Elena Sazhina

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.

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.

Radiative Heating of Semi-Transparent Diesel Fuel Droplets

Absorption spectra of four types of diesel fuel are studied experimentally in the range between 0.2 μm and 6 μm. The ageing process of fuels is simulated by prolonged boiling. The average absorption efficiency factor of droplets is assumed to be proportional to ar b d, where r d is the droplet radius, and a and b are polynomial functions of external gas temperature. Explicit expressions for a and b are derived for diesel fuel droplets in various realistic droplet radii and external gas temperature ranges for all four types of fuel.

The shell autoignition model: a new mathematical formulation

The equations of the Shell model are reexamined with a view to their more effective implementation into a computational fluid dynamics code. The simplification of the solution procedure without compromising accuracy is achieved by replacing time as an independent variable with the fuel depletion, which is the difference between the initial fuel concentration and the current one. All the other variables used in this model, including temperature, concentration of oxygen, radicals, intermediate and branching agents are expressed as functions of fuel depletion. Equations for the temperature and concentration of the intermediate agent are of the first order and allow analytical solutions. The concentrations of oxygen and fuel are related via an algebraic equation which is solved in a straightforward way. In this case the numerical solution of five coupled first-order ordinary differential equations is reduced to the solution of only two coupled first-order differential equations for the concentration of radicals and branching agent. It is possible to rearrange these equations even further so that the equation for the concentration of the radicals is uncoupled from the equation for the branching agent. In this case the equation for the concentration of radicals becomes a second-order ordinary differential equation. This equation is solved analytically in two limiting cases and numerically in the general case. The solution of the first-order ordinary differential equation for the concentration of the branching agent and the solution of the first-order differential equation for time are presented in the form of integrals containing the concentration of the radicals obtained earlier. This approach allows the central processing unit (CPU) time to be more than halved and makes the calculation of the autoignition process using the Shell model considerably more effective.

Modelling of the gas to fuel droplets radiative exchange

Abstract The results of the implementation of the thermal radiation transfer model into the commercial computational fluid dynamics (CFD) code VECTIS of Ricardo Consulting Engineers and its application to modelling the fuel droplets radiative exchange with gas in a Diesel engine cylinder are reported. The P-1 model with Marshak boundary conditions at the droplets’ surfaces is shown to be the most suitable for modelling the thermal radiation transfer in a Diesel engine where the contribution of soot allows the combustible charge to be approximated as an optically thick medium. The results of the implementation of this model were tested for the idealised case where droplet evaporation and burning are ignored, and the gas temperature is kept constant. In this case the equation for droplet heating in gaseous media, taking into account the effects of convection and thermal radiation, is resolved analytically and numerically (based on the VECTIS CFD code). Analytical results are obtained in two limiting cases where the effects of radiation dominate over or are dominated by the effects of convection. Possible time dependence of gas temperature, radiation temperature, and/or convective heat transfer coefficient is accounted for. Solutions obtained for spherical droplets are generalized for the case of droplets having the forms of prolate and oblate spheroids. Good agreement between the analytical and numerical results endorses the approximations on which the analytical solutions are based and the VECTIS numerical results. It is shown that thermal radiation noticeably accelerates the droplet evaporation, which is reflected in a more rapid decrease in the droplet diameter when compared to the case, when thermal radiation is ignored. The asymptotic values of droplet surface temperature are shown to be independent of thermal radiation.

The application of the Global Quasi-Linearisation technique to the analysis of the cyclohexane/air mixture autoignition

The paper is focused on the application of the recently developed Global-Quasi-Linearization (GQL) method to a specific problem of the cyclohexane/air autoignition in a rapid compression machine environment. A simplified autoignition mechanism including 50 species has been used in the analysis based on the customised computational fluid dynamics (CFD) package FLUENT and the new GQL method. The results predicted by FLUENT are shown to be very close to the results predicted by the zero dimensional code SPRINT, developed at the University of Leeds. The application of the GQL method shows that further substantial reduction of the mechanism is possible without significant loss of accuracy. The method is shown to be an efficient tool for identification and approximations of low-dimensional invariant system manifolds.

Dynamic Decomposition of ODE Systems: Application to Modelling of Diesel Fuel Sprays

A new method of decomposition of multiscale systems of ordinary differential equations is suggested. The suggested approach is based on the comparative analysis of the magnitudes of the eigenvalues of the matrix JJ*, where J is the local Jacobi matrix of the system under consideration. The proposed approach provides with the separation of the variables into fast and slow ones. The hierarchy of the decomposition is subject of variation with time, therefore, this decomposition is called dynamic. Equations for fast variables are solved by a stiff ODE system solver with the slow variables taken at the beginning of the time step. This is considered as a zeroth order solution for these variables. The solution of equations for slow variables is presented in a simplified form, assuming linearised variations of these variables during the time evolution of the fast variables. This is considered as the first order approximation for the solution for these variables or the first approximation for the fast manifold. The new approach is applied to numerical simulation of diesel fuel spray heating, evaporation and the ignition of fuel vapour/ air mixture. The results show advantages of the new approach when compared with the one proposed by the authors earlier and the conventional CFD approach used in computational fluid dynamics codes, both from the point of view of accuracy and CPU efficiency.