1. Introduction
Natural Gas (NG) is considered as an appropriate alternative for internal combustion engines due to its cleaner combustion, relative lower cost and rich reserves [
1,
2]. It is generally applied in the form of mono- or dual-fuel engines, such as spark ignition natural gas engines, natural gas/diesel engines and CNG-H
2 engines [
3,
4,
5]. For spark ignition (SI) natural gas engines, the further thermal efficiency improvement is constrained by a knocking phenomenon that commonly occurs in gas-fueled SI engines [
6]. Knocking is the noise transmitted through the engine structure when a portion of the end-gas (the mixture of fuel, air and residual gas) ignites spontaneously before the propagating flame arrival. When this abnormal combustion process takes place, there will be an extremely rapid chemical energy release in the end-gas, resulting in high local pressure and the propagation of pressure waves of substantial amplitude across the combustion chamber, which may cause the chamber to resonate at its natural frequency [
7]. Knocking primarily occurs under wild-open-throttle operating conditions, which leads to a direct constraint on engine performance. In addition, since knocking probability increases with higher temperature and pressure of the end-gas, it also constrains the engine efficiency by limiting the maximum compression ratio. Therefore, it is important for an engine designer to achieve the desired normal combustion behavior while holding the engine propensity to knock at a minimum.
Two broad categories of experimental based methods are used to detect the knocking phenomenon in a certain natural gas engine: the former one is based on direct measurement, like an intensified charge coupled detector (ICCD) camera and Laser-induced Fluorescence (LIF) imaging [
8,
9]; other methods [
10,
11] are based on indirect measurement such as in-cylinder pressure analysis, cylinder block vibration, exhaust gas temperature, etc. On the other hand, simulation models enable engineers to explore the details comprehensively during the design period in order to determine the best case, saving research time and development cost. In general, numerical simulation of the natural gas engine working process is classified as follows: the mean value model, zero-dimensional model, quasi-dimensional model and multi-dimensional model [
12]. The mean value model is not primarily intended for engine development, but it is efficient for integrated system research, thus it is usually based on a large amount of engine test data and has scarcely no ability to predict [
13,
14]. For knocking prediction simulation models, the main objective is to characterize the end-gas temperature, which has a direct effect on knocking occurring. It is difficult for the zero-dimensional model to achieve this goal since the in-cylinder temperature and species concentrations are assumed to be uniform throughout the cylinder [
15]. The multi-dimensional simulation model (or Computational Fluid Dynamics model, CFD) provides most details of in-cylinder parameters, while it is usually time-consuming and hard to implement [
16]. The quasi-dimensional model is a kind of simplified phenomenological model that divides the combustion chamber into several zero-dimensional zones according to the distribution pattern of the flame position or injection space. In each zone, certain physical and chemical processes are considered, like fuel-air mixing, flame propagation and species concentration changes, which determine the temperature and pressure in each zone. Thus, the quasi-dimensional model does better work in balancing low computational cost and high prediction accuracy [
17,
18].
The two-zone model is considered to be the simplest quasi-dimensional model and usually consists of a burnt zone and an unburnt zone. For diesel engines, Hohlbaum [
19] separates the in-cylinder space into two cylindrical zones by a flat flame front, in which the primary oxidation is assumed to take place until equilibrium, i.e., the components O, H, O
2, H
2O, CO, CO
2 and OH are in chemical equilibrium. Heider [
20] adopted another way to divide the combustion chamber, a drop-shaped reaction zone surrounded by the fuel spray boundary and an unburnt gas zone occupying the remaining volume. The air–fuel ratio in reaction zone is assumed to be constant throughout the working cycle, thus the mass change in reaction zone is completely determined by the heat release rate. Rakopoulos [
21] built a two-zone combustion model of a diesel engine with an upgraded jet mixing sub-model, in which the burnt zone is further divided into several sub-zones depending on the number of injector nozzle holes. Gonca [
22,
23] used a zero-dimensional two-zone combustion model, which is divided into two zones as burnt and unburnt gas regions, to calculate nitric oxide (NO) emission, torque, brake power, brake efficiency and specific fuel consumption of a Miller cycled diesel engine. For gas engines, Fiveland and Assanis developed a two-zone model for homogeneous charge compression ignition (HCCI)combustion engines, which couples an adiabatic core zone and a boundary layer heat transfer zone [
24]. Their research integrates complex chemical kinetics with models of turbulence-based heat transfer and gas exchange processes for a four-stroke cycle. It provides boundary layer thickness and mass fraction for better hydrocarbon quenching prediction. Ibrahim and Bari [
25] compared exhaust gas recirculation (EGR) and lean-burn strategies employed in a natural gas SI engine using a two-zone model, in which the burnt zone was shaped by the spherical flame. A turbulent flame propagation model [
26] was applied to obtain the explicit relations for the flame development angle and rapid burning angle as function of engine design and operating variables. Galindo [
27] characterized a two-zone sub-model for the gas phase in a three-zone diesel engine model, in which the mass and energy balance between burnt zone and unburnt zone can also be theoretically applied to gas engine. Zhang [
28] described a two-zone homogeneous charge compression ignition (HCCI) combustion sub-model in the hardware-in-the-loop (HIL) simulation environment, where the in-cylinder charge is divided into the well-mixed and unmixed zones as the result of charge mixing. Simplified fluid dynamics are used to predict the residual gas fraction before the combustion phase starts, which defines the mass of the unmixed zone, during real-time simulations. Reyes [
29] developed a two-zone thermodynamic combustion diagnosis model to analyze the combustion process and cycle-to-cycle variations in a spark ignition engine fueled with natural gas/hydrogen mixtures. The two-zone model considers a spherical flame front centered at the spark plug, and solves the intersection of the flame front with the piston, cylinder head and cylinder wall, in order to provide the values of the flame radius corresponding to the burned mass volume and the surfaces for heat to the piston and walls. In conclusion, two-zone models work better in natural gas SI engines than in diesel engines since the basic space division theory is what happens exactly in SI engine combustion chambers as the flame propagates throughout the cylinder and separates the combustion chamber. However, most researchers put emphasis on the spherical flame propagation process and rely on complicated reaction mechanisms to obtain the emission concentration, which would increase the model complexity and computational cost to some extent.
In this paper, an in-cylinder process model of natural gas SI engine is built into the MATLAB/SIMULINK (R2012a, MathWorks, Natick, MA, USA) environment [
30], which provides the prediction of engine performance, NO emission and knocking performance. The model consists of a single-zone compression sub-model, a two-zone combustion sub-model and a single-zone expansion sub-model. The overall computational cost is decreased by using cylindrical division theory and a basic reaction mechanism when developing the two-zone combustion sub-model. The heat release rate is firstly calculated from the measured in-cylinder pressure and the obtained Vibe parameters will be used to simulate the energy release of natural gas. After model validation with engine test data, the effect of boundary parameters variation and knocking factors on engine performance will be discussed under different engine working conditions.