RK-model:
Simulation of mixture formation and combustion in diesel

      Simulation method of RK-model was developed by Prof. Razleytsev in 1990-1994. After this method was modified and complemented by Dr. Kuleshov [1, 2, 3]. RK-model takes into account:

• - shape of the injection profile including split injection;
• - drop sizes;
• - direction of sprays in the combustion chamber;
• - dynamic of evolution of fuel sprays;
• - dynamic of swirl;
• - interaction of sprays with an air swirl and walls.

      The method takes into account conditions of evolution of each fuel spray and wall surface flows generated by sprays, and also interaction between wall surface flows. RK-model allows determination the emission of soot and emission of NO depending on mixture formation and combustion conditions. The software makes it possible to find the optimum of piston bowl shape, fuel sprays directions, diameters and numbers of nozzles, intensity of air swirl and the injection profile shape.

     Main principles of RK-model are similar with Hiroyasu combustion model, though there are considerable differences. The RK-model provides more detailed modeling of:
-  fuel sprays and walls interaction,
-  interaction of near wall flows formed by sprays among themselves.
More detailed comparison of Hiroyasu and RK-model is presented in page >>.

     At simulation, the assumption is made that the heat release process consists of four main phases. They differ by physical and chemical peculiarities and factors limiting the rate of the process:

• Induction period.
• Premixed combustion phase.
• Mixing-controlled combustion phase.
• Late combustion phase after the ending of fuel injection.

Distribution of fuel in a diesel spray

Notations: 1 - Dilute outer sleeve of a spray. 2 - Dense axial core of free spray. 3 - Dense forward front. 4 - Dilute outer surrounding of a near wall flow (NWF). 5 - Dense core of a NWS on a piston bowl surface. 6 - Forward front of a NWF. 7 - Axial conical core of a NWF.

            Fig.1.   Diagram of a diesel spray.

      Evolution of a free spray consists of two main phases:
         - Initial phase of pulsing evolution.
         - Basic phase of cumulative evolution. See details in...

      Amount of fuel getting in the characteristic zones with different conditions of evaporation and burning are calculated during movement of  sprays. In a list of these zones, except listed above, zones on a piston crown, on a cylinder liner and on a cylinder head are included.

      Trajectories of free sprays and movement of near wall flows formed by sprays are calculated in view of influence of tangential air swirl and angle of clash between spray and wall. The intensity of an air swirl is set by swirl ratio Rs (or swirl number). Rs is a relation between swirl angular velocity w_s (in the combustion chamber at the end of compression) and crank rotation velocity w_c:  

Rs = w_s / w_c.

Example: Calculation of fuel sprays evolution in combustion chamber of tractor diesel CMD

Fig. 2. Results of simulation of mixture formation in tractor diesel CMD (rpm=1800, BMEP=7.7 Bar).

      The given example presents the comparison between the result of calculation of fuel sprays evolution and NWF movement with the experimental film-gramme of NWF in the combustion chamber of a tractor diesel CMD (rpm=1800, BMEP=7.7 Bar). The experimental data are obtained of GSKBD (Ukraine). The intensity of air swirl in the combustion chamber at the TDC corresponds to swirl ratio Rs=3.15. On the diagrams it is shown how much fuel in each moment of time has got to the characteristic zones.

Evaporation of sprayed fuel in volume and on a combustion chamber walls

     During injection of fuel and evolution of fuel sprays the rate of combustion is limited mainly by the rate of evaporation. While spray is free the forward front and the dilute outer surrounding of a spray are zones of intensive heat exchange and evaporation of sprayed fuel. In high-speed and dense axial flow core the warming is low and evaporation of drops are insignificant.
      At clash of spray with a wall, the evaporation rate of fuel accumulated in forward front is reduced sharply to a minimum at the moment of end of stacking of front on a wall. It is caused by the lower (in comparison with gas) temperature of a wall, reduction of blow of drops, condensation of drops-gas mixture on a wall, merge and interfusion of vanguard drops with more cold drops flying up to a wall. After stacking of front on a wall the biphase mixture begins to be distributed on a wall outside the limits of a cone of spray. The evaporation rate of fuel in a wall surface zone is increased, though remains smaller than in the volume of the chamber. When the fuel is distributed on the surface of the piston a part of fuel can penetrate into a clearance between the piston crown and a head of the cylinder. Fuel get on the head and on a cylinder liner.
     The evaporation rate of fuel arriving in each zone of intensive heat exchange is equal to a sum of evaporation rates of separate drops. The evaporation of each drop before and after ignition of fuel is simulated by the Sreznevsky's equation.
The fuel equipment of boosted diesels provides rather uniform similar atomizing of fuel, especially on the basic phase of injection. Therefore, the calculation of evaporation of fuel can be carried out on a base of an average Sauter drop diameter  d₃₂.
      Constants of evaporation of fuel in various zones are determined with the purpose of calculation of evaporation rate. The estimation of constants is made by known equation in which are entered:
- Nusselt's criterion for process of diffusion;
- Factor of a diffusion for fuel vapors;
- Pressure of saturated steams;
- Density of liquid fuel;
- Characteristic pressure and temperatures including temperatures of walls.
    

Combustion of sprayed fuel

     After termination of induction period en explosive distribution of a flame on an activated mixture in an environment of sprays occurs. The value of the first maximum of heat release rate curve depends on the following factors:
- the amount of fuel evaporated in the induction period;
- degree of vapor activation;
- the relation between evaporation rate during flare and mass of injected fuel;
- quality of fuel atomizing and distribution;
- time of evaporation;
- physical, chemical, thermodynamic and gasdynamic characteristics of a fuel-air mixture.

     After initial flare and combustion of fuel vapours have formed in the induction period, the heat release rate is determined, in general by rates of evaporation and burning out of the products of incomplete combustion in volume of   cylinder. The latter depends on the average concentration of unused oxygen in volume.

     In the period of late combustion phase, after termination of injection and termination of sprays evolution, decrease of combustion rate occurs. It is connected with reduction of weight of unburned fuel and with a limiting role of process of a diffusion in this period. Flame disintegrates into a lot of the centers around the local congestion of fuel in core of spray. If the significant part of fuel is allocated on a wall of a piston bowl, especially on the surfaces near to the head of the cylinder, in the interval of 15-30 degrees of CA after TDC, on the curves of heat release rate one more small peak is observed. It is connected with the indignation and destruction of quasi-laminar wall surface layer at sharp expansion of a gas above the appropriate surface.

Example: Calculation of heat release rate in a tractor diesel CMD.

 

Fig. 3. Comparison of calculated and experimental curves of heat release rate dx/dCA. (rpm=1800, BMEP=7.7 Bar.)

      The submitted technique provides carrying out the calculation of combustion in engines both with the volumetric and with the film mixing processes.

Example: Calculation of mixture formation and combustion  in the medium-speed marine diesel engine at full load.

Example: Calculation of mixture formation and combustion  in the high-speed automobile diesel engine.

Visualization of mixture formation

Spray #1 (short)

Notations: Environ. - Fuel fraction allocated in dilute outer sleeve of free spray and in the surrounding of NWF. Jet.Core - Fuel fraction allocated in dense core of free spray. Pst.Wall - Fuel fraction allocated in NWF. Cyl.Head - Fuel fraction settled on cylinder head surface. Cyl.Wall - Fuel fraction settled on cylinder liner surface.

      Results of simulation of mixture formation and combustion in different diesels at different operating modes are presented in following pages:

• High-speed diesel over whole operating range.
• Medium-speed diesel D49 over locomotive characteristic.
• Truck diesel YaMZ-238D over whole operating range.
• Truck diesel KamAZ-7405 over external curve.

All calculations are carried out with identical empiric coefficients.

REFERENCE

1. A.S. Kuleshov : ”Model for predicting air-fuel mixing, combustion and emissions in DI diesel engines over whole operating range”, SAE Paper No. 2005-01-2119, 2005.

2. A.S. Kuleshov: "Use of Multi-Zone DI Diesel Spray Combustion Model for Simulation and Optimization of Performance and Emissions of Engines with Multiple Injection", SAE Paper No 2006-01-1385, 2006.

3. A.S. Kuleshov: "Multi-Zone DI Diesel Spray Combustion Model and its application for Matching the Injector Design with Piston Bowl Shape", SAE Paper No 2007-01-1908, 2007.

 

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