Quantitative Analysis of Water Injection Mass and Timing Effects on Oxy-Fuel Combustion Characteristics in a GDI Engine Fuelled with E10

Abstract

The climate change issue has become a growing concern due to the increasing greenhouse gas emissions. To achieve carbon neutrality for mitigating the climate problem, the oxy-fuel combustion (OFC) technique on internal combustion engines (ICEs) has attracted much attention. Furthermore, the water injection (WI) strategy was proven effective in improving the combustion process and thermal efficiency in engines under OFC mode. However, WI strategy effects on gasoline direct injection (GDI) engines fuelled with gasoline–alcohol blends have not been reported. This study quantitatively analysed WI mass and timing effects on oxy-fuel combustion performance from a GDI engine fuelled with E10 (10% ethanol and 90% gasoline in mass) by simulation. The results show that equivalent brake-specific fuel consumption (BSFC_E) shows a monotonically decreasing trend with the increase in the water–fuel mass ratio ($R_{wf}$) from 0 to 0.2. However, further increasing $R_{wf}$ would cause a deterioration in BSFC_E due to the enhanced cooling effects of water vaporisation. Moreover, an appropriate water injection timing ($t_{WI}$) could be explored for improving OFC performance, especially for large $R_{wf}$ conditions. The difference in BSFC_E between $t_{WI}$ = −100°CA and $t_{WI}$ = −60°CA can be up to around 6.3 g/kWh by increasing $R_{wf}$ to 0.6.

1. Introduction

In the past few years, global warming concerns have become more serious, and extreme heat conditions appear more frequently [1]. Achieving the goals of carbon peaking and carbon neutrality has been proposed to minimise carbon dioxide (CO₂) emissions for mitigating global warming issues. Hence, various carbon reduction technologies have been implemented in the transportation sector, such as battery electric vehicles (BEVs) [2], ammonia or hydrogen fuel engines [3,4], and fuel cell vehicles [5]. These technologies have attracted much attention because of their carbon-free characteristics. However, it is still very valuable and attractive to achieve CO₂ capture and storage for internal combustion engines (ICEs), which account for the largest proportion of transportation power sources nowadays.

As shown in the chemical process of Equation (1), the combustion products of oxy-fuel combustion (OFC) technology proposed by Yaverbaum are almost CO₂ and H₂O, which has been an attractive alternative for decreasing and capturing carbon emissions [6,7,8,9]. Figure 1 shows a schematic diagram of a novel OFC system with carbon capture and storage (CCS) in the application of ICE. During the working process, intake air can be replaced by pure oxygen and CO₂ from exhaust gas recirculation (EGR). Hence, without N₂ involved in combustion, NO_X emissions can be totally eliminated. Moreover, the extra CO₂ can be compressed by a compressor after separating from H₂O, and then easily captured and stored into a tank.

$${\mathrm{C}}_{\mathrm{x}}{\mathrm{H}}_{\mathrm{y}}{\mathrm{O}}_{\mathrm{z}}+\left(\mathrm{x}+\frac{\mathrm{y}}{4}-\frac{\mathrm{z}}{2}\right){\mathrm{O}}_2\to {\mathrm{xCO}}_2+\frac{\mathrm{y}}{2}{\mathrm{H}}_2\mathrm{O}$$

(1)

When comparing OFC mode to conventional air combustion (CAC) mode, the differences in physicochemical properties between CO₂ and N₂ should be noticed and stressed, as shown in

Table 1. Physicochemical properties of CO₂ and N₂ (1000 k, 0.1 MPa) [10,11].

Property	CO2	N2	Ratio (CO2/N2)
Molecular weight	44	28	157%
Specific heat capacity (kJ/kgK)	1.2343	1.1674	106%
Kinematic viscosity (m2/s)	7.69 × 10−5	1.2 × 10−4	63.1%
Thermal diffusivity (m2/s)	1.1 × 10−4	1.7 × 10−4	64.4%
Mass diffusivity of O2 (m2/s)	9.8 × 10−5	1.3 × 10−4	77.8%
Thermal conductivity (W/mK)	7.057 × 10−2	6.599 × 10−2	107%
Prandtl number	0.7455	0.7022	106%
Emissivity and absorptivity	>0	~0	-

[10,11]. First and foremost, the molecular weight of CO₂ is 57% higher than that of N₂. Moreover, the specific heat capacity of CO₂ is 106% of N₂. Hence, compared to N₂, the mole heat capacity of CO₂ is considerably higher, which would negatively impact the combustion rates and temperature under OFC mode. Second, the thermal diffusivity of CO₂ is only 64.4% of N₂. Moreover, the mass diffusivity speed of O₂ in CO₂ is 22.2% lower than the conditions of N₂. These factors can help reduce the heat release rate and slow chemical reactions during the early combustion stage. Moreover, the thermal conductivity of CO₂ is very close to that of N₂, which would not easily cause discrepancies in the combustion.

Hence, although using OFC technology in engines has excellent potential for carbon reduction, controlling the engine combustion process and maintaining thermal efficiency under OFC mode is challenging. Ditaranto et al. [12] indicated that the low thermal diffusivity properties of CO₂ would lead to more heat loss than conventional air combustion, resulting in lower thermal efficiency. It was also found that the flame characteristics in OFC mode are closely related to the oxygen concentration. Li et al. [13] conducted some numerical investigations of OFC combustion on dual-fuel spark ignition (SI) engines. The results suggested that with the increase in oxygen mass fraction, significant changes can be seen in combustion characteristics, leading to a reduction in brake-specific fuel consumption (BSFC). Yu et al. [14] reported that a high oxygen fraction could accelerate combustion and improve the maximum pressure rise rate. It indicated that pure O₂ with no inert gas would produce an excessively fast combustion rate accompanying abnormal pressure rise rates of more than 4 MPa/CA. The powerful waves of engine super knock would rapidly occur across the combustion chamber with substantial amplitude, significantly damaging the engine.

Moreover, in order to further improve the combustion process and thermal efficiency, the water injection (WI) strategy has been implemented for engines under OFC mode. Bilger et al. [15] proposed a new conception of the internal combustion Rankine cycle (ICRC) engine, which employs preheated water directly injected into engine cylinders to control combustion. The key research progresses on the effects of WI strategy on the combustion characteristics in engines under OFC mode over the past decade are summarised in

Table 2. Research summary of WI strategy in engines under OFC mode.

Publication Year	Focusing Parameter	Engine Type	Fuel	Main Authors
2013	WI mass, timing, pressure	PFI, SI	Propane	Yu et al. [14]
2014	WI temperature	PFI, SI	Propane	Fu et al. [16]
2014	WI mass, temperature	PFI, SI	Propane	Wu et al. [17]
2017	WI mass	HCCI, CI	N-heptane	Kang et al. [18]
2018	WI mass, timing, temperature	CI	N-heptane	Kang et al. [19]
2021	WI mass, timing, temperature	Dual-injection, SI	Gasoline	Li et al. [20]

.

Based on a single-cylinder port fuel injection (PFI) engine fuelled with propane, Yu et al. [14] studied the combustion performance under a quasi-ICRC engine after replacing air with oxygen as an oxidant. The study demonstrated that adding water to the combustion chamber could inhibit the spontaneous combustion of the air–fuel mixture by reducing the in-cylinder temperature. Meanwhile, the engine thermal efficiency could be improved by extending the constant pressure process caused by water evaporation at the beginning of the power stroke. Fu et al. [16] demonstrated that owing to the acceleration of the water vaporisation process, a higher WI temperature would help further improve cylinder pressure and engine thermal efficiency in a PFI engine under ICRC mode. For example, under the conditions of 2.9 ms fuel injection duration and 120 °C WI temperature, the engine indicated work and indicated thermal efficiency could be improved by 10.3% and 3.1%, respectively. Wu et al. [17] provided new insights into the solution for improving thermal efficiency by investigating the effects of WI duration and pressure in a PFI engine under OFC mode. It was reported that the thermal efficiency could be improved from 32.1% to 41.5%, and the higher WI pressure can make greater use of vaporisation heat, leading to higher thermal efficiency. Kang et al. [18] designed a WI system to explore its potential in stabilising the combustion process in an N-heptane homogeneous charge compression ignition (HCCI) engine under OFC mode. It was found that a suitable WI strategy helps maintain the engine thermal efficiency and mitigate combustion instability. A strategy using 120 °C and 35 MPa WI would be helpful to eliminate the phenomenon of abnormal combustion. Based on KIVA, Kang et al. [19] established a CFD model of an oxy-fuel diesel engine fuelled with N-heptane to study the feasibility of utilising WI strategies in affecting engine thermal efficiency. The study demonstrated that combustion stability is sensitive to WI timing, which can be fixed near the engine top dead centre of firing. In addition, Li et al. [20] investigated WI effects on OFC characteristics in a dual-injection SI engine fuelled with gasoline. The research indicated that all three fuel injection conditions of GDI, 50% PFI plus 50% GDI and PFI would lead to different performances of cylinder pressure and combustion phasing by changing the value of WI mass, timing, or temperature. It demonstrated that appropriate WI strategies would be beneficial in optimising key combustion characteristics, which leads to relatively low fuel consumption.

From existing studies of OFC engines, the WI strategy has been proven as a potential benefit for the combustion process and thermal efficiency. Most of these studies focused on engines fuelled with propane, N-heptane, or gasoline. However, almost no research was reported about the effects of WI strategies on a gasoline direct injection (GDI) engine fuelled with gasoline–alcohol blends. Furthermore, with more stringent emission regulations in recent years, ethanol has been a clean burning fuel and common additive worldwide with the advantages of reducing emissions and enhancing anti-knock capacity.

Therefore, a quantitative analysis was provided in this study for investigating the WI mass and timing effects on OFC characteristics in a GDI engine fuelled with E10 (10% ethanol and 90% gasoline in mass, which is 9.3% ethanol and 90.7% gasoline in volume). The impacts of WI on OFC GDI engines fuelled with the gasoline−ethanol blend were initially explored. The findings of this study will significantly contribute to understanding the role of WI in the OFC process. Furthermore, the findings will provide novel information and theoretical guidance for improving the fuel economy of GDI engines fuelled with E10 under OFC mode.

2. Research Approach and Numerical Method

2.1. Engine and Experimental Facilities

The engine test was conducted on a 2.0-litre turbocharged four-cylinder GDI engine. The details of the engine technical specifications are listed in

Table 3. Engine specifications.

Item	Content
Engine type	Four-cylinder; four-stroke
Bore × Stroke (mm)	82.5 × 92
Displacement (L)	2.0
Fuel system	GDI
Intake system	Turbocharged
Compression ratio	9.6:1
Rated speed (rpm)	5500
Rated power (kW)	160
Maximum torque (N·m)	320

, and the schematic diagram of the engine testbed is presented in Figure 2.

During the test, an electrical dyno and a programable electronic control unit (ECU) were mainly used to control the key engine operating parameters, such as speed, torque, ignition, and fuel injection timing. The transient cylinder pressure traces were measured with plug-type transducers (AVL-GH13Z), an amplifier (Kistler 5018A), and a combustion analyser (AVL 641).

To eliminate the cycle-to-cycle fluctuations’ interference, the average cylinder pressure from two hundred consecutive cycles was used in this work. The spark timings were optimised to be the minimum advance for maximum brake torque (MBT) or the knock-limited spark advance (KLSA). Before the test, E10 fuel was obtained by thoroughly mixing 10% ethanol with 90% gasoline in mass (9.3% ethanol and 90.7% gasoline in volume). The properties of the gasoline and ethanol are listed in

Table 4. Fuel properties [13].

Fuel Type	Ethanol	Gasoline
Chemical formula	C2H5OH	C5-C12
Density (20 °C) (kg/L)	0.789	0.73
Relative molecular mass	46	95–120
Gravimetric oxygen content (%)	34.78	<1
Research octane number	107	95
Boiling range (°C)	78	30–200
Kinematic viscosity (20 °C) (mm2/s)	1.52	0.71
Dynamic viscosity (20 °C) (mPa·s)	1.2	0.52
Low heating value (kJ/kg)	26,900	44,300
Surface tension (20 °C) (mN/m)	21.97	22
Latent heat of vaporisation (kJ/kg)	840	370
Laminar flame speed (20 °C) (m/s)	0.5	0.33
Stoichiometric air–fuel ratio	8.95	14.7

.

2.2. Research Approach and Model Description

In this study, an engine model was established and developed by GT-Power, which has been widely used in the research of SI engines [21,22]. The settings of pipe geometry, engine displacement, cylinder, valve profile, and other parameters were consistent with engine specifications. The engine of this study was operated at 2000 rpm-10 bar brake mean effective pressure (BMEP), a typical medium-high load of engine urban operating conditions. The conversion from CAC mode to OFC mode in this simulation is achieved by replacing N₂ with CO₂. Figure 3 presents the design of the WI components adopted in this study, which can directly inject water into the cylinder and are more convenient for practical engine implementation.

Throughout this study, the WI pressure and water temperature are kept at 60 bar and 298 K, respectively. As shown in Equation (2), WI mass is represented by the water/fuel ratio ($R_{wf}$) to make the parameters more visual. In addition, the other key parameters are fixed to control the variables in the investigation process, such as the intake oxygen mass fraction, intake temperature, and throttle angle.

$$R_{wf}=\frac{m_{water}}{m_{fuel}}$$

(2)

where $m_{water}$ and $m_{fuel}$ are water and fuel injection mass per engine working cycle, respectively.

$t_{WI}$ represents the WI timing. ${\phi }_{CA50}$ is the crank angle (CA) at 50% of cumulative released heat; $P_M$ is the peak value of cylinder pressure. The equivalent brake-specific fuel consumption (BSFC_E) is used to assess the fuel consumption, as shown in Equation (3) [23]. Compared to BSFC, the advantage of BSFC_E is that different fuels can be converted to equivalent gasoline consumption based on heating values [24,25,26,27].

$${\mathrm{BSFC}}_{\mathrm{E}}=\frac{{\tau }_F\times 1000}{P}\times \frac{\left(0.1\times H_E\right)\times \left(0.9\times H_G\right)}{H_G}$$

(3)

where $P$ (kW) is engine brake power; ${\tau }_F$ (kg/h) is the fuel consumption rate of oxygen and fuel under actual conditions; and $H_E$ and $H_G$ are the low heating value of ethanol and gasoline, respectively.

In order to accurately predict the combustion process and heat transfer processes, “SI turbulent flame combustion” and “Woschni” submodels are chosen in this study, as shown in Equations (4) and (5) [28].

$$S_L=\left(B_m-B_{\varnothing }{\left(\varnothing -{\varnothing }_m\right)}^2\right){\left(\frac{T_u}{T_{ref}}\right)}^{\alpha }{\left(\frac{p}{p_{ref}}\right)}^{\beta }f\left(D\right)$$

(4)

where $S_L$ is laminar flame speed; $B_m$ is maximum laminar speed; $B_{\varnothing }$ is laminar speed roll-off value; $\varnothing$ is in-cylinder equivalence ratio; ${\varnothing }_m$ is equivalence ratio at maximum speed; $T_u$ is unburned gas temperature; $T_{ref}$ is 298 K; $p$ is pressure; $p_{ref}$ is 101.325 kPa; $\alpha$ is temperature exponent; $\beta$ is pressure exponent; and $f\left(D\right)$ is the dilution effect.

$$h=110d^{-0.2}{P}^{0.8}{T}^{-0.53}{\left[C_1{c}_m+C_2\frac{V_S{T}_1}{P_1{V}_1}\left(P-P_0\right)\right]}^{0.8}$$

(5)

where $h$ is the heat transfer coefficient; $d$ is the cylinder bore diameter; $P$ is the cylinder pressure; $T$ is the in-cylinder mean gas temperature; $C_1$ is a constant related to the airflow velocity coefficient; $c_m$ is the mean piston speed; $C_2$ is a constant related to the combustion chamber; $V_S$ is the cylinder volume; $T_1$, $P_1$, and $V_1$ are cylinder temperature, pressure, and volume, respectively; and $P_0$ is the cylinder pressure at the beginning of the compression stroke.

3. Results and Discussion

3.1. Model Validation

In order to ensure the accuracy of the simulation results, it was necessary to perform model validation. Moreover, the model’s effectiveness was further guaranteed and enhanced by checking the time-step sensitivity. Figure 4 presents the comparison of the cylinder pressure between the experimental and simulation results in the conditions of 2000 rpm-2 bar, 2000 rpm-6 bar, and 2000 rpm-10 bar under CAC mode. The corresponding torques of these conditions are 31.8 N·m, 95.4 N·m, and 159 N·m, respectively. It can be found that the curves’ peaks of simulation are just around 2% higher than those of the experiment. Moreover, the peaks’ locations of the relevant curves are well matched. In general, the overall trends of cylinder pressure match well, indicating that the model is capable of making a reliable prediction.

3.2. Quantitative Analysis of WI Mass on OFC Performance

In this section, the first step is to optimise the engine spark timing to be MBT under OFC mode without WI. The relevant trends for BSFC_E and ${\phi }_{CA50}$ can be seen in Figure 5.

With the spark timing advances from −58°CA to −72°CA, BSFC_E decreases from 321.078 g/kWh to 311.35 g/kWh, which is the lowest value of the presented curve. Meanwhile, ${\phi }_{CA50}$ has an apparent change of 8.6°CA, which advances from 11.8°CA to 3.2°CA. However, with further advancing spark timing from −72°CA to −90°CA, BSFC_E shows an obvious growing trend and reaches 320.827 g/kWh at −90°CA spark timing. ${\phi }_{CA50}$ shows a monotonous decrease tendency from 3.2°CA to −6.2°CA. The deterioration of BSFC_E is closely related to the excessive early ${\phi }_{CA50}$, which would negatively impact the effective use of energy, leading to a deterioration in BSFC_E. Hence, it is found that −72°CA is the optimal spark timing, which was fixed as a base in this study.

In order to explore the effects of WI mass on OFC performance, this section mainly evaluates BSFC_E, in-cylinder temperature, heat-release rate (HRR), $P_M$ and ${\phi }_{CA50}$ under different $R_{wf}$. In addition, to focus on the quantitative analysis of WI mass, $t_{WI}$ is fixed at −60°CA in the study of this section.

As shown in Figure 6, $R_{wf}$ has a significant influence on BSFC_E. Compared to other conditions, a relatively low level of BSFC_E can be found under the condition of zero water injection ($R_{wf}$ = 0). By increasing $R_{wf}$ from 0 to 0.2, BSFC_E shows a monotonically decreasing trend and reaches a minimum of 310.836 g/kWh at $R_{wf}$ = 0.2. This phenomenon can be attributed to the increase in oxygen concentration caused by injecting water [14]. When $R_{wf}$ is larger than 0.2, a rebound trend occurs. By further increasing $R_{wf}$, BSFC_E rises rapidly and achieves a maximum of 323.445 g/kWh at $R_{wf}$ = 0.9. Afterwards, BSFC stablises at approximately 323 g/kWh, indicating that the deterioration is counteracted by increased oxygen concentration. The variation of $R_{wf}$ can be further explained and explored through the results of the combustion characteristics, as follows.

Figure 7 shows the effects of $R_{wf}$ on the in-cylinder temperature. The shapes and locations of these in-cylinder temperature curves are generally similar. However, a downward trend can be found by increasing $R_{wf}$. The maximum in-cylinder temperature decreases from 2227 K to 2108 K with the increase in $R_{wf}$ from 0 to 0.3. Subsequently, the maximum values reduce to 2001 K, 1950 K, and 1941 K under the conditions of $R_{wf}$ = 0.6, $R_{wf}$ = 0.9, and $R_{wf}$ = 1.2, respectively. This trend is mainly attributed to the enhanced effects of heat absorption with a large amount of vapourised water, which could effectively decrease the in-cylinder temperature.

With the increase in $R_{wf}$, HRR shows a similar tendency with that of the in-cylinder temperature, as presented in Figure 8. Under the conditions of $R_{wf}$ = 0 or $R_{wf}$ = 0.3, the peaks of the HRR curves are higher than for other conditions. The variations of in-cylinder temperature and HRR suggest that WI could obviously inhibit the heat release process of a GDI engine fuelled with E10 under OFC mode.

Regarding the $P_M$ and ${\phi }_{CA50}$, it can be seen that by increasing $R_{wf}$ from 0 to 0.6, $P_M$ has a gradual reduction from 54.6 bar to 49.8 bar and ${\phi }_{CA50}$ is postponed from 3.2°CA to 5.7°CA, as shown in Figure 9. Moreover, when $R_{wf}$ is larger than 0.6, $P_M$ and ${\phi }_{CA50}$ are generally stable. This demonstrates that although a large amount of injected water could provide more working medium and a higher oxygen concentration, the combustion phasing is still retarded because of the strong cooling effects during water vaporisation, leading to an adverse impact on BSFC_E.

3.3. Quantitative Analysis of WI Timing on OFC Performance

As a key influencing factor, the effects of $t_{WI}$ on OFC performance should also be clearly noted. Figure 10 shows the impacts of $t_{WI}$ on BSFC_E. In general, under the conditions of small $R_{wf}$, BSFC_E remains at a relatively stable level by changing $t_{WI}$. In particular, BSFC_E is largely unaffected by $t_{WI}$ when $R_{wf}$ is 0.1 and 0.2. The lowest value of BSFC_E is 310.735 g/kWh, which appears at $t_{WI}$ = −100°CA and $R_{wf}$ = 0.1.

However, under the conditions of large $R_{wf}$, an apparent deterioration of BSFC_E can be found with an inappropriate $t_{WI}$. For example, when $R_{wf}$= 0.6, BSFC_E could be increased to 320.992 g/kWh and 319.726 g/kWh for $t_{WI}$ = −100°CA and $t_{WI}$ = −30°CA, respectively. The gap in BSFC_E between $t_{WI}$ = −100°CA and $t_{WI}$ = −60°CA can be up to around 6.3 g/kWh. This demonstrates that BSFC_E is particularly sensitive to $t_{WI}$ under high $R_{wf}$ conditions, which should be of concern for a GDI engine operating under OFC mode.

To explore the reasons for the variation in BSFC_E affected by $t_{WI}$, the change in HRR is studied under $R_{wf}$= 0.1 and $R_{wf}$ = 0.6, as shown in Figure 11. The overall trend is that HRR could be influenced by continuously changing $t_{WI}$, and the degree of influence can be enhanced with a higher $R_{wf}$. When $R_{wf}$= 0.1, the HRR peak only increases by 2 J/°CA, while the phase just advances from 5.6°CA to 4.4°CA. Under $R_{wf}$ = 0.6, as $t_{WI}$ postpones from −80°CA to −40°CA, the phase of the HRR peak monotonically advances from 7.2°CA to 4.2°CA. Meanwhile, the peak of HRR is increased by approximately 7 J/°CA. This suggests that the excessively advanced $t_{WI}$ could result in sufficient water vaporisation, which postpones the heat release and combustion phase. Therefore, it is essential to look for an optimal $t_{WI}$ to increase thermal efficiency, especially under the conditions of large $R_{wf}$.

As shown in Figure 12, the in-cylinder temperature can be influenced by the variation of $t_{WI}$. Under $R_{wf}$ = 0.1, as $t_{WI}$ postpones from −80°CA to −40°CA, the maximum in-cylinder temperature increases from 2175 K to 2191 K, with an improvement of around 16 K. Furthermore, the degree of influence on in-cylinder temperature is increased significantly with a higher $R_{wf}$. When the $R_{wf}$ reaches 0.6, the relevant improvement of maximum in-cylinder temperature can be up to 64 K. This can be attributed to the fact that stronger cooling effects can be achieved with a relatively high amount of injected water under $t_{WI}$ = −80°CA.

Figure 13 shows the variation in $P_M$ and ${\phi }_{CA50}$ with different $t_{WI}$. The $P_M$ shows a monotonic increasing trend as $t_{WI}$ postpones from −100°CA to −30°CA. Under $R_{wf}$ = 0.1, $P_M$ has an improvement of around 2.3 bar. Meanwhile, the change in magnitude is about 11 bar under $R_{wf}$ = 0.6. On the contrary, ${\phi }_{CA50}$ shows a highly advanced trend by postponing $t_{WI}$. When $t_{WI}$ postpones from −100°CA to −30°CA, an advance of about 1.5°CA can be seen in ${\phi }_{CA50}$ under $R_{wf}$ = 0.1, whilst an advance of about 7°CA occurs under $R_{wf}$ = 0.6. By postponing $t_{WI}$, the variation characteristics of $P_M$ and ${\phi }_{CA50}$ are mainly because the short water vaporisation period weakens the inhibition impact on combustion.

From Figure 13, it is notable that when $t_{WI}$ is −40°CA and −30°CA, the distinction of these combustion characteristics between $R_{wf}$ = 0.1 and $R_{wf}$ = 0.6 become quite slight. That is because under the conditions of a late $t_{WI}$, the effects of $t_{WI}$ on $P_M$ and ${\phi }_{CA50}$ become relatively small due to the shorter water vaporisation period before combustion.

4. Conclusions

The OFC technique has shown great potential in achieving zero CO₂ emissions from conventional GDI engines. To further improve the fuel economy of engines under OFC mode, this study numerically investigates the effects of WI strategies on OFC characteristics in a GDI engine fuelled with E10. The main conclusions can be listed as follows.

• Under OFC mode without WI strategy, the optimum BSFC_E is 311.35 g/kWh by advancing spark timing to −72°CA.
• BSFC_E shows a monotonically decreasing trend by increasing $R_{wf}$ from 0 to 0.2, due to the increasing oxygen concentration caused by the decomposition of water.
• With the increase in $R_{wf}$ from 0.2 to 0.9, strong cooling effects significantly decrease the in-cylinder temperature and postpone the heat release. Hence, a deterioration is caused owing to a larger $R_{wf}$.
• In general, BSFC_E is largely unaffected by $t_{WI}$ when $R_{wf}$ is 0.1 and 0.2. BSFC_E can be optimised to 310.735 g/kWh under the condition of $t_{WI}$ = −100°CA and $R_{wf}$ = 0.1.
• Under the conditions of a late $t_{WI}$, the effects of $t_{WI}$ on $P_M$ and ${\phi }_{CA50}$ become relatively small due to the shorter water vaporisation period before combustion.
• An appropriate $t_{WI}$ is very important to improve the OFC performance under large $R_{wf}$ conditions. When $R_{wf}$ reaches 0.6, the gap in BSFC_E between $t_{WI}$ = −100°CA and $t_{WI}$ = −60°CA can be up to around 6.3 g/kWh.

According to the findings of this study, water injection mass and timing have been proven to effectively impact the combustion characteristics and fuel economy of GDI engines fuelled with E10 under OFC mode. Several proposals can be forwarded as follows regarding the prospects for future studies in the specific knowledge area.

First, some other key parameters of WI strategy can be explored and studied for GDI engines under OFC mode. For instance, increasing the WI pressure could be a potential solution to optimise the combustion process and fuel efficiency by shorting the WI duration under the conditions of fixed WI mass. The change in WI temperature is also a factor that affects combustion quality, which can be a research direction.

Second, it is necessary to investigate OFC GDI engines fuelled with a high ethanol ratio in the gasoline–alcohol blends. Changing the ethanol ratio in blends impacts the fuel’s physicochemical properties, thereby resulting in a significant discrepancy in engine performance.

Third, it is also valuable to study the most suitable EGR rate to impact fuel performance for OFC engines fuelled with gasoline–alcohol blends. In the meantime, oxygen consumption rates should be noted, which will be a cost factor during the operation of OFC engines.