## 1 Introduction  
Diesel engine combustion is an unsteady and discontinuous process, in which the fuel chemical energy is transferred to the work medium internal energy. Due to its complicated energy conversion process, modeling the diesel engine combustion is quite challenging to both engine designers and users [1]. When the engine is applied in an integrated system such as the diesel engine control system, after-treatment system, ship propulsion system, etc., the combustion details are not the main concern, but the main performance parameters of the engine, such as engine work, peak pressure, peak temperature, are strongly affected by the engine combustion process. A suitable approach on fitting diesel engine combustion process with a few parameters is useful for combustion modeling, where the mathematics analysis is essentially required to solve the rooting finding problems in particular for the experimental investigation, because plenty of experimental data needs to be handled and used in the multi-dimensional system of equations [2, 3]. Diesel engine combustion process is varied in comparison with the other combustion machines, resulting in the specific theoretical investigation method. Recently there has been lots of diesel engine combustion research using both theoretical and experimental approaches. With the rapid development of three-dimension numerical calculation technology, the diesel engine combustion can be simulated in quite detailed ways to obtain the detailed combustion information [4, 5]. A three-dimension simulation of diesel engine combustion requires the turbulence flow model, spray model and combustion model, among which the turbulence flow model plays an important role. Normally there are three ways to model the turbulence flow of the engine: Large Eddy Simulation (LES), Direct Numerical Simulation (DNS) and Reynolds-Averaged Navier-Stokes (RANS) [6]. [PERSON] et al. developed the LES together with a finite-rate chemistry model to investigate the engine dual-fuel ignition process [7]. [PERSON] et al. proposed the compressible Eulerian numerical model to describe how liquid fuel injector nozzle geometry and operation strategies influence gas phase fuel distribution [8]. [PERSON] et al. used the renormalization group K-epsilon model to describe the turbulent flow field and predict the soot particles evolution [9]. When modeling the turbulent flow, it is important to calculate the average chemical reaction rate and the turbulent combustion rate of fuel [10,11]. [PERSON] et al. used the characteristic time combustion model coupled with the chemical kinetic mechanism to study the mixture formation's influence on the smoke [12]. [PERSON] et al. studied the methyl esters of soybean and coconuts formed by spray combustion and related emissions of the diesel engine and further to the effect of EGR on these biodiesel fuel combustion [13]. The diesel engine spray models are mainly divided into homogeneous gaseous jet models and gas-liquid two phase models, and the latter use the gas and liquid two phases in modeling engine spray process [14, 15, 16]. Besides the three-dimension approaches in modeling the engine combustion process, the multi-zone models are also efficient tools. Compared with the commonly used single-zone models, the multi-zone models take into account the instantaneous details of combustion process, such as the formation and development of fuel spray, the relative motion of fuel droplets and air. A popularly used multi-zone combustion model is [PERSON]'s fuel droplet evaporation combustion model [17], which includes the fuel injection sub-model, combustion thermodynamic calculation sub-model and emission generation sub-model. [PERSON] et al. used the in-cylinder steam injection method to establish a two-zone combustion model to research the waste heat recovery and NOx emission control [18]. [PERSON] et al. built a two-dimension combustion model to study the effect of electric fields on the combustion characteristics of a lean-burning methane air mixture [19]. [PERSON] et al.