested by Abramzon and Sirignano (1989). A modified version of the TAB (Taylor analogy breakup) model was used for modeling the droplet breakup process. It is pointed out that the ETC model leads to the prediction of shorter spray penetration, in agreement with experimental data, when compared with the ITC model. The effect of the liquid phase model on predicted gas pressure in diesel engines is shown to be relatively weak. The predicted amounts of fuel vapor, O2, CO2, CO, and NO are strongly affected by the choice of the liquid phase model but practically unaffected by the choice of the gas phase model.
ABSTRACT The results of recent developments of analytical vortex ring models and the applications of these models to interpretation of the experimentally observed dynamics of vortex ring–like structures in gasoline sprays, under... more
ABSTRACT The results of recent developments of analytical vortex ring models and the applications of these models to interpretation of the experimentally observed dynamics of vortex ring–like structures in gasoline sprays, under non-evaporating conditions, are summarised. Analytical formulae in the limit of small Reynolds numbers (Re), are compared with numerical solutions. Particular attention is focused on the generalised vortex ring model in which the time evolution of the thickness of the vortex ring core L is approximated as , where a and b are constants (1 ≤ b ≤ 1/2). This model incorporates both the laminar model for b=1/2 and fully turbulent model for b=1/4. The values of velocities in the region of maximal vorticity, predicted by the generalised vortex ring model, are compared with the results of experimental studies of fuel droplets distributed in vortex ring-like structures in two gasoline injectors, under cold-start, engine-like conditions. Liquid iso-octane at a temperature of 22 °C was injected at a frequency of 1 Hz and a pressure of 100 bar (direct injection) and 3.5 bar (port injection) into air at atmospheric pressure and a temperature of 20 °C. Phase Doppler Anemometry was performed over a fine measurement grid that covered the whole spray. The decaying phase of fuel injection showed the most clearly defined vortex rings. The identification of their locations in each time step permitted the determination of the velocities of their displacement in the axial and radial directions. Although the radial component of velocity in both these regions is equal to zero, the location of both changes with time. This leads to an effective radial velocity component; the latter depends on b. Most of the values of the axial velocity of the vortex rings lie between the theoretically predicted values corresponding to the late stage of vortex ring development and b=1/4 (fully developed turbulence) and 1/2 (laminar case).
The paper presents a new approach to the modelling of heating and evaporation of dual-fuel droplets with a specific application to blends of biodiesel (represented by the widely used soybean methyl ester, SME) and Diesel fuels in... more
The paper presents a new approach to the modelling of heating and evaporation of dual-fuel droplets with a specific application to blends of biodiesel (represented by the widely used soybean methyl ester, SME) and Diesel fuels in conditions representative of internal combustion engines. The original compositions, with up to 105 components of Diesel and biodiesel fuels, are replaced with a smaller number of components and quasi-components using the recently introduced multi-dimensional quasi-discrete (MDQD) model. Transient diffusion of these components and quasi-components in the liquid phase and temperature gradient and recirculation inside droplets are taken into account. The results are compared with the predictions of the case when blended biodiesel/Diesel fuel droplets are represented by pure biodiesel fuel or pure Diesel fuel droplets. It is shown that droplet evaporation time and surface temperature predicted for 100% SME, representing pure biodiesel fuel, are close to those ...
Research Interests:
Some recently developed approaches to the hydrodynamic, kinetic and molecular dynamic modelling of mono- and multi-component droplet heating and evaporation are discussed. New approaches to taking into account the effect of the moving... more
Some recently developed approaches to the hydrodynamic, kinetic and molecular dynamic modelling of mono- and multi-component droplet heating and evaporation are discussed. New approaches to taking into account the effect of the moving boundary during droplet evaporation on droplet heating for mono- and multi-component droplets are summarised. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution to the species diffusion equation inside droplets, is described. A quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets, and its application to modelling the heating and evaporation of realistic Diesel and gasoline fuel droplets are described. A new kinetic algorithm, taking into account the effect of inelastic collisions, is reviewed. The results of applications of molecular dynamics simulations to study the evaporation of n-dodecane droplets are described.
Research Interests:
A new approach to numerical simulation of two-phase, two-dimensional flows (sprays or two-phase jets), based on a combination of the full Lagrangian method for the dispersed phase and the mesh-free vortex blob method for the carrier... more
A new approach to numerical simulation of two-phase, two-dimensional flows (sprays or two-phase jets), based on a combination of the full Lagrangian method for the dispersed phase and the mesh-free vortex blob method for the carrier phase, is suggested. The problem of calculation of all parameters in both phases (including particle concentration) is reduced to the solution of a high-order system of ordinary differential equations, describing transient processes in both carrier and dispersed phases. This allows one to study in detail local zones of particle accumulation in complex transient flows, including those with multiple intersections of particle trajectories and the formation of “folds” in the concentration field of the dispersed phase. The new approach is applied to modelling of the time evolution of a two-phase Lamb vortex and the development of an impulse two-phase jet. These examples involve the formation of local zones of particle accumulation and regions of multiple intersections of particle trajectories. The correct simulation of these flow features is expected to involve serious difficulties when the conventional Eulerian/Lagrangian methods, described in the literature, are used.
A brief review of models of diesel fuel spray penetration, developed at the University of Brighton, are presented. These refer to the initial stage of spray penetration and the two-phase flow stage, when the relative velocity between... more
A brief review of models of diesel fuel spray penetration, developed at the University of Brighton, are presented. These refer to the initial stage of spray penetration and the two-phase flow stage, when the relative velocity between droplets and gas can be ignored. The predictions of the two-phase models of spray penetration are compared with the results of experimental studies. A rapid compression diesel spray rig, based at Brighton University, and a high-pressure dimethyl ether spray chamber, based at Chungbuk National University, have been used. In both cases the experimental results are shown to be in agreement with the prediction of theoretical models.
The main features of the previously developed model for two-component droplet heating and evaporation into a neutral gas (nitrogen) are summarised. The results of functionality testing of this model for heat and mass transfer between two... more
The main features of the previously developed model for two-component droplet heating and evaporation into a neutral gas (nitrogen) are summarised. The results of functionality testing of this model for heat and mass transfer between two parallel plates are reviewed. New results of the application of the model to the analysis of a twocomponent (n-dodecane and p-dipropylbenzene) droplet’s heating and evaporation in a high pressure background gas (nitrogen) in Diesel engine-like conditions are presented. As in the case of the previously developed similar models, the model used in the analysis is based on the introduction of the kinetic region in the immediate vicinity of the droplets and the hydrodynamic region. The model is tested for the analysis of heating and evaporation of a droplet with initial radius and temperature equal to 5 μm and 300 K, respectively, immersed into gas with temperatures 1000 K and 700 K for several mixtures of n-dodecane and p-dipropylbenzene. It is shown that the increase in mass fraction of p-dipropylbenzene and kinetic effects lead to the increase in predicted droplet evaporation time. It is shown that the kinetic effects increase with increasing gas temperature and molar fraction of p-dipropylbenzene.
Abstract A meshless method for modelling of 2D transient, non-isothermal, gas-droplet flows with phase transitions, based on a combination of the viscous-vortex and thermal-blob methods for the carrier phase with the Lagrangian approach... more
Abstract A meshless method for modelling of 2D transient, non-isothermal, gas-droplet flows with phase transitions, based on a combination of the viscous-vortex and thermal-blob methods for the carrier phase with the Lagrangian approach for the dispersed phase, is developed. The one-way coupled, two-fluid approach is used in the analysis. The method makes it possible to avoid the ‘remeshing’ procedure (recalculation of flow parameters from Eulerian to Lagrangian grids) and reduces the problem to the solution of three systems of ordinary differential equations, describing the motion of viscous-vortex blobs, thermal blobs, and evaporating droplets. The gas velocity field is restored using the Biot–Savart integral. The numerical algorithm is verified against the analytical solution for a non-isothermal Lamb vortex and some asymptotic results known in the literature. The method is applied to modelling of an impulse two-phase cold jet injected into a quiescent hot gas, taking into account droplet evaporation. Various flow patterns are obtained in the calculations, depending on the initial droplet size: (i) low-inertia droplets, evaporating at a higher rate, form ring-like structures and are accumulated only behind the vortex pair; (ii) large droplets move closer to the jet axis, with their sizes remaining almost unchanged; and (iii) intermediate-size droplets are accumulated in a curved band whose ends trail in the periphery behind the head of the cloud, with larger droplets being collected at the front of the two-phase region.
ABSTRACT Modelling of gasoline fuel droplet heating and evaporation processes is investigated using several approximations of this fuel. These are quasi-components used in the quasi-discrete model and the approximations of these... more
ABSTRACT Modelling of gasoline fuel droplet heating and evaporation processes is investigated using several approximations of this fuel. These are quasi-components used in the quasi-discrete model and the approximations of these quasi-components (Surrogate I (molar fractions: 83.0% n-C6H14 + 15.6% n-C10H22 + 1.4% n-C14H30) and Surrogate II (molar fractions: 83.0% n-C7H16 + 15.6% n-C11H24 + 1.4% n-C15H32)). Also, we have used Surrogate A (molar fractions: 56% n-C7H16 + 28% iso-C8H18 + 17% C7H8) and Surrogate B (molar fractions: 63% n-C7H16 + 20% iso-C8H18 + 17% C7H8), originally introduced based on the closeness of the ignition delay of surrogates to that of gasoline fuel. The predictions of droplet radii and temperatures based on three quasi-components and their approximations (Surrogates I and II) are shown to be much more accurate than the predictions using Surrogates A and B.
The analysis of the processes in sprays, taking into account the contribution of all spatial and temporal scales, is not feasible in most cases due to its complexity. The approach used in most applications is based on separate analysis of... more
The analysis of the processes in sprays, taking into account the contribution of all spatial and temporal scales, is not feasible in most cases due to its complexity. The approach used in most applications is based on separate analysis of the processes at various scales, and the analysis of the link between these processes. This approach is demonstrated for the
Recently developed approaches to the hydrodynamic, kinetic, and molecular dynamic modeling of fuel droplet heating and evaporation are reviewed. Two new solutions to the heat conduction equation, taking into account the effect of the... more
Recently developed approaches to the hydrodynamic, kinetic, and molecular dynamic modeling of fuel droplet heating and evaporation are reviewed. Two new solutions to the heat conduction equation, taking into account the effect of the moving boundary during transient heating of an evaporating droplet, are discussed. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterra integral equation of the second kind. The new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. An alternative approach to the same problem has been based on the assumption that the time evolution of a droplet's radius, Rd (t), is known. For sufficiently small time steps, the time evolutions of droplet surface temperatures and radii predicted by both approaches coincide. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution to the species diffusion equation inside droplets, is discussed. Two new solutions to the equation, describing the diffusion of species during multi-component droplet evaporation taking into account the effects of the moving boundary, are presented. A quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets is described. The predictions of the model, taking into account the effects of the moving boundary during the time steps on the solutions to the heat transfer and species diffusion equations, are discussed. A new algorithm, based on simple approximations of the kinetic results, suitable for engineering applications, is discussed. The results of kinetic modeling, taking into account the effects of inelastic collisions, and applications of molecular dynamics simulations to study the evaporation of n-dodecane droplets are briefly summarized. The most challenging and practically important unsolved problems with regard to the modeling of droplet heating and evaporation are summarized and discussed.
A new model for fuel spray penetration (location of spray tip) is suggested and validated against available experimental data. Simple analytical expressions for fuel spray penetration are derived in two limiting cases: the initial stage... more
A new model for fuel spray penetration (location of spray tip) is suggested and validated against available experimental data. Simple analytical expressions for fuel spray penetration are derived in two limiting cases: the initial stage and the two-phase flow regime. At the initial stage, the effects of droplet drag and entrainment of air are accounted for. In the case of

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Previously developed droplet heating and evaporation models, taking into account temperature gradient, recirculation, and species diffusion within droplets, and their application to the analysis of commercial automotive fuel droplets are... more
Previously developed droplet heating and evaporation models, taking into account temperature gradient, recirculation, and species diffusion within droplets, and their application to the analysis of commercial automotive fuel droplets are reviewed. It is shown that the most efficient analysis of Diesel fuel droplet heating and evaporation is based on the MDQD (multi-dimensional quasi-discrete) model, taking into account the contribution of all groups of hydrocarbons in automotive fuels. The main features of this model are summarised and its new application to the analysis of droplets in Diesel engine-like conditions, taking into account time-dependent velocities, is described. In the MDQD model, Diesel fuel is approximated by six groups of components: alkanes, cycloalkanes, bicycloalkanes, alkylbenzenes, indanes & tetralines, naphthalenes, and three characteristic components C19H34 (tricycloalkane), C13H12 (diaromatic), and C14H10 (phenanthrene). It is shown that errors in estimated temperatures and evaporation times in typical Diesel engine conditions, using the approximation of Diesel fuel by 15 quasi-components/components compared to the case when all 98 components are taken into account, are up to 1% and 3%, respectively. This is acceptable in most engineering applications. This approximation has also reduced CPU time by about 6 times compared with the case when the contribution of 98 components is taken into account. The approximations of Diesel fuel with n-dodecane (widely used in engineering modelling) and 20 alkane components lead to under-prediction of the evaporation time by over 50% and 22%, respectively.
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"A detailed comparative analysis of transport and thermodynamic properties of biodiesel fuels and components of these fuels is presented. Five types of biodiesel fuels are considered: Palm Methyl Ester, produced from palm oil; Hemp... more
"A detailed comparative analysis of transport and thermodynamic properties of biodiesel fuels and
components of these fuels is presented. Five types of biodiesel fuels are considered: Palm Methyl
Ester, produced from palm oil; Hemp Methyl Esters, produced from hemp oil in the Ukraine and
European Union; Rapeseed oil Methyl Ester, produced from rapeseed oil in the Ukraine; and Soybean
oil Methyl Ester, produced from soybean oil. Up to 16 components (methyl esters in most cases) of
these fuels are considered. The results are applied to the analysis of biodiesel fuel droplet heating and
evaporation in conditions relevant to internal combustion engines, using the model described
elsewhere."
Research Interests:
Research Interests:
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The main features of the previously developed model for two-component droplet heating and evaporation into a neutral gas (nitrogen) are summarised. The results of functionality testing of this model for heat and mass transfer between two... more
The main features of the previously developed model for two-component droplet heating and evaporation into a
neutral gas (nitrogen) are summarised. The results of functionality testing of this model for heat and mass transfer
between two parallel plates are reviewed. New results of the application of the model to the analysis of a twocomponent
(n-dodecane and p-dipropylbenzene) droplet’s heating and evaporation in a high pressure background
gas (nitrogen) in Diesel engine-like conditions are presented. As in the case of the previously developed similar
models, the model used in the analysis is based on the introduction of the kinetic region in the immediate vicinity of
the droplets and the hydrodynamic region. The model is tested for the analysis of heating and evaporation of a droplet
with initial radius and temperature equal to 5 μm and 300 K, respectively, immersed into gas with temperatures 1000
K and 700 K for several mixtures of n-dodecane and p-dipropylbenzene. It is shown that the increase in mass
fraction of p-dipropylbenzene and kinetic effects lead to the increase in predicted droplet evaporation time. It is shown
that the kinetic effects increase with increasing gas temperature and molar fraction of p-dipropylbenzene.
Research Interests: