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Turbulent combustion and flow processes occurring in direct injection internal combustion engine are dominated by mixing throughout the engine cycle. This mixing is caused by several events such as direct fuel injection and piston movement; these events take place at different crank angle degrees within the engine cycle. Therefore, the mixing time will vary with the mixing intensity during the combustion the engine cycle and cannot be constant. In this work we are usinguse a time based mixing model developed by Pasternak et al. based on a previously developed Curl mixing model [41 and 51].
The purposeidea of the model is to account for different mixing times throughout the engine cycle; to be. able to achieve that, tThe engine cycle was divided*…show more content…*

The mixing process in this regime is expected to be the shortest during the engine cycle. This regime corresponds to the highest value of the scalar dissipation rate (figure 1b) [5]. In the initial phase of the fuel injection process the scalar dissipation rate does not change significantly, unless a visible heat release rate occurs. Thus, the mixing time during the fuel injection period (SOI to EOI) was assumed to be constant. The longest phase of the Diesel combustion is the diffusive combustion mode represented by regime III in figure 1a. Figure 2 shows that in this regime the decay of the scalar dissipation rate is observed. The decay of the scalar dissipation rate and the profile of the mixing time are assumed to follow an exponential function, which can be used to describe the decay of a passive scalar in turbulent flows (e.g. [59]). Based on scalar dissipation rate data, it is assumed that the exponential character of the mixing time starts where injection ends and ends roughly where the mixing controlled combustion phase is completed. It has also been assumed that in regimes I and IV mixing intensity can be represented by a constant*…show more content…*

It affects the value of the mixing time in regime I and, together with parameter B in regimes III and IV. The parameter B is given as B=ln(2)/t″, where t″ denotes the half time for the exponential part of the mixing time. The parameter t’ defines intensity of the mixing during the fuel injection phase. The parameters A0 and B have the most influence on the model’s performance. In general, A0 influences the anchorage of the exponential part of the mixing time whereas B affects its slope. It should be noted that the durations of each of the mixing sub-process (τI, τII, τIII, τIV) are also model parameters that can be subjected to some fine adjustments from their defined values above. In general however, the mixing time for the complete engine cycle can be described (Equation (9)) using two parameters, i.e. A0 and t″. Other model parameters, including the duration of each of the mixing sub-process and also parameter t’ can be well assigned prior to simulations. This, in turn means that in practice, the complete SRM-DI based engine model can be validated against experimental data using only these two parameters A0 and t’’. Detailed description of the model and its validation can be found in

The mixing process in this regime is expected to be the shortest during the engine cycle. This regime corresponds to the highest value of the scalar dissipation rate (figure 1b) [5]. In the initial phase of the fuel injection process the scalar dissipation rate does not change significantly, unless a visible heat release rate occurs. Thus, the mixing time during the fuel injection period (SOI to EOI) was assumed to be constant. The longest phase of the Diesel combustion is the diffusive combustion mode represented by regime III in figure 1a. Figure 2 shows that in this regime the decay of the scalar dissipation rate is observed. The decay of the scalar dissipation rate and the profile of the mixing time are assumed to follow an exponential function, which can be used to describe the decay of a passive scalar in turbulent flows (e.g. [59]). Based on scalar dissipation rate data, it is assumed that the exponential character of the mixing time starts where injection ends and ends roughly where the mixing controlled combustion phase is completed. It has also been assumed that in regimes I and IV mixing intensity can be represented by a constant

It affects the value of the mixing time in regime I and, together with parameter B in regimes III and IV. The parameter B is given as B=ln(2)/t″, where t″ denotes the half time for the exponential part of the mixing time. The parameter t’ defines intensity of the mixing during the fuel injection phase. The parameters A0 and B have the most influence on the model’s performance. In general, A0 influences the anchorage of the exponential part of the mixing time whereas B affects its slope. It should be noted that the durations of each of the mixing sub-process (τI, τII, τIII, τIV) are also model parameters that can be subjected to some fine adjustments from their defined values above. In general however, the mixing time for the complete engine cycle can be described (Equation (9)) using two parameters, i.e. A0 and t″. Other model parameters, including the duration of each of the mixing sub-process and also parameter t’ can be well assigned prior to simulations. This, in turn means that in practice, the complete SRM-DI based engine model can be validated against experimental data using only these two parameters A0 and t’’. Detailed description of the model and its validation can be found in

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