Sergei Sazhin

A model for fuel spray penetration

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 the two-phase flow, it is assumed that the spray droplets have the same velocities as the entrained air. The characteristic time of droplet break-up in the spray is estimated for both bag and stripping break-up mechanisms. For realistic diesel spray parameters, the droplet break-up takes place almost immediately after the droplets leave the nozzle. This leads to a considerable shortening of the initial stage and a rapid conversion of the flow to the two-phase stage. This allows the analysis to be restricted to the two-phase flow approximation for this type of spray. The expressions for spray penetration derived in this paper give more accurate predictions compared with those suggested earlier.

A detailed modelling of the spray ignition process in diesel engines

The Shell autoignition model with the value of the pre-exponential factor in the rate of production of the intermediate agent (A f4) in the range between 3×106 and 6×1O6 has been applied to the detailed modelling of the ignition process in monodisperse and polydisperse sprays based on a computational fluid dynamics (CFD) code. The mass balance in the Shell model has been improved to ensure bener physical consistency and more effective numerical implementation. Based on the analysis of the ignition in a monodisperse spray it is pointed out that in the case of droplets with the initial radius (R d0) about or greater than 6 μm the physical ignition delay dominates over the chemical ignition delay, while for the smaller droplets with R d0≤2.5 μm the opposite is true. The start of the ignition processis predicted near the periphery of both monodisperse and polydisperse sprays in agreement with current understanding of this phenomenon. The observed ignition delay for a monodisperse spray agrees with the available experimental data. The ignition stage of the polydisperse Diesel combustion predicted by the model agrees with available experimental data for a medium duty truck Diesel engine, provided that the fine tuning of the parameter A f4 is performed and additional constants. such as concentration limits, are introduced.

Droplets and sprays

1.-Introduction 2.-Spray Formation and Penetration 3.-Heating of Non-evaporating Droplets 4.-Heating and Evaporation of Mono-component Droplets 5.-Heating and Evaporation of Multi-component Droplets 6.-Kinetic Modelling of Droplet Heating and Evaporation 7.-Heating, Evaporation and Autoignition of Sprays.

Thermal ignition analysis of a monodisperse spray with radiation

The system of equations describing the effects of heating, evaporation, and combustion of fuel droplets in a monodisperse spray is simplified assuming that the Nusselt and Sherwood numbers are equal to 2. The radiative energy exchange between fuel droplets surface and gas is described by using the P-1 model with Marshak boundary conditions. The chemical term is presented in the Arrhenius form with the pre-exponential factor calculated from the enthalpy equation, using the Shell autoignition model. The resultant, singularly perturbed system of ordinary differential equations is analyzed, based on the geometrical version of the integral manifold method. The ignition process is subdivided into two stages: droplet evaporation and ignition of the gaseous mixture. Results predicted by the analytical solutions are compared with those predicted by the CFD package VECTIS. It is suggested that the analytical solution underpredicts the evaporation time. A considerably better agreement between the evaporation times predicted by VECTIS and the proposed theory is achieved when the gas temperature is assumed to be equal to the local temperature in the vicinity of droplets. The effects of thermal radiation are significant, especially at high temperatures and with large droplets, and cannot be ignored.

The Shell autoignition model: applications to gasoline and diesel fuels

The applications of the Shell model to modelling autoignition in gasoline and diesel engines are reported. The complexities of modelling autoignition in diesel sprays have been highlighted. In contrast to autoignition in gasoline engines, autoignition of diesel fuel sprays takes place at a wide range of equivalence ratios and temperatures. This makes it necessary to impose flammability limits to restrict the range of equivalence ratios in which the autoignition model is active. The autoignition chemical delay for n-dodecane is shown to be much less than the physical delay due to the droplet transit time, atomization, heating, evaporation and mixing. This enables the use of the less accurate but more computer efficient Shell model for diesel fuel chemical autoignition. Since experimental data for the chemical autoignition delay for n-dodecane are not available, this study of the applicability of the Shell model to diesel fuels is based on data for n-heptane. The ignition time delays for premixed n-heptane predicted by calculations using the kinetic rate parameters corresponding to the primary reference fuel, RON70, show good agreement with experimental results when Af4 (preexponential factor in the rate of production of the intermediate agent) was chosen in the range between 3×106 and 6×106. It is pointed out that the difference between the end-of-compression temperature, as predicted by the adiabatic law, and the actual end-of-compression temperature, taking into account the exothermic reactions at the end of compression, needs to be accounted for. The relation between the two temperatures is approximated by a linear function. It is considered that this approach can be extended to n-dodecane.

Heating and evaporation of semi-transparent diesel fuel droplets in the presence of thermal radiation

Absorption and scattering spectral efficiency factors for spherical semi-transparent fuel droplets are approximated by simple analytical expressions as functions of imaginary and real parts of the complex index of refraction and the diffraction parameters of droplets. These expressions are applied to the modelling of thermal radiation transfer in Diesel engines. On the basis of the P-1 approximation, which is applicable due to the large optical thickness of combustion products, various ways of spectral averaging for absorption and scattering coefficients are suggested. Assuming that the concentration of fuel droplets is small, the scattering effects are ignored and the analysis is focused on approximations for the absorption coefficient. The average absorption coefficient of droplets is shown to be proportional to ard2+b, where rd is the droplet radii, and a and b are quadratic functions of gas temperature. Explicit expressions for a and b are derived for diesel fuel droplets in the range 5–50 μm and gas temperatures in the range 1000–3000 K. The expression for the average absorption coefficient of droplets is implemented into the research version of VECTIS CFD code of Ricardo Consulting Engineers. The effect of thermal radiation on heating and evaporation of semi-transparent diesel fuel droplets is shown to be considerably smaller when compared with the case of black opaque droplets.

Absorption of thermal radiation in a semi-transparent spherical droplet: a simplified model

The boundary-value problem for calculation of differential absorption of thermal radiation is formulated based on the modified DP0 approximation. The solution of this problem is supplemented by simple analytical approximations for the normalised absorbed radiation power. The latter is used together with the analytical approximation for the efficiency factor of absorption, suggested earlier. The resulting simplified model is applied to the specific problem of absorption of thermal radiation by a diesel fuel droplet. Two types of diesel fuel have been considered. It is pointed out that the radial distribution of absorbed thermal radiation power is non-monotonic. The power absorbed in the droplet core is shown to be rather large and almost homogeneous. Also, the absorbed power is large in the vicinity of the droplet surface, but is minimal in the intermediate region. It is pointed out that the variations of the refractive index of diesel fuel with wavelengths can smooth the predicted radial dependence of the thermal radiation power, absorbed in diesel fuel droplets.

A simplified non-isothermal model for droplet heating and evaporation

A simple model for heating and evaporation of non-isothermal droplets is suggested. This model is based on the parabolic approximation of the temperature profiles inside droplets. The d-squared law of droplet evaporation is modified to take into account droplet heating. Comparison with numerical solutions of the transient problem for moving droplets shows the applicability of this approximation to modelling the heating and evaporation processes of fuel droplets in diesel engines. The simplicity of the model makes it particularly convenient for implementation into multidimensional CFD codes to replace the widely used model of isothermal droplets.

Spectral properties of diesel fuel droplets

Absorption spectra of several types of diesel fuel are studied experimentally. Index of refraction of these fuels is calculated using subtractive Kramers - Kronig analysis. The ageing process of fuels is simulated by prolonged boiling. Radiative properties of diesel fuel droplets are calculated using the Mie theory and a simplified approach, based on approximations of absorption and scattering efficiency factors. It is pointed out that the accuracy of the simplified approach is sufficient for practical applications in the visible and infrared ranges, for various types of diesel fuel, and for droplet radii in the range from 5 to 50 mm. The monodisperse approximation is shown to be applicable for the analysis of infrared radiative properties of realistic polydisperse diesel fuel sprays. q 2002 Elsevier Science Ltd. All rights reserved.

A parabolic temperature profile model for heating of droplets

A model for convective heating of droplets, which takes into account their finite thermal conductivity, is suggested. This model is based on the assumption of the parabolic temperature profile in the droplets. A rigorous numerical solution, without restrictions on temperature profiles inside droplets, is compared with predictions of the parabolic temperature profile and isothermal models