The research object of this paper is a two-cylinder horizontally opposed spark-ignition two-stroke piston engine with reed valve intake. Gasoline is selected as the fuel, and its main physicochemical properties are as follows: density of 0.70 - 0.75 kg/L, flash point of −45˚C - −25˚C, freezing point of −80˚C, theoretical air-fuel ratio of 14.8, and lower heating value of 44000 kJ/kg. The main technical parameters are listed in Table 1.

Table 1. Main technical parameters of the engine.

The one-dimensional performance simulation calculation of engine is also defined as thermodynamic cycle calculation. To efficiently and accurately reproduce the actual operating conditions of the engine, the whole calculation process is divided into four parts: gas exchange process, heat transfer process, combustion process, and the unsteady gas dynamic process of the intake and exhaust system [17]. The one-dimensional performance simulation model established by GT-Power is shown in Figure 1.

GT-Power possesses quasi-three-dimensional simulation capability for engine calculation. It can not only analyze key performance parameters such as power output, fuel consumption and emission characteristics, but also simulate the variations of pressure, temperature and mass flow along the gas flow path inside the engine. In addition to the simulation of steady-state operating conditions, the software can accurately predict the transient operating processes. Accordingly, reasonable initial and boundary conditions can be provided for the subsequent three-dimensional numerical simulation. Table 2 presents the initial and boundary conditions obtained from one-dimensional simulation under the specified operating conditions: engine speed of 5400 r/min, 100% throttle opening, ignition advance angle of 29˚CA, fuel injection timing of −130˚CA, single-cycle fuel injection quantity of 2.38 mg, and injection duration of 12˚CA.

Figure 1.One-dimensional performance simulation model diagram.

Table 2.Initial and boundary conditions for simulation calculation.

In this paper, only a single cylinder is selected as the research object for the three-dimensional simulation, and the crankcase modeling is omitted. Therefore, the established three-dimensional engine simulation model mainly consists of three domains: the scavenge passage, the exhaust passage, and the cylinder with combustion chamber. The adopted physical models are specified as follows: the RNG k-ε model for turbulence, the KH-RT model for droplet breakup, the Wall Film model for droplet impingement, the Frossling model for fuel evaporation, the L-type Energy Source model for ignition, and the SAGE model for combustion. In this study, the SAGE combustion model is adopted to simulate and calculate the in-cylinder combustion process of the engine. The chemical reaction mechanism employs an isooctane mechanism developed by Dalian University of Technology, which contains 41 species and 124 reaction steps [18].

Proposed by Tuns [19], a multi-step chemical reaction mechanism can be expressed in the following form:

where V ′ m , r and V ″ m , r represent the stoichiometric coefficients of reactants and products, respectively. Herein, m denotes the chemical species, r stands for the elementary reaction, R is the total number of reaction steps, and X m refers to the chemical formula of the species m . The net production rate of each chemical species can be calculated by Equation (1).

where ω ˙ m denotes the net production rate, M is the total number of chemical species, and V m , r in the above equation is defined as:

The reaction progress parameter q r of the r reaction step is expressed by the following equation:

where [ X m ] is the molar concentration of the species m , k f r and k r r denote the forward r and reverse rate coefficients of the reaction, respec-tively.

For a given computational cell, the governing equations based on mass conservation and energy conservation can be solved.

where V is the volume, T is the temperature, P is the pressure, ω ˙ m represents the net production rate of species m , and h ¯ m and c ¯ p , m are the molar specific enthalpy and molar constant-pressure specific heat capacity of species m , respectively.

Figure 2 presents the fluid domain of the engine.

Figure 2.Internal flow field model of the engine.

This paper defines several cross-sections for subsequent cloud contour analysis, as shown in Figure 3. The symmetry planes along the X-axis and Y-axis of the cylinder are defined as the Y-Z cross-section and X-Z cross-section, respectively. The plane 3 mm away from the X-Z cross-section is defined as the X-Z-3 cross-section.

Figure 3.Schematic of the defined cross-sections.

Mesh quality is one of the direct factors affecting the accuracy of numerical simulation results [20]. Converge software provides tools to control mesh size and realize the coarsening or refining of the base mesh. It mainly includes two encryption strategies: fixed embedding, which improves mesh accuracy by fixed refinement at designated positions and moments, and adaptive mesh refinement, which adjusts mesh size according to flow fluctuation and moving boundary conditions. In engine simulation, the two methods are generally used cooperatively. In this model, two layers of spherical fixed refinement regions with radii of 3 mm and 1 mm are established around the spark plug at the ignition moment, with refinement levels of 2 and 3 respectively. During fuel injection, a conical fixed refinement region is arranged along the fuel spray path with a refinement level of 2. Meanwhile, adaptive mesh refinement is activated with a refinement level of 1. The mesh refinement configuration is shown in Figure 4. Local mesh refinement in key working stages captures critical flow phenomena and effectively improves the accuracy of simulation results.

To ensure the reliability of simulation results, basic grid sizes of 1.4 mm, 1.2 mm, 1.0 mm and 0.8 mm listed in Table 3 are selected for comparative analysis. Figure 5 shows the variation curves of the calculated average in‑cylinder pressure of the engine simulation model under different basic mesh sizes. It can be observed that the influence of mesh size on the average in‑cylinder pressure gradually decreases as the basic mesh size declines. The average in‑cylinder pressure of Case 1 is slightly higher than that of Case 2, while the mesh number of Case 1 is far larger. Considering comprehensively the calculation accuracy and time cost, a basic mesh size of 1 mm is finally determined.

Table 3.Number of meshes used.

Figure 4.Mesh refinement conditions in the calculation.

Figure 5.Curves of in-cylinder average pressure variation under different basic mesh dimensions.

Since the crankcase is omitted in the present simulation, the compression process of fresh air inside the crankcase cannot be calculated. However, the pressure in the actual crankcase varies significantly during engine operation, and a constant pressure boundary condition will exert a considerable impact on the simulation accuracy. Therefore, a pressure boundary condition varying with the crank angle must be specified at the inlet of the scavenge passage. This boundary condition was calculated and acquired through one-dimensional simulation, as illustrated in Figure 6.

Figure 6.Average pressure variation curve in the crankcase.

Figure 7 presents the variation of spray penetration distance under different fuel injection timings. The spray penetration distance is defined as the maximum distance between the spray front and the nozzle along the injection direction. The injection timing exerts a significant effect on spray penetration characteristics. An earlier injection timing corresponds to a lower in‑cylinder back pressure and a higher peak spray penetration distance. Among all cases, the injection timing of −140˚CA shows the maximum peak penetration distance of 44 mm, leading to the highest risk of fuel wall impingement. By contrast, the timing of −120˚CA has the minimum peak penetration distance of 37 mm, which results in insufficient spray development and a high risk of inadequate mixture formation. Combined with the analysis of spray penetration distance, fuel atomization quality and combustion performance, the injection timing of −130˚CA is determined as the optimal solution. It can effectively avoid fuel wall wetting, ensure sufficient spray development and promote the uniform formation of in‑cylinder mixture.

Figure 7.Spray penetration distance variation curves at different fuel injection timings.

The fuel atomization effect during injection is commonly evaluated by the fineness and uniformity of fuel droplets. Finer droplets with a more uniform distribution indicate superior atomization quality. The droplet fineness is generally characterized by the Sauter Mean Diameter (SMD), which is defined as the ratio of the total volume of all droplets to their total surface area. The mathematical expression is as follows:

In the formula, N t o t represents the number of droplet diameter groups; N i is the total number of droplets with the diameter of d i ; d i denotes the droplet diameter.

Here is the fully polished, academically standardized English translation, consistent with your previous CFD/two‑stroke engine terminology: Figure 8 illustrates the variation of droplet Sauter Mean Diameter (SMD) under different fuel injection timings. It can be seen that the peak SMD values under various injection timings remain approximately 0.20 mm, indicating that the initial droplet size produced during injection is barely affected by injection timing. After the end of injection, secondary breakup and fuel evaporation occur under the influence of in‑cylinder airflow, causing a rapid reduction in SMD. A later injection timing corresponds to a lower SMD in the stable stage, presenting a clear regular trend. The −120˚CA case exhibits the smallest stable SMD and the best atomization performance, yet it faces the risk of insufficient mixture preparation. In contrast, the early injection condition of −140˚CA allows fuel to reside in the cylinder for an excessively long period, which aggravates droplet coalescence and wall wetting, consequently increasing droplet size before combustion and deteriorating overall atomization quality. For timings ranging from −125˚CA to −130˚CA, the SMD remains at a moderate level with sufficient evaporation time, achieving a reasonable balance between atomization quality and mixture formation duration. In terms of fuel atomization alone, the late injection strategy at −120˚CA shows distinct advantages. Nevertheless, practical engine calibration requires comprehensive consideration of combustion phasing, power performance, and emission characteristics. By compromising atomization performance and mixture preparation time, the range of −125˚CA to −130˚CA is identified as the optimal injection interval for balancing atomization behavior and combustion efficiency.

Figure 9 shows the variation of in‑cylinder fuel vapor mass at different fuel injection timings. It can be observed that, during the injection period under all tested timings, the in‑cylinder fuel vapor mass rises rapidly at first and then tends to stabilize. The injection timing exerts a significant influence on fuel evaporation characteristics. As the injection timing is delayed, the final stable value of gaseous fuel inside the cylinder increases gradually. The −140˚CA condition presents the lowest stable vapor mass of 1.98 mg. The value rises to 2.05 mg at −135˚CA and further increases to 2.18 mg at −130˚CA. The stable vapor mass continues to increase slightly at −125˚CA and −120˚CA, reaching 2.28 mg and 2.30 mg, respectively, with only a minor discrepancy between the two cases. An excessively advanced injection timing induces severe fuel wall wetting, which causes a temporary decline in gaseous fuel mass and imposes adverse effects on combustion and emissions. By contrast, the range of −120˚CA to −125˚CA effectively avoids wall wetting caused by overly early injection while maintaining sufficient evaporation duration. This enables the in‑cylinder fuel vapor mass to reach a relatively high level by the late compression stroke, thereby forming the optimal injection advance angle range for fuel evaporation performance.

Figure 8.Fuel sauter mean diameter variation curves at different fuel injection timings.

Figure 9.In-cylinder fuel vapor mass variation curves at different fuel injection timings.

Figure 10 presents the in‑cylinder equivalence ratio distribution of the mixture at the ignition moment under different fuel injection timings. It can be seen that the mixture distribution is the most uniform at the injection timing of −140˚CA. The advanced injection provides a longer mixing time for fuel and air. Meanwhile, the exhaust port is largely open during injection, and the strong in‑cylinder tumble flow facilitates fuel diffusion. Nevertheless, an excessively early injection timing causes a large number of fuel droplets to be directly discharged from the cylinder during injection. Considerable fuel vapor also flows out of the cylinder before the exhaust port closes, resulting in an overall low equivalence ratio of the combustible mixture. As the injection timing is delayed, the equivalence ratio gradually increases in the region near the exhaust port. This indicates that fuel tends to accumulate in this area under retarded injection. The shortened mixing time between fuel and air restricts the diffusion of high‑concentration fuel to leaner regions, thereby further raising the local equivalence ratio.

Figure 10.Contour distribution of mixture equivalence ratio at ignition under different fuel injection timings.

Figure 11 shows the equivalence ratio of the mixture near the spark plug at the ignition moment under different fuel injection timings. It is observed that the equivalence ratio around the spark plug gradually increases as the injection timing is retarded.

At the injection timing of −130˚CA, the equivalence ratio near the spark plug reaches 1.05 at ignition, which deviates by only 5% from the stoichiometric value and is conducive to reliable ignition. When the injection timing is delayed to −125˚CA and −120˚CA, the local equivalence ratio rises to 1.20 and 1.28, corresponding to deviations of 20% and 28%, respectively. An over-rich mixture tends to cause incomplete combustion and even ignition failure.

In contrast, with advanced injection timings of −135˚CA and −140˚CA, the equivalence ratio around the spark plug decreases to 0.87 and 0.74, with deviations of 13% and 26%. An overly lean mixture leads to unstable combustion and further induces cycle-to-cycle variation and misfire.

Figure 11.Mixture equivalence ratio at spark plug during ignition under different fuel injection timings.

Figure 12(a) illustrates the variation of in-cylinder average pressure at different fuel injection timings. It can be observed that the peak in-cylinder average pressure first increases and then delays with the retardation of injection timing. At the injection timing of −130˚CA, the peak in-cylinder pressure reaches the maximum value of 3.4 MPa, which is significantly higher than 3.1 MPa at −120˚CA. Meanwhile, the peak occurs within a reasonable range of 10˚CA - 15˚CA, indicating a more sufficient combustion process and higher power output capacity. This condition realizes maximum work output and avoids knock and excessive mechanical load caused by an overly rapid pressure rise.

Figure 12(b) presents the variation of in-cylinder average temperature under various injection timings. As the injection timing is retarded, the peak in-cylinder average temperature also rises first and then declines. The maximum peak temperature of 2200 K appears at −130˚CA, with its peak position occurring the earliest. This demonstrates that the fuel combustion is more sufficient under this operating condition, which maximizes the combustion efficiency and efficiently converts combustion heat energy into piston work.

The results reveal that the regulation effect of injection timing on combustion phase directly determines the power performance and thermal efficiency of the engine. Accordingly, −130˚CA is the optimal injection advance angle that balances combustion sufficiency and operational stability under the present condition.

(a) (b)

Figure 12.Variation curves for multiple in-cylinder combustion parameters under different fuel injection timings. (a) In-cylinder average pressure variation curve; (b) In-cylinder average temperature variation curve.

Figure 13 presents the contour nephograms of in‑cylinder temperature distribution during the combustion process under different fuel injection timings. As illustrated, the high‑temperature region in the cylinder is the smallest at the crank angle of −17˚CA, while nearly the entire in‑cylinder area maintains a high and relatively uniform temperature at 33˚CA. As the injection timing is retarded from −140˚CA to −120˚CA, the overall in‑cylinder temperature level increases gradually. The high‑temperature zone changes from local concentration to uniform distribution across the whole cylinder, and the temperature gradient decreases significantly. This is attributed to the shortened ignition delay and improved fuel‑air mixing efficiency under retarded injection, which promotes sufficient combustion reactions and uniform flame propagation. At the injection timing of −130˚CA, an optimal balance between temperature field uniformity and combustion intensity is achieved, yielding high combustion efficiency and providing a direct reference for the optimization of the corresponding fuel injection strategy.

Figure 13.Temperature distribution contours of X-Z, Y-Z and X-Y-2 cross-sections inside cylinder under different fuel injection timings.