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Engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine
Simulation Modelling Practice and Theory 19 (2011) 734–751
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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine M.M. Rahman ⇑, Mohammed Kamil, Rosli A. Bakar Automotive Engineering Centre, Faculty of Mechanical Engineering, Universiti Malaysia Pahang Tun Abdul Razak Highway, 26300 Gambang, Kuantan, Pahang, Malaysia
a r t i c l e
i n f o
Article history: Received 7 November 2009 Received in revised form 4 October 2010 Accepted 9 October 2010 Available online 15 October 2010 Keywords: Direct injection Injection timing Air fuel ratio Speed Hydrogen fuel
a b s t r a c t This paper presents the engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine. The 4-cylinder direct injection hydrogen engine model was developed utilizing the GT-Power commercial software. This model employed one dimensional gas dynamics to represent the flow and heat transfer in the components of engine model. Sequential pulse injectors are adopted to inject hydrogen gas fuel within the compression stroke. Injection timing was varied from 110° before top dead center (BTDC) until top dead center (TDC) timing. Engine speed was varied from 2000 rpm to 6000 rpm, while the equivalence ratio was varied from 0.2 to 1.0. The validation was performed with the existing previous experimental results. The negative effects of the interaction between ignition timing and injection duration was highlighted and clarified. The results showed that optimum injection timing and engine performance are related strongly to the air fuel ratio and engine speed. The acquired results show that the air fuel ratio and engine speed are strongly influence on the optimum injection timing and engine performance. It can be seen that the indicated efficiency increases with increases of AFR while decreases of engine speed. The power and torque increases with the decreases of AFR and engine speed. The indicated specific fuel consumption (ISFC) decreases with increases of AFR from rich conditions to lean while decreases of engine speed. The injection timing of 60° BTDC was the overall optimum injection timing with a compromise. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction With increasing concern about the energy shortage and environmental protection, research on improving engine fuel economy, hydrogen fueled engine is being developed into a hydrogen fueled engine with manifold injection, direct injection or duel injection according to the fuel supply method [1–4]. Of course, the hydrogen fueled engine with direct injection can fundamentally keep backfires from occurring so it can be utilized as a high powered hydrogen power system if the reliability of high pressure direct injection valve is secured [5,6]. Hydrogen gas is characterized by a rapid combustion speed, wide combustible limit and low minimum ignition energy. Such characteristics play a role to decrease engine cycle variation for the safety of combustion. However, it is frequently observed that the values of cycle variation for hydrogen-fueled engines with direct injection are higher than those of hydrogen-fueled engines with manifold injection or those of gasoline engines, due to a decrease in the mixing period by direct injection in the process of compressing hydrogen gas [7–9]. In today’s modern world, where new technologies are introduced every day, transportation’s energy use is increasing rapidly. ⇑ Corresponding author. Tel.: +60 9 4242246; fax: +60 9 4242202. E-mail address: mustafi[email protected] (M.M. Rahman). 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.10.006
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Fossil fuel particularly petroleum fuel is the major contributor to energy production and the primary fuel for transportation. Rapidly depleting reserves of petroleum and decreasing air quality raise questions about the future. As world awareness about environment protection increases so does the search for alternative to petroleum fuels. Hydrogen can be used as a clean alternative to petroleum fuels and its use as a vehicle fuel is promising in the effects to establish environmentally friendly mobility systems. So far, extensive studies investigated hydrogen fueled internal combustion engines (H2ICE) with external mixture formation fuel delivery system [10,11]. However, the operation of these engines subjected to abnormal combustion, such as pre-ignition, backfire and knocking. Moreover, the power outputs of these hydrogen engines are about 30% less than those of gasoline engines [12]. Therefore the premixed-charge spark ignition engines fueled with hydrogen can be used for significantly limited operation range [13]. It is a common conclusion achieved by many researchers that abnormal combustion can be controlled by direct injection (DI) of hydrogen in-side the cylinder [13–15]. Direct injection H2ICE requires optimized operation strategies that enable the availability of high power output as well as the abolition of critical exhaust gas emission in combination with high efficiencies. Several parameters need to be optimized. Optimization of spark timing, valve timing, combustion chamber geometry, injection parameters such as injection timing, injection duration, injection pressure and nozzle hole numbers/arrangement, swirls intensity, etc. are indeed important to achieve an engine performance level competitive to that in the modern direct-injection diesel engines [15]. Injection timing plays a critical role in the phasing of the combustion, and hence the emissions and torque production. Therefore, extensive number of studies indicated the significance of optimization for ignition timing [15–17]. White et al. [18] suggested that late injection can minimize the residence time that a combustible mixture is exposed to in-cylinder hot spots and allow for improved mixing of the intake air with the residual gases. This selection can control pre-ignition problem. The main challenge for selecting the proper ignition timing that is in-cylinder injection requires hydrogen–air mixing in a very short time. For early injection (i.e., coincident with inlet valve closure (IVC)), maximum available mixing times range from approximately 20 ms to 4 ms across the speed range 1000–5000 rpm. In practice, to avoid pre-ignition, start of injection (SOI) is retarded with respect to IVC and mixing times are further reduced. Regarding the behavior of the performance characteristic with ignition timing, there are several contradictories in the literature. Eichlseder et al. [3] found that at low loads (or low equivalence ratio (h)), indicated efficiency (IE) increases with retard of SOI. The increase was shown to be due to the decrease in the compression work caused by differences in mixture gas properties and charge mass with retarded SOI. The authors also found their study at high loads, IE first increases and then decreases with retard of SOI. The reversing trend is assumed to be a consequence of an unfavorable mixture formation. However, Kim et al. [17] reported the contradictory results to Eichlseder et al. [3] results, where they find that, for both low and high loads, indicated efficiency decreases monotonically with retard of SOI. These contradictory findings may be a result of differences in mixture formation [18]. Much effort has been devoted to optimize the injection timing which is ranging from IVC until the top dead center (i.e. within the compression stroke). However, Mohammadi et al. [15] optimized the injection timing for three ranges: during the intake stroke, where they prevented backfire. However, thermal efficiency and output power are limited by knock due to reduction in volumetric efficiency; at compression stroke, where they prevented knock and gives an increase in thermal efficiency and maximum output power; and at later stage of compression stroke, where they achieved thermal efficiency higher than 38.9% and brake mean effective pressure 0.95 MPa. This study attempts to optimize injection timing that gives the best performance of a 4-cylinders direct injection. The 4-cylinder direct injection hydrogen fueled engine model is developed for this purpose. The effects of air fuel ratio, engine speed on engine performance and the optimum injection timing on the engine performance such as indicated efficiency, indicated specific fuel consumption, power and torque for direct injection hydrogen fueled engine. 2. Engine modeling 2.1. Engine performance parameters The brake mean effective pressure (BMEP) can be defined as the ratio of the brake work per cycle Wb to the cylinder volume displaced per cycle Vd, and it can be expressed as [19]:
BMEP ¼
Wb Vd
ð1Þ
Eq. (1) can be rewrite for the four stroke engine as:
BMEP ¼
2Pb NV d
where Pb is the brake power, and N is the rotational speed.
ð2Þ
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Brake efficiency (gb) can be defined as the ratio of the brake power Pb to the engine fuel energy as:
P
gb ¼ _ b mf ðLHVÞ
ð3Þ
_ f is the fuel mass flow rate and LHV is the lower heating value of hydrogen. where m _ f per unit brake power output and can be exThe brake specific fuel consumption (BSFC) represents the fuel flow rate m pressed as [19]:
BSFC ¼
_f m Pb
ð4Þ
The volumetric efficiency (gv) of the engine defines as the mass of air supplied through the intake valve during the intake _ a Þ by comparison with a reference mass, which is that mass required to perfectly fill the swept volume under period ðm the prevailing atmospheric conditions, and can be expressed as:
gv ¼
_a m qai V d
ð5Þ
where qai is the inlet air density. The burning rate (Xb) of combustion process was modeled using Wiebe function, which can be expressed as:
" nþ1 # h hi X b ¼ 1 exp a Dh
ð6Þ
where h is the crank angle, hi is the start of combustion, Dh is the combustion period and a and n are adjustable constants. Furthermore, the heat transfer in-side the cylinder was modeled using a formula which is closely emulates the classical Woschni correlation. Based on this correlation, the heat transfer coefficient hc can be expressed as:
hc ¼ 3:26B0:2 p0:8 T 0:55 w0:8
ð7Þ
where B is the bore in meters, p is the pressure in kPa, T is temperature in K and w is the average cylinder gas velocity in m/s. The hydrogen gas fuel was injected directly in-side the cylinders using the four sequential pulse fuel injectors. The AFR was imposed for the injectors. Then, the injected fuel rate was estimated using [20]:
3 _ delivery ¼ gv qref NV d ðFARÞ m 2ðPwÞ
ð8Þ
_ delivery is the injector delivery rate (g/s), qref the reference density used to calculate volumetric efficiency (kg/m3), FAR where m is the fuel air ratio and Pw is the injection duration (°CA). The 4-cylinders were then connected together through the engine part which translates the force acting on each piston into the crankshaft (brake) power. In the engine model: engine type was 4-stroke type; the number of cylinders is set to four; the configuration in-line had been chosen; and simulation with prescribed engine speed was specified rather than engine load. Furthermore, engine friction model was imposed to model friction in the engine. The friction mean effective pressure (FMEP) was modeled based on [21]: 2
FMEP ¼ 0:4 þ ð0:005 P max Þ þ ð0:09 Speedmp Þ þ ð0:0009 Speedmp Þ
ð9Þ
where Speedmp represents the mean piston speed and Pmax is the peak cylinder pressure. 2.2. Engine modeling The engine model for an in-line 4-cylinder direct injection engine was developed for this study. Engine specifications for the base engine are tabulated in Table 1. The specific values of input parameters including the AFR, engine speed, and Table 1 Engine specification. Engine parameter
Value
Unit
Bore Stroke Connecting rod length Piston pin offset Total displacement Compression ratio Inlet valve close, IVC Exhaust valve open, EVO Inlet valve open, IVO Exhaust valve close, EVC
100 100 220 1.00 3142 9.5 96 125 351 398
mm mm mm mm cm3 °CA °CA °CA °CA
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injection timing were defined in the model. The boundary condition of the intake air was defined first in the entrance of the engine. The air enters through a bell-mouth orifice to the pipe. The discharge coefficients of the bell-mouth orifice were set to 1 to ensure the smooth transition as in the real engine. The pipe of bell-mouth orifice with 0.07 m of diameter and 0.1 m of length are used in this model. The pipe connects in the intake to the air cleaner with 0.16 m of diameter and 0.25 m of length was modeled. The air cleaner pipe identical to the bell-mouth orifice connects to the manifold. A log style manifold was developed from a series of pipes and flow-splits. The intake system of the present study model is shown in Fig. 1. The total volume for each flow-split was 256 cm3. The flow-splits compose from an intake and two discharges. The intake draws air from the preceding flow-split. One discharge supplies air to adjacent intake runner and the other supplies air to the next flow-split. The last discharge pipe was closed with a cup to prevent any flow through it because there is no more flow-split. The flow-splits are connected with each other via pipes with 0.09 m diameter and 0.92 m length. The junctions between the flow-splits and the intake runners were modeled with bell-mouth orifices. The discharge coefficients were also set to 1 to assure smooth transition, because in most manifolds the transition from the manifold to the runners is very smooth. The intake runners for the 4-cylinders were modeled as four identical pipes with .04 m diameter and 0.1 m length. Finally the
Fig. 1. Intake system model.
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intake runners were linked to the intake ports which were modeled as pipes with 0.04 m diameter and 0.08 length. The air mass flow rate in e intake port was used for hydrogen flow rate based on the imposed AFR. The second major part of the engine model is the powertrain model which is shown in Fig. 2. In the powertrain, the induced air passes through the intake cam-driven type valves with 45.5 mm of diameter to the cylinders. The valve lash (mechanical clearance between the cam lobe and the valve stem) was set to 0.1 mm. The overall temperature of the head, piston and cylinder for the engine parts are listed in Table 2. The temperature of the piston is higher than the cylinder head and cylinder block wall temperature because this part is not directly cooled by the cooling liquid or oil. The last major part in the present model is the exhaust system which is shown in Fig. 3. The exhaust runners were modeled as rounded pipes with 0.03 m inlet diameter, and 80° bending angle for runners 1 and 4; and 40° bending angle of runners 2 and 3. Runners 1 and 4, and runners 2 and 3 are connected before enter in a flow-split with 169.646 cm3 volume. Conservation of momentum is solved in 3-dimentional flow-splits even though the flow in GT-Power is otherwise based on a one-dimensional version of the Navier–Stokes equation. Finally a pipe with 0.06 m diameter and 0.15 m length connects the last flow-split to the environment. Exhaust system walls temperature was calculated using a model embodied in each pipe and flow-split. Table 3 are listed the parameters used in the exhaust environment of the model.
Fig. 2. Powertrain model.
M.M. Rahman et al. / Simulation Modelling Practice and Theory 19 (2011) 734–751 Table 2 Temperature of the mail engine parts. Components
Temperature (K)
Cylinder head Cylinder block wall Piston
550 450 590
Fig. 3. Exhaust system model.
Table 3 Parameters used in the exhaust environment. Parameters
Value
Unit
External environment temperature Heat transfer coefficient Radiative temperature Wall layer material Layer thickness Emissivity
320 15 320 Steel 3 0.8
K W/m2 K K mm
739
740
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3. Model validation The experimental results obtained from Mohammadi et al. [15] were used for the purpose of validation in this study. Engine specifications of Mohammadi et al. [15] and present single cylinder direct injection engine model are listed in Table 4. For the purpose of validation, single cylinder direct injection engine model converted to 4-cylinder direct injection model. Fig. 4 shows the single cylinder direct injection engine model. Engine speed and AFR were fixed at 1200 rpm and 57.216 (u = 0.6) respectively in this comparison. Injection timing was varied from 130 °CA BTDC until 70 °CA BTDC to be coincident with Mohammadi et al. [15]. The correlation of brake thermal efficiency of the baseline model and experimental results obtained from Mohammadi et al. [3] is shown in Fig. 5. It can be seen that the brake thermal efficiency are good match with the experimental results. Only small deviation was obtained due to the difference between the engine operation conditions that are not mentioned in Mohammadi et al. [15]. However, considerable coincident between the single cylinder model and experimental results can be recognized in spite of the mentioned model differences. 4. Results and discussion A lean mixture is one in which the amount of fuel is less than stoichiometric mixture. This leads to fairly easy to get an engine start. Furthermore, the combustion reaction will be more complete. Additionally, the final combustion temperature is lower reducing the amount of pollutants. The air–fuel ratio (AFR) was varied from rich limit (AFR = 27.464:1 based on mass where the equivalence ratio (u = 1.2) to a very lean limit (AFR = 171.65 where (u = 0.2) and engine speed varied from 2500 rpm to 4500 rpm. BMEP is a good parameter for comparing engines with regard to design due to its independent on the engine size and speed. The results in the following section show the engine performance behavior with injection timing for each condition under investigation. In order to check the validity and accuracy of the present model, comparison with published experimental results in the literature. The effect of AFR with injection timing on the engine performance parameters including efficiency, brake specific fuel consumption, power, and torque were discussed. The effects of engine speed with injection timing on the engine performances are also investigated. 4.1. Variation in air fuel ratio on engine performance Fig. 6 shows the effect of air–fuel ratio on the brake mean effective pressure. It can be seen that BMEP decreases with increases of AFR and speed. This decrease happens with two different behaviors. For rich mixtures (low AFR), BMEF decreases almost linearly, then BMEP falls with a non-linear behavior. Higher linear range can be recognized for higher speeds. For 4500 rpm, the linear range is continuing until AFR of 42.9125 (u = 0.8). The non-linear region becomes more predominant at lower speeds and the linear region cannot be specified there. The total drop of BMEP within the studied range of AFR was 8.08 bar for 4500 rpm compared with 10.91 bar for 2500 rpm. At lean operating conditions (AFR = 171.65, (u = 0.2 the engine gives maximum power (BMEP = 1.635 bar) at lower speed 2500 rpm) compared with the power (BMEP = 0.24 bar) at speed 4500 rpm. Fig. 7 shows the variation of the brake thermal efficiency with the air fuel ratio for the selected speeds. Brake power is the useful part as a percentage from the intake fuel energy. The fuel energy is also covered the friction losses and heat losses (heat loss to surroundings, exhaust, enthalpy and coolant load). Therefore lower values of gb can be seen in Fig. 7. It can be observed that the brake thermal efficiency is increases nearby the richest condition (AFR ffi 35) and then decreases with increases of AFR and speed. The operation within a range of AFR from 38.144 to 42.91250 (u = 0.9–0.8) gives the maximum values for gb for all speeds. Maximum gb of 35.4% at speed 2500 rpm can be seen compared with 26.3% at speed 4500 rpm. Unaccepted efficiency gb of 3.7% can be seen at very lean conditions with AFR of 171.65 (u = 0.2 for speed of 4500 rpm while a value of 23.86% was recorded at the same conditions with speed of 2500 rpm. Clearly, rotational speed has a major effect in the behavior of gb with AFR. Higher speeds lead to higher friction losses. Table 4 Specifications of the engines models.
*
Engine parameter
Mohammadi et al. (2007)
Present model
Unit
Bore Stroke Connecting rod length Piston pin offset Total displacement Compression ratio Inlet valve close, IVC Exhaust valve open, EVO Inlet valve open, IVO Exhaust valve close, EVC
102 105 NA* NA 857 11.5 580 130 360 380
102 105 220 1.00 858 11.5 624° 125° 351° 398°
Mm Mm Mm Mm cm3
NA = not available.
ATDC ATDC ATDC ATDC
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Fig. 4. Single cylinder direct injection model.
Fig. 5. Comparison between published experimental results [15] and present single cylinder direct injection engine model based on brake efficiency.
Fig. 6. Variation of brake mean effective pressure with air fuel ratio for various engine speeds.
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Fig. 7. Variation of brake thermal efficiency with air fuel ratio.
Fig. 8. Variation of brake specific fuel consumption with air fuel ratio.
Fig. 8 depicts the behavior of the brake specific fuel consumption BSFC with AFR. It is easy to perceive from the figure that there is an optimum minimum value of BSFC occurred within a range of AFR from 38.144 (u = 0.9) to 49.0428 (u = 0.7) for the selected range of speed. At very lean conditions, higher fuel consumption can be noticed. After AFR of 114.433 (u = 0.3) the BSFC rises up rapidly, especially for high speeds. At very lean conditions with AFR of 171.65 (u = 0.2), a BSFC of 125.87 g/kW h was observed for the speed of 2500 rpm; while it was 809 g/kW h for 4500 rpm. Fig. 9 shows how the AFR can affect the maximum temperature in-side the cylinder. In general, lower temperatures are required due to the reduction of pollutants. It is clearly demonstrated how the increase in the AFR can decrease the maximum cylinder temperature with a severe steeped curve. But for rich mixtures, the maximum cylinder temperature drops down with a linear manner. The effect of the engine speed on the relationship between maximum cylinder temperatures with AFR seems to be minor. At rich operating conditions (AFR = 27.464, u = 1.2) and a speed of 3000 rpm, a maximum cylinder temperature of 2767 K was recorded. This temperature dropped down to 1345 K at AFR of 171.65 (u = 0.2). This lower temperature inhibits the formation of NOx pollutants. In fact this feature is one of the major motivations toward hydrogen fuel.
4.2. Variation in speed on engine performance Fig. 10 shows the variation of the volumetric efficiency with the engine speed for different air equivalence ratio. Leaner mixture gives the higher volumetric efficiency. The maximum volumetric efficiency was observed 85% at lean conditions
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Fig. 9. Variation of maximum cylinder temperature with air fuel ratio.
Fig. 10. Effect of engine speed against volumetric efficiency for different equivalence ratio.
with AFR = 171.65 (u = 0.2) and 2500 rpm whereas volumetric efficiency decreases at high speed due to the frictional losses. In the first part of the curve, higher speed lead to higher volumetric efficiency because of the high speed gives high vacuum at the intake port and consequent larger air flow rate that goes in-side the cylinder. Fig. 11 shows the variation of the power with engine speed. Greater power can be generated by increasing displacement, brake mean effective pressure and engine speed. The engine mass increases with increases of displacement and also takes up space, both are contrary to automobile design trends. For this reason, most modern engines are smaller but run at higher speeds and often turbocharged or supercharged to increase BMEP. Modern gasoline automobile engines usually have brake power output per displacement of 40–80 kW/L [21]. Clearly, power increases with increases of engine speed at certain level. The power decreases at higher engine speed after certain level due to the friction losses and becomes the dominant factor at very high speed. AFR has a strong effect in specifying the speed that gives maximum power. At AFR of 171.65 (u = 0.2), a maximum power obtained of 10.7 kW at 2500 rpm while AFR of 42.912 (u = 0.8), a maximum power of 94 kW obtained at 4500 rpm; and at AFR 27.464 (u = 1.2), a maximum power of 104.3 kW at 3500 rpm. But, for many gasoline engines, maximum power occurs at about 6000–7000 rpm. In fact this is another desired feature for hydrogen engines. The reported power at lean mixture is low and unacceptable. Fig. 12 illustrates the influence of variable engine speed on the torque. For all the range of studies AFR: at low speed, torque increases as engine speed increases. As engine speed increases further, torque reaches a maximum and then decreases as
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Fig. 11. Effect of engine speed against power.
Fig. 12. Variation of torque with engine speed.
shown in Fig. 12. The point of maximum torque is called maximum brake torque speed (MBT). A major goal in the design of a modern automobiles engine is to flatten the torque vs. speed curve, and to have high torque at both high and low speed. But, it is important to clarify here, that toque vs. speed curve for hydrogen is flatten compared to gasoline. The BMTs for the present hydrogen engine occurred at 2500 rpm; and their values are: 178 N m at equivalence ratio of 0.6; and 294 N m at 2500 rpm with stoichiometric operation. Hydrogen has long since been attempted as a fuel for the internal combustion engine. In general, it is desirable to have maximum volumetric efficiency for engine. The importance of efficiency is more critical for hydrogen engines because of the hydrogen fuel displaces large amount of incoming air due to its low density (0.0824 kg/m3 at 25 °C and 1 atm.). This reason reduces the efficiency to high extent. A stoichiometric mixture of hydrogen and air consists of approximately 30% hydrogen by volume, whereas a stoichiometric mixture of fully vaporized gasoline and air consists of approximately 2% gasoline by volume [18]. Therefore, the low efficiency for hydrogen engine is expected compared to gasoline engine works with same operating conditions and physical dimension. However, the higher efficiencies can be gained with direct injection of hydrogen, which can be shown in Fig. 7. The maximum value of efficiency for the selected range of speed was around 85%. At further higher engine speed beyond these values, the flow into the engine during at least part of the intake process becomes chocked. Once this condition occurs, further increases in engine speed decrease the flow rate significantly. Thus, the efficiency decreases sharply because of the higher speed is accompanied by some phenomenon that have negative influence on efficiency. These phenomenon include the charge heating in the manifold and higher friction flow losses which increase
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as the square of engine speed. Due to dissociation at high temperatures following combustion, molecular oxygen is present in the burned gases under stoichiometric conditions. Thus some additional fuel can be added and partially burned. This increases the temperature and the number of moles of the burned gases in the cylinder. These effects increases the pressure were given increase power and mean effective pressure [20]. The AFR for optimum fuel consumption at a given load depends on the details of chamber design (including compression ratio) and mixture preparation quality. It varies for a given chamber with the part of throttle load and speed range [20]. It is clearly seen (Fig. 8) that the higher fuel is consumed at higher speeds due to the greater friction losses that can occur at high speeds. The value BSFC at speed of 2500 rpm was doubled around two times at speed of 4000 rpm; however the same value was doubled around five times at speed of 4500 rpm. This is because of very lean operation conditions can lead to unstable combustion and more lost power due to a reduction in the volumetric heating value of the air/hydrogen mixture. Most modern gasoline automobiles have maximum torque per displacement in the range of 80 to 110 N m/L with some as high as 140 N m/L. The maximum torque obtained of 200–400 N m, usually at engine speed around 4000–6000 rpm (gasoline engines) [21]. Fig. 12 shows the torque of direct injection hydrogen-fueled engines with respect to variation in engine speed and air–fuel ratio. It is thought to be attributable to many factors such as: (i) the heterogeneity of air–fuel mixture may be increased at every cycle due to the decrease of the mixing period by direct injection into the cylinder in the early period of compression, (ii) the heterogeneity of air–fuel mixture may be also increased with decrease of penetration depth because of lightweight of hydrogen, and (iii) the combustion performance of the hydrogen–air mixture is lowered because direct injection hydrogen-fueled engines are configured by modifying only the fuel supply system without changing the shape of the combustion chamber of the gasoline engine. It is obvious that speed reduction increases mechanical losses. This disadvantage can be solved by supercharging. Supercharging also helps to cool off the cylinders. Hydrogen combustion converts two diatomic molecules to triatomic molecule [22,23]. Therefore, hydrocarbon combustion increases entropy, hence irreversibility. Since 90% of irreversibility comes from combustion process, second-law efficiency increases in favor of hydrogen [11]. Whilst experimental data are not available to verify these predictions, the authors are presented here to illustrate some of the insights that this type of simulation tool may provide to future engine systems designers.
4.3. Effects of air fuel ratio on injection timing In the present model, hydrogen was injected into the cylinder within a timing range started just before IVC (96° BTDC) until TDC (0°). AFR was varied from stoichiometric condition (AFR = 34.33, u = 1.0) to very lean limit (AFR = 171.65, u = 0.2). Amount of hydrogen injected in one cycle is approximately 22 mg/cycle with injection pulse duration of 4.4 ms. Engine speed was considered 3000 rpm for the evaluation of AFR effect on the engine performance. Fig. 13 shows the variation of indicated efficiency with injection timing with respect to changes in AFR. It can be clearly seen that for indicated efficiency increases with increases of AFR, however, the maximum indicated efficiency obtained at AFR = 85.825 (u = 0.4). The indicated efficiency slightly increases with advances of injection timing towards TDC until certain position then decreases sharply except AFR = 85.825 (u = 0.4) which is not effective due to the unstable engine operation especially the occurrence of interaction between the injection and spark timings. The spark timing of this study is considered at 95 BTDC. The rate indicated efficiency drop is higher for the richer mixtures (lower AFR) than the lean mixture. This leads to more narrow range of injection timing that can be controlled for rich mixtures. Optimum injection timing found to be 60°
Fig. 13. Variation of indicated efficiency with injection timing for various air fuel ratios.
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BTDC for stoichiometric condition (u = 1.0) which gives the indicated efficiency of 39.33%, however, optimum injection timing was obtained 10° BTDC for lean condition (u = 0.2). The indicated efficiency increases continuously with decreases of injection timing for AFR = 85.825. Fig. 14 depicts the indicated specific fuel consumption with the injection timing for various AFR. It is seen from the figure that the ISFC decreases with increases of AFR from rich conditions to lean except AFR = 85.825 (u = 0.4). It can be also seen that the ISFC decreases with advances of injection timing towards TDC until the certain position for all AFR and sharply increases except AFR = 85.825, which is undesirable. It can be found that the rapid increases of ISFC for rich conditions after the optimum injection timing. Lowest value of ISFC was occurred 68.3 g/kW h for AFR = 85.825 at 20° BTDC. For stoichiometric conditions, the minimum value of ISFC found to be 76.313 g/kW h at 60° BTDC. The ISFC increase sharply after occurs the lowest value. This indicates that ISFC is very critical for the injection timing at rich operation conditions. Fig. 15 shows the variation of power with injection timing with respect to changes the AFR. It is clearly observed that the power increases with the decreases of AFR i.e. the lean condition (u = 0.2) to rich conditions (u = 1.0) for all cases. Apparently, power increases slightly with advances of injection timing towards TDC until certain level then decreases sharply except the lean mixtures. Optimum injection timing strongly depends on the AFR conditions. The maximum power found to be 89.38 kW for rich mixture condition (u = 1.0) at injection timing of 60° BTDC while it was 34.3 kW for u = 0.4 at injection
Fig. 14. Variation of indicated specific fuel consumption with injection timing for various air fuel ratios.
Fig. 15. Variation of power with injection timing for various air fuel ratios.
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timing of 20° BTDC. It is observed that rate of change rapidly decreases for rich conditions due to the interaction between the injection duration and the ignition timing. Fig. 16 shows that the effect of injection timing on the torque response for various AFR. It can be seen from the figure that the same trends was found like as the power response. The AFR are strongly related to the torque from rich conditions to lean. It can be seen that the toque increases with decreases of AFR i.e. torque decreases rich mixtures to lean mixtures. The torque slightly increases with advances of injection timing towards TDC until certain level and then decreases rapidly except the lean conditions due to interaction between the injection duration and ignition timing. The maximum torque found to be 284.5 N m at 60° BTDC for u = 1.0 and while it found to be 109 N m at 10° BTDC for u = 0.4.
4.4. Engine speed influence on injection timing In the present model, hydrogen was injected into the cylinder within a timing range started just before IVC (96° BTDC) until TDC (0°). AFR was varied. Amount of hydrogen injected in one cycle is approximately 22 mg/cycle with injection pulse duration of 4.4 ms. Engine speed was varied from 2000 rpm to 6000 rpm. Stoichiometric condition was fixed throughout the investigation.
Fig. 16. Variation of torque output with injection timing for various air fuel ratios.
Fig. 17. Variation of indicated efficiency with injection timing for various engine speeds.
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Fig. 17 shows the variation of indicated thermal efficiency with the injection timing for the changes of engine speed. It can be seen that the indicated efficiency increases with decreases of engine speed. From the acquired results, indicated efficiency increases slightly with advances of injection timing towards TDC for all engine speed range. It is also seen that the slightly increase of indicated efficiency until about 30° BTDC for 2000 rpm then it drops down. The rate of change in indicated efficiency is higher for higher speed and drop occurs early in higher speeds. For very high speeds, the drop happens earlier due to the early interaction between the injection duration and ignition timing. Optimum injection timing under speeds from 2000 rpm to 5000 rpm was in the range (40–80°) BTDC while the optimum injection timing for 6000 rpm was 100° BTDC. Obviously, engine speed has a strong contribution in specifying the optimum injection timing. The very limited acceptable injection timing range occurs for high speeds. The selection of the proper injection timing is crucial not only for performance aspects, but also for stable operation. However, one should keep in mind that this situation, described currently, is for stoichiometric condition. It was extensively emphasized by related studies that stable stoichiometric operation is not simple in hydrogen engines and it is accompanied by lot of difficulties. So, with higher AFR best situation is expected. The variation of engine speed on the indicated efficiency is shown in Fig. 18 for stoichiometric operation and injection timing of 100° BTDC. It can be seen that the maximum indicated efficiency is 38.55% corresponding to engine speed 2500 rpm. This variation of indicated efficiency is primarily due to the variation of the volumetric efficiency.
Fig. 18. Effect of engine speed on indicated efficiency.
Fig. 19. Variation of ISFC with injection timing for various engine speeds.
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Fig. 19 shows the influence of injection timing on ISFC for different engine speeds. Lower engine speeds operation consumes smaller amounts of hydrogen as well as permits wider range for injection timing. The inverse is true for higher speeds where very limited range is available for injection timing. For 2000 rpm, the fuel consumption rates are acceptable throughout the studied range with injection timing of 60° BTDC being the optimum. At injection timing of 100° BTDC, minimum hydrogen consumed at 6000 rpm. Fig. 20 illustrates the variation of power with injection timing with respect to changes the engine speed. It can be seen that the power gained increases with increases of engine speed except 6000 rpm case. However, this happens due to the interaction between injection duration and ignition timing. So, it does not represent the normal situation. This occurs at injection timing in the vicinity of TDC. The maximum power of 123 kW was gained at injection timing of 100° BTDC for 5000 rpm, while the optimum injection timing that gives at 2000 rpm was 40° BTDC and maximum power of 59 kW. The power shows a maximum at engine speed 5000 rpm. It is also observed that the power gained decreases at 6000 rpm due to the increase in the friction losses. The variation of engine speed on the power gained is shown in Fig. 21 for stoichiometric operation and injection timing of 100° BTDC. From the acquired results, the power increases slightly with advances of injection timing towards TDC for all engine speed range. It is also seen that the slightly increase of power until about 30° BTDC for 2000 rpm then it drops down.
Fig. 20. Variation of power output with injection timing for various engine speeds.
Fig. 21. Effect of engine speed on power.
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Fig. 22. Variation of torque output with injection timing for various engine speeds.
The rate of change in power is higher for higher speed and drop occurs early in higher speeds. For very high speeds, the drop happens earlier due to the early interaction between the injection duration and ignition timing and friction losses. Fig. 22 shows the trends of torque with injection timing with the interaction of engine speed effect. Higher torques is produced at lower speed with extra advantages of more acceptable operation range of injection timing. The severe drop with high speed introduces a challenge for injection timing optimization. Based on torque measure, the optimum injection timing throughout the studied speeds, ranged from 40° BTDC at 2000 rpm until 100° BTDC at 6000 rpm. This extended range imposes more control difficulties. However, compromise solutions can be applied. As a whole, there is optimum injection timing that gives the maximum efficiency, maximum power and torque and minimum desired indicated specific fuel consumption. This optimum injection timing strongly depends on the air fuel ratio and engine speed. Shorter injection duration is required at lean conditions compared to rich conditions. Long injection duration can interact with spark timing which is highly undesirable because of it causes the unstable operation. Therefore, short injection duration is reflected in more extended acceptable injection range. Although, spark timing is restricted with injection timing, the stable operation can be obtained in wide range of engine speed as long as spark timing is adequately selected. 5. Conclusion A computational model was developed for 4-cylinder direct injection hydrogen fueled engine. The influence of air fuel ratio and engine speed with injection timing was investigated. The main results are summarized as follows: (i) At very lean conditions with low engine speeds, acceptable BMEP can be reached, while it is unacceptable for higher speeds. Lean operation leads to small values of BMEP compared with rich conditions. (ii) Maximum brake thermal efficiency can be reached at mixture composition in the range of (u = 0.9–0.7) and it decreases dramatically at leaner conditions. (iii) The desired minimum BSFC occurs within a mixture composition range of (u = 0.7–0.9). The operation with very lean condition (u < 0.2) and high engine speeds (>4500) consumes unacceptable amounts of fuel. (iv) Higher volumetric efficiency emphasizes that direct injection of hydrogen is a strong candidate solution to solve the problem of the low volumetric efficiencies of hydrogen engine. (v) Maximum brake torque speed for hydrogen engine occurs at lower speed compared with gasoline engines. MBT values are accepted. (vi) AFR has strong impact on the injection timing. Adding more hydrogen to the mixture (ascent toward richer mixtures) retards optimum injection timing from TDC timing. (vii) The engine performance is strongly depends on the engine speed. The engine speed 2500 rpm gives the maximum indicated efficiency. (viii) Optimum injection timing depends also strongly on engine speed. Lower speeds advances optimum injection timing toward TDC timing. (ix) As a compromise, injection timing of 60° BTDC can be considered as optimum for the present engine. However, this is for constant injection timing. The recommended operation is with different injection timing bases on AFR and engine speed.
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(x) Interaction between injection duration and spark timing is strongly undesired and can result in unstable operation. This is was apparent by the unaccepted performance parameters during interaction period. Avoidance of this interaction should take priority in specifying injection timing. (xi) Spark timing is another parameter that should be optimized for hydrogen engines, especially direct injection hydrogen engines. The optimum values of spark timing and injection timing are related strongly. The best way of optimizing injection timing is to fix spark timing on maximum brake torque timing.
Acknowledgement The authors would like to express their deep gratitude to Universiti Malaysia Pahang (UMP) for provided the laboratory facilities and financial support under project No. RDU090393. References [1] J.T. Lee, Y.Y. Kim, J.A. Caton, 2002. The development of a dual injection hydrogen fueled engine with high power and high efficiency, in: Proceedings of the 2002 Fall Technical Conference of the ASEM Internal Combustion Engine Division, p. 323–333. [2] F. William, S. Stockhausen et al. 2002. Ford P2000 Hydrogen Engine Design and Vehicle Development Program, SAE 2002-01-0240. [3] H. Eichlseder, T. Wallner, R. Freymann, J. Ringler, 2003. The Potential of Hydrogen Internal Combustion Engines in a Future Mobility Scenario, SAE Paper No. 2003012267. [4] Y.Y. Kim, J.T. Lee, G.H. Choi, An investigation on the cause of cycle variation in direct injection hydrogen fueled engines, Int. J. Hydrogen Energy 30 (2005) 69–76. [5] C.A. MacCarley, W.D. Van Vorst, Electronic fuel injection techniques for hydrogen energy, Int. J. Hydrogen Energy 5 (1980) 179–203. [6] J.T. Lee, Y.Y. Kim, C.W. Lee, J.A. Caton, An investigation of a cause of backfire and its control due to crevice volumes in a hydrogen fueled engine, Trans ASME 123 (2001) 204–210. [7] Y. Nakagawa, M. Nakai, K. Hamai, A study of the relationship between cycle-to-cycle variations of combustion and heat release delay in a spark-ignited engine, JSME 25 (1982) 54–60. [8] J.M. Kim, Y.T. Kim, S.Y. Lee, J.T. Lee, 1995. Performance Characteristics of Hydrogen Fueled Engine with the Direct Injection and Spark Ignition System, SAE Paper No. 952498. [9] K.S. Varde, G.A. Frame, Development of a high-pressure hydrogen injection for SI engine and results of engine behavior, Int. J. Hydrogen Energy 10 (11) (1985) 743–748. [10] W.F. Stockhausen, R.J. Natkin, D.M. Kabat, L. Reams, X. Tang, S. Hashemi, S.J. Szwabowski, V.P. Zanardelli, 2002. Ford P2000 Hydrogen Engine Design and Vehicle Development Program, SAE Paper No. 2002-01-0240. [11] E. Kahraman, C. Ozcanlı, B. Ozerdem, An experimental study on performance and emission characteristics of a hydrogen fuelled spark ignition engine, Int. J. Hydrogen Energy 32 (2007) 2066–2072. [12] X. Tang, D.M. Kabat, R.J. Natkin, W.F. Stockhausen, J. Heffel, 2002. Ford P2000 Hydrogen Engine Dynamometer Development, SAE Paper No. 2002-010242. [13] T. Tsujimura, A. Mikami, N. Achiha, 2003. A Study of Direct Injection Diesel Engine Fueled with Hydrogen, SAE Paper No. 2003-01-0761. [14] H. Rottengruber, M. Berckmüller, G. Elsässer, N. Brehm, C. Schwarz, 2004. Direct-injection Hydrogen SI-engine Operation Strategy and Power Density Potentials, SAE Paper No. 2004-01-2927. [15] A. Mohammadi, M. Shioji, Y. Nakai, W. Ishikura, E. Tabo, Performance and combustion characteristics of a direct injection SI hydrogen engine, Int. J. Hydrogen Energy 32 (2007) 296–304. [16] R. Sierens, S. Verhelst, S. Verstraeten, 2005. An overview of hydrogen fuelled internal combustion engines, in: Proc. Int. Hydrogen Energy Congress and Exhibition IHEC 2005, Istanbul, Turkey, 13–15 July 2005. [17] Y.Y. Kim, J.T. Lee, J.A. Caton, The development of a dual-Injection hydrogen-fueled engine with high power and high efficiency, J. Eng. Gas Turbines and Power, ASME 128 (2006) 203–212. [18] C.M. White, R.R. Steeper, A.E. Lutz, The hydrogen-fueled internal combustion engine: a technical review, Int J. Hydrogen Energy 31 (2006) 1292–1305. [19] J.B. Heywood, Internal Combustion Engine Fundamentals, first ed., McGraw-Hill, London, 1988. pp. 1–930, ISBN-10: 007028637X. [20] C.R. Ferguson, A.T. Kirkpatrick, International Combustion Engines: Applied Thermosciences, second ed., John Wiley and Sons, Inc., New York, 2001. pp. 1–384, ISBN-10: 0471356174. [21] W.W. Pulkrabek, Engineering Fundamentals of the Internal Combustion Engines, second ed., Prentice Hall, New York, 2003. ISBN: 9780131405707. [22] C.D. Rakopoulos, D.C. Kyritsis, Comparative second law analysis of internal combustion engine operation for methane, methanol and dodecane fuels, Energy 26 (7) (2001) 705–722. [23] C.D. Rakopopoulos, M.A. Scott, D.C. Kyritsis, E.G. Giakoumis, Availability analysis of hydrogen/natural gas blends combustion in internal combustion engines, Energy 33 (2) (2008) 248–255.
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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine M.M. Rahman ⇑, Mohammed Kamil, Rosli A. Bakar Automotive Engineering Centre, Faculty of Mechanical Engineering, Universiti Malaysia Pahang Tun Abdul Razak Highway, 26300 Gambang, Kuantan, Pahang, Malaysia
a r t i c l e
i n f o
Article history: Received 7 November 2009 Received in revised form 4 October 2010 Accepted 9 October 2010 Available online 15 October 2010 Keywords: Direct injection Injection timing Air fuel ratio Speed Hydrogen fuel
a b s t r a c t This paper presents the engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine. The 4-cylinder direct injection hydrogen engine model was developed utilizing the GT-Power commercial software. This model employed one dimensional gas dynamics to represent the flow and heat transfer in the components of engine model. Sequential pulse injectors are adopted to inject hydrogen gas fuel within the compression stroke. Injection timing was varied from 110° before top dead center (BTDC) until top dead center (TDC) timing. Engine speed was varied from 2000 rpm to 6000 rpm, while the equivalence ratio was varied from 0.2 to 1.0. The validation was performed with the existing previous experimental results. The negative effects of the interaction between ignition timing and injection duration was highlighted and clarified. The results showed that optimum injection timing and engine performance are related strongly to the air fuel ratio and engine speed. The acquired results show that the air fuel ratio and engine speed are strongly influence on the optimum injection timing and engine performance. It can be seen that the indicated efficiency increases with increases of AFR while decreases of engine speed. The power and torque increases with the decreases of AFR and engine speed. The indicated specific fuel consumption (ISFC) decreases with increases of AFR from rich conditions to lean while decreases of engine speed. The injection timing of 60° BTDC was the overall optimum injection timing with a compromise. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction With increasing concern about the energy shortage and environmental protection, research on improving engine fuel economy, hydrogen fueled engine is being developed into a hydrogen fueled engine with manifold injection, direct injection or duel injection according to the fuel supply method [1–4]. Of course, the hydrogen fueled engine with direct injection can fundamentally keep backfires from occurring so it can be utilized as a high powered hydrogen power system if the reliability of high pressure direct injection valve is secured [5,6]. Hydrogen gas is characterized by a rapid combustion speed, wide combustible limit and low minimum ignition energy. Such characteristics play a role to decrease engine cycle variation for the safety of combustion. However, it is frequently observed that the values of cycle variation for hydrogen-fueled engines with direct injection are higher than those of hydrogen-fueled engines with manifold injection or those of gasoline engines, due to a decrease in the mixing period by direct injection in the process of compressing hydrogen gas [7–9]. In today’s modern world, where new technologies are introduced every day, transportation’s energy use is increasing rapidly. ⇑ Corresponding author. Tel.: +60 9 4242246; fax: +60 9 4242202. E-mail address: mustafi[email protected] (M.M. Rahman). 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.10.006
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Fossil fuel particularly petroleum fuel is the major contributor to energy production and the primary fuel for transportation. Rapidly depleting reserves of petroleum and decreasing air quality raise questions about the future. As world awareness about environment protection increases so does the search for alternative to petroleum fuels. Hydrogen can be used as a clean alternative to petroleum fuels and its use as a vehicle fuel is promising in the effects to establish environmentally friendly mobility systems. So far, extensive studies investigated hydrogen fueled internal combustion engines (H2ICE) with external mixture formation fuel delivery system [10,11]. However, the operation of these engines subjected to abnormal combustion, such as pre-ignition, backfire and knocking. Moreover, the power outputs of these hydrogen engines are about 30% less than those of gasoline engines [12]. Therefore the premixed-charge spark ignition engines fueled with hydrogen can be used for significantly limited operation range [13]. It is a common conclusion achieved by many researchers that abnormal combustion can be controlled by direct injection (DI) of hydrogen in-side the cylinder [13–15]. Direct injection H2ICE requires optimized operation strategies that enable the availability of high power output as well as the abolition of critical exhaust gas emission in combination with high efficiencies. Several parameters need to be optimized. Optimization of spark timing, valve timing, combustion chamber geometry, injection parameters such as injection timing, injection duration, injection pressure and nozzle hole numbers/arrangement, swirls intensity, etc. are indeed important to achieve an engine performance level competitive to that in the modern direct-injection diesel engines [15]. Injection timing plays a critical role in the phasing of the combustion, and hence the emissions and torque production. Therefore, extensive number of studies indicated the significance of optimization for ignition timing [15–17]. White et al. [18] suggested that late injection can minimize the residence time that a combustible mixture is exposed to in-cylinder hot spots and allow for improved mixing of the intake air with the residual gases. This selection can control pre-ignition problem. The main challenge for selecting the proper ignition timing that is in-cylinder injection requires hydrogen–air mixing in a very short time. For early injection (i.e., coincident with inlet valve closure (IVC)), maximum available mixing times range from approximately 20 ms to 4 ms across the speed range 1000–5000 rpm. In practice, to avoid pre-ignition, start of injection (SOI) is retarded with respect to IVC and mixing times are further reduced. Regarding the behavior of the performance characteristic with ignition timing, there are several contradictories in the literature. Eichlseder et al. [3] found that at low loads (or low equivalence ratio (h)), indicated efficiency (IE) increases with retard of SOI. The increase was shown to be due to the decrease in the compression work caused by differences in mixture gas properties and charge mass with retarded SOI. The authors also found their study at high loads, IE first increases and then decreases with retard of SOI. The reversing trend is assumed to be a consequence of an unfavorable mixture formation. However, Kim et al. [17] reported the contradictory results to Eichlseder et al. [3] results, where they find that, for both low and high loads, indicated efficiency decreases monotonically with retard of SOI. These contradictory findings may be a result of differences in mixture formation [18]. Much effort has been devoted to optimize the injection timing which is ranging from IVC until the top dead center (i.e. within the compression stroke). However, Mohammadi et al. [15] optimized the injection timing for three ranges: during the intake stroke, where they prevented backfire. However, thermal efficiency and output power are limited by knock due to reduction in volumetric efficiency; at compression stroke, where they prevented knock and gives an increase in thermal efficiency and maximum output power; and at later stage of compression stroke, where they achieved thermal efficiency higher than 38.9% and brake mean effective pressure 0.95 MPa. This study attempts to optimize injection timing that gives the best performance of a 4-cylinders direct injection. The 4-cylinder direct injection hydrogen fueled engine model is developed for this purpose. The effects of air fuel ratio, engine speed on engine performance and the optimum injection timing on the engine performance such as indicated efficiency, indicated specific fuel consumption, power and torque for direct injection hydrogen fueled engine. 2. Engine modeling 2.1. Engine performance parameters The brake mean effective pressure (BMEP) can be defined as the ratio of the brake work per cycle Wb to the cylinder volume displaced per cycle Vd, and it can be expressed as [19]:
BMEP ¼
Wb Vd
ð1Þ
Eq. (1) can be rewrite for the four stroke engine as:
BMEP ¼
2Pb NV d
where Pb is the brake power, and N is the rotational speed.
ð2Þ
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Brake efficiency (gb) can be defined as the ratio of the brake power Pb to the engine fuel energy as:
P
gb ¼ _ b mf ðLHVÞ
ð3Þ
_ f is the fuel mass flow rate and LHV is the lower heating value of hydrogen. where m _ f per unit brake power output and can be exThe brake specific fuel consumption (BSFC) represents the fuel flow rate m pressed as [19]:
BSFC ¼
_f m Pb
ð4Þ
The volumetric efficiency (gv) of the engine defines as the mass of air supplied through the intake valve during the intake _ a Þ by comparison with a reference mass, which is that mass required to perfectly fill the swept volume under period ðm the prevailing atmospheric conditions, and can be expressed as:
gv ¼
_a m qai V d
ð5Þ
where qai is the inlet air density. The burning rate (Xb) of combustion process was modeled using Wiebe function, which can be expressed as:
" nþ1 # h hi X b ¼ 1 exp a Dh
ð6Þ
where h is the crank angle, hi is the start of combustion, Dh is the combustion period and a and n are adjustable constants. Furthermore, the heat transfer in-side the cylinder was modeled using a formula which is closely emulates the classical Woschni correlation. Based on this correlation, the heat transfer coefficient hc can be expressed as:
hc ¼ 3:26B0:2 p0:8 T 0:55 w0:8
ð7Þ
where B is the bore in meters, p is the pressure in kPa, T is temperature in K and w is the average cylinder gas velocity in m/s. The hydrogen gas fuel was injected directly in-side the cylinders using the four sequential pulse fuel injectors. The AFR was imposed for the injectors. Then, the injected fuel rate was estimated using [20]:
3 _ delivery ¼ gv qref NV d ðFARÞ m 2ðPwÞ
ð8Þ
_ delivery is the injector delivery rate (g/s), qref the reference density used to calculate volumetric efficiency (kg/m3), FAR where m is the fuel air ratio and Pw is the injection duration (°CA). The 4-cylinders were then connected together through the engine part which translates the force acting on each piston into the crankshaft (brake) power. In the engine model: engine type was 4-stroke type; the number of cylinders is set to four; the configuration in-line had been chosen; and simulation with prescribed engine speed was specified rather than engine load. Furthermore, engine friction model was imposed to model friction in the engine. The friction mean effective pressure (FMEP) was modeled based on [21]: 2
FMEP ¼ 0:4 þ ð0:005 P max Þ þ ð0:09 Speedmp Þ þ ð0:0009 Speedmp Þ
ð9Þ
where Speedmp represents the mean piston speed and Pmax is the peak cylinder pressure. 2.2. Engine modeling The engine model for an in-line 4-cylinder direct injection engine was developed for this study. Engine specifications for the base engine are tabulated in Table 1. The specific values of input parameters including the AFR, engine speed, and Table 1 Engine specification. Engine parameter
Value
Unit
Bore Stroke Connecting rod length Piston pin offset Total displacement Compression ratio Inlet valve close, IVC Exhaust valve open, EVO Inlet valve open, IVO Exhaust valve close, EVC
100 100 220 1.00 3142 9.5 96 125 351 398
mm mm mm mm cm3 °CA °CA °CA °CA
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injection timing were defined in the model. The boundary condition of the intake air was defined first in the entrance of the engine. The air enters through a bell-mouth orifice to the pipe. The discharge coefficients of the bell-mouth orifice were set to 1 to ensure the smooth transition as in the real engine. The pipe of bell-mouth orifice with 0.07 m of diameter and 0.1 m of length are used in this model. The pipe connects in the intake to the air cleaner with 0.16 m of diameter and 0.25 m of length was modeled. The air cleaner pipe identical to the bell-mouth orifice connects to the manifold. A log style manifold was developed from a series of pipes and flow-splits. The intake system of the present study model is shown in Fig. 1. The total volume for each flow-split was 256 cm3. The flow-splits compose from an intake and two discharges. The intake draws air from the preceding flow-split. One discharge supplies air to adjacent intake runner and the other supplies air to the next flow-split. The last discharge pipe was closed with a cup to prevent any flow through it because there is no more flow-split. The flow-splits are connected with each other via pipes with 0.09 m diameter and 0.92 m length. The junctions between the flow-splits and the intake runners were modeled with bell-mouth orifices. The discharge coefficients were also set to 1 to assure smooth transition, because in most manifolds the transition from the manifold to the runners is very smooth. The intake runners for the 4-cylinders were modeled as four identical pipes with .04 m diameter and 0.1 m length. Finally the
Fig. 1. Intake system model.
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intake runners were linked to the intake ports which were modeled as pipes with 0.04 m diameter and 0.08 length. The air mass flow rate in e intake port was used for hydrogen flow rate based on the imposed AFR. The second major part of the engine model is the powertrain model which is shown in Fig. 2. In the powertrain, the induced air passes through the intake cam-driven type valves with 45.5 mm of diameter to the cylinders. The valve lash (mechanical clearance between the cam lobe and the valve stem) was set to 0.1 mm. The overall temperature of the head, piston and cylinder for the engine parts are listed in Table 2. The temperature of the piston is higher than the cylinder head and cylinder block wall temperature because this part is not directly cooled by the cooling liquid or oil. The last major part in the present model is the exhaust system which is shown in Fig. 3. The exhaust runners were modeled as rounded pipes with 0.03 m inlet diameter, and 80° bending angle for runners 1 and 4; and 40° bending angle of runners 2 and 3. Runners 1 and 4, and runners 2 and 3 are connected before enter in a flow-split with 169.646 cm3 volume. Conservation of momentum is solved in 3-dimentional flow-splits even though the flow in GT-Power is otherwise based on a one-dimensional version of the Navier–Stokes equation. Finally a pipe with 0.06 m diameter and 0.15 m length connects the last flow-split to the environment. Exhaust system walls temperature was calculated using a model embodied in each pipe and flow-split. Table 3 are listed the parameters used in the exhaust environment of the model.
Fig. 2. Powertrain model.
M.M. Rahman et al. / Simulation Modelling Practice and Theory 19 (2011) 734–751 Table 2 Temperature of the mail engine parts. Components
Temperature (K)
Cylinder head Cylinder block wall Piston
550 450 590
Fig. 3. Exhaust system model.
Table 3 Parameters used in the exhaust environment. Parameters
Value
Unit
External environment temperature Heat transfer coefficient Radiative temperature Wall layer material Layer thickness Emissivity
320 15 320 Steel 3 0.8
K W/m2 K K mm
739
740
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3. Model validation The experimental results obtained from Mohammadi et al. [15] were used for the purpose of validation in this study. Engine specifications of Mohammadi et al. [15] and present single cylinder direct injection engine model are listed in Table 4. For the purpose of validation, single cylinder direct injection engine model converted to 4-cylinder direct injection model. Fig. 4 shows the single cylinder direct injection engine model. Engine speed and AFR were fixed at 1200 rpm and 57.216 (u = 0.6) respectively in this comparison. Injection timing was varied from 130 °CA BTDC until 70 °CA BTDC to be coincident with Mohammadi et al. [15]. The correlation of brake thermal efficiency of the baseline model and experimental results obtained from Mohammadi et al. [3] is shown in Fig. 5. It can be seen that the brake thermal efficiency are good match with the experimental results. Only small deviation was obtained due to the difference between the engine operation conditions that are not mentioned in Mohammadi et al. [15]. However, considerable coincident between the single cylinder model and experimental results can be recognized in spite of the mentioned model differences. 4. Results and discussion A lean mixture is one in which the amount of fuel is less than stoichiometric mixture. This leads to fairly easy to get an engine start. Furthermore, the combustion reaction will be more complete. Additionally, the final combustion temperature is lower reducing the amount of pollutants. The air–fuel ratio (AFR) was varied from rich limit (AFR = 27.464:1 based on mass where the equivalence ratio (u = 1.2) to a very lean limit (AFR = 171.65 where (u = 0.2) and engine speed varied from 2500 rpm to 4500 rpm. BMEP is a good parameter for comparing engines with regard to design due to its independent on the engine size and speed. The results in the following section show the engine performance behavior with injection timing for each condition under investigation. In order to check the validity and accuracy of the present model, comparison with published experimental results in the literature. The effect of AFR with injection timing on the engine performance parameters including efficiency, brake specific fuel consumption, power, and torque were discussed. The effects of engine speed with injection timing on the engine performances are also investigated. 4.1. Variation in air fuel ratio on engine performance Fig. 6 shows the effect of air–fuel ratio on the brake mean effective pressure. It can be seen that BMEP decreases with increases of AFR and speed. This decrease happens with two different behaviors. For rich mixtures (low AFR), BMEF decreases almost linearly, then BMEP falls with a non-linear behavior. Higher linear range can be recognized for higher speeds. For 4500 rpm, the linear range is continuing until AFR of 42.9125 (u = 0.8). The non-linear region becomes more predominant at lower speeds and the linear region cannot be specified there. The total drop of BMEP within the studied range of AFR was 8.08 bar for 4500 rpm compared with 10.91 bar for 2500 rpm. At lean operating conditions (AFR = 171.65, (u = 0.2 the engine gives maximum power (BMEP = 1.635 bar) at lower speed 2500 rpm) compared with the power (BMEP = 0.24 bar) at speed 4500 rpm. Fig. 7 shows the variation of the brake thermal efficiency with the air fuel ratio for the selected speeds. Brake power is the useful part as a percentage from the intake fuel energy. The fuel energy is also covered the friction losses and heat losses (heat loss to surroundings, exhaust, enthalpy and coolant load). Therefore lower values of gb can be seen in Fig. 7. It can be observed that the brake thermal efficiency is increases nearby the richest condition (AFR ffi 35) and then decreases with increases of AFR and speed. The operation within a range of AFR from 38.144 to 42.91250 (u = 0.9–0.8) gives the maximum values for gb for all speeds. Maximum gb of 35.4% at speed 2500 rpm can be seen compared with 26.3% at speed 4500 rpm. Unaccepted efficiency gb of 3.7% can be seen at very lean conditions with AFR of 171.65 (u = 0.2 for speed of 4500 rpm while a value of 23.86% was recorded at the same conditions with speed of 2500 rpm. Clearly, rotational speed has a major effect in the behavior of gb with AFR. Higher speeds lead to higher friction losses. Table 4 Specifications of the engines models.
*
Engine parameter
Mohammadi et al. (2007)
Present model
Unit
Bore Stroke Connecting rod length Piston pin offset Total displacement Compression ratio Inlet valve close, IVC Exhaust valve open, EVO Inlet valve open, IVO Exhaust valve close, EVC
102 105 NA* NA 857 11.5 580 130 360 380
102 105 220 1.00 858 11.5 624° 125° 351° 398°
Mm Mm Mm Mm cm3
NA = not available.
ATDC ATDC ATDC ATDC
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Fig. 4. Single cylinder direct injection model.
Fig. 5. Comparison between published experimental results [15] and present single cylinder direct injection engine model based on brake efficiency.
Fig. 6. Variation of brake mean effective pressure with air fuel ratio for various engine speeds.
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Fig. 7. Variation of brake thermal efficiency with air fuel ratio.
Fig. 8. Variation of brake specific fuel consumption with air fuel ratio.
Fig. 8 depicts the behavior of the brake specific fuel consumption BSFC with AFR. It is easy to perceive from the figure that there is an optimum minimum value of BSFC occurred within a range of AFR from 38.144 (u = 0.9) to 49.0428 (u = 0.7) for the selected range of speed. At very lean conditions, higher fuel consumption can be noticed. After AFR of 114.433 (u = 0.3) the BSFC rises up rapidly, especially for high speeds. At very lean conditions with AFR of 171.65 (u = 0.2), a BSFC of 125.87 g/kW h was observed for the speed of 2500 rpm; while it was 809 g/kW h for 4500 rpm. Fig. 9 shows how the AFR can affect the maximum temperature in-side the cylinder. In general, lower temperatures are required due to the reduction of pollutants. It is clearly demonstrated how the increase in the AFR can decrease the maximum cylinder temperature with a severe steeped curve. But for rich mixtures, the maximum cylinder temperature drops down with a linear manner. The effect of the engine speed on the relationship between maximum cylinder temperatures with AFR seems to be minor. At rich operating conditions (AFR = 27.464, u = 1.2) and a speed of 3000 rpm, a maximum cylinder temperature of 2767 K was recorded. This temperature dropped down to 1345 K at AFR of 171.65 (u = 0.2). This lower temperature inhibits the formation of NOx pollutants. In fact this feature is one of the major motivations toward hydrogen fuel.
4.2. Variation in speed on engine performance Fig. 10 shows the variation of the volumetric efficiency with the engine speed for different air equivalence ratio. Leaner mixture gives the higher volumetric efficiency. The maximum volumetric efficiency was observed 85% at lean conditions
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Fig. 9. Variation of maximum cylinder temperature with air fuel ratio.
Fig. 10. Effect of engine speed against volumetric efficiency for different equivalence ratio.
with AFR = 171.65 (u = 0.2) and 2500 rpm whereas volumetric efficiency decreases at high speed due to the frictional losses. In the first part of the curve, higher speed lead to higher volumetric efficiency because of the high speed gives high vacuum at the intake port and consequent larger air flow rate that goes in-side the cylinder. Fig. 11 shows the variation of the power with engine speed. Greater power can be generated by increasing displacement, brake mean effective pressure and engine speed. The engine mass increases with increases of displacement and also takes up space, both are contrary to automobile design trends. For this reason, most modern engines are smaller but run at higher speeds and often turbocharged or supercharged to increase BMEP. Modern gasoline automobile engines usually have brake power output per displacement of 40–80 kW/L [21]. Clearly, power increases with increases of engine speed at certain level. The power decreases at higher engine speed after certain level due to the friction losses and becomes the dominant factor at very high speed. AFR has a strong effect in specifying the speed that gives maximum power. At AFR of 171.65 (u = 0.2), a maximum power obtained of 10.7 kW at 2500 rpm while AFR of 42.912 (u = 0.8), a maximum power of 94 kW obtained at 4500 rpm; and at AFR 27.464 (u = 1.2), a maximum power of 104.3 kW at 3500 rpm. But, for many gasoline engines, maximum power occurs at about 6000–7000 rpm. In fact this is another desired feature for hydrogen engines. The reported power at lean mixture is low and unacceptable. Fig. 12 illustrates the influence of variable engine speed on the torque. For all the range of studies AFR: at low speed, torque increases as engine speed increases. As engine speed increases further, torque reaches a maximum and then decreases as
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Fig. 11. Effect of engine speed against power.
Fig. 12. Variation of torque with engine speed.
shown in Fig. 12. The point of maximum torque is called maximum brake torque speed (MBT). A major goal in the design of a modern automobiles engine is to flatten the torque vs. speed curve, and to have high torque at both high and low speed. But, it is important to clarify here, that toque vs. speed curve for hydrogen is flatten compared to gasoline. The BMTs for the present hydrogen engine occurred at 2500 rpm; and their values are: 178 N m at equivalence ratio of 0.6; and 294 N m at 2500 rpm with stoichiometric operation. Hydrogen has long since been attempted as a fuel for the internal combustion engine. In general, it is desirable to have maximum volumetric efficiency for engine. The importance of efficiency is more critical for hydrogen engines because of the hydrogen fuel displaces large amount of incoming air due to its low density (0.0824 kg/m3 at 25 °C and 1 atm.). This reason reduces the efficiency to high extent. A stoichiometric mixture of hydrogen and air consists of approximately 30% hydrogen by volume, whereas a stoichiometric mixture of fully vaporized gasoline and air consists of approximately 2% gasoline by volume [18]. Therefore, the low efficiency for hydrogen engine is expected compared to gasoline engine works with same operating conditions and physical dimension. However, the higher efficiencies can be gained with direct injection of hydrogen, which can be shown in Fig. 7. The maximum value of efficiency for the selected range of speed was around 85%. At further higher engine speed beyond these values, the flow into the engine during at least part of the intake process becomes chocked. Once this condition occurs, further increases in engine speed decrease the flow rate significantly. Thus, the efficiency decreases sharply because of the higher speed is accompanied by some phenomenon that have negative influence on efficiency. These phenomenon include the charge heating in the manifold and higher friction flow losses which increase
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as the square of engine speed. Due to dissociation at high temperatures following combustion, molecular oxygen is present in the burned gases under stoichiometric conditions. Thus some additional fuel can be added and partially burned. This increases the temperature and the number of moles of the burned gases in the cylinder. These effects increases the pressure were given increase power and mean effective pressure [20]. The AFR for optimum fuel consumption at a given load depends on the details of chamber design (including compression ratio) and mixture preparation quality. It varies for a given chamber with the part of throttle load and speed range [20]. It is clearly seen (Fig. 8) that the higher fuel is consumed at higher speeds due to the greater friction losses that can occur at high speeds. The value BSFC at speed of 2500 rpm was doubled around two times at speed of 4000 rpm; however the same value was doubled around five times at speed of 4500 rpm. This is because of very lean operation conditions can lead to unstable combustion and more lost power due to a reduction in the volumetric heating value of the air/hydrogen mixture. Most modern gasoline automobiles have maximum torque per displacement in the range of 80 to 110 N m/L with some as high as 140 N m/L. The maximum torque obtained of 200–400 N m, usually at engine speed around 4000–6000 rpm (gasoline engines) [21]. Fig. 12 shows the torque of direct injection hydrogen-fueled engines with respect to variation in engine speed and air–fuel ratio. It is thought to be attributable to many factors such as: (i) the heterogeneity of air–fuel mixture may be increased at every cycle due to the decrease of the mixing period by direct injection into the cylinder in the early period of compression, (ii) the heterogeneity of air–fuel mixture may be also increased with decrease of penetration depth because of lightweight of hydrogen, and (iii) the combustion performance of the hydrogen–air mixture is lowered because direct injection hydrogen-fueled engines are configured by modifying only the fuel supply system without changing the shape of the combustion chamber of the gasoline engine. It is obvious that speed reduction increases mechanical losses. This disadvantage can be solved by supercharging. Supercharging also helps to cool off the cylinders. Hydrogen combustion converts two diatomic molecules to triatomic molecule [22,23]. Therefore, hydrocarbon combustion increases entropy, hence irreversibility. Since 90% of irreversibility comes from combustion process, second-law efficiency increases in favor of hydrogen [11]. Whilst experimental data are not available to verify these predictions, the authors are presented here to illustrate some of the insights that this type of simulation tool may provide to future engine systems designers.
4.3. Effects of air fuel ratio on injection timing In the present model, hydrogen was injected into the cylinder within a timing range started just before IVC (96° BTDC) until TDC (0°). AFR was varied from stoichiometric condition (AFR = 34.33, u = 1.0) to very lean limit (AFR = 171.65, u = 0.2). Amount of hydrogen injected in one cycle is approximately 22 mg/cycle with injection pulse duration of 4.4 ms. Engine speed was considered 3000 rpm for the evaluation of AFR effect on the engine performance. Fig. 13 shows the variation of indicated efficiency with injection timing with respect to changes in AFR. It can be clearly seen that for indicated efficiency increases with increases of AFR, however, the maximum indicated efficiency obtained at AFR = 85.825 (u = 0.4). The indicated efficiency slightly increases with advances of injection timing towards TDC until certain position then decreases sharply except AFR = 85.825 (u = 0.4) which is not effective due to the unstable engine operation especially the occurrence of interaction between the injection and spark timings. The spark timing of this study is considered at 95 BTDC. The rate indicated efficiency drop is higher for the richer mixtures (lower AFR) than the lean mixture. This leads to more narrow range of injection timing that can be controlled for rich mixtures. Optimum injection timing found to be 60°
Fig. 13. Variation of indicated efficiency with injection timing for various air fuel ratios.
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BTDC for stoichiometric condition (u = 1.0) which gives the indicated efficiency of 39.33%, however, optimum injection timing was obtained 10° BTDC for lean condition (u = 0.2). The indicated efficiency increases continuously with decreases of injection timing for AFR = 85.825. Fig. 14 depicts the indicated specific fuel consumption with the injection timing for various AFR. It is seen from the figure that the ISFC decreases with increases of AFR from rich conditions to lean except AFR = 85.825 (u = 0.4). It can be also seen that the ISFC decreases with advances of injection timing towards TDC until the certain position for all AFR and sharply increases except AFR = 85.825, which is undesirable. It can be found that the rapid increases of ISFC for rich conditions after the optimum injection timing. Lowest value of ISFC was occurred 68.3 g/kW h for AFR = 85.825 at 20° BTDC. For stoichiometric conditions, the minimum value of ISFC found to be 76.313 g/kW h at 60° BTDC. The ISFC increase sharply after occurs the lowest value. This indicates that ISFC is very critical for the injection timing at rich operation conditions. Fig. 15 shows the variation of power with injection timing with respect to changes the AFR. It is clearly observed that the power increases with the decreases of AFR i.e. the lean condition (u = 0.2) to rich conditions (u = 1.0) for all cases. Apparently, power increases slightly with advances of injection timing towards TDC until certain level then decreases sharply except the lean mixtures. Optimum injection timing strongly depends on the AFR conditions. The maximum power found to be 89.38 kW for rich mixture condition (u = 1.0) at injection timing of 60° BTDC while it was 34.3 kW for u = 0.4 at injection
Fig. 14. Variation of indicated specific fuel consumption with injection timing for various air fuel ratios.
Fig. 15. Variation of power with injection timing for various air fuel ratios.
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timing of 20° BTDC. It is observed that rate of change rapidly decreases for rich conditions due to the interaction between the injection duration and the ignition timing. Fig. 16 shows that the effect of injection timing on the torque response for various AFR. It can be seen from the figure that the same trends was found like as the power response. The AFR are strongly related to the torque from rich conditions to lean. It can be seen that the toque increases with decreases of AFR i.e. torque decreases rich mixtures to lean mixtures. The torque slightly increases with advances of injection timing towards TDC until certain level and then decreases rapidly except the lean conditions due to interaction between the injection duration and ignition timing. The maximum torque found to be 284.5 N m at 60° BTDC for u = 1.0 and while it found to be 109 N m at 10° BTDC for u = 0.4.
4.4. Engine speed influence on injection timing In the present model, hydrogen was injected into the cylinder within a timing range started just before IVC (96° BTDC) until TDC (0°). AFR was varied. Amount of hydrogen injected in one cycle is approximately 22 mg/cycle with injection pulse duration of 4.4 ms. Engine speed was varied from 2000 rpm to 6000 rpm. Stoichiometric condition was fixed throughout the investigation.
Fig. 16. Variation of torque output with injection timing for various air fuel ratios.
Fig. 17. Variation of indicated efficiency with injection timing for various engine speeds.
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Fig. 17 shows the variation of indicated thermal efficiency with the injection timing for the changes of engine speed. It can be seen that the indicated efficiency increases with decreases of engine speed. From the acquired results, indicated efficiency increases slightly with advances of injection timing towards TDC for all engine speed range. It is also seen that the slightly increase of indicated efficiency until about 30° BTDC for 2000 rpm then it drops down. The rate of change in indicated efficiency is higher for higher speed and drop occurs early in higher speeds. For very high speeds, the drop happens earlier due to the early interaction between the injection duration and ignition timing. Optimum injection timing under speeds from 2000 rpm to 5000 rpm was in the range (40–80°) BTDC while the optimum injection timing for 6000 rpm was 100° BTDC. Obviously, engine speed has a strong contribution in specifying the optimum injection timing. The very limited acceptable injection timing range occurs for high speeds. The selection of the proper injection timing is crucial not only for performance aspects, but also for stable operation. However, one should keep in mind that this situation, described currently, is for stoichiometric condition. It was extensively emphasized by related studies that stable stoichiometric operation is not simple in hydrogen engines and it is accompanied by lot of difficulties. So, with higher AFR best situation is expected. The variation of engine speed on the indicated efficiency is shown in Fig. 18 for stoichiometric operation and injection timing of 100° BTDC. It can be seen that the maximum indicated efficiency is 38.55% corresponding to engine speed 2500 rpm. This variation of indicated efficiency is primarily due to the variation of the volumetric efficiency.
Fig. 18. Effect of engine speed on indicated efficiency.
Fig. 19. Variation of ISFC with injection timing for various engine speeds.
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Fig. 19 shows the influence of injection timing on ISFC for different engine speeds. Lower engine speeds operation consumes smaller amounts of hydrogen as well as permits wider range for injection timing. The inverse is true for higher speeds where very limited range is available for injection timing. For 2000 rpm, the fuel consumption rates are acceptable throughout the studied range with injection timing of 60° BTDC being the optimum. At injection timing of 100° BTDC, minimum hydrogen consumed at 6000 rpm. Fig. 20 illustrates the variation of power with injection timing with respect to changes the engine speed. It can be seen that the power gained increases with increases of engine speed except 6000 rpm case. However, this happens due to the interaction between injection duration and ignition timing. So, it does not represent the normal situation. This occurs at injection timing in the vicinity of TDC. The maximum power of 123 kW was gained at injection timing of 100° BTDC for 5000 rpm, while the optimum injection timing that gives at 2000 rpm was 40° BTDC and maximum power of 59 kW. The power shows a maximum at engine speed 5000 rpm. It is also observed that the power gained decreases at 6000 rpm due to the increase in the friction losses. The variation of engine speed on the power gained is shown in Fig. 21 for stoichiometric operation and injection timing of 100° BTDC. From the acquired results, the power increases slightly with advances of injection timing towards TDC for all engine speed range. It is also seen that the slightly increase of power until about 30° BTDC for 2000 rpm then it drops down.
Fig. 20. Variation of power output with injection timing for various engine speeds.
Fig. 21. Effect of engine speed on power.
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Fig. 22. Variation of torque output with injection timing for various engine speeds.
The rate of change in power is higher for higher speed and drop occurs early in higher speeds. For very high speeds, the drop happens earlier due to the early interaction between the injection duration and ignition timing and friction losses. Fig. 22 shows the trends of torque with injection timing with the interaction of engine speed effect. Higher torques is produced at lower speed with extra advantages of more acceptable operation range of injection timing. The severe drop with high speed introduces a challenge for injection timing optimization. Based on torque measure, the optimum injection timing throughout the studied speeds, ranged from 40° BTDC at 2000 rpm until 100° BTDC at 6000 rpm. This extended range imposes more control difficulties. However, compromise solutions can be applied. As a whole, there is optimum injection timing that gives the maximum efficiency, maximum power and torque and minimum desired indicated specific fuel consumption. This optimum injection timing strongly depends on the air fuel ratio and engine speed. Shorter injection duration is required at lean conditions compared to rich conditions. Long injection duration can interact with spark timing which is highly undesirable because of it causes the unstable operation. Therefore, short injection duration is reflected in more extended acceptable injection range. Although, spark timing is restricted with injection timing, the stable operation can be obtained in wide range of engine speed as long as spark timing is adequately selected. 5. Conclusion A computational model was developed for 4-cylinder direct injection hydrogen fueled engine. The influence of air fuel ratio and engine speed with injection timing was investigated. The main results are summarized as follows: (i) At very lean conditions with low engine speeds, acceptable BMEP can be reached, while it is unacceptable for higher speeds. Lean operation leads to small values of BMEP compared with rich conditions. (ii) Maximum brake thermal efficiency can be reached at mixture composition in the range of (u = 0.9–0.7) and it decreases dramatically at leaner conditions. (iii) The desired minimum BSFC occurs within a mixture composition range of (u = 0.7–0.9). The operation with very lean condition (u < 0.2) and high engine speeds (>4500) consumes unacceptable amounts of fuel. (iv) Higher volumetric efficiency emphasizes that direct injection of hydrogen is a strong candidate solution to solve the problem of the low volumetric efficiencies of hydrogen engine. (v) Maximum brake torque speed for hydrogen engine occurs at lower speed compared with gasoline engines. MBT values are accepted. (vi) AFR has strong impact on the injection timing. Adding more hydrogen to the mixture (ascent toward richer mixtures) retards optimum injection timing from TDC timing. (vii) The engine performance is strongly depends on the engine speed. The engine speed 2500 rpm gives the maximum indicated efficiency. (viii) Optimum injection timing depends also strongly on engine speed. Lower speeds advances optimum injection timing toward TDC timing. (ix) As a compromise, injection timing of 60° BTDC can be considered as optimum for the present engine. However, this is for constant injection timing. The recommended operation is with different injection timing bases on AFR and engine speed.
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(x) Interaction between injection duration and spark timing is strongly undesired and can result in unstable operation. This is was apparent by the unaccepted performance parameters during interaction period. Avoidance of this interaction should take priority in specifying injection timing. (xi) Spark timing is another parameter that should be optimized for hydrogen engines, especially direct injection hydrogen engines. The optimum values of spark timing and injection timing are related strongly. The best way of optimizing injection timing is to fix spark timing on maximum brake torque timing.
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