Applying a Diesel Spray Model With Different Size Distribution Functions to High Pressure Diesel Spray Cases
In diesel engine sprays, smaller sized droplets aid the combustion process, thus reducing emissions. Thus, it is important for diesel engine spray models to satisfactorily represent hydrodynamic mechanisms. A further development of a diesel spray model th
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Abstract In diesel engine sprays, smaller sized droplets aid the combustion process, thus reducing emissions. Thus, it is important for diesel engine spray models to satisfactorily represent hydrodynamic mechanisms. A further development of a diesel spray model that uses different size distribution functions has been presented. In this model transport equations are constructed to calculate three moments of the droplet size distribution, a fourth moment is calculated from a gamma size distribution function, while the results of the droplet break up process are derived from an assumed size distribution function. Together these present the complete hydrodynamics characterisation of the diesel spray. The motivation for using different size distributions is to reduce the complexity of the spray modelling process and reduce the computational expense. The model has been applied to high-pressure diesel spray cases with the experimental data characterised by diesel spray penetration at different injection pressure values. The results from the model indicate that diesel spray penetration is over predicted at the start of injection but this improves as the fuel injection progresses. Keywords Droplet size distribution function Modelling Droplet break up
Nomenclature n(r) Q Q0
Droplet size moments Sprays
Number size distribution Droplet moment Total number
F2012-A02-011 E. G. Nwabueze (&) Midlands Simulation Group, School of Technology, University of Wolverhampton, Wolverhampton, UK e-mail: [email protected]
SAE-China and FISITA (eds.), Proceedings of the FISITA 2012 World Automotive Congress, Lecture Notes in Electrical Engineering 189, DOI: 10.1007/978-3-642-33841-0_25, Springer-Verlag Berlin Heidelberg 2013
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E. G. Nwabueze
Q1 Q2 Q3 r t U x
Sum of radii, m Sum of squares of radii, m2 Sum of cubes of radii, m3 Radius, m Time, s Velocity, ms-1 Coordinate direction, m
Greek Symbols e a
Dissipation Rate, m2s-3 Nondimensional size parameter
Subscripts 32 i i, j l
Sauter mean Moment index Velocity component Liquid
Acronyms DDM
Discrete droplet model
1 Introduction With the increased concerns in the emission levels from automobiles, representing diesel engine sprays more accurately in spray models is essential to aiding the understanding of the structure of the sprays and also in optimising the injection design process. Diesel spray models in use typically present the complete hydrodynamic nature of diesel sprays by tracking computational droplet classes, the so-called Discrete Droplet Model (DDM) method, with its pioneers including Dukowicz [1], and Gosman and John [2]. Each of these droplet classes represents a large number of droplets of the same size, temperature and velocity. Changes in these variables for each droplet class are computed by solving the ordinary differential equations governing the mass, energy, and momentum conservation for a representative droplet member of the class. The liquid and gas phases are linked using source terms in the equations. However, this method can be com
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