The noted above sub-models were integrated into full-cycle engine simulation software together with library of non-linear programming procedures, allowing multidimensional optimization of DI diesel engine working parameters to reach prescribed emissions regulations norms. List of optimized parameters includes: CR, EGR, injection profile shape, fuel injection pressure, port timings (IVC), boost pressure, power for turbocharger assistance, injection timing, nozzles hole number, diameter and inclination angle of nozzles. Two variants of piston bowl were investigated. In the research there was done an optimization of working parameters of medium speed diesel engine at few operating points with account of weighting coefficients of the points. At each operating point the problem of optimization has individual peculiarities and an individual set of independent variables and restrictions. The expression for objective function of conjoint optimization of SFC, NOx and PM was proposed. Procedures of Rosenbrock, Powell and other were used for optimum search. Restrictions were accounted by penalty function method. Controlling algorithms for EGR booster driving, injection timing, Common Rail pressure, turbocharger assist for locomotive performance were obtained. To provide a required injection profile shape being obtained in optimization a modification of injector was carried out. There were optimized fuel pipe line diameter and dimensions of internal elements of injector: control valve, orifice and internal volume. The injection profile was simulated with hydrodynamic simulation software INJECT.

A.S. Kuleshov, A.V. Kozlov, K. Mahkamov  "Self-Ignition delay Prediction in PCCI direct injection diesel engines using multi-zone spray combustion model and detailed chemistry" 2010.
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ABSTRACT
 A multi-zone direct-injection (DI) diesel combustion model has been implemented for full cycle simulation of a turbocharged diesel engine. The above combustion model takes into account the following features of the spray dynamics:
 • the detailed evolution process of fuel sprays;
 • interaction of sprays with the in-cylinder swirl and the walls of the combustion chamber;
 • the evolution of a Near-Wall Flow (NWF) formed as a result of a spray-wall impingement as a function of the impingement angle and the local swirl velocity;
 • interaction of Near-Wall Flows formed by adjacent sprays;
 • the effect of gas and wall temperatures on the evaporation rate in the spray and NWF zones.
 In the model each fuel spray is split into a number of specific zones with different evaporation conditions including in zones formed on the cylinder liner surface and on the cylinder head. The piston bowl in the modelling process is assumed to have an arbitrary axi-symmetric shape. The combustion model considers all known types of injectors including non-central and side injection systems. A NOx calculation sub-model uses detailed chemistry analysis which considers 199 reactions of 33 species. A soot formation calculation sub-model used is the phenomenological one and takes into account the distribution of the Sauter Mean Diameter in injection process. The ignition delay sub-model implements two concepts. The first concept is based on calculations using the conventional empirical equations. In the second approach the ignition delay period is estimated using relevant data in the calculated comprehensive 4-D map of ignition delays. This 4-D map is developed using CHEMKIN detailed chemistry simulations which take into account effects of the temperature, the pressure, the Air/Fuel ratio and the EGR. The above approach is also planned to be used in future for calculations of ignition delays in diesel engines fuelled by bio-fuels. The model has been validated using published experimental data obtained on high- and medium-speed engines. Comparison of results demonstrates a good agreement between theoretical and experimental sets of data.
 The above sub-models were integrated into DIESEL-RK software, which is a full-cycle engine simulation tool, allowing more advanced analysis of PCCI and HCCI diesels.
 

A.S. Kuleshov: "Multi-Zone DI Diesel Spray Combustion Model for Thermodynamic Simulation of Engine with PCCI and High EGR Level", SAE Paper No 2009-01-1956, 2009.

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ABSTRACT
A multi-zone, direct-injection (DI) diesel combustion model, the so-called RK-model, has been developed and implemented in a full cycle simulation of a turbocharged engine. The combustion model takes into account:
• transient evolution of fuel sprays,
• interaction of sprays with swirl and walls,
• evolution of near-wall flow formed after spray-wall impingement depending on impingement angle and local swirl velocity,
• interaction of Near-Wall Flows (NWF) formed by adjacent sprays,
• influence of temperatures of gas and walls in the zones on evaporation rate.
In the model the fuel spray is split into a number of specific zones with different evaporation conditions including zone on the cylinder liner and on the cylinder head. The piston bowl is assumed to be a body of revolution with arbitrary shape. The combustion model supports central and non-central injector as well as the side injection system. NOx formation model uses Detail Kinetic Mechanism (199 reactions with 33 species). Soot formation model is phenomenological. The general equation for prediction of ignition delay period was derived as for conventional engines as for engines with PCCI where pilot injection timing achieved 130 CA deg. before TDC. The model has been validated by experimental data obtained from high-speed, medium-speed and low-speed engines over the whole operating range; a good agreement has been achieved without recalibration of the model for different operating modes.
General equations for prediction of spray tip penetration, spray angle and ignition delay for low temperature combustion and high temperature combustion were derived and validated with the published data obtained for different diesels including diesels with multiple injection system and injection timing varied from very early up to after the TDC.
To make a computational optimization of multiple injection strategy possible, the full cycle thermodynamic engine simulation software DIESEL-RK has been supplied with library of nonlinear optimization procedures.

Kuleshov, A. and Mahkamov, K.  Multi-zone diesel fuel spray combustion model for the simulation of a diesel engine running on biofuel. // Proc. Mechanical Engineers Vol. 222, Part A, Journal of Power and Energy. pp. 309 – 321. 2008.

ABSTRACT
A mathematical model for the calculation of the multi-zone diesel fuel spray combustion process in compression ignition engines is refined in order to expand its capability to describe the operation of diesel engines running on different bio-fuel blends. As an illustration of the capacity of the proposed model to accurately describe the working process numerical simulations of a Caterpillar diesel engine operating on diesel oil and different SME blends are presented in this paper. A comparison of these theoretical results with published experimental data for the SME 20% and 40% blends shows good agreement. As the proposed model provides a fairly accurate prediction of the heat release rate during the combustion process and the levels of NOx and PM emission formations the model may be used for the optimisation of the engine’s design and its working process parameters.

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.
Download and see paper on SAE web site.

ABSTRACT
A multi-zone, direct-injection (DI) diesel combustion model, the so-called RK-model, has been developed and implemented in a full cycle turbocharged engine simulation code. The combustion model takes into account:
• transient evolution of fuel sprays;
• interaction of sprays with swirl and walls;
• evolution of near-wall flow formed after spray-wall impingement depending on impingement angle and swirl;
• interaction of near-wall flows formed by adjacent sprays.

In the model the fuel spray is divided into a number of zones with different evaporation conditions. The piston bowl is assumed to be a body of revolution with arbitrary side shape. Submodels of soot and NOx formation are included. The model has been validated by experimental data obtained for high-speed, medium-speed and low-speed engines over the whole operating range; a good agreement has been achieved without recalibration for different operating modes.
Predictions of spray tip penetration, spray angle and ignition delay were validated by the published data obtained for different diesels including diesels with multiple injection system and injection timing after the TDC. Formulas for computation of these characteristics were derived.
Computational research and optimization of sprayer nozzles orientation for different piston bowl shapes has been performed. Analysis of fuel sprays evolution in contact with walls as well as distribution of fuel in characteristic zones has been done for part load and full capacity. Conclusion about dependence of optimal piston bowl shape on BMEP was made.

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
Download and see paper on SAE web site.

ABSTRACT
A multi-zone, direct-injection (DI) diesel combustion model, the so-called RK-model, has been developed and implemented in a full cycle simulation of a turbocharged engine. The combustion model takes into account:
• transient evolution of fuel sprays,
• interaction of sprays with swirl and walls,
• evolution of near-wall flow formed after spray-wall impingement depending on impingement angle and swirl, fuel-air mixing,
• interaction of near-wall flows formed by adjacent sprays,
• evaporation conditions for different zones.
In the model the fuel spray is divided into a number of zones with different evaporation conditions. The piston bowl is assumed to be a body of revolution of otherwise arbitrary shape. Submodels of soot and NOx formation are included. The model has been validated by experimental data obtained from high-speed and medium-speed engines over the whole operating range; a good agreement has been achieved without recalibration for different operating modes.
Predictions of spray tip penetration, spray angle and ignition delay were validated by the published data obtained for diesels with multiple injection system and injection timing after the TDC. Formulas for computation of these characteristics were derived.
Results obtained without recalibration of the RK-model demonstrate good agreement between the calculated and experimental heat release rate curves as well as between integral engine parameters for diesels with multiple injection being considered.
To make a computational research of multiple injection strategy possible, the full cycle thermodynamic engine simulation software DIESEL-RK has been supplied with an additional tool for parametric setting of multiple injection profile by specifying a fuel fraction and delay after previous injection for each fuel portion. These parameters can be used as arguments of optimization in a future research.
 

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.
Download and see paper on SAE web site.

ABSTRACT
A multi-zone model of diesel sprays evolution and combustion named as RK-model has been developed. The model with submodels of NO and soot formation has been implemented into ICE thermodynamic analysis software (DIESEL-RK). The RK-model takes into account: the shape of injection profile, including split injection; drop sizes; direction of each spray in the combustion chamber; the swirl intensity; the piston bowl shape. Evolution of wall surface flows generated by each spray depends on the spray and wall impingement angle and the swirl intensity. Interaction between near-wall flows (further named wall surface flows) generated by the adjacent sprays is taken into account. The method considers hitting of fuel on the cylinder head and liner surfaces. The evaporation rate in each zone is determined by Nusselt number for the diffusion process, the pressure and the temperature, including temperatures of different walls where a fuel spray gets. A parametric study of the swirl intensity effect has been performed and a good agreement with experimental data was obtained. The calculations results allow describing the phenomenon of increased fuel consumption with increase of swirl ratio over the optimum value. The model has been used for simulation of different engines performances. The calculated results obtained for high-speed, truck and medium-speed diesels have shown a good agreement of SFC, power, smoke and NO emissions with the experimental data over the whole operating range, including modes of idling and 7...10% capacity. The model does not require recalibration for different operating modes of a diesel engine.
 

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