Tailoring Engine Piston for Carbon-Neutral Polyoxymethylene Dimethyl Ethers: From Diesel Comparison to Fuel-Specific Co-Optimization

Abstract

Polyoxymethylene dimethyl ethers (PODE) is a promising carbon-neutral synthetic fuel for reducing emissions in compression ignition engines. This study employed a progressive optimization from operating parameters alone to co-optimization with operating and geometric parameters to improve engine performance, and the coupling among fuel properties, injection strategies, and piston geometry is elucidated by comparing the combustion and emission characteristics of diesel and PODE. Compared to diesel, the high oxygen content and superior atomization of PODE promote rapid combustion and lower exhaust losses, albeit with larger heat transfer losses that limit net thermal efficiency gains. Consequently, the optimization priority shifts from enhancing mixture preparation for diesel to managing flame/wall interactions for PODE. From parameter-only tuning to co-optimization, diesel adopts a lower injection pressure to alleviate the fast combustion rate, paired with a shrunken bowl bottom pocket to compensate for the lower spray momentum; PODE prioritizes a lower injection pressure and an elevated side pocket to mitigate flame/wall interactions and suppress heat transfer losses. Under co-optimization, PODE achieves a 2.1% improvement in thermal efficiency and a 14.3% reduction in nitrogen oxides (NOx) relative to parameter-only optimization; both gains are more pronounced than those for diesel. These insights provide a theoretical basis for designing high-efficiency engines with carbon-neutral fuels.

1. Introduction

Diesel engines serve as the primary power source for transportation and industrial sectors; however, they still face the challenge of overcoming the trade-off between nitrogen oxides (NOx) and soot emissions, while simultaneously improving thermal efficiency and reducing carbon emissions. Although various advanced combustion modes have been proposed to address these issues, their practical implementation remains limited by narrow operating ranges, low operational stability, and increased injection complexity, etc., hindering their large-scale commercialization in the near term [1]. Therefore, further improvement of conventional diesel engines is still essential, and numerical optimization offers a viable pathway to maximize their potential in complying with increasingly more stringent regulations in the future.

Current advancements in conventional diesel engines primarily focus on the optimization of injection parameters and intake conditions. A multiple-injection strategy is capable of alleviating combustion rates, reducing combustion noise, lowering unburned emissions, and improving thermal efficiency, which has become the predominant approach for enhancing diesel combustion [1,2]. High-pressure injection significantly enhances fuel atomization and fuel/air mixing [3], thereby effectively mitigating the trade-off between NOx and soot [4]. Intake boosting is frequently coupled with engine downsizing or the Miller cycle to supply sufficient oxygen for complete combustion. The larger intake density not only increases output power but also improves brake thermal efficiency (BTE) [5].

Although the aforementioned strategies can reduce pollutant emissions and improve thermal efficiency, their potential for engine decarbonization remains marginal. Consequently, the achievement of life-cycle carbon neutrality in internal combustion engines necessitates a transition from fossil-derived fuels toward carbon-neutral alternatives, such as polyoxymethylene dimethyl ethers (PODE), which can be synthesized utilizing renewable energy. The PODE molecule features high oxygen content (approximately 47 wt%) and no carbon/carbon bonds, which promotes clean combustion with lower emissions of carbon monoxide (CO), hydrocarbons (HC), and soot [6,7]. Furthermore, the low viscosity and high cetane number (approximately 78) of PODE enhance atomization and ignition, respectively, which can synergistically promote combustion completeness and improve cold-start reliability [8].

Optical experiments by Zhang et al. [9] revealed that PODE exhibited a shorter ignition delay and a faster combustion rate compared to diesel, facilitating more complete diffusion combustion and lower unburned emissions. In a constant-volume chamber, Mazari [10] investigated the spray and combustion characteristics of PODE/diesel blends. Although the injection duration of PODE/diesel blends was longer than that of diesel due to its lower heating value (LHV), the PODE/diesel blend demonstrated superior atomization and fuel/air mixing. Specifically, the shorter spray penetration and lift-off length of the blends improved combustion efficiency, achieving a simultaneous reduction in soot and NOx emissions by 78.2% and 31.3%, respectively. These findings were corroborated by the engine evaluations of Liu et al. [11], which showed substantial decreases in HC, CO, and soot emissions with a larger PODE blending ratio. Although the inherent trade-off between NOx and soot persisted, the simultaneous reduction of both emissions at higher PODE ratios underscored the potential of PODE fuel for achieving clean and high-efficiency combustion.

Furthermore, piston geometry dictates in-cylinder flow dynamics, fuel/wall impingement, and subsequent fuel/air mixture preparation, so it evidently affects flame propagation, combustion efficiency, and thermal efficiency [12,13]. Given the intricate interaction between spray development and piston geometry, the optimal piston configuration is intrinsically dependent on the physicochemical properties of direct-injected fuel [14]. Due to the significant differences between PODE and diesel, particularly in cetane number, oxygen content, and viscosity [15], a dedicated re-optimization of the piston geometry is imperative when PODE is introduced as a primary fuel [16].

Current methodologies of piston geometry optimization predominantly rely on comparative screening of the established configurations, including toroidal, U-type, hemispherical, re-entrant, and stepped-lip pistons. Comparative studies by Manjunath et al. [17] and Pham et al. [18] identified the re-entrant piston as the optimal configuration for reducing fuel consumption and soot emissions, owing to its ability to enhance airflow motion and fuel/air mixing. Complementarily, parametric reconstruction offers a more flexible framework for piston optimization by decomposing piston geometry into key design variables. However, the four-parameter reconstructions proposed by Sener et al. [19] and Rafael et al. [20] were restricted to specific structures and lacked the versatility of more complex piston geometries. Subsequently, Guo et al. [21] developed a six-parameter reconstruction approach capable of reproducing more sophisticated piston structures. Their optimized design effectively divided the spray plume into two distinct jets targeting separate spatial regions, thereby maximizing air utilization and accelerating fuel/air mixing.

Despite these advances in PODE-fueled engines, existing optimization efforts have primarily focused on injection strategies tailored to its unique spray and combustion characteristics. However, systematic investigations into piston geometries specifically designed for PODE to fully exploit its physicochemical advantages remain scarce. More importantly, operating parameters and piston geometry are inherently coupled through their effects on spray/wall interaction, fuel/air mixing, and the combustion process, necessitating their integrated consideration to fully exploit their synergistic effects and maximize engine performance. Furthermore, existing parametric reconstruction methods still struggle to reproduce the advanced complex piston structure with high fidelity, restricting comprehensive exploration across diverse piston geometries. To address the above research gaps, this study integrates an advanced parametric reconstruction method for piston geometry with high-fidelity computational fluid dynamics (CFD) and an efficient optimization algorithm. This framework enables a comprehensive co-optimization of both operating parameters and piston structure for diesel and PODE. The optimal piston configuration customized for each fuel is identified, and the fundamental correlation among fuel properties, operating parameters, and piston geometry is elucidated, which provides essential insights for fuel-specific engine design and facilitates the commercial application of PODE-fueled engines.

2. Computational Methods

2.1. Numerical Models

This study utilizes the three-dimensional simulation platform KIVA@DUT [22,23] to investigate the combustion and emission formation processes of diesel and PODE fuels in a conventional compression ignition engine. The generalized renormalization group (gRNG) k-ε turbulence model [24] was adopted to reproduce the in-cylinder turbulent flow characteristics. Fuel spray dynamics were simulated by an enhanced Kelvin-Helmholtz/Rayleigh-Taylor (KH-RT) breakup model [25] and an improved spray collision model [26]. The spray/wall impingement process was accurately tracked by the model proposed by Zhang et al. [27]. The wall heat transfer model developed by Cao et al. [28] was implemented to quantify the heat flux density across various combustion processes.

To accurately simulate the ignition and combustion characteristics of diesel or PODE fuels, the CHEMKIN solver [29] was coupled with KIVA@DUT by treating each computational cell as a perfectly stirred reactor. A simplified surrogate model was adopted for diesel fuel, whose physical and chemical properties were represented by n-dodecane and n-heptane, respectively. The PODE fuel was modeled as a blend of PODE₃, PODE₄, PODE₅, and PODE₆, with respective mass fractions of 44.8%, 28.2%, 17.1%, and 9.9% [30]. A combined chemical reaction mechanism was constructed by coupling the diesel surrogate mechanism from Chang et al. [31] with the PODE oxidation mechanism from Huang et al. [32]. Furthermore, the extended Zeldovich mechanism was used to predict NOx emissions.

During numerical simulation, a variable time step ranging from 1.0 × 10⁻¹² to 5.0 × 10⁻⁵ s was employed in this study, depending on the convergence behavior of the implicit solver. The allowable relative errors for the implicit solution of mass diffusion, momentum diffusion, heat diffusion, and turbulent kinetic energy diffusion are all set to 1.0 × 10⁻³, whereas that for the pressure iteration is set to 1.0 × 10⁻⁴. To ensure the consistency of the calculations, the same numerical convergence criteria are applied in the subsequent validation and optimization for different fuels and piston geometries.

2.2. Numerical Model Validation

Diesel and PODE are separately investigated and optimized in this study, and the properties of the two fuels are compared in Table 1 [33]. Compared with diesel, PODE has a considerably higher cetane number, a markedly lower auto-ignition temperature, and wider flammability limits, indicating its higher reactivity. However, the LHV of PODE is substantially lower than that of diesel, which means that considerably more PODE is required to maintain the same engine load.

Table 1. Comparison of fuel properties between diesel and PODE.

Property	Diesel	PODE
Density (kg/m3)	834	1047
Latent heat of vaporization (kJ/kg)	250	359
Cetane number	51	75.5
Lower heating value (MJ/kg)	42.5	21.77
Auto-ignition temperature (K)	463~613	398~513
Flammability limit (%vol)	0.6~6.5	1.5~10.5

The engine used in this work was a heavy-duty four-cylinder engine, which was modified into a single-cylinder configuration by deactivating the other cylinders. The main specifications of the test engine are summarized in Table 2. The intake air was boosted by an external air compressor. Two surge tanks were installed upstream of the intake pipe and downstream of the exhaust pipe, respectively, damping the pressure fluctuations traveling along both ducts. The temperature of the intake charge was adjusted by a heating unit mounted downstream of the intake tank. The injector was mounted at the center of the cylinder and features an 8-hole nozzle with a hole diameter of 0.217 mm and a spray included angle of 143°.

Table 2. Tested engine specifications.

Parameters	Value
Bore	127 mm
Stroke	165 mm
Compression ratio	18.5
Intake valve closing	−145 °CA ATDC
Exhaust valve opening	120 °CA ATDC
Piston geometry

To validate the reliability of the numerical model, a comprehensive comparison between experiment and simulation was performed under different indicated mean effective pressures (IMEP) and engine speeds. Main injection timing and injection pressure were calibrated to achieve the maximum thermal efficiency at each operating condition. A small pilot injection mass was consistently employed across the experiment to mitigate combustion rate and prevent engine knock. The operating parameters under different conditions are summarized in Table 3.

Table 3. Experimental operating parameters for model validation.

IMEP	Speed	Fuel Mass	Pilot Mass	Pilot Injection	Main Injection	Injection Pressure
2.63 MPa	1200 rpm	0.276 g	0.002 g	−9.1 °CA ATDC	1.6 °CA ATDC	131.9 MPa
2.03 MPa	1200 rpm	0.198 g	0.002 g	−7.5 °CA ATDC	−1.0 °CA ATDC	117.0 MPa
1.23 MPa	1200 rpm	0.118 g	0.002 g	−8 °CA ATDC	−1.2 °CA ATDC	106.5 MPa
2.60 MPa	1000 rpm	0.276 g	0.002 g	−9.8 °CA ATDC	0.8 °CA ATDC	109.8 MPa
1.13 MPa	1000 rpm	0.118 g	0.002 g	−13.2 °CA ATDC	−1.6 °CA ATDC	99.6 MPa

A series of experiments was conducted, and the key metrics, including peak pressure (P_max), intake air flow, indicated thermal efficiency (ITE), and NOx emissions, are compared between prediction and experiment, as shown in Figure 1. However, although various metrics were measured, few in-cylinder pressure traces were recorded in the experiment. Therefore, the available experimental pressure data are very limited. Owing to the lack of directly measured wall temperatures, the temperatures of the piston, cylinder head, and liner were all prescribed as 500 K, 470 K, and 450 K, respectively.

Figure 1. Comparison between experiment and simulation for a diesel engine. (a) Comparison of pressure; (b) Comparison of P_max; (c) Comparison of intake flow; (d) Comparison of ITE; (e) Comparison of NOx emissions.

First, a mesh independence study was performed at an engine speed of 1200 rpm and an IMEP of 2.03 MPa. Three meshes with average mesh sizes of 2.0, 1.6, and 1.2 mm were evaluated, which are referred to as the coarse, medium, and fine meshes. To save computational cost, a 45° sector mesh corresponding to one injector nozzle hole was adopted, as shown in Table 2. As shown in Figure 1a, the peak pressure predicted with the coarse mesh is higher than the measured value. When the mesh is refined to the medium and fine levels, the predicted pressure agrees well with the measured profile. Since the medium and fine meshes yield very similar pressures, the medium mesh is finally adopted as a compromise between prediction accuracy and computational cost. After determining the optimal mesh size, the numerical model was validated by a comprehensive comparison against the experimental data. The results demonstrated good agreement in pressure evolution, peak pressures, and intake airflow rates between simulation and experiment. The relative prediction deviations of P_max and intake flow rates are 0.45% and 3.83%, respectively. Furthermore, the variations in the measured ITE and NOx were also consistently reproduced by the numerical simulation. The underprediction of ITE in the simulations was attributed to the restricted computational period from intake valve closing (IVC) to exhaust valve opening (EVO), which excluded the gas exchange effects inherent in the experiment.

Given the scarcity of experimental data for pure PODE-fueled engines, the model validation for PODE was performed on an alternative engine operating, with its engine specifications and operating parameters listed in Table 4. As seen in Figure 2, the implemented numerical models accurately capture the combustion process and ITE for the PODE-fueled engine. Although an underestimation is observed in the predicted ITE and NOx emissions compared to the measurements, their variations with injection timing remain remarkably close to the measurements. It should be noted that the validations of PODE and diesel were conducted on two different engines, which inevitably limits the generality of the validation results. To address this concern, extensive validations of the models have been performed across diverse engines featuring different compression ratios (CR) and piston geometry, various fuels, and different combustion modes. It can be found that both the in-cylinder pressure and the emissions are accurately reproduced under these widely varying conditions [34,35,36]. These results collectively demonstrate the reliability of the employed numerical models; consequently, the validation performed on the small-bore PODE-fueled engine provides sufficient confidence for extending the models to the large-bore engine and the subsequent optimization.

Table 4. PODE-fueled engine specifications and operating parameters.

Parameters	Value
Bore	83.1 mm
Stroke	92.0 mm
CR	16.7
Intake valve closing	−130 °CA ATDC
Exhaust valve opening	94 °CA ATDC
Fuel mass	0.0194 g
Injection timing	−45 °CA ATDC
Injection pressure	90 MPa
Piston geometry

Figure 2. Comparison between experiment and simulation for a PODE-fueled engine. (a) Comparison of pressure and HRR; (b) Comparison of ITE and NOx emissions.

2.3. Parametric Reconstruction of Piston Geometry

Sixteen geometric variables are employed to parametrically reconstruct diverse piston bowl profiles, which are systematically categorized into positional, length, and angular variables. As illustrated in Figure 3, four positional variables (z₁, x₂, z₂, and x₃) define the coordinates of Points 1–3, dictating the bowl depth and radial length. Eight length variables encompass six radii of Circles A–E (R_a, R_b, R_c, R_d1, R_d2, and R_e) and two lengths of piston lip segment (l₃₄ and l_4t5), which, respectively, adjust arc curvatures and the piston lip size. In addition, four angular variables are also used to shape the piston bowl geometry; specifically, β₁, β₂, and ε₁ collectively control the inclination of the stepped-lip region, while γ specifically governs the contour of the bowl floor. To ensure fluid-dynamic smoothness, tangential continuity is maintained across all geometric segments, with the exception of the junction between the piston bowl and top at Point 3. The minimum radius of the circle is restricted to 1 mm to avoid excessive local curvature. When the piston geometry is varied, the piston bowl volume changes accordingly. Since the displacement is kept constant throughout the optimization, the CR varies synchronously with the piston geometry. In addition, when the piston geometry is optimized using the parametric reconstruction method, the computational mesh is regenerated accordingly. Nevertheless, the average mesh size is kept constant throughout to ensure consistent numerical accuracy across all designs. A comprehensive description of the reconstruction methodology can be found in the dissertation of Cai [36].

Figure 3. Illustration of parametric reconstruction for piston geometry.

2.4. Optimization Setup

A non-dominated sorting genetic algorithm (NSGA-II) was employed to perform co-optimization of piston geometry and operating parameters. Through iterative evolution, optimal individuals are determined based on non-dominated ranking and crowding distance. These individuals then undergo crossover and mutation to generate promising candidates, progressively improving multiple optimized objectives over successive generations [37,38]. The optimized parameters and their allowable ranges remain identical for both diesel and PODE fuels, as summarized in Table 5.

Table 5. Optimized parameters and their variation ranges.

Operating Parameters	Ranges	Geometric Parameters	Ranges
TIVC (K)	370~400	z1	0.5~0.77
SOI2–SOI1 (°CA)	3~10	x2	0.38~0.57
SOI2 (°CA ATDC)	−14~6	z2	0.54~0.75
PInj (MPa)	80~240	x3	0.43~0.67
CR	18.5~22.0	Ra	0.15~0.57
		Rb	0.2~0.38
		Rc	0.51~0.99
		Rd1	0.01~0.99
		Rd2	0.1~0.99
		Re	0.01~0.75
		l34	0.5~0.9
		l4t5	0.2~0.99
		β1	0.3~0.97
		β2	0.1~1
		ε1	0.03~0.99
		γ	0.01~0.55

The optimization is conducted at the condition characterized by an IMEP of 2.03 MPa and an engine speed of 1200 rpm, which corresponds to the operating condition with the highest thermal efficiency across the operating map. The optimized operating parameters include the in-cylinder initial temperature at intake valve closing (T_IVC), the dwell time between two injections (SOI₂–SOI₁), the main injection timing (SOI₂), and the injection pressure (P_Inj). According to the experiment, a small pilot injection mass is used to mitigate engine knock, so it is not optimized here. The 16 optimized piston parameters are described in Section 2.3. Since modification to the piston bowl inherently changes the CR, it is constrained within the range of 18.5 to 22.0 to prevent excessively high P_max at higher loads.

Given the inherently soot-free combustion of PODE, the disadvantages of diesel would become even more pronounced if soot emissions were additionally considered. Thus, the optimization objectives for both fuels were confined to fuel consumption and NOx emissions. Due to the different LHV of diesel and PODE, the equivalent indicated specific fuel consumption (EISFC) is introduced for fair comparison between the two fuels, which is defined in Equation (1) [39].

$$\mathit{EISFC}={\displaystyle \frac{m_{\mathrm{f}}\times {\mathit{LHV}}_{\mathrm{f}}}{W_{\mathrm{i}}{\times \mathit{LHV}}_{\mathrm{d}}}}={\displaystyle \frac{m_{\mathrm{f}}\times {\mathit{LHV}}_{\mathrm{f}}}{{\mathit{LHV}}_{\mathrm{d}}}}\times {\displaystyle \frac{1}{{\int }_{\mathrm{IVC}}^{\mathrm{EVO}}\mathit{pdV}}}$$

(1)

where m_f is the mass of direct-injected fuel; W_i represents the indicated work performed from IVC to EVO, obtained by integrating the cylinder pressure and volume; LHV_f and LHV_d, respectively, represent the LHV of direct-injected fuel and diesel.

To ensure stable and reliable engine operation, the optimization was constrained by a P_max limit of 21 MPa and a ringing intensity (RI) threshold of 5 MW/m², which is defined according to Equation (2) [40].

$$\mathrm{RI}={\displaystyle \frac{1}{2\gamma }}{\displaystyle \frac{{\left[0.05{\left(\frac{\mathit{dp}}{\mathit{dt}}\right)}_{\max }\right]}^2}{p_{\max }}}\sqrt{\mathit{\gamma R}{T}_{\max }}$$

(2)

where γ is the specific heat ratio, (dp/dt)_max is the maximum pressure rise rate, p_max and T_max are the in-cylinder maximum pressure and temperature, and R is the ideal gas constant. The population size and the number of generations were set to 600 and 8, respectively, yielding a total of 4800 CFD evaluations. The crossover and mutation probabilities were 0.5 and 0.1. Optimization convergence was assessed using the inverted generational distance (IGD) [41]; when the change in IGD between two consecutive generations fell below 0.002, the population was considered to have converged to the Pareto front.

3. Results and Discussion

3.1. Comparison Between Diesel and PODE Base Cases

Based on the original piston, the engine is operated with diesel or PODE under the identical operating parameters, which are named Diesel_Base and PODE_Base, respectively. The in-cylinder pressures and heat release rates (HRR) of the two base cases are compared in Figure 4, and their combustion phasings and energy distributions are shown in Figure 5. The ITE is obtained by dividing the net work by the total fuel energy. Heat transfer losses are evaluated using Newton’s cooling law, based on the temperature difference between near-wall cells and the wall surface. Combustion losses are determined by summing the energy of all unburned species. Since the four energy components sum to 100%, the exhaust losses are calculated by difference from the other three terms [42].

Figure 4. Comparison of pressure and HRR between PODE_Base and Diesel_Base.

Figure 5. Comparison between PODE_Base and Diesel_Base. (a) Comparison of combustion phasing; (b) Comparison of energy distribution.

Since the LHV of PODE is approximately half that of diesel, its injection duration must be significantly extended to maintain the equivalent total fuel energy under the same injection pressure. Consequently, the higher energy density of diesel leads to a more concentrated initial heat release than PODE, characterized by a higher P_max, as well as a shorter interval between the crank angle at which 10% of the total energy is released (CA10) and the crank angle at which 50% of the total energy is released (CA50) [43].

Despite the prolonged injection duration of PODE compared to that of diesel, its superior atomization and diffusion characteristics enhance fuel/air mixing, facilitating a higher overall combustion rate and a shorter combustion duration from CA10 to the crank angle at which 90% of the total energy is released (CA90). Compared to Diesel_Base, the shortened combustion duration of PODE_Base effectively reduces exhaust losses, while its superior mixture preparation promotes more complete combustion, as seen in Figure 5b. These synergistic effects ultimately account for the larger ITE of PODE_Base relative to Diesel_Base.

To further elucidate the reason for the different combustion rates between diesel and PODE, the in-cylinder temperature and equivalence ratio distributions of Diesel_Base and PODE_Base are illustrated in Figure 6. The wider high-temperature distribution observed for PODE reveals that PODE spray exhibits better breakup and diffusion behaviors, resulting in more thorough fuel/air mixing (i.e., lower local equivalence ratio) and a more intense overall combustion rate. Beyond the influences of fuel physical properties, the chemical reaction kinetics are also compared between diesel and PODE by analyzing the spatial distributions of equivalence ratio, temperature, and HRR at the respective CA50 timing in Figure 7. Under the identical equivalence ratio and combustion temperature, the HRR of PODE is much faster than that of diesel, owing to its shorter molecular chain length and inherent oxygen content [44]. Therefore, both the physical and chemical properties of PODE contribute to its faster combustion rate, which effectively reduces exhaust losses and improves combustion efficiency. In addition, owing to the superior diffusion characteristics and faster combustion rate of PODE, it is found from Figure 6 that the high-temperature combustion region in PODE_Base is larger than that in Diesel_Base, which leads to its higher NOx emissions [45].

Figure 6. Comparison of temperature and equivalence ratio distributions between two base cases at 19 °CA ATDC (iso-line denotes equivalence ratio). (a) Distributions of Diesel_Base; (b) Distributions of PODE_Base.

Figure 7. Distribution of temperature, equivalence ratio, and HRR distributions for two fuels at their respective CA50 timing. (a) Distribution of Diesel_Base; (b) Distribution of PODE_Base.

Although the physicochemical properties of PODE inherently favor high thermal efficiency, the analysis for Figure 6 reveals that the intensified combustion process of PODE elevates peak temperatures, expands the high-temperature reaction zone, and shifts the flame closer to the piston bowl surfaces. These higher localized temperatures inevitably increase NOx formation, and the intensified flame/wall interaction is identified as the primary reason for the elevated heat transfer losses of PODE_Base. Consequently, the distinct physicochemical properties of diesel and PODE yield disparate combustion and emission behaviors, necessitating a fuel-specific optimization for PODE [46]. Specifically, the piston geometry must be co-optimized with operating parameters to align with PODE’s unique spray and oxidation characteristics, which is crucial for mitigating heat transfer losses and maximizing the thermodynamic potential of PODE-fueled engines.

3.2. Optimization of Operating Parameters Alone

Based on the original piston, an optimization of four key operating parameters is first performed for each fuel within the variation ranges listed in Table 5. The performance metrics for both fuels are quantitatively compared in Figure 8. The optimal cases from the final evolution population are, respectively, designated as Diesel Optimal Cases and PODE Optimal Cases, with the base cases of the two fuels introduced as benchmarks.

Figure 8. Distributions of EISFC and NOx for all the optimized cases and representative cases.

Through the optimization of operating parameters, both fuels achieve substantial reductions in EISFC without compromising NOx emissions relative to their respective base cases. Comparative analysis reveals that PODE Optimal Cases generally exhibit lower EISFC than Diesel Optimal Cases. However, the advantage of PODE is accompanied by higher NOx emissions, highlighting a distinct trade-off relationship between EISFC and NOx.

The distributions of the optimal operating parameters are compared in Figure 9 to reveal the different tuning strategies for both fuels. First, the optimized T_IVC is generally lower than the base cases for both fuels. The reduced T_IVC increases the charge density, which not only augments the oxygen supply for complete combustion but also increases the heat capacity of the charge mixture to lower combustion temperature. Second, the optimal injection dwell (SOI₂-SOI₁) of both fuels converges at approximately 7 °CA. This specific interval ensures that the pilot injection effectively triggers the ignition of the main injection while avoiding detrimental pulse-to-pulse interactions that would degrade combustion efficiency [47].

Figure 9. Parameter distributions of optimal cases for diesel and PODE.

The primary difference in the optimized operating parameters between diesel and PODE lies in SOI₂ and P_Inj. Diesel favors a late SOI₂ and a high P_Inj, while PODE achieves optimal performance through an early SOI₂ and a low P_Inj. To investigate the reason for their different injection strategies, two representative cases with the lowest EISFC are selected from the two sets of optimal cases illustrated in Figure 8, designated as Diesel_Para and PODE_Para, respectively. Additionally, another PODE optimal case featuring a late SOI₂ and a high P_Inj is also incorporated for comparative analysis and designated as PODE_SOI2.

The in-cylinder pressure and HRR of the five representative cases are compared in Figure 10, with their operating parameters listed in Table 6. Compared to the base cases, the implementation of late SOI₂ and high P_Inj can enhance fuel/air mixing and intensify the combustion process for either diesel or PODE, subsequently yielding higher peaks of HRR and pressure, as observed for Diesel_Para and PODE_SOI2 in Figure 10. In contrast, the PODE_Para case adopts an early SOI₂ and a low P_Inj, which exhibits an advanced ignition timing, a slower combustion speed, and a lower peak HRR.

Figure 10. Pressure and HRR of representative cases fueled with diesel or PODE.

Table 6. Operating parameters of base case, Diesel_Para, PODE_Para, and PODE_SOI2.

Parameter	Range	Base Case	DieselPara	PODEPara	PODESOI2
TIVC (K)	370~400	386.0	370.35	373.05	371.56
SOI2-SOI1 (°CA)	3~10	6.5	5.3	8.7	4.8
SOI2 (°CA ATDC)	−14~6	−1.0	1.7	−6.7	0.9
PInj (MPa)	80~240	131.0	230.6	86.2	185.1

To elucidate the distinct injection strategies for diesel and PODE, Figure 11 compares the combustion phasings and energy distribution between the base cases and the three representative optimized cases. The above analysis indicates that the lower ITE of Diesel_Base than PODE_Base is primarily attributed to its longer combustion duration and higher exhaust losses. Accordingly, the optimization for diesel-fueled engines effectively addresses this weakness by leveraging higher P_Inj to enhance fuel/air mixing, thereby reducing exhaust losses and increasing ITE. Although the heat transfer losses of Diesel_Para increase simultaneously, they are outweighed by the substantial reduction in exhaust losses, yielding a net gain in ITE. Furthermore, by delaying the SOI₂, Diesel_Para effectively suppresses the rapid combustion rate, thereby mitigating rough combustion and knock while maintaining high thermal efficiency.

Figure 11. Comparison among the five representative cases. (a) Comparison of combustion phasing; (b) Comparison of energy distributions.

In contrast, due to the superior physical and chemical properties of PODE, PODE_Base already achieves rapid fuel/air mixing and high combustion rates. Consequently, when late SOI₂ and high P_Inj are also adopted for PODE (i.e., PODE_SOI2), the improvements in combustion completeness and exhaust losses reduction are marginally limited. Figure 12 further illustrates the influence of different injection strategies on heat transfer through the visualization of temperature distribution. Compared to PODE_Base, PODE_SOI2 exacerbates spray impingement due to its higher P_Inj. Thus, the high-temperature combustion region in PODE_SOI2 not only expands over a larger area but also propagates closer to the piston surface, thereby intensifying heat transfer losses. In contrast, by adopting a lower P_Inj in PODE_Para, the high-temperature regions are substantially reduced, and the spatial distribution of combustion zones is optimized, as seen in Figure 12c. Therefore, the adoption of a lower P_Inj for PODE is necessary to prevent the excessive expansion of high-temperature flame toward the piston surface.

Figure 12. Comparison of in-cylinder temperature distributions at 17 °CA ATDC. (a) Distribution of PODE_Base; (b) Distribution of PODE_SOI2; (c) Distribution of PODE_Para.

However, an excessively low P_Inj prolongs injection duration and retards combustion phasing, which is detrimental to thermal efficiency [48]. Therefore, the optimal injection strategy for PODE adopts an advanced SOI₂ to compensate for the elongated combustion duration caused by the reduced P_Inj. In summary, the different injection strategies adopted for diesel and PODE stem from their distinct fuel properties. Owing to the inferior atomization and diffusion characteristics of diesel, Diesel_Para employs a high P_Inj and a retarded SOI₂ to enhance the diesel/air mixing and reduce exhaust losses, while maintaining an appropriate combustion rate. In contrast, PODE relies on its superior atomization and diffusion characteristics to promote fuel/air mixing. Thus, PODE_Para adopts a reduced P_Inj and an early SOI₂ to shorten spray penetration, effectively reducing heat transfer losses while maintaining an optimal combustion phasing.

3.3. Co-Optimization of Operating Parameters and Piston Geometry

The preceding analysis substantiates the correlation between fuel physicochemical properties and the corresponding optimal injection strategy. Beyond injection parameters, the piston geometry, serving as a key spatial boundary constraint, also shows significant impacts on spray development and mixture formation [49]. Consequently, a co-optimization of operating parameters and piston geometry is performed for diesel and PODE, and the matching mechanism among fuel properties, operating parameters, and piston topology is revealed to maximize overall engine performance. The co-optimized parameters and their corresponding variation ranges are listed in Table 5.

Figure 13 compares the EISFC and NOx of optimal cases for diesel and PODE under two optimization frameworks: the optimization of operating parameters alone and the co-optimization of both operating parameters and piston geometry. The optimal cases from the two frameworks are designated as Optimal cases and Optimal + Geo cases, respectively. In addition, the base cases of diesel and PODE are also introduced into Figure 13 as benchmarks. The results demonstrate that the co-optimization framework effectively transcends the performance limitations of parameter-alone tuning, enabling further improvement in both EISFC and NOx emissions for both fuels. Notably, PODE fuel exhibits a more pronounced performance improvement than diesel under the co-optimization framework.

Figure 13. Comparison between optimization of operating parameters alone and co-optimization of operating parameters and piston geometry. (a) Comparison for diesel; (b) Comparison for PODE.

Figure 14 compares the distributions of the operating parameters and CR for the Optimal + Geo cases of diesel and PODE. A comparative analysis of Figure 9 and Figure 14 reveals that the co-optimized operating parameters differ from those under parameter-alone optimization. The co-optimized CR for both fuels is larger than the original one, while the optimal CR for PODE is lower than that for diesel to prevent premature ignition and subsequent degradation of ITE, which is driven by the higher cetane number and superior atomization characteristics of PODE. Although the optimal T_IVC under co-optimization aligns with that under parameter-alone optimization, diesel requires a relatively higher T_IVC to promote fuel vaporization and mixture preparation under a high-CR environment. Consistent with Figure 9, the co-optimized SOI₂ for PODE is more advanced than that for diesel. However, the optimal SOI₂ for both fuels under co-optimization is earlier than that under parameter-alone optimization. In addition, a substantial reduction in P_Inj is observed for diesel under co-optimization, which is related to its piston modification.

Figure 14. Parameter distributions of co-optimized cases for diesel and PODE.

Subsequently, the influences of piston geometrical parameters and CR on engine performance are quantitatively evaluated. Based on the optimized cases during evolution, the sensitivity coefficients of each geometric parameter regarding EISFC and NOx were extracted using a Random Forest regression model, as illustrated in Figure 15a. The Random Forest is configured with 1000 regression trees, which is sufficient to ensure a stable ranking of the variable importance while keeping the computational cost moderate. At each split, a randomly selected subset of one-third of the design variables is evaluated, which decorrelates the individual trees and reduces the variance of the ensemble. The trees are grown without depth limitation so that the nonlinear and interactive effects among the design variables can be fully captured, and the minimum number of samples required at a leaf node is set to unity to keep the model bias low.

Figure 15. Statistical analysis of EISFC and NOx to piston geometrical parameters for both diesel and PODE. (a) Sensitivity analysis; (b) Correlation analysis.

According to sensitivity analysis, the engine performance of diesel is primarily governed by z₂, R_a, β₁, γ, R_e, and CR. In contrast, the high-sensitivity parameters for PODE shift to R_a, R_c, l_4t5, ε₁, γ, and CR. Furthermore, to elucidate the relationship between these geometrical parameters and optimization targets, Pearson correlation coefficients were calculated for both fuels, as shown in Figure 15b. The results demonstrate that the distribution of high-correlation parameters is highly consistent with their influence rankings, validating the accuracy and representativeness of these identified key geometric parameters.

Based on sensitivity and correlation analyses, the engine performances of the two fuels are both strongly correlated with R_a, γ, and CR, suggesting that the three parameters are fuel-independent. A high CR is theoretically recognized to improve ITE, which is successfully realized in the Optimal + Geo cases by adopting a shallow flat piston that features a reduced R_a and an increased γ. Conversely, x₂, z₂, R_e, R_c, l_4t5, and ε₁ exhibit pronounced fuel-specific influences. In diesel-fueled engines, x₂ exhibits a positive correlation with EISFC, while z₂ and R_e are strongly negatively correlated with both EISFC and NOx. Thus, the optimal piston geometry for diesel is characterized by a reduced x₂ along with larger z₂ and R_e. In contrast, R_c and l_4t5 display a positive correlation with EISFC and NOx for PODE, whereas ε₁ shows a significant negative correlation. Consequently, the optimal piston design for PODE features smaller R_c and l_4t5 coupled with an increased ε₁.

To further examine the discrepancy in the optimized piston geometries between the two fuels, two representative cases with the lowest EISFC are selected from two sets of Optimal + Geo cases for in-depth analysis, designated as Diesel_Co-opt and PODE_Co-opt, respectively. By comparing the optimized piston profiles against the base case in Figure 16, it is evident that the configurations of the two representative cases show strong consistency with the statistical results identified in Figure 15. Compared to the original piston, the optimal designs for both fuels achieve a larger CR by reducing piston depth and piston bowl volume. Regarding the specific geometrical features, the optimal piston for diesel adopts a lower x₂ as well as larger z₂ and R_e, resulting in the upward and centripetal migration of the bowl bottom pocket toward the cylinder axis. This optimized structure effectively shortens spray development distance to enhance the guiding effects of the piston wall on spray development and mixture formation. The optimal piston for PODE employs a reduced R_c and l_4t5 as well as an increased ε₁ to narrow the bowl rim width, reduce the side pocket volume, and increase the second-step inclination, which effectively suppresses excessive spray diffusion.

Figure 16. Comparison of piston geometry between co-optimization and base case for two fuels. (a) Comparison of geometrical parameters; (b) Comparison of piston geometry between baseline and Diesel_Co-opt; (c) Comparison of piston geometry between baseline and PODE_Co-opt.

In addition to the difference in the optimal piston geometry between diesel and PODE, Figure 17 further compares the pressures of two co-optimized cases with their base cases, and their operating parameters are summarized in Table 7. The higher CR adopted in both Diesel_Co-opt and PODE_Co-opt enhances not only the in-cylinder thermal conditions but also the flow intensity. Thus, a more advanced ignition timing and a higher P_max are achieved compared to the respective base cases, contributing to the reduced EISFC. Although Diesel_Co-opt still maintains a larger P_max than PODE_Co-opt, their difference is much smaller than that observed between Diesel_Base and PODE_Base.

Figure 17. Comparison of combustion process between co-optimization and base case for two fuels.

Table 7. Comparison of operating parameters among representative cases.

Parameter	Base Case	DieselCo-Opt	PODECo-Opt
TIVC (K)	386.0	377.94	376.12
SOI2-SOI1 (°CA)	6.5	7.6	3.3
SOI2 (°CA ATDC)	−1.0	−0.8	−5.3
PInj (MPa)	131.0	99.9	113.0
CR	18.5	21.7	19.8

Finally, the benefits of co-optimization are demonstrated in Figure 18 by comparing EISFC, NOx emissions, P_max, and energy distribution among three distinct scenarios: base case, parameter-alone optimization, and co-optimization. The results indicate that parameter-alone optimization already significantly reduces EISFC for both fuels, while maintaining a comparable NOx emissions level to the base case. The co-optimization of piston geometry and operating parameters successfully exploits their synergistic interaction to yield a further reduction in EISFC.

Figure 18. Comparison of energy distribution and NOx among the three representative cases. (a) Comparison for diesel; (b) Comparison for PODE.

It is worth noting that the improvement achieved by co-optimization stems from both the increased CR and the optimized piston geometry. To separate their individual contributions, two additional cases, Diesel_CR and PODE_CR, are designed for diesel and PODE based on the baseline and co-optimized cases; they retain the original piston geometry while adopting the optimized CR by reducing the distance between top dead center and cylinder head. The comparison of energy distributions and NOx among the three cases is shown in Figure 18. Since the three representative cases of each fuel maintain nearly identical NOx levels, the comparison is focused on their difference in ITE. Although Diesel_CR accelerates combustion and yields a 1% higher ITE than Diesel_base, its exhaust losses remain considerably larger than those of Diesel_co-opt due to the absence of the mixing enhancement provided by the optimized piston geometry, resulting in its ITE being 0.4% lower than Diesel_co-opt. Similarly, the higher ambient density associated with the larger CR in PODE_CR suppresses the PODE spray diffusion, which reduces the heat transfer losses relative to PODE_base. Nevertheless, without the optimized piston geometry, the heat transfer losses are still 2.5% larger than those of PODE_co-opt. The above results reveal that increasing the CR alone cannot fully exploit the potential of the engine performance; hence, the co-optimization of both CR and piston geometry is imperative [50].

After the individual effects of the CR and piston geometry are quantified, the correlation between the piston geometry and the fuel properties is investigated. From the energy distribution perspective illustrated in Figure 19, the dominant mechanisms driving performance improvements are different for the two fuels. As the optimization strategy transitions from base case to parameter-alone, and ultimately to co-optimization, the EISFC reduction in the diesel-fueled engine stems primarily from a continuous decrease in exhaust losses. Conversely, the EISFC gain in the PODE-fueled engine is predominantly attributed to the sustained mitigation of heat transfer losses. These findings demonstrate that the physicochemical properties of injected fuel dictate distinct evolutionary pathways for improving engine performance.

Figure 19. Comparison between co-optimization and base case for diesel and PODE. (a) Engine performance; (b) Geometry parameters.

In order to explain the impacts of fuel physicochemical properties on the optimization strategy, Figure 20 compares the in-cylinder temperature and equivalence ratio distributions of the base cases and the co-optimized cases at 4 °CA after CA50 between both fuels. Given that diesel exhibits a lower cetane number and inferior diffusion characteristics compared to PODE, Diesel_Co-opt is allowed to adopt a higher CR. Owing to the positive effects of a high CR on thermal conditions and tumble flow, together with the 14.2% enhancement of turbulent kinetic energy achieved by the optimized piston, a reduced P_Inj is employed to alleviate the combustion rate under high-CR and optimized piston conditions. To compensate for the lower spray momentum, the bowl bottom pocket was migrated toward the cylinder axis to strengthen the guiding effect of the piston on spray diffusion. This architectural refinement not only expands the spatial volume for fuel/air mixing in the upper bowl but also promotes a stronger tumble motion in the bowl, effectively mitigating fuel deposition at the bowl bottom, as seen in Figure 20. Consequently, the fuel/air mixing rate in Diesel_Co-opt is significantly enhanced, and the combustion duration is markedly shortened, leading to a substantial reduction in both exhaust losses and EISFC.

Figure 20. Comparison of equivalence ratio and temperature between co-optimized cases and base cases for diesel and PODE at 4 °CA after CA50.

Due to the superior diffusion characteristics of PODE, the high-temperature region of PODE combustion locates closer to the piston surface, resulting in higher heat transfer losses. Thus, PODE_Co-opt adopts a lower P_Inj to shorten spray penetration and shift the high-temperature region away from the piston surface. However, a reduced P_Inj prolongs the combustion duration, deteriorating EISFC, which is compensated by advancing SOI₂. Complementing the P_Inj reduction, the piston geometry is optimized specifically for PODE by incorporating a smaller and more elevated side pocket. This modification not only reduces turbulent kinetic energy by 22%, thereby diminishing air entrainment and its effect on spray breakup, but also effectively weakens the guiding influence of the step structure on spray development, which further repositions the combustion region away from the piston surface. In summary, the optimal piston geometries for diesel and PODE are dependent on their optimized injection parameters, which are inherently governed by the specific physicochemical properties of each fuel.

4. Conclusions

This study presents a comprehensive analysis of the combustion and emission characteristics of diesel and PODE fuels in compression ignition engines. Through the co-optimization of both operating and geometric structural parameters, the engine performance of the two fuels is substantially improved. The results elucidate the intricate coupling among fuel properties, optimal operating parameters, and optimal piston geometry, providing a theoretical foundation for the practical application of PODE fuel in carbon-neutral power systems. The main conclusions are as follows.

(1)

Benefiting from the higher oxygen content and superior atomization characteristics, PODE exhibits a faster combustion rate than diesel under the same piston and operating parameters. This significantly reduces exhaust loss and yields a 0.7% improvement in ITE. However, the enhanced atomization also leads to a larger high-temperature combustion zone near the piston surface. Consequently, heat transfer losses of PODE combustion increase, which in turn limits its net improvement in thermal efficiency.

(2)

Diesel and PODE require distinct optimal operating strategies owing to their different fuel properties. A high P_inj and late SOI₂ strategy is adopted for diesel to enhance fuel/air mixing and maintain favorable combustion phasing, which reduces exhaust losses and improves thermal efficiency. Conversely, increasing P_inj shows a marginal effect on the combustion rate of PODE; a low P_inj and an advanced SOI₂ are more suitable for PODE to reduce heat transfer losses and increase ITE.

(3)

Compared with optimizing the operating parameters alone, the co-optimization of both the operating parameters and the piston geometry yields further improvements in ITE and NOx emissions for both fuels, with PODE exhibiting a more pronounced improvement. Relative to parameter-only tuning, PODE achieves a 2.1% improvement in ITE and a 14.3% reduction in NOx emissions, underscoring the stronger potential for co-optimization.

(4)

The mechanisms driving performance improvements follow distinct pathways dictated by fuel properties: diesel efficiency gains stem primarily from minimized exhaust losses via enhanced mixing rates, whereas PODE improvements are driven by the mitigation of heat transfer losses. This underscores a shift in optimization priorities from mixing enhancement for diesel to flame/wall interaction management for PODE.

(5)

The optimal piston geometries for diesel and PODE are correlated to their respective operating parameters and fuel properties. The optimal piston for diesel focuses on enhancing spray diffusion and tumble motion via bowl-bottom refinement to compensate for its inferior diffusion, while the optimal piston for PODE prioritizes shifting high-temperature regions away from the cylinder walls through elevated side pockets to suppress its inherent high heat transfer losses.

It should be noted that the spray-included angle shows a strong correlation with the piston geometry, which should be optimized together in future work. Moreover, the piston optimization is performed at only one medium operating condition via numerical simulation. Its performance over a wider range of operating conditions requires further evaluation and experimental verification, which will be addressed in our future work.