The problem of the numerical computation of the penetration and vaporization of two-dimensional unsteady sprays is considered. This topic is of interest in the field of modeling of combustion in direct injection, internal combustion engines with self-ignition (Diesel), or spark ignition (stratified charge). The spray equation, which is the governing equation and, in this application, exhibits six independent variables, is numerically solved using an upwind difference scheme which is first-order accurate and explicit in time. The problem is set up both as a boundary value problem and an equivalent initial value problem. The boundary value formulation is preferable for applications. A study of the numerical error of the initial value problem is undertaken by comparing the numerical solution with an analytical one. The analytical solution is obtained by discretizing the spray, reducing the spray equation to a set of ordinary differential equations, solving these equations in closed form, and reconstructing the solution for the entire spray by integrating the contributions from the individual, discretized spray parcels. It is concluded that the selected numerical method yields sufficiently accurate results in reasonable computational time. However, the practical usefulness of the model is presently limited due to the simplifying assumptions that were made in order to concentrate on the formulation of the problem, the method of solution, and computational time and accuracy. a,b B C D d,,d 2 f h,,H 2 k P Pr r 'inj r 30 R Re Re L s t A/ T u V,V1,V2 "injWe Nomenclature = constants of the Weber/Reynolds correlation = coefficient in the initial distribution function sVcrn 7 = constant in the Nukiyama-Tanasawa initial distribution function in the drop radius space, cm-1 = drop drag coefficient = constants in the initial Gauss distribution functions in the velocity space, cm/s = droplet distribution function, s 2 /cm 5 = ( = diVdO time rate of change of drop velocity following the drop, cm/s 2 = constants in the initial Gauss distributions in the physical space, cm = modified vaporization rate constant, g/cm s = pressure, dyn/cm 2 = gas Prandtl number = radius of the drop, cm = injector nozzle radius, cm = volume-number average radius, cm = time rate of change of drop radius, cm/s = drop Reynolds number = liquid jet Reynolds number = a coordinate = time, s = time step for the numerical integration of the spray equation, s = gas temperature, K = gas velocity, cm/s = liquid drop coordinates in the velocity space, cm/s = centers of the initial Gauss distributions in the velocity space, cm/s = liquid injection velocity, cm/s = liquid jet Weber number

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A divided-chamber, stratified-charge engine was operated at different speeds and loads, and with two prechamber nozzle sizes. Pressure was recorded and flame propagation was filmed through a transparent head. For each condition, several sets of data were taken and the experimental scatter identified. Pressure and flame propagation were then computed with a two-dimensional model and compared with the measured ones. Several quantities which influence the computed results were not directly measured in the experiment and assumptions had to be made about them in the model. They include amount and state of cylinder air and residual products, turbulence, and wall heat transfer. A turbulent diffusivity, an overall reaction rate, and a wall heat loss proportional to the heat released thus were adopted in the model. The same set of model constants was used for all cases and, through successive iterations, adequate agreement of computed and measured results was obtained. For this specific engine design and set of operating conditions, it was found necessary to account for the turbulence generated by the prechamber jet in order to reproduce main chamber combustion properly. In spite of uncertainties about both the measured quantities and the model, this first detailed comparison of engine combustion data also shows again that the model can be used to interpret and extrapolate engine data. Such capabilities are useful in the stages of development and optimization of engines.

Effect of progress variable definition on the mass burning rate of premixed laminar flames predicted by the Flamelet Generated Manifold method, Combustion Theory and Modelling,