Fuel Droplet Heating and Evaporation: Analysis of Liquid and Gas Phase Models (original) (raw)
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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 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.
Models for droplet heating and evaporation: an application to biodiesel, diesel and gasoline fuels
International Journal of Engineering Systems Modelling and Simulation, 2017
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.
New approaches to the modelling of multi-component fuel droplet heating and evaporation
Journal of Physics: Conference Series, 2015
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.
Modelling of Automotive Fuel Droplet Heating and Evaporation
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%.
2007
A review of liquid and gas phase models for fuel droplet heating and evaporation, suitable for implementation into CFD codes with a view to modelling the processes in Diesel engines, is presented. To describe properties of 'hot' Diesel fuel sprays, new sub-models for spray break-up, droplet heating and evaporation and Shell autoignition were implemented into the KIVA II CFD code. This customised version of the KIVA II code was used to simulate autoignition in Diesel engines. The results of simulation were shown to be consistent with in-house experimental data referring to autoignition timing at in-cylinder pressures from 5 to 9 MPa and an injection pressure of 160 MPa. The autoignition delay time is shown to be sensitive to the choice of liquid phase models for droplet heating, but not sensitive to the choice of gas phase models. It is recommended that the effective thermal conductivity liquid phase model and the gas phase model taking into account the effects of finite thickness of the thermal boundary layer are used for the simulation of the ignition process in Diesel engines. Some recent non-traditional developments of the models referring to droplet heating and evaporation are discussed. These are the model based on the coupled solution for the liquid and gas phases, the kinetic model of evaporation, and the dynamic decomposition technique for the solution of ordinary differential equations describing droplet heating and evaporation and the ignition of the fuel vapour/air mixture.
MODELLING OF DROPLET HEATING, EVAPORATION AND BREAK-UP: RECENT DEVELOPMENTS
Multiphase, 2006
Several new approaches to the modelling of liquid droplet heating and evaporation by convection and radiation from the surrounding hot gas are reviewed. The finite thermal conductivity of the liquid, recirculation within droplets, time dependence of gas temperature and the convection heat transfer coefficient are taken into account. The relatively small contribution of thermal radiation to droplet heating allows us to describe it by a simplified model, which does not consider the variation of radiation absorption inside the droplets. In the case of stationary droplets a coupled solution of the heat conduction equation for gas and liquid phases is obtained. A transient modification of Newton's law is introduced via a correction to either the gas temperature or convection heat transfer coefficient. The solution is analysed using values of parameters relevant to liquid fuel droplet heating in a diesel engine. Since gas diffusivity in this case is more than an order of magnitude larger than liquid diffusivity, for practical applications in computational fluid dynamics (CFD) codes, this model can be simplified by assuming that droplet surface temperature is fixed. Moreover, if the initial stage of droplet heating (a few μs) can be ignored then the steady-state solution for the gas phase can be applied for the analysis of droplet heating. This solution is described in terms of the steady-state convection heat transfer coefficient. All transient effects in this case are accounted for by liquid phase models. A decomposition technique for the solution of the system of ODEs, based on the geometrical version of the integral manifold method, is described. A comparative analysis of hydrodynamic and kinetic approaches to the problem of diesel fuel droplet evaporation is described. The kinetic approaches are based on a simplified analysis of the Boltzmann equation and its direct numerical solution. Kinetic models predict longer evaporation times and higher droplet temperature compared with the hydrodynamic model. It is recommended that kinetic effects are taken into account when modelling the evaporation process of diesel fuel droplets in realistic internal combustion engines. The preliminary results predicted by deterministic and stochastic models of droplet break-up, both implemented into the KIVA-2 code, are compared with high-speed video images of diesel sprays.
Modelling of biodiesel and Diesel fuel droplet heating and evaporation
New results of the investigation of biodiesel fuel droplet heating and evaporation, using previously developed models, are presented. Temperature gradient, recirculation and species diffusion within the droplets are taken into account. The results of calculations, taking into account the contribution of all components of biodiesel fuels (up to 16) and assuming that these fuels can be treated as a one component fuel, are discussed. It is pointed out that there are serious problems with the application of the approach, based on the analysis of diffusion of individual components, to the modelling of heating and evaporation of realistic Diesel fuel droplets, as the latter include more than 100 components. In our earlier papers, a new approach to the modelling of heating and evaporation of multi-component droplets, suitable for the case when a large number of components are present in the droplets, was suggested. This approach was based on the introduction of quasi-components, and the model was called the 'quasi-discrete' model. It is pointed out that there are two main problems with the application of the quasi-discrete model to realistic Diesel fuels. Firstly, even if we restrict our analysis to alkanes alone, it appears not to be easy to approximate this distribution with a reasonably simple distribution function. Secondly, the contributions of other hydrocarbon families in addition to alkanes cannot be ignored in any realistic model of Diesel fuels. Some results of the development of the generalised multi-dimensional version of the quasi-discrete model and its application to realistic Diesel fuel droplets are presented.
State of the Art of Fuel Droplet Evaporation
International Journal of Heat and Technology, 2022
The process of fuel droplet evaporating is one of the most important factors that directly affect the efficiency of the combustion process. Therefore, the current study reviews previous studies that focused on the process of evaporation of a drop of fuel. The review is divided into points. The first part is concerned with modeling of the evaporation process under different initial condition and temperature of the droplet. The second part present the experimental studies concerned with measuring the evaporation time of the droplet, as well as the shape of the droplet during the evaporation process. Most of the studies related to this subject can be divided into three categories: The first category is the studies that are concerned with the process of heating the droplet and studying the evaporation time for different types of fuels or by adding nanomaterials to the fuel and studying their effect on the evaporation process. The second category is the studies concerned with the mechanics of droplet evaporation and the study of droplet shape. The third category is the studies that focus on studying the effect of initial conditions, such as temperature and pressure, as well as the concentration of gasses surrounding the drop and their types. There are other studies concerned with projecting the electric field onto the drop during the evaporation process and studying its effect.
A self-consistent kinetic model for droplet heating and evaporation
A new kinetic model for heating and evaporation of Diesel fuel droplets is suggested. The model is based on the introduction of the kinetic region in the immediate vicinity of the heated and evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. Diesel fuel is approximated by n-dodecane or a mixture of 80% n-dodecane and 20% p-dipropylbenzene. In both cases, the evaporation coefficient is assumed equal to 1. The values of temperature and vapour density at the outer boundary of the kinetic region are inferred from the equirement that both heat flux and mass flux of vapour (or vapour components) in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions should be equal. Initially, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following the above-mentioned procedure, are used to calculate the corrected values of hydrodynamic heat and mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region etc. It is shown that this process quickly converges for the cases analysed in the paper, and it leads to self-consistent values for both heat and mass fluxes. The model is applied to the analysis of heating and evaporation of Diesel fuel droplets with initial radii and temperature equal to 5 lm and 300 K, immersed into gas with temperatures in the range 800–1200 K and pressure equal to 30 bar. It is shown that in all cases the kinetic effects lead to a decrease in droplet surface temperature and an increase in the evaporation time. The kinetic effects on the droplet evaporation time are shown to increase with increasing gas temperatures.