Effects of Water Injection Strategies on Oxy-Fuel Combustion Characteristics of a Dual-Injection Spark Ignition Engine

: Currently, global warming has been a serious issue, which is closely related to anthropogenic emission of Greenhouse Gas (GHG) in the atmosphere, particularly Carbon Dioxide (CO 2 ). To help achieve carbon neutrality by decreasing CO 2 emissions, Oxy-Fuel Combustion (OFC) technology is becoming a hot topic in recent years. However, few ﬁndings have been reported about the implementation of OFC in dual-injection Spark Ignition (SI) engines. This work numerically explores the effects of Water Injection (WI) strategies on OFC characteristics in a practical dual-injection engine, including GDI (only using GDI), P 50 -G 50 (50% PFI and 50% GDI) and PFI (only using PFI). The ﬁndings will help build a conceptual and theoretical foundation for the implementation of OFC technology in dual-injection SI engines, as well as exploring a solution to increase engine efﬁciency. The results show that compared to Conventional Air Combustion (CAC), there is a signiﬁcant increase in BSFC under OFC. Ignition delay ( θ F ) is signiﬁcantly prolonged, and the spark timing is obviously advanced. Combustion duration ( θ C ) of PFI is a bit shorter than that of GDI and P 50 -G 50 . There is a small beneﬁt to BSFC under a low water-fuel mass ratio ( R wf ). However, with the further increase of R wf from 0.2 to 0.9, there is an increment of 4.29%, 3.6% and 3.77% in BSFC for GDI, P 50 -G 50 and PFI, respectively. As WI timing ( t WI ) postpones to around − 30 ◦ CA under the conditions of R wf ≥ 0.8, BSFC has a sharp decrease of more than 6 g/kWh, and this decline is more evident under GDI injection strategy. The variation of maximum cylinder pressure ( P max ) and combustion phasing is less affected by WI temperature ( T WI ) compared to the effects of R wf or t WI . BSFC just has a small decline with the increase of T WI from 298 K to 368 K regardless of the injection strategy. Consequently, appropriate WI strategies are beneﬁcial to OFC combustion in a dual-injection SI engine, but the beneﬁt in fuel economy is limited.


Introduction
The global warming crisis has apparently been a severe problem over the last few decades. Furthermore, the 10 warmest years on record have occurred since 1998, with the 4 warmest years occurring since 2014 [1]. Hence, carbon neutrality has become a desperate need to resolve the climate crisis, as it is closely linked to anthropogenic Greenhouse Gas (GHG) emissions, particularly Carbon Dioxide (CO 2 ) [2][3][4]. To help achieve carbon neutrality by decreasing CO 2 emissions, a variety of new technologies have been developed for passenger vehicles, such as hybrid electric, plug-in hybrid electric, lithium-ion battery electric, solar-powered, fuel-cell electric, etc. [5][6][7].
However, due to the relatively high cost and low torque output, these technologies are rarely utilised in non-road mobile machineries, such as vessels and boats. In order to realise zero CO 2 emissions in conventional Internal Combustion Engine (ICE) fuelled with fossil fuels, Oxy-Fuel Combustion (OFC) technology with Carbon Capture and Storage (CCS) has been an attractive alternative in recent decades. Yaverbaum initially proposed OFC technology, which was afterward widely applied in power stations [8][9][10][11][12]. Equation (1) and Table 1 present the OFC reaction process and the gas physicochemical properties, respectively. The discrepancies of physicochemical properties between CO 2 and nitrogen have significant impacts on OFC and Conventional Air Combustion (CAC). The chemical reaction indicates that OFC can take advantage of eliminating nitrogen during the combustion process. The comparison of gas properties shows that CO 2 heat capacity is much higher than nitrogen on a mole basis. Besides, both the thermal diffusivity and oxygen diffusion of CO 2 are much lower than those of nitrogen. Regarding the study of OFC technology in Spark Ignition (SI) engines, Bilger [15] initially proposed a new approach named Internal Combustion Rankine Cycle (ICRC) in 1999. In recent years, Wu et al. [16][17][18][19][20][21][22][23][24][25] made a significant contribution to ICRC implementation in Port Fuel Injection (PFI) SI engines fuelled with propane under 40% to 70% oxygen volume fraction. Water Injection (WI) has been a proven method to control oxy-fuel combustion process of ICRC engines based on some findings [17][18][19][20][21]. Engine performance could be directly affected by the timing, duration, pressure, mass and temperature of WI. Thermal efficiency and indicated work could be enhanced by an appropriate rate of EGR matches with ignition timing and increased WI temperature. Li et al. [26] initially investigated the impacts of intake charge on OFC in a dual-injection SI engine fuelled with gasoline under GDI, P-G and PFI three injection strategies.
Based on this literature survey about OFC implementation in SI engines, most of them focused on PFI engines fuelled propane. However, few studies have been reported about the implementation of OFC in GDI engines or dual-injection SI engines. However, Gasoline Direct Injection (GDI) technology has become the mainstream of SI engines in academia and industry [27][28][29][30][31][32][33][34][35]. In 2005, an advanced technology named dual-injection was commercially applied to SI engines by Toyota [36]. Furthermore, with the advantages of flexible fuel injection, dual-injection SI engines have been a hot topic for researchers in recent years [37][38][39][40][41][42]. The thermal efficiency, gaseous and particulate emissions have been investigated in this type of engine by using gasoline plus various fuels such as methanol, ethanol and 2,5-dimethylfuran.
Therefore, the investigation of the effects of WI strategies on combustion characteristics of OFC in a dual-injection SI engine fuelled with gasoline was firstly reported in this article. It will provide valuable insight into the effects of WI strategies on OFC characteristics in a Therefore, the investigation of the effects of WI strategies on combustion characteristics of OFC in a dual-injection SI engine fuelled with gasoline was firstly reported in this article. It will provide valuable insight into the effects of WI strategies on OFC characteristics in a practical dual-injection engine, including GDI (only using GDI), P50-G50 (50% PFI and 50% GDI) and PFI (only using PFI). The findings will help build the conceptual and theoretical foundation for the OFC implementation in dual-injection SI engines, as well as exploring a solution to increase engine efficiency. This work belongs to the 'RIVER' project, which was proposed to develop a novel non-carbon boat with an environmentfriendly powertrain system. The overview of the designed novel 'RIVER' system can be depicted in Figure 1, which mainly includes the subsystems of oxygen feeding, intake organisation, CO2 capture and storage. Pure oxygen is mixed with recirculated gas (CO2), then the mixture will enter into engine combustion chambers. Besides, the excess CO2 can be captured in a storage tank to achieve zero carbon emissions.

Research Approach and Key Parameters
In order to keep this numerical study well organised, the procedure can be summarised in Figure 2. First, the validation of this model is performed based on the experimental data of 2000 rpm-10 bar BMEP under CAC mode. Second, as nitrogen is replaced by CO2, engine operation converts into the OFC mode with nitrogen replaced by CO2, a comparison in performance between CAC and OFC is presented. Finally, the effects of WI mass, WI timing and WI temperature on OFC characteristics are explored and analysed in turn.

Research Approach and Key Parameters
In order to keep this numerical study well organised, the procedure can be summarised in Figure 2. First, the validation of this model is performed based on the experimental data of 2000 rpm-10 bar BMEP under CAC mode. Second, as nitrogen is replaced by CO 2 , engine operation converts into the OFC mode with nitrogen replaced by CO 2 , a comparison in performance between CAC and OFC is presented. Finally, the effects of WI mass, WI timing and WI temperature on OFC characteristics are explored and analysed in turn.
In order to increase the efficiency of water utilisation for optimising OFC process, it is usually injected directly into the engine chamber by a separated injector [17][18][19][20][21]. Figure 3 shows the schematic of two representatives.
The system presented in Figure 3a is adopted in this numerical study, which advantage is compact size, simple structure and control measure. A container coupled with a pump is utilised to deliver water to a rail. Afterward, water will be directly injected into combustion chambers with the assistance of an air booster. The booster provides a high WI pressure to enhance water droplets' breakup, diffusion and vaporisation.
The other strategy in Figure 3b does not include storage for water supply. Instead, the water vapour in the exhaust gas can be condensed and separated, then heated up prior to being recirculated and injected into the combustion chambers. The advantage of this system is that overall thermal efficiency can be improved by the benefit of water vaporisation inside the cylinder chamber and the waste heat recovery from the exhaust gas.  In order to increase the efficiency of water utilisation for optimising OFC pr is usually injected directly into the engine chamber by a separated injector [17-21 3 shows the schematic of two representatives.
The system presented in Figure 3a is adopted in this numerical study, w vantage is compact size, simple structure and control measure. A container coup a pump is utilised to deliver water to a rail. Afterward, water will be directly injec combustion chambers with the assistance of an air booster. The booster provide WI pressure to enhance water droplets' breakup, diffusion and vaporisation.
The other strategy in Figure 3b does not include storage for water supply. the water vapour in the exhaust gas can be condensed and separated, then heated to being recirculated and injected into the combustion chambers. The advantag system is that overall thermal efficiency can be improved by the benefit of water sation inside the cylinder chamber and the waste heat recovery from the exhaust (a) WI with a water tank (b) WI without a water tank In order to make the parameters more visually, WI mass is parameterised b fuel mass ratio ( ) in Equation (2).

=
Here, (mg/cycle) and (mg/cycle) denotes the injection quantity of w  In order to increase the efficiency of water utilisation for optimising OFC process, it is usually injected directly into the engine chamber by a separated injector [17][18][19][20][21]. Figure  3 shows the schematic of two representatives.
The system presented in Figure 3a is adopted in this numerical study, which advantage is compact size, simple structure and control measure. A container coupled with a pump is utilised to deliver water to a rail. Afterward, water will be directly injected into combustion chambers with the assistance of an air booster. The booster provides a high WI pressure to enhance water droplets' breakup, diffusion and vaporisation.
The other strategy in Figure 3b does not include storage for water supply. Instead, the water vapour in the exhaust gas can be condensed and separated, then heated up prior to being recirculated and injected into the combustion chambers. The advantage of this system is that overall thermal efficiency can be improved by the benefit of water vaporisation inside the cylinder chamber and the waste heat recovery from the exhaust gas.
(a) WI with a water tank (b) WI without a water tank In order to make the parameters more visually, WI mass is parameterised by waterfuel mass ratio ( ) in Equation (2 Here, (mg/cycle) and (mg/cycle) denotes the injection quantity of water and fuel per engine cycle, respectively. WI timing and WI temperature is abbreviated with and , respectively. Brake Specific Fuel Consumption (BSFC) is introduced to evaluate fuel consumption. 10 , 50 and 90 represents the Crank Angle (CA) where 10%, 50% and 90% of the total heat has been released, respectively. Ignition delay ( ) represents the period between In order to make the parameters more visually, WI mass is parameterised by water-fuel mass ratio (R w f ) in Equation (2).
Here, τ w (mg/cycle) and τ f (mg/cycle) denotes the injection quantity of water and fuel per engine cycle, respectively. WI timing and WI temperature is abbreviated with t W I and T W I , respectively. Brake Specific Fuel Consumption (BSFC) is introduced to evaluate fuel consumption. ϕ CA10 , ϕ CA50 and ϕ CA90 represents the Crank Angle (CA) where 10%, 50% and 90% of the total heat has been released, respectively. Ignition delay (θ F ) represents the period between spark timing and ϕ CA10 . Combustion duration (θ C ) denotes the period between ϕ CA10 and ϕ CA90 .
During the study, engine operation is kept at a typical mid-high load of 2000 revolutions per minute (rpm) and 10 bar Brake Mean Effective Pressure (BMEP). The spark timings are fixed under the conditions of R w f = 0. WI pressure is maintained at 60 bar to ensure the injected water is in the liquid state. The water boiling point at 60 bar is around 549 K, which is much higher than the WI temperature (298 K to 368 K) in this study. Besides, to make the investigation process more explicit, the throttle opening angle, fuel injection timings, intake temperature and Oxygen Mass Fraction (OMF) remain constant with CAC mode throughout this study.

Engine and Testbed
The model of numerical study is set up based on a practical turbocharged dualinjection SI engine fuelled with gasoline. The engine specifications and testbed overview are presented in Table 2 and Figure 4, respectively. The used fuel of this study is commercial gasoline, which physical and chemical parameters are shown in Table 3. Regarding the data collection and analysis of the test, cylinder pressure is measured and analysed by sparkplug type piezo-electric sensors (AVL-GH13Z), a crank sensor (Kistler 2614CK1), a charge amplifier (Kistler 5018A) and a combustion analyser (AVL 641). The pressure data are recorded and averaged by 200 consecutive cycles to ensure the accuracy of measurements. A direct current electrical dynamometer measures and controls the engine's speed and torque in real-time. A programmable Electronic Control Unit (ECU) is used to adjust the ignition, fuel injection and other engine operating parameters. The air-fuel ratio is kept constant at stoichiometric ratio (lambda = 1 ± 0.01). The uncertainties of the measured parameters in the test are shown in Table 4 by the root mean square method.      Table 4. Uncertainties of measured parameters.

Model Description
The model used in this study is set up based on GT-Power software, which is an industry-standard simulation software and widely used both industry and academia to predict combustion performance of SI engines [43][44][45][46].
In this model, the engine configuration settings are according to its detailed specifications, such as basic geometry of pipes, engine displacement, cylinder bore, connecting rod length, valves, etc. The heat transfer process in ICE can be classified into thermal conduction, thermal convection, thermal radiation and thermal vaporisation. The heat transfer submodel is set to be 'Woschni model', which was put forward to provide an instantaneous, spatially averaged heat transfer coefficient for the evaluation of heat transfer rate to the cylinder walls [47][48][49]. Some key correlations in the 'Woschni model' are given by Equations (3)-(5).
Here, Q W is total heat transferred; h is heat transfer coefficient; A i is heat absorbing area of the surfaces; T is in-cylinder mean gas temperature; T wi is mean surface temperature of A i ; ϕ is CA; d is cylinder bore diameter; P is cylinder pressure; T is in-cylinder mean gas temperature; C 1 is a constant related to airflow velocity coefficient; c m is mean piston speed; w c is gas velocity caused by combustion; C 2 is a constant related to combustion chamber; Energies 2021, 14, 5287 7 of 24 V S is cylinder volume; P 0 is cylinder pressure when the engine is started. T 1 , P 1 and V 1 is cylinder temperature, pressure and volume at the beginning of compression, respectively.
The 'SI turbulent flame combustion model' is chosen and set up for the submodel of combustion and heat transfer. This submodel is commonly used to predict the in-cylinder burn rate, knocking occurrence and emissions for SI engines [43]. Moreover, the flamewall interactions can be calculated in this submodel according to the settings of cylinder geometry, spark location, head region and piston cup. Some key formulas are presented as Equations (6)- (9).
Here, S L is laminar flame speed; S L,0 is laminar flame speed under the condition of 298 K and 101.325 kPa; T u is unburned gas temperature; T re f is 298 K; α is temperature exponent; p is pressure; p re f is 101.325 kPa; β is pressure exponent; B m is maximum laminar speed; B O is laminar speed roll-off value; O is in-cylinder equivalence ratio; O m is equivalence ratio at maximum speed; f (D) is dilution effect; D is mass fraction of the residuals in the unburned zone; λ DEM is dilution effect multiplier.

Figures 5 and 6 show the model validation by comparing cylinder pressure and Heat
Release Rate (HRR) between experimental and simulation results at 2000 rpm-10 bar under CAC mode with GDI, P 50 -G 50 and PFI three injection strategies. The time-step sensitivity has also been considered to assure the accuracy of the simulation results further. It can be observed that the cylinder pressure and HRR curves in experimental conditions have a good match with those of simulation. Furthermore, the magnitude and position for the peaks of curves are correctly predicted. Therefore, this model is eligible to make a reasonable prediction in this study. can be observed that the cylinder pressure and HRR curves in experimental conditions have a good match with those of simulation. Furthermore, the magnitude and position for the peaks of curves are correctly predicted. Therefore, this model is eligible to make a reasonable prediction in this study.  It can be seen that the peaks of HRR under OFC are generally about 8 degrees ad vanced than CAC. The peaks of HRR curves decrease from around 110 J/CA of CAC to 9 J/CA of OFC. This is mainly because the engine knocking would occur with the exces sively advanced sparking timing at 2000 rpm-10 bar under CAC, and it can be easil avoided since the thermal diffusivity of CO2 is much lower than that of nitrogen.    Figures 8 and 9 shows the comparison of BSFC, spark timing, and between CAC and OFC. It can be seen that BSFC is 317.269 g/kWh, 317.519 g/kWh and 317.524 g/kWh for GDI, P50-G50 and PFI, respectively. There is a significant increase of around 68 g/kWh compared to that of the CAC mode. This is mainly because the thermal diffusivity of CO2 is much lower than nitrogen, resulting in a great difference in flame transmission, which would increase the heat loss under OFC. Even though there are also offset effects caused by the higher thermal conductivity of CO2 than that of nitrogen.

Comparison between CAC and OFC
The behaviour can be further explained by the significantly advanced spark timing and prolonged under OFC compared to CAC. It is similar to some previous findings of oxy-fuel burners, which conclude that the ignition delay of a mixture of O2/CO2 is significantly higher than that of an O2/N2 mixture with a similar oxygen fraction [50,51].
Besides, there is no significant difference in between OFC and CAC. In the meantime, the of PFI under OFC is 25.5 degrees, which is a bit shorter than 26.8 degrees of GDI and 26 degrees of P50-G50. This can be attributed to that compared to P50-G50 and GDI, a more homogenous gas-fuel mixture under PFI strategy can help accelerate flame development. It can be seen that the peaks of HRR under OFC are generally about 8 degrees advanced than CAC. The peaks of HRR curves decrease from around 110 J/CA of CAC to 90 J/CA of OFC. This is mainly because the engine knocking would occur with the excessively advanced sparking timing at 2000 rpm-10 bar under CAC, and it can be easily avoided since the thermal diffusivity of CO 2 is much lower than that of nitrogen. Figures 8 and 9 shows the comparison of BSFC, spark timing, θ F and θ C between CAC and OFC. It can be seen that BSFC is 317.269 g/kWh, 317.519 g/kWh and 317.524 g/kWh for GDI, P 50 -G 50 and PFI, respectively. There is a significant increase of around 68 g/kWh compared to that of the CAC mode. This is mainly because the thermal diffusivity of CO 2 is much lower than nitrogen, resulting in a great difference in flame transmission, which would increase the heat loss under OFC. Even though there are also offset effects caused by the higher thermal conductivity of CO 2 than that of nitrogen.
The behaviour can be further explained by the significantly advanced spark timing and prolonged θ F under OFC compared to CAC. It is similar to some previous findings of oxy-fuel burners, which conclude that the ignition delay of a mixture of O 2 /CO 2 is significantly higher than that of an O 2 /N 2 mixture with a similar oxygen fraction [50,51].

Effects of WI Mass on OFC Performance
The effects of are discussed in this section, which includes the analysis of BSFC, maximum cylinder pressure ( ), 50 , HRR and in-cylinder temperature under three injection strategies (GDI, P50-G50 and PFI). Meanwhile, in order to make the research objective clear and straightforward, and is fixed at −60 °CA and 298 K, respectively.
As shown in Figure 10, BSFC is quite sensitive to . With the increase of from 0 to 0.2, there is a small decrease in BSFC regardless of the injection strategy. The lowest BSFC is each 316.647 g/kWh, 316.497 g/kWh and 316.358 g/kWh for GDI, P50-G50 and PFI, which has a slight saving rate of 0.196%, 0.322% and 0.367% than that of = 0, respectively. This can be attributed to the increased working medium and oxygen atom concentration from injected water.

Effects of WI Mass on OFC Performance
The effects of are discussed in this section, which includes the analysis of BSFC, maximum cylinder pressure ( ), 50 , HRR and in-cylinder temperature under three injection strategies (GDI, P50-G50 and PFI). Meanwhile, in order to make the research objective clear and straightforward, and is fixed at −60 °CA and 298 K, respectively.
As shown in Figure 10, BSFC is quite sensitive to . With the increase of from 0 to 0.2, there is a small decrease in BSFC regardless of the injection strategy. The lowest BSFC is each 316.647 g/kWh, 316.497 g/kWh and 316.358 g/kWh for GDI, P50-G50 and PFI, which has a slight saving rate of 0.196%, 0.322% and 0.367% than that of = 0, respectively. This can be attributed to the increased working medium and oxygen atom concentration from injected water. Besides, there is no significant difference in θ C between OFC and CAC. In the meantime, the θ C of PFI under OFC is 25.5 degrees, which is a bit shorter than 26.8 degrees of GDI and 26 degrees of P 50 -G 50 . This can be attributed to that compared to P 50 -G 50 and GDI, a more homogenous gas-fuel mixture under PFI strategy can help accelerate flame development.

Effects of WI Mass on OFC Performance
The effects of R w f are discussed in this section, which includes the analysis of BSFC, maximum cylinder pressure (P max ), ϕ CA50 , HRR and in-cylinder temperature under three injection strategies (GDI, P 50 -G 50 and PFI). Meanwhile, in order to make the research objective clear and straightforward, t W I and T W I is fixed at −60 • CA and 298 K, respectively.
As shown in Figure 10, BSFC is quite sensitive to R w f . With the increase of R w f from 0 to 0.2, there is a small decrease in BSFC regardless of the injection strategy. The lowest BSFC is each 316.647 g/kWh, 316.497 g/kWh and 316.358 g/kWh for GDI, P 50 -G 50 and PFI, which has a slight saving rate of 0.196%, 0.322% and 0.367% than that of R w f = 0, respectively. This can be attributed to the increased working medium and oxygen atom concentration from injected water. However, an overall growth trend can be observed in BSFC with the further increas of from 0.2 to 0.9, which is an increment of 4.29%, 3.6% and 3.77% for GDI, P50-G and PFI, respectively. Moreover, by further increasing from 0.9 to 2.0, the trend o BSFC would become quite stable. This indicates that an excessive amount of injected wate will increase BSFC. However, the deterioration is not serious due to water's positive effec on combustion by the increased working medium and oxygen concentration.
The variations can be further explained in Figures 11 and 12, which show the effect of on combustion characteristics by , 50 , HRR and in-cylinder temperatur It demonstrates that the changing trends in combustion characteristics are similar for GD P50-G50 and PFI. With the increase of from 0 to 0.6, has a reduction of aroun 4.5 bar and 50 is delayed by around 2.5 degrees. With further increased , bot and 50 remain broadly stable with a minor fluctuation. In the meantime, HR However, an overall growth trend can be observed in BSFC with the further increase of R w f from 0.2 to 0.9, which is an increment of 4.29%, 3.6% and 3.77% for GDI, P 50 -G 50 and PFI, respectively. Moreover, by further increasing R w f from 0.9 to 2.0, the trend of BSFC would become quite stable. This indicates that an excessive amount of injected water will increase BSFC. However, the deterioration is not serious due to water's positive effect on combustion by the increased working medium and oxygen concentration.
The variations can be further explained in Figures 11 and 12, which show the effects of R w f on combustion characteristics by P max , ϕ CA50 , HRR and in-cylinder temperature. It demonstrates that the changing trends in combustion characteristics are similar for GDI, P 50 -G 50 and PFI. With the increase of R w f from 0 to 0.6, P max has a reduction of around 4.5 Energies 2021, 14, 5287 13 of 24 bar and ϕ CA50 is delayed by around 2.5 degrees. With further increased R w f , both P max and ϕ CA50 remain broadly stable with a minor fluctuation. In the meantime, HRR and in-cylinder temperature are also sensitive to R w f . Under all the three injection strategies, as the R w f increases from 0 to 1.0, the peak of HRR is postponed by around 1 degree whilst the peak of in-cylinder temperature reduces about 180 K. Afterwards, HRR and in-cylinder temperature will be less affected by further increasing R w f .   Figure 13 presents the effects of t W I on BSFC under three injection strategies (GDI, P 50 -G 50 and PFI). Meanwhile, T W I is held constant at 298 K in this section.

Effects of WI Timing on OFC Performance
On the whole, the relatively lower BSFC generally appear with low R w f . The lowest BSFC appears on the operating condition of 't W I = −70 • CA, R w f = 0.1', 't W I = −70 • CA, R w f = 0.2' and 't W I = −70 • CA, R w f = 0.2' for GDI, P 50 -G 50 and PFI, respectively. The corresponding values are each 316.638 g/kWh, 316.383 g/kWh and 316.172 g/kWh, which provides a limited benefit of 0.199%, 0.358% and 0.426% than that of R w f = 0, respectively.
Besides, it can be observed that BSFC is less affected by t W I under the conditions of low R w f . On the conditions of R w f ≤ 0.5, the fluctuation of BSFC is generally kept in a narrow range with the delay of t W I from −100 • CA to −30 • CA under all three injection strategies.
Under the conditions of high R w f (R w f ≥ 0.8), BSFC is strongly affected by t W I . As t W I postpones from −100 • CA to −30 • CA, BSFC has a sharp decrease of more than 6 g/kWh. Furthermore, this trend becomes more obvious under GDI injection strategy. Because the negative effects on the gas-fuel mixture from the vaporisation process of injected water are a bit stronger under GDI. The variation of BSFC can be attributed to the combustion characteristics, which are presented with P max , ϕ CA50 , HRR and in-cylinder temperature in Figures 14 and 15.
As shown in Figure 14, P max shows a monotonic increase with the delay of t W I from −100 • CA to −30 • CA. The decreased tendency is more apparent under the conditions of R w f = 1.0, particularly with GDI strategy. In the meantime, ϕ CA50 generally shows a decreasing trend to around 5 • CA at t W I = −30 • CA, which is also helpful to improve fuel efficiency. Figure 15 shows the effects of t W I on HRR and in-cylinder temperature under GDI with R w f = 1.0. With the postpone of t W I from −100 • CA to −40 • CA, the peak of HRR is advanced by 4.5 • CA, and the peak of in-cylinder temperature is significantly increased by 247 K. With the delay of t W I , the improvement in combustion performance is mainly because the cooling effect is getting weaker by reducing the period of water vaporisation. Under the conditions of high ( ≥ 0.8), BSFC is strongly affected by . As postpones from −100 °CA to −30 °CA, BSFC has a sharp decrease of more than 6 g/kWh. Furthermore, this trend becomes more obvious under GDI injection strategy. Because the negative effects on the gas-fuel mixture from the vaporisation process of injected water are a bit stronger under GDI. The variation of BSFC can be attributed to the combustion characteristics, which are presented with , 50 , HRR and in-cylinder temperature in Figures 14 and 15.
As shown in Figure 14, shows a monotonic increase with the delay of from −100 °CA to −30 °CA. The decreased tendency is more apparent under the conditions of = 1.0, particularly with GDI strategy. In the meantime, 50 generally shows a decreasing trend to around 5 °CA at = −30 °CA, which is also helpful to improve fuel efficiency. Figure 15 shows the effects of on HRR and in-cylinder temperature under GDI with = 1.0. With the postpone of from −100 °CA to −40 °CA, the peak of HRR is advanced by 4.5 °CA, and the peak of in-cylinder temperature is significantly increased by 247 K. With the delay of , the improvement in combustion performance is mainly because the cooling effect is getting weaker by reducing the period of water vaporisation.
(a) GDI     Figure 16 shows the effects of T W I on BSFC under GDI, P 50 -G 50 and PFI injection strategies. In the meantime, t W I is fixed at −60 • CA in this section. It can be seen that BSFC is not sensitive to T W I , it generally has a small decline with the increase of T W I from 298 K to 368 K regardless of the injection strategy. The most significant decline is just around 3.5 g/kWh under R w f = 1.0. Besides, the lowest BSFC are each 316.291 g/kWh, 316.068 g/kWh and 315.884 g/kWh, providing a limited saving rate of 0.308%, 0.457% and 0.516% than that of R w f = 0, respectively. Figure 17 presents the effects of T W I on P max and ϕ CA50 under R w f = 0.2, 0.6 and 1.0. The variation of P max and ϕ CA50 is less affected by T W I compared to the effects of R w f or t W I . By increasing T W I from 298 K to 368 K, P max just presents an increase of around 0.5 bar, and whilst ϕ CA50 would be advanced by about 0.25 degrees. This is mainly because that by increasing T W I , the suppression of combustion would become slightly weaker during the process of heat absorption by the cooling effect of water. Moreover, increasing T W I would accelerate the vaporisation rate of water, leading to fewer negative effects on combustion [52].

Effects of WI Temperature on OFC Performance
This can also be explained by Figure 18, which is one example to show the effects of T W I on HRR and in-cylinder temperature. It shows that by increasing T W I from 308 K to 368 K, the peak of HRR and in-cylinder temperature have a slight increase of 0.47 J/CA and 19.5 K, respectively. Figure 16 shows the effects of on BSFC under GDI, P50-G50 and PFI injection strategies. In the meantime, is fixed at −60 °CA in this section. It can be seen that BSFC is not sensitive to , it generally has a small decline with the increase of from 298 K to 368 K regardless of the injection strategy. The most significant decline is just around 3.5 g/kWh under = 1.0. Besides, the lowest BSFC are each 316.291 g/kWh, 316.068 g/kWh and 315.884 g/kWh, providing a limited saving rate of 0.308%, 0.457% and 0.516% than that of = 0, respectively. Figure 17 presents the effects of on and 50 under = 0.2, 0.6 and 1.0. The variation of and 50 is less affected by compared to the effects of or . By increasing from 298 K to 368 K, just presents an increase of around 0.5 bar, and whilst 50 would be advanced by about 0.25 degrees. This is mainly because that by increasing , the suppression of combustion would become slightly weaker during the process of heat absorption by the cooling effect of water. Moreover, increasing would accelerate the vaporisation rate of water, leading to fewer negative effects on combustion [52].

Effects of WI Temperature on OFC Performance
This can also be explained by Figure 18, which is one example to show the effects of on HRR and in-cylinder temperature. It shows that by increasing from 308 K to 368 K, the peak of HRR and in-cylinder temperature have a slight increase of 0.47 J/CA and 19.5 K, respectively.

Conclusions
In order to eliminate CO 2 emissions from ICE for achieving carbon neutrality and mitigating global warming, the implementation of OFC technology in a dual-injection SI engine fuelled with gasoline was numerically studied. This study systematically explores the effects of WI strategies (mass, timing, temperature) on OFC characteristics in a dualinjection SI engine. The findings offer some important insights to help understand the performance and optimisation of dual-injection SI engine under OFC mode fuelled with gasoline. The main conclusions are summarised as follows.

1.
Compared to CAC mode, it can be seen that the peaks of HRR under OFC are generally about 8 degrees advanced than CAC. The peaks of HRR curves decrease from around 110 J/CA of CAC to 90 J/CA of OFC. Furthermore, there is a significant increase of around 68 g/kWh in BSFC under OFC. θ F is significantly prolonged, and the spark timing is obviously advanced. Besides, θ C of PFI is a bit shorter than that of GDI and P 50 -G 50 .

2.
With the increase of R w f , P max and in-cylinder temperature is reduced, while ϕ CA50 and the peak of HRR is postponed. There is a small benefit to BSFC under low R w f . However, with the further increase of R w f from 0.2 to 0.9, there is an increment of 4.29%, 3.6% and 3.77% in BSFC for GDI, P 50 -G 50 and PFI, respectively.

3.
On the whole, the relatively lower BSFC generally appear with low R w f . The lowest BSFC appears on the operating condition of 't W I = −70 • CA, R w f = 0.1', 't W I = −70 • CA, R w f = 0.2' and 't W I = −70 • CA, R w f = 0.2' for GDI, P 50 -G 50 and PFI, respectively.

4.
Under the conditions of R w f ≥ 0.8, BSFC is strongly affected by t W I . As t W I postpones to around −30 • CA, with the improvement in combustion performance, BSFC has a sharp decrease of more than 6 g/kWh, and this decline is more evident under GDI injection strategy. 5.
The variation of P max and ϕ CA50 is less affected by T W I compared to the effects of R w f or t W I . BSFC generally has a small decline with the increase of T W I from 298 K to 368 K regardless of the injection strategy. P max just presents an increase of around 0.5 bar, and whilst ϕ CA50 would be advanced by about 0.25 degrees. 6.
It is feasible to implement appropriate WI strategies to control OFC characteristics and performance of a dual-injection SI engine, but the benefit in fuel economy is limited. 7.
The findings of this study are beneficial to establish a conceptual and theoretical foundation for the implementation of OFC technology in dual-injection SI engines, as well as increasing the efficiency of this kind of engine. In future works, the engine efficiency under the OFC mode will be expected to further improve by various optimisation research, such as the effects of different kinds of fuel injection, intake charge components, variable valve actuation, etc.