Pre-Mixed Combustion Model Description

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4.1.5 Diffusion Controlled Combustion

Using a frequency based approach, the characteristics of the diffusion controlled combustion are defined by the mixing time τ Diff and the mass of vaporized fuel m FuelVapDiff available. , 4.16 The mixing time τ Diff is defined as the ratio of the characteristic diffusion length scale l Diff and the mass transfer velocity u’ 4.17 where the characteristic length scale l Diff is given as a function of the instanta- neous in-cylinder volume V Cyl , the number of injection nozzle orifices n Nozzle , and the specific airfuel ratio for the transferred mass λ Diff . 4.18 As a function of the actual airfuel ratio at SOC λ SOC and the burned mass frac- tion ζ , the specific airfuel ratio for the transferred mass λ Diff mainly accounts for the decreasing mass of oxygen available during combustion. 4.19 Given that the mixing of air and fuel during diffusion controlled combustion is a highly turbulent process, a velocity u’ derived from the instantaneous turbulence intensity is used as characteristic velocity for calculations concerning the mass trans- fer. Assuming a spatially homogeneous in-cylinder turbulence distribution at all times, five key effects contribute to an increase in turbulent kinetic energy: intake flow, swirl, quench flow, injection and combustion. As a common approximation, the contributions of the intake and quench flows, as well as the swirl to the turbulence intensity are taken to be proportional to the square of the mean piston velocity c m a.k.a. background turbulence. The characteristic velocity u’ is thus defined as 4.20 where the effects of injection and combustion on the turbulent kinetic energy are described as functions of the rate of fuel injected m FuelInj , the nozzle exit velocity u , the in-cylinder mass m Cyl and the burning rate m FuelBurn . 4.21 m· FuelBurnDiff c 3 m FuelVapDiff τ Diff -------------------------- ⋅ = τ Diff l Diff u --------- = l Diff V Cyl λ Diff n Nozzle ⋅ ------------------------------ ⎝ ⎠ ⎛ ⎞ 1 3 ⁄ = λ Diff f λ SOC ζ , = u c g c m 2 ⋅ c Inj k Inj c Comb k Comb ⋅ + ⋅ + = dk Inj dt ----------- c InjF f Formation m· FuelInj ⋅ c InjD f ⋅ Dissipation k Inj l Inj , – = 37 4.22 Superposition of Premixed and Diffusion Controlled Combustion