Heating Of Fuel Droplets Research Articles

The Effects of Multistage Fuel-Oxidation Chemistry, Soot Radiation, and Real Gas Properties on the Operation Process of Compression Ignition Engines

The objectives of the study are to reveal the influence of multistage fuel-oxidation chemistry, thermal radiation of soot during the combustion of a small (submillimeter size) fuel droplet, and real gas effects on the operation process of compression ignition engines. The use of the multistage oxidation chemistry of iso-octane in the zero-dimensional approximation reveals the appearance of different combinations of cool, blue, and hot flames at different compression ratios and provides a kinetic interpretation of these phenomena that affect the heat release function. Cool flames are caused by the decomposition of alkyl hydroperoxide, during which a very reactive radical, OH, is formed. Blue flames are caused by the decomposition of H2O2 with the formation of OH. Hot flames are caused by the chain branching reaction between atomic hydrogen and molecular oxygen with the formation of OH and O. So-called “double” cool flames correspond to the sequential appearance of a separated cool flame and a low-intensity blue flame rather than two successive cool flames. The use of a one-dimensional model of fuel droplet heating, evaporation, autoignition, and combustion at temperatures and pressures relevant to compression ignition engines shows that the thermal radiation of soot during the combustion of small (submillimeter size) droplets is insignificant and can be neglected. The use of real gas caloric and thermal equations of state of the matter in a three-dimensional simulation of the operation process in a diesel engine demonstrates the significant effect of real gas properties on the engine pressure diagram and on the NO and soot emissions: real gas effects reduce the maximum pressure and mass-averaged temperature in the combustion chamber by about 6 and 9%, respectively, increases the autoignition delay time by a 1.6 crank angle degree, increase the maximum heat release rate by 20%, and reduce the yields of NO and soot by a factor of 2 and 4, respectively.

Combustion of Fuel Surrogates: An Application to Gas Turbine Engines

The previously developed approaches for fuel droplet heating and evaporation processes, mainly using the Discrete Multi Component Model (DMCM), are investigated for the aerodynamic combustion simulation. The models have been recently improved and generalised for a broad range of bio-fossil fuel blends so that the application areas are broadened with an increased accuracy. The main distinctive features of these models are that they consider the impacts of species’ thermal conductivities and diffusivities within the droplets in order to account for the temperature gradient, transient diffusion of species and recirculation. A formulation of fuel surrogates is made using the recently introduced model, referred to as “Complex Fuel Surrogate Model (CFSM)”, and analysing their heating, evaporation and combustion characteristics. The CFSM is aimed to reduce the full composition of fuel to a much smaller number of components based on their mass fractions, and to formulate fuel surrogates. Such an approach has provided a proof of concept with the implementation of the developed model into a commercial CFD code ANSYS Fluent. A case study is made for the CFD modelling of a gas turbine engine using a kerosene fuel surrogate, which is the first of its kind. The surrogate is proposed using the CFSM, with the aim to reduce the computational time and improve the simulation accuracy of the CFD model.

Modelling of multi-component kerosene and surrogate fuel droplet heating and evaporation characteristics: A comparative analysis

A Discrete Component Model (DCM) is applied to study the heating and evaporation of suspended kerosene and kerosene surrogate droplets. The effects of natural convection are taken into account using the Churchill approximation, whilst the effects of heat addition from the supporting fibre are modelled using the assumption that heat supplied via the fibre is uniformly distributed within the droplet volume. The results of taking into account and ignoring the above effects are investigated. It is shown that the effect of supporting fibre can be ignored in the analysis of these droplets. In contrast, the effect of natural convection cannot be ignored. The time evolution of droplet radii predicted by the DCM, taking into account the effects of natural convection and supporting fibre, is shown to be close to experimental predictions of this parameter for gas temperatures in the range 500 °C to 700 °C. The heating and evaporation of kerosene droplets are compared with those for droplets of various kerosene surrogate fuels, including eleven surrogate fuels proposed in the literature, and two original compositions. Considering the balance between the heating and evaporation characteristics of droplets we conclude that those of the original surrogate SU1 and the modified Utah surrogate are the closest to those of kerosene droplets.

Blended E85–Diesel Fuel Droplet Heating and Evaporation

The multidimensional quasi-discrete (MDQD) model is applied to the analysis of heating and evaporation of mixtures of E85 (85 vol % ethanol and 15 vol % gasoline) with diesel fuel, commonly known as “E85–diesel” blends, using the universal quasi-chemical functional group activity coefficients model for the calculation of vapor pressure. The contribution of 119 components of E85–diesel fuel blends is taken into account, but replaced with smaller number of components/quasi-components, under conditions representative of diesel engines. Our results show that high fractions of E85–diesel fuel blends have a significant impact on the evolutions of droplet radii and surface temperatures. For instance, droplet lifetime and surface temperature for a blend of 50 vol % E85 and 50 vol % diesel are 23.2% and up to 3.4% less than those of pure diesel fuel, respectively. The application of the MDQD model has improved the computational efficiency significantly with minimal sacrifice to accuracy. This approach leads to a s...

Ethanol/Gasoline Droplet Heating and Evaporation: Effects of Fuel Blends and Ambient Conditions

This paper focuses on the modeling of blended ethanol/gasoline fuel droplet heating and evaporation in conditions representative of internal combustion engines. The effects of ambient conditions (ambient pressure, ambient temperature, and radiative temperature) and ethanol/gasoline fuel blend ratios on multicomponent fuel droplet heating and evaporation are investigated using the analytical solutions to the heat-transfer and species diffusion equations. The ambient pressures, gas and radiative temperatures, and ethanol/gasoline fuel ratios are considered in the ranges of 3–30 bar, 400–650 K, 1000–2000 K, and 0% (pure gasoline)–100% (pure ethanol), respectively. Transient diffusion of 21 hydrocarbons, temperature gradient, and recirculation inside droplets are accounted for using the discrete component model. The droplet lifetimes of all mixtures decrease when ambient temperatures increase, under all ambient pressures (3–30 bar). The combination of ethanol and gasoline fuels has a noticeable impact on drop...

Models for droplet heating and evaporation: an application to biodiesel, diesel and gasoline fuels

This paper presents our recent progress in the modelling of automotive fuel droplet heating and evaporation processes in conditions close to those in direct-injection internal-combustion engines. Three types of automotive-fuels are considered: biodiesel, diesel and gasoline fuels. Modelling of biodiesel fuel droplets is based on the application of the discrete component (DC) model. A distinctive feature of this model is that it is based on the analytical solutions to the transient heat conduction and species diffusion equations in the liquid phase, taking into account the effects of recirculation. The application of the DC model to fossil fuels (containing potentially hundreds of components), however, is computationally expensive. The modelling of these fuels is based on the recently introduced multi-dimensional quasi-discrete (MDQD) model. This model replaces a large number of components in diesel and gasoline fuels with a much smaller number of quasi-components/components without losing the main features of the original DC model. The MDQD model is shown to accurately predict droplet temperatures and evaporation times and to be much more computationally efficient than the DC model. The main features of these models and their applications to three types of automotive fuel droplets are summarised and discussed.

Modelling of blended Diesel and biodiesel fuel droplet heating and evaporation

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 predicted for pure Diesel fuel. Also, it is shown that the approximations of the actual compositions of B5 (5% SME and 95% Diesel) and B50 (50% SME and 50% Diesel) dual-fuels by 17 quasi-components/components, using the MDQD model, lead to under-predictions in droplet lifetimes by up to 9% and 4%, respectively, under the same engine conditions. The application of the latter model has resulted in above 83% reduction in CPU time compared to the case when all 105 components are taken into account using the discrete component model.

Modelling of automotive fuel droplet heating and evaporation: mathematical tools and approximations

New mathematical tools and approximations developed for the analysis of automotive fuel droplet heating and evaporation are summarised. The approach to modelling biodiesel fuel droplets is based on the application of the Discrete Component Model (DCM), while the approach to modelling Diesel fuel droplets is based on the application of the recently developed multi-dimensional quasi-discrete model. In both cases, the models are applied in combination with the Effective Thermal Conductivity/Effective Diffusivity model and the implementation in the numerical code of the analytical solutions to heat transfer and species diffusion equations inside droplets. It is shown that the approximation of biodiesel fuel by a single component leads to under-prediction of droplet evaporation time by up to 13% which can be acceptable as a crude approximation in some applications. The composition of Diesel fuel was simplified and reduced to only 98 components. The approximation of 98 components of Diesel fuel with 15 quasi-components/components leads to under-prediction of droplet evaporation time by about 3% which is acceptable in most engineering applications. At the same time, the approximation of Diesel fuel by a single component and 20 alkane components leads to a decrease in the evaporation time by about 19%, compared with the case of approximation of Diesel fuel with 98 components. The approximation of Diesel fuel with a single alkane quasi-component (C14.763H31.526) leads to under-prediction of the evaporation time by about 35% which is not acceptable even for qualitative analysis of the process. In the case when n-dodecane is chosen as the single alkane component, the above-mentioned under-prediction increases to about 44%.

Modelling of biodiesel fuel droplet heating and evaporation: Effects of fuel composition

A comparative analysis of predictions of several models of biodiesel fuel droplet heating and evaporation in realistic Diesel engine-like conditions is presented. Nineteen types of biodiesel fuels composed of methyl esters are used for the analysis. It is shown that the model, based on the assumption that the diffusivity of species in droplets is infinitely fast and the liquid thermal conductivity is infinitely large, under-predicts the droplet evaporation time compared with the model taking into account the effects of finite diffusivity and conductivity, by up to about 15%. A similar under-predictions of the model in which the transient diffusion of species is ignored and the liquid thermal conductivity is assumed to be infinitely large, is shown to be about 26%. The latter result is not consistent with the earlier finding, based on the analysis of only five types of biodiesel fuels and different input parameters, in which it was shown that the deviations between the evaporation times predicted by these models do not exceed about 5.5%. As in the case of Diesel and gasoline fuel droplets, for biodiesel droplets the multi-component models predict higher droplet surface temperatures at the final stages of droplet evaporation and longer evaporation times than for the single-component models. This is related to the fact that at the final stages of droplet evaporation the mass fraction of heavier species, which evaporate more slowly than the lighter species and have higher boiling temperatures, increases at the expense of lighter species.

New approaches to the modelling of multi-component fuel droplet heating and evaporation

The previously suggested quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets is described. The dependence of density, viscosity, heat capacity and thermal conductivity of liquid components on carbon numbers n and temperatures is taken into account. The effects of temperature gradient and quasi-component diffusion inside droplets are taken into account. The analysis is based on the Effective Thermal Conductivity/Effective Diffusivity (ETC/ED) model. This model is applied to the analysis of Diesel and gasoline fuel droplet heating and evaporation. The components with relatively close n are replaced by quasi-components with properties calculated as average properties of the a priori defined groups of actual components. Thus the analysis of the heating and evaporation of droplets consisting of many components is replaced with the analysis of the heating and evaporation of droplets consisting of relatively few quasi-components. It is demonstrated that for Diesel and gasoline fuel droplets the predictions of the model based on five quasi-components are almost indistinguishable from the predictions of the model based on twenty quasi-components for Diesel fuel droplets and are very close to the predictions of the model based on thirteen quasi-components for gasoline fuel droplets. It is recommended that in the cases of both Diesel and gasoline spray combustion modelling, the analysis of droplet heating and evaporation is based on as little as five quasi-components.

A multi-dimensional quasi-discrete model for the analysis of Diesel fuel droplet heating and evaporation

A new multi-dimensional quasi-discrete model is suggested and tested for the analysis of heating and evaporation of Diesel fuel droplets. As in the original quasi-discrete model suggested earlier, the components of Diesel fuel with close thermodynamic and transport properties are grouped together to form quasi-components. In contrast to the original quasi-discrete model, the new model takes into account the contribution of not only alkanes, but also various other groups of hydrocarbons in Diesel fuels; quasi-components are formed within individual groups. Also, in contrast to the original quasi-discrete model, the contributions of individual components are not approximated by the distribution function of carbon numbers. The formation of quasi-components is based on taking into account the contributions of individual components without any approximations. Groups contributing small molar fractions to the composition of Diesel fuel (less than about 1.5%) are replaced with characteristic components. The actual Diesel fuel is simplified to form six groups: alkanes, cycloalkanes, bicycloalkanes, alkylbenzenes, indanes & tetralines, and naphthalenes, and 3 components C19H34 (tricycloalkane), C13H12 (diaromatic), and C14H10 (phenanthrene). It is shown that the approximation of Diesel fuel by 15 quasi-components and components, leads to errors in estimated temperatures and evaporation times in typical Diesel engine conditions not exceeding about 3.7% and 2.5% respectively, which is acceptable for most engineering applications.

Transient Heating and Evaporation of Moving Fuel Droplets

In combustion devices involving direct injection of low-volatility liquid fuels (e.g., bio-oils from pyrolysis process), transient heating and vaporization of fuel droplets is a controlling factor in ignition and combustion of the fuel vapor/air mixture. As a result, some experimental and numerical efforts have been made on this topic. In this paper, a comprehensive 3D model that addresses the internal flow circulation, heat and mass transfer within a moving droplet has been successfully developed. The model is calibrated by analytical solutions for simplified cases and validated by experimental results available in literature. The model not only reliably produces all the details that help to achieve an in-depth understanding of the underlying physical processes and to derive simplified models for liquid fuel droplet heating and evaporation, but also can be readily reformulated for modeling of conversion of solid fuel particles.

Modelling of biodiesel fuel droplet heating and evaporation

Biodiesel fuel droplet heating and evaporation is investigated using the previously developed models, taking into account temperature gradient, recirculation, and species diffusion within droplets. The analysis is focused on four types of biodiesel fuels: Palm Methyl Ester, Hemp Methyl Esters, Rapeseed oil Methyl Ester, and Soybean oil Methyl Ester. These fuels contain up to 15 various methyl esters and possibly small amounts of unspecified additives, which are treated as methyl esters with some average characteristics. Calculations are performed using two approaches: (1) taking into account the contribution of all components of biodiesel fuels (up to 16); and (2) assuming that these fuels can be treated as a one component fuel with averaged transport and thermodynamic coefficients. It is pointed out that for all types of biodiesel fuel the predictions of the multi-component and single component models are rather close (the droplet evaporation times predicted by these models differ by less than about 5.5%). This difference is much smaller than observed in the case of Diesel and gasoline fuel droplets, and is related to the fact that in the case of Diesel and gasoline fuel droplets the contribution of components in a wide range of molar masses and enthalpies of evaporation needs to be taken into account, while in the case of biodiesel fuels the main contribution comes from the components in a narrow range of molar masses, boiling temperatures and enthalpies of evaporation. As in the case of Diesel and gasoline fuel droplets, the multi-component model predicts higher droplet surface temperature and longer evaporation times than the single component model.

Modelling of heating and evaporation of gasoline fuel droplets: A comparative analysis of approximations

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.

Physical Continuous Model of Heating, Evaporation and Ignition of Polydisperse Fuel Droplets

A new modeling of heating and evaporation of fuel droplets and ignition of a fuel vapour/ air mixture in continuousform is suggested. The size distribution of fuel droplets is assumed to be continuous and found from thesolution of the kinetic equation for the probability density function (PDF). The semi-transparency of droplets, thedifference between the gas temperature and the external temperature are take into account. The model represent indimensionless from, and the dynamics of the system is present in term of the dynamics of a multi-scale, singularlyperturbed system (SPS)

DROPLET HEATING AND EVAPORATION−RECENT RESULTS AND UNSOLVED PROBLEMS

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.

Transient heating of an evaporating droplet

Two new solutions to the heat conduction equation, describing transient heating of an evaporating droplet, are suggested. 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. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. This approach can be considered as the generalisation of the approach currently used in all research and commercial CFD codes known to us (e.g. KIVA, FLUENT, PHOENICS), in which it is assumed that droplet radius is constant during the timestep. The new analytical solution has been incorporated into a zero-dimensional CFD code and applied to the analysis of Diesel fuel droplet heating and evaporation in typical engine conditions. The results have been compared with those which follow from the conventional (traditional) approach to modelling droplet heating and evaporation, based on the assumption that the droplet radius is constant over the timestep (but changes from one step to another). It has been pointed out that the new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. The relative difference between evaporation times is shown to be practically independent of the values of the initial droplet radii and to increase with increasing gas temperatures. Larger timesteps can be used in the case of the new approach compared with the conventional one to achieve the same accuracy of calculation. It is recommended that the effect of a moving boundary on droplet heating is taken into account in modelling droplet heating and evaporation in CFD codes.

Kinetic modelling of fuel droplet heating and evaporation: calculations and approximations

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.

Numerical Modeling of Droplet Transient Heating and Evaporation

Several approaches to numerical modelling of liquid droplet heating and evaporation by convection and radiation from the surrounding hot gas are discussed. The finite thermal conductivity of liquid, recirculation in droplets, and time dependence of gas temperature and the convection heat transfer coefficient are taken into account. For the constant and almost constant convection heat transfer coefficient the new analytical solutions of the heat conduction equation inside droplets are incorporated into the numerical code. For the abitrary convection heat transfer coefficient the numerical solution of the latter equation is replaced by the numerical solution of the Volterra integral equation of the second kind. Direct comparison between these approaches shows that the solution based on the assumption of constant convective heat transfer coefficient is the most computer efficient for implementation into numerical codes. The results of the application of this approach to the numerical modelling of fuel droplet heating and evaporation in conditions relevant to diesel engines are briefly discussed. This approach is more effective than the approach based on the numerical solution of the discretised heat conduction equation inside the droplet, and more accurate than the solution based on the parabolic temperature profile model. The relatively small contribution of thermal radiation to droplet heating allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets.

Approximate Analysis of Thermal Radiation Absorption in Fuel Droplets

The values of absorption coefficients of gasoline fuel (BP Pump Grade 95 RON ULG (research octane number unleaded gasoline)), 2,2,4-trimethylpentane (CH 3 ) 2 CHCH 2 C(CH 3 ) 3 (iso-octane) and 3-pentanone CH 3 CH 2 COCH 2 CH 3 have been measured experimentally in the range of wavelengths between 0.2 μm and 4 μm. The values of the indices of absorption, calculated based on these coefficients, have been compared with those previously obtained for low sulphur ESSO AF1313 diesel fuel. These values are generally lower for pure substances (e.g., iso-octane and 3-pentanone) than for diesel and gasoline fuels. The values of the average absorption efficiency factor for all fuels are approximated by a power function aR b d , where R d is the droplet radius a and b in turn are approximated by piecewise quadratic functions of the radiation temperature, with the coefficients calculated separately in the ranges of droplet radii 2-5 μm, 5-50 μm, 50-100 μm, and 100-200 μm for all fuels. This new approximation is shown to be more accurate compared with the case when a and b are approximated by quadratic functions or fourth power polynomials of the radiation temperature, with the coefficients calculated in the whole range 2-200 μm. This difference in the approximations of a and b, however, is shown to have little effect on modeling of fuel droplet heating and evaporation in conditions typical for internal combustion engines, especially in the case of diesel fuel and 3-pentanone.