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Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine
international journal of hydrogen energy xxx (xxxx) xxx
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Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine Ling-Zhi Bao, Bai-Gang Sun, Qing-He Luo*, Xi Wang, Qing-Yu Niu School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
highlights The traditional pressure correction method is not suitable for DI hydrogen engine. The polytropic index is sensitive to the concentration of hydrogen. Advancing injection of hydrogen increases the polytropic index. Average polytropic index of the DI hydrogen engine is approximately 1.32.
article info
abstract
Article history:
Hydrogen is regarded as a promising alternative fuel in the future. The direct-injection (DI)
Received 22 January 2020
hydrogen engine has been demonstrated to offer large power without the risk of abnormal
Received in revised form
combustion. For the engine test of combustion analysis, the piezoelectric transducer
23 February 2020
measures the dynamic cylinder pressure data rather than the absolute one. The traditional
Accepted 1 March 2020
method of absolute cylinder pressure correction is normally based on the polytropic index.
Available online xxx
This paper investigated the polytropic index effects by injection duration, start timing of injection and speed based on a 2.0 L direct-injection hydrogen engine. The experiments
Keywords:
found that, since the injection of large volume hydrogen leads to approximately 0.8 bar
Polytropic index
increase of cylinder pressure in the compression stroke, the traditional correct method is
Direct injection hydrogen engine
not suitable for the DI hydrogen engine. What’s more, the polytropic index drops from 2.2
Combustion analysis
to 1.22 with the changes of the crank angle and is sensitive to the concentration of the
Cylinder pressure correction
hydrogen. The study of the instantaneous polytropic index can not only be used to calculate the accurate heat release rate but also guide the research of the heat transfer of the DI hydrogen engine. The average polytropic index of 1.32 provides a new reference for the absolute cylinder pressure correction of the DI hydrogen engine. © 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Currently, the growing consumption of foil fuels has accelerated the energy crisis. It is necessary to implement alternative
energy sources[1]. Hydrogen, as a prominent selection for the renewable and sustainable energy carrier in the future, has a wide range of sources [2,3]. There are mainly two options to utilize pure hydrogen powering the vehicle, one is by the
* Corresponding author. E-mail address: [email protected] (Q.-H. Luo). https://doi.org/10.1016/j.ijhydene.2020.03.006 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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hydrogen fuel cell with high efficiency and zero emissions[4]. The second approach is to apply hydrogen in an internal combustion engine that can utilize the mature industry, achieve high brake thermal efficiency and guarantee high reliability and low price [5]. The characteristics of high heating value, wide flammable range, low ignition energy, and free carbon emissions make hydrogen an ideal fuel [6]. At the same time, these properties make the combustion of hydrogen engines unique from other fueled spark-ignition engines. To investigate and compare this process by quantitative analysis, the combustion diagnosis is implemented. In detail, the cylinder pressure data is used to calculate the heat release rate of combustion, the indicated mean effective pressure, the timing of 50% fuel burned, the energy loss of heat transfer, etc. The basic parameters needed including the geometry of the cylinder, the valve timing, as well as the polytropic index. Therefore, the heat release rate can be obtained by the Rassweiler-Withrow method, as follow:
Qnet ¼
EOC X
Vi þVi1 2
i¼SOC
g pi pi1 VVi1i g1
(1)
where Qnet is the heat release rate; SOC and EOC are the starting and the ending crank angle of combustion separately, V is the cylinder volume calculated by the piston motion and g represents the polytropic index of the compression stroke. Among these parameters, the polytropic index is a variable data determined by the engine working conditions. It is measured by experiment and greatly affects the accuracy of calculation which has been widely investigated by researchers. Lee et al. [7] established a new model with the considering of heat loss to estimate the polytropic index for the real-time application based on a 1.6 L diesel engine. Svete et al. [8] analyzed the polytropic index in the frequency domain and found that the dynamic process of compression can be considered as adiabatic in gasoline engines. Lapuerta et al. [9] studied the factors of heat exchange and the leakage of gases affecting the polytropic index calculation on a reciprocating gasoline SI (Spark Ignition) engine and concluded that polytropic index can also be used to research the heat transfer of the engine according to the equation: dQ Cv P ¼ ðk gÞ dV R
(2)
where, Q is the energy of heat exchange, Cv is the constantpressure special heat, k is the heat specific ratio and g represents the polytropic index. The compression stroke is more adiabatic with a higher polytropic index closing to the heat specific ratio. Hence, the study of the polytropic index can not only improve the accuracy of the combustion analyzer but also reflect the process of heat transfer. However, the former studies are mainly based on the traditional internal combustion engines. The polytropic index is sensitive to the alternative fuels applied since different fuels lead to diverse components of mixed gases in the cylinder of the compression stroke. Luo et al. [10] put forward that the polytropic index of a 2.0 L port fuel injection hydrogen engine ranges from 1.28 to 1.35, which is different from the gasoline engine. Therefore,
the polytropic index of the hydrogen engine is worth being investigated considering the unique physical properties of the gaseous fuel. The study of the hydrogen internal compression engine can be divided into the port fuel injection (PFI) and direct injection (DI) spark-ignited according to the mixture formation types. In terms of the PFI engine, a part load efficiency can be relatively high [11], with a long mixing time of hydrogen-air gases, but low power output [12]. Most researchers pay attention to the DI engine nowadays, which has been demonstrated to offer very high efficiencies, with controllable emissions [13]. It can not only solve the problem of abnormal combustion such as backfire and preignition [14] but also reach a high brake mean effective pressure of approximately 16 MPa [15]. Since the direct injection of hydrogen provides full freedom in injection, the effect and the mechanism of injection strategies have been extensively investigated [16e18]. However, few papers pay attention to the changing of the polytropic index of the compression stroke which is greatly affected by the hydrogen injection. In this paper, the effect of injection, equivalence ratio and engine speed on the polytropic index have been investigated based on the experimental data of a 2.0 L direct-injection engine.
Materials and method Experimental equipment Experiments are implemented on a 2.0 L, four strokes, naturally aspirated direct-injection hydrogen engine. The schematic diagram is described as Fig. 1 with parameters shown in Table 1. A CW250 eddy current dynamometer was equipped to measure the speed and torque of the engine. The H2 volume flow was monitored by CMF010 and CMF025 Coriolis mass flowmeters (measurement deviation: ±0.1%FSa) and the air mass flow was measured by a thermal mass flowmeter (measurement deviation: ±1%FSa). The outward-opening hydrogen injector was placed in the cylinder head, near the valves and injection pressure was adjusted according to the speed and load. A Kistler cylinder pressure transducer 6118 was used to obtain the cylinder pressure and the electric control unit (ECU) was based on the Motohawk system. The data measuring system mainly included temperature (Pt100 and K type thermocouple), the pressure of intake and exhaust pipe (Kistler 4045 A), atmospheric temperature and moisture. The NOx emission and oxygen concentration in the exhaust before and after TWC were measured by the Horiba 7110 and the AVL DiGas 4000 Light.
Measurements of the polytropic index The experiments were conducted after the warm-up of the engine. The temperature of coolant and oil was stabilized at 90 C and 100 C respectively to achieve high efficiency. The appropriate variable valve timing of 2000 rpm was set as the intake vale closing at 140 CA (negative represents the crank angle before the top dead center). For a naturally aspirated DI
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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Fig. 1 e Sketch of the direct injection hydrogen engine. (1-Air filter, 2- Air mass flow meter, 3-Throttle valve, 4-Hydrogen pipe, 5-Hydrogen direct injector, 6-spark plug combined with cylinder pressure sensor, 7-Exhaust gas analysis before TWC 8-Exhaust gas analysis after TWC,9-Hydrogen carbon fiber wound bottle, 10-Pressure reducing valve, 11-Hydrogen mass flow meter, 12-Secondary pressure reducing valve, 13-Dynamometer).
hydrogen engine, the controlling strategy of hydrogen injection will be adjusted by the various working conditions. Here the injection pressure is 10 MPa when the engine operates at a lean equivalence ratio, early injection (220 CA) in the intake stroke will promote the formation of the homogeneous hydrogen-air mixing gases. However, the advancing injection of hydrogen takes up the limited space of cylinder, and the fresh air will be pushed back to the intake ports. Therefore, it is wise to inject near the crank angle of the intake valve closing (140 CA). According to the definition, the polytropic index in this paper is calculated by: g¼
dp=p dv=v
(3)
Here the volume of the cylinder is obtained from the law of piston motion, and the pressure is measured by the Kistler combustion analyzer. Considering the large cyclic variation of the hydrogen engine [19], the data come from an average of 200 cycles. However, calculation directly following equation (3) will lead to a wrong result. Because there is a relation between the cylinder pressure data and the polytropic index in the arithmetic of the combustion analyzer. They influence each other and the principle is explained specifically as follows. To avoid the contradiction of the calculation, it is necessary to study the absolute pressure correction of the DI hydrogen engine.
Table 1 e Parameters of the 2.0 L direct-injection hydrogen engine. Engine type
Hydrogen engine
Bore Stroke Cylinders Compression ratio Exhaust valve open Exhaust valve close Inlet valve open Inlet valve close Engine speed
88 mm 82 mm 4 10:1 40 BBDC 4 BTDC 20 ATDC 80 ABDC 1000 rpme6000 rpm
Absolute cylinder pressure correction of the DI hydrogen engine The principle of a cylinder pressure sensor is when the pressure change, the quartz piezoelectric transducer releases the electric charges correspondingly. After the treatment of the charge amplifier, we can obtain the change of pressure by Ref. [20]: pðqÞ ¼
EðqÞ Ebias Ks
(4)
where, pðqÞ is the cylinder pressure of the corresponding crank angle, EðqÞ is the measured voltage, Ebias and Ks refer to the sensor offset voltage and sensor gain. Since the value of Ebias is random and changes cycle by cycle. Hence, it is important to correct the cylinder pressure and find its zero points to gain absolute pressure. There are mainly two measures of zeropoint correction [21], using the pressure of intake manifold or through the calculation by the polytropic index. The first one assumes that the cylinder pressure equals the pressure of intake manifolds when the intake valve closes, and this cannot be applied to a direct injection hydrogen engine. Because if the injector still operates when the intake values close, there is a difference between the cylinder pressure and intake manifolds pressure due to the injection of hydrogen. The second method supposes a part of the pressure curve fits the polytropic process as pVg ¼ const
(5)
Thereby, the pressure offset value is calculated by g p1 Dp ¼ 1
p2 g
V1 V2
(6)
V1 V2
Normally the crank angles of p1 and p2 are recommended as 100 CA and 65 CA. The pressure offset Dp is then subtracted from the cycle pressure values to achieve the absolute pressure, namely the whole cycle pressure data are moved
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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Fig. 2 e Cylinder pressure changes with the crank angle for motoring and different injection pressures.
down by Dp. Hence, according to equation (3) and equation (6), the polytropic index is associated with the cylinder pressure and affect each other. Fig. 2 shows the influence of hydrogen injection on the cylinder pressure in the compression stroke. The DI hydrogen engine was operated at 2000 rpm, throttle wide open condition, the injection pressure of 8 MPa and 10 MPa with an equivalence ratio of 0.4. The spark advanced angle is 10 CA. The start of injection (SOI) timing is adjusted to 160 CA and the injection process lasted 3.4 ms with 10 MPa injection pressure and 4.7 ms with 8 MPa injection pressure. In other words, the injection lasted 61.2 CA and 84.6 CA separately. The motoring data of 2000 rpm was measured simultaneously to guarantee the identical temperature of the coolant and other factors. Therefore, the cylinder pressure was corrected by assuming the pressure of the intake stroke of the motoring is the same as others. As shown in Fig. 2, the cylinder pressure of two working conditions is slightly higher than the motoring one during the period of hydrogen injection. Then the gap of two pressures increases gradually due to the compression of the piston, reaching 4 bar at the timing of the spark. After
ignition, the cylinder pressure of 10 MPa injection pressure rises drastically and reaching a maximum of 36.3 bar, compared to the 21.7 bar of the motoring. The zoom-in Fig. 3 displays the compression stroke in detail. At the timing of the intake valve closing (-140 CA), the cylinder pressure of working conditions is 0.2 bar larger than the pressure of the motoring and the intake manifolds. When the injection finishes at a crank angle of 80 CA, the pressure difference reaches 0.6 bar. Higher injection pressure ends up with a slightly higher pressure of approximately 0.8 bar. The first measure of absolute pressure correction cannot be applied to the DI hydrogen engine. It demonstrates that the injection of hydrogen results in the changing of the cylinder pressure in the compression stroke. Furthermore, this conclusion is only appropriate to the DI hydrogen engine, excluding the PFI hydrogen, gasoline or natural gas engine. Because the issues exist on the gaseous fuel engine are amplified by the extremely low density of hydrogen. As shown in Table 2, although the heat value of hydrogen is twice as large as the one of methane, the volumetric heat value of hydrogen is 10.6 MJ/m3, compared to 32.5 of methane. Therefore, hydrogen accounts for over 29% of the cylinder volume, while methane takes up approximately 10% at the stoichiometric ratio. In terms of the PFI hydrogen engine, the formation of hydrogen-air gases occurs in the manifold in the intake stroke. Thus, the component of mixing gases in the compression stroke of the DI hydrogen engine experiences the most change, and the polytropic index will be different. The second method of absolute cylinder pressure correction cannot be implemented on the DI hydrogen engine. In summary, due to the injection of a large volume of hydrogen in the compression stroke, the traditional method of the cylinder pressure correction is not suitable for the DI hydrogen engine. What’s more, accurate calculation of the polytropic index should base on the absolute cylinder pressure. The polytropic index has to be recalculated, and an appropriate value for cylinder pressure correction needs to be verified.
Results and discussion Effects of the duration of hydrogen injection To investigate the effects of duration of hydrogen injection on the polytropic index of the compression stroke, the experiments test various duration from 4 ms to 6 ms with an engine speed of 2000 rpm, wide-open throttle vale, coolant
Table 2 e Hydrogen properties compared with methane and iso-octane at 300 K and 1 atm. Property
Fig. 3 e Pressure of cylinder and intake manifold changes with the crank angle for motoring and working conditions.
Density (kg/m3) Lower heat value (MJ/kg) Stoichiometric ratio (kg/kg) Volumetric heat value (MJ/m3) Volume fraction at stoichiometric ratio (%)
Hydrogen Methane Iso-octane 0.08 120 34.2 10.6 29%
0.65 50 17.1 32.5 10%
692 44.3 15 e e
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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temperature of 90 C. The intake valve of this condition was adjusted to close at-140 CA and the start of injection timing was also set as 140 CA. Therefore, the cylinder pressure can be corrected by the intake manifold pressure and the motoring data in advance. As shown in Fig. 4, the polytropic index of the direct injection hydrogen engine first decreases drastically to approximately 1.37. After a turning point, which corresponding to the crank angle of the end of the injection, it keeps stable for a while, declines gradually and reaches the bottom of approximately 1.22. The range of the compression process is defined as 60 CA to 10 CA considering the ends of the 6 ms injection and the sparking timing. At the beginning of the compression process (-60 CA), the polytropic index of 6 ms duration is slightly higher than the others because adding hydrogen increases the incompressibility of the mixing gases and end up with a high compress pressure. However, it drops to the lowest at 1.23 at the spark angle of 10 CA. The polytropic index of 4 ms durations shows an opposite trend, it reaches 1.35 with a crank angle of 60 CA and decreases to 1.25. This phenomenon can be explained by Newton’s law of heat transfer as follows. Q ¼ a Tg Tw
(7)
where, Q is the heat flux, a is the heat transfer coefficient, Tg and Tw represent the temperature of gas and wall respectively. The thermal conductivity of hydrogen-air gases ascends with the increase of the equivalence ratio [10]. At the same time, there is a positive correlation between the heat transfer coefficient and thermal conductivity. Hence, the heat flux of gases near the top dead center enlarges with the increasing of the duration of injection and results in the decreasing of the polytropic index. In terms of the polytropic index for the absolute cylinder pressure correction, Fig. 5 displays the change of the average value with injection durations for different calculation ranges. The calculation starts from (60 CA), lasting 10 CA, 30 CA, and 50 CA respectively. The mean value of the whole compression stroke (60 CA ~ -10 CA) rises slightly with the increasing of the injection duration, which mainly clusters between 1.32 and 1.33. Without including the crank angle near
Fig. 4 e Polytropic index changes with the crank angle for various injection durations.
5
Fig. 5 e Polytropic index changes with injection duration for different average calculation windows.
the top dead center, the average value of short calculation range changes significantly, from 1.35 to 1.38 (60 CA ~ 50 CA). This can be explained by the balance of the effects between the concentration of hydrogen and the effect of heat transfer as mentioned above. Therefore, the polytropic index for the absolute cylinder pressure correction is approximately 1.32 for various injection durations.
Effects of the start timing of hydrogen injection The timing of hydrogen injection is an important factor for the controlling strategy of the direct injection hydrogen engine since it determines the distribution and local equivalence ratio of mixed gases in the cylinder, thereby affect the process of the combustion. In the experiments, when the injection finishes before the intake valve closing, hydrogen will take up the volume of the cylinder and causing the backflow of fresh air in the intake manifolds. Therefore, the conditions can be approximately regarded as the port fuel injection. Fig. 6 displays the polytropic index comparison between the PFI and DI hydrogen
Fig. 6 e Polytropic index comparison between port fuel injection and direct injection hydrogen engine.
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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engines. During the compression stroke from the intake valve closing (140 CA) to the spark angle (20 CA), the polytropic index of PFI increases gradually from 1.2 to 1.31. While for direct injection, it first increases dramatically, reaches the peak at 2.2, fluctuates for a moment then declines to a turning point at 90 CA, which is the same crank angle as the end of the injection. Then it drops steadily to approximately 1.28 which displays a different pattern. Hence, the selection of the SOI is crucial and the injection of hydrogen leads to a violent fluctuation of the polytropic index. The following experiments are conducted with the speed of 2000 rpm and the injection duration of 4 ms. The SOI timing was adjusted from 160 CA to 125 CA and the spark advanced angle was fixed at 10 CA. As shown in Fig. 7, the curve mainly shows the same trend as mentioned above. The turning points corresponding to the end of the injection arrange in order. In detail, the polytropic index of SOI-160 CA, 150 CA are larger than the one of SOI-140 CA and 130 CA at the beginning of the compression process. Because the early injection is beneficial to the formation of rich homogeneous hydrogen-air gases that increases the polytropic index. At the spark angle (-10 CA), the polytropic index of the SOI-140 CA is the lowest at 1.23. For the rest of the terms, the polytropic index mainly clusters between 1.25 and 1.27 and the one of SOI -130 CA ranks the first. This can be explained by the mass of hydrogen injected into the cylinder changes with the SOI of injection. As shown in Fig. 8, the flow rate of hydrogen rises steadily and reach the peak at 1.973 kg/h with SOI -140 CA, before declining drastically to 1.928 kg/h with retarded injection. The injection takes place before 140 CA encounters the problem of the backflow of the hydrogen to the intake manifolds. While injection occurs after the closing of the intake valves (-140 CA) will be influenced by the increasing cylinder backpressure with constant duration and injection pressure. As shown in Fig. 9, the average value (60 CA ~ -50 CA) of the polytropic index decreases drastically from 1.385 to 1.34. without the balance of the effect of heat transfer as explained above. However, the average value of (60 CA ~ -10 CA) first declines from 1.34 to 1.32 with the advancing of SOI, touches the bottom at 1.32 with SOI -140 CA and keeps stable after
Fig. 8 e Hydrogen flow rate changes with SOI.
Fig. 9 e Polytropic index changes with SOI for various average calculation windows.
that. Hence, the average polytropic index of early injection is larger than the one of retarded injection. For the injection starts after the closing of the intake valves, the average polytropic index can be set as 1.32.
Effects of engine speed
Fig. 7 e Polytropic index changes with the crank angle for different start timing of injection.
In order to test the effects of engine speed, the throttle valve was set as wide open, injection duration 4 ms, injection SOI140 CA. The speed was adjusted from 1500 rpm to 4000 rpm. As shown in Fig. 10, the curve represents 4000 rpm fluctuate drastically compared with others since fast engine speed accelerates the moving of piston, leading to the fluctuation of cyclic pressure. Besides, the polytropic index rises for high engine speed, and this can be explained in two aspects. For one thing, the mass of leakage gas from the cylinder reduces with the increase of speed and the compression stroke is more similar to an adiabatic process. For another, the temperature of the piston and the cylinder wall rises with the increasing number of working cycles per second. Therefore, the decrease of temperature difference in equation (7) results in the declination of heat flux. Furthermore, according to the Woschni
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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a function of the crank angle reflects the extent of heat transfer of the engine. In addition, the average polytropic index can be used to correct pressure and calculate the heat release rate. In this paper, the characteristic of the polytropic index of a 2.0 L DI hydrogen engine effects by the injection duration, the SOI of injection and the engine speed has been investigated. From the above analysis we can get the following conclusions:
Fig. 10 e Polytropic index changes with the crank angle for various engine speeds.
Fig. 11 e Polytropic index changes with the engine speed for different average calculation windows.
heat transfer model [22], the increasing of the piston moving velocity leads to the decreasing heat transfer coefficient. Hence, the polytropic index rises with the increase of engine speeds. The average polytropic index changes with engine speed are displayed in Fig. 11. The average value of 4000 rpm stands out among different speeds, reaching 1.33 with the calculation of 60 CA to 10 CA. Because the injection of 4000 rpm lasts 4 ms and the end of the injection locates at 45 CA. The part of hydrogen injection is included in the calculation leads to the increase of the polytropic index. Considering the large difference of short-range calculation, the average polytropic index for the effects of speed is approximately 1.32 with a range of 60 CA to 10 CA.
Conclusion The polytropic index is an important parameter in the combustion diagnosis. The polytropic index which is measured as
1. There exists a contradiction between the polytropic index and the cylinder pressure. The polytropic index is obtained from the cylinder pressure signal, while the cylinder pressure data is corrected by the polytropic index. Thus, the calculation should base on the pressure data corrected by other methods. 2. The injection of a large volume of hydrogen during the compression stroke results in the change of cylinder pressure and the pressure difference can reach 0.8 bar. Therefore, the traditional absolute pressure correction method is not suitable for the DI hydrogen engine. In this paper, the cylinder pressure data were first corrected by the motoring with the same operating conditions to guarantee the accuracy of the calculation. 3. The injection of hydrogen will lead to a dramatic increase and a violent fluctuation of the polytropic index. After the injection, the polytropic index changes with the crank angle decreases drastically from 2.2 to 1.37, then it declines gradually to approximately 1.22 at the spark angle. 4. The average polytropic index of compression stroke rises with the ascending of the injection duration, the advancing of the SOI timing and the increasing of the engine speed. The calculation range of (60 CA ~ -10 CA) is appropriate for the absolute pressure correction, and the average polytropic index can be approximately set as 1.32. 5. The gas properties have a significant influence on the heat transfer of the hydrogen internal combustion engines. Hence, it is necessary to take the components of mixed hydrogen-air gases into account of the heat transfer model for the DI hydrogen engine.
Acknowledgement The financial support of the works Funded by China Postdoctoral Science Foundation (PFCPSF 2018M641215) is greatly acknowledged.
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[4] Ouyang L, Cao Z, Wang H, Hu R, Zhu M. Application of dielectric barrier discharge plasma-assisted milling in energy storage materials-A review. J Alloy Compd 2017;691:422e35. [5] Verhelst S. Recent progress in the use of hydrogen as a fuel for internal combustion engines. Int J Hydrogen Energ 2014;39:1071e85. [6] Verhelst S, Wallner T. Hydrogen-fueled internal combustion engines. Prog Energ Combust 2009;35:490e527. [7] Lee Y, Min K. Estimation of the polytropic index for incylinder pressure prediction in engines. Appl Therm Eng 2019;158:113703. I, Kutin J. Investigation of polytropic [8] Svete A, Bajsic corrections for the piston-in-cylinder primary standard used in dynamic calibrations of pressure sensors. Sensor Actuator Phys 2018;274:262e71. [9] Lapuerta M, Armas O, Molina S. Study of the compression cycle of a reciprocating engine through the polytropic coefficient. Appl Therm Eng 2003;23:313e23. [10] Luo Q, Sun B, Tian H. The characteristic of polytropic coefficient of compression stroke in hydrogen internal combustion engine. Int J Hydrogen Energ 2014;39:13787e92. [11] Wang X, Sun B, Luo Q. Energy and exergy analysis of a turbocharged hydrogen internal combustion engine. Int J Hydrogen Energ 2019;44:5551e63. [12] Luo Q, Hu J, Sun B, Liu F, Wang X, Li C, et al. Effect of equivalence ratios on the power, combustion stability and NOx controlling strategy for the turbocharged hydrogen engine at low engine speeds. Int J Hydrogen Energ 2019;44:17095e102. [13] Mohammadi A. Shioji M Performance and combustion characteristics of a direct injection SI hydrogen engine. Int J Hydrogen Energ 2007;32:296e304.
[14] Takagi Y, Oikawa M, Sato R, Kojiya Y, Mihara Y. Near-zero emissions with high thermal efficiency realized by optimizing jet plume location relative to combustion chamber wall, jet geometry and injection timing in a directinjection hydrogen engine. Int J Hydrogen Energ 2019;44:9456e65. [15] Wimmer A, Wallner T, Ringler J, Gerbig F. H2-Direct injection-A highly promising combustion concept. SAE International; 2005. [16] Li Y, Gao W, Zhang P, Ye Y, Wei Z. Effects study of injection strategies on hydrogen-air formation and performance of hydrogen direct injection internal combustion engine. Int J Hydrogen Energ 2019;44:26000e11. [17] Rahman KM, Kawahara N, Matsunaga D, Tomita E, Takagi Y, Mihara Y. Local fuel concentration measurement through spark-induced breakdown spectroscopy in a direct-injection hydrogen spark-ignition engine. Int J Hydrogen Energ 2016;41:14283e92. [18] Fathi V, Nemati A, Khalilarya S, Jafarmadar S. The effect of the initial charge temperature under various injection timings on the second law terms in a direct injection SI hydrogen engine. Int J Hydrogen Energ 2011;36:9252e9. [19] Sun B, Zhang D, Liu F. Cycle variations in a hydrogen internal combustion engine. Int J Hydrogen Energ 2013;38:3778e83. [20] Lee K, Kwon M, Sunwoo M, Yoon M. An in-cylinder pressure referencing method based on a variable polytropic coefficient. SAE International; 2007. [21] Brunt MFJ, Pond CR. Evaluation of techniques for absolute cylinder pressure correction. SAE International; 1997. [22] Demuynck J, De Paepe M, Huisseune H, Sierens R, Vancoillie J, Verhelst S. On the applicability of empirical heat transfer models for hydrogen combustion engines. Int J Hydrogen Energ 2011;36:975e84.
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine Ling-Zhi Bao, Bai-Gang Sun, Qing-He Luo*, Xi Wang, Qing-Yu Niu School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
highlights The traditional pressure correction method is not suitable for DI hydrogen engine. The polytropic index is sensitive to the concentration of hydrogen. Advancing injection of hydrogen increases the polytropic index. Average polytropic index of the DI hydrogen engine is approximately 1.32.
article info
abstract
Article history:
Hydrogen is regarded as a promising alternative fuel in the future. The direct-injection (DI)
Received 22 January 2020
hydrogen engine has been demonstrated to offer large power without the risk of abnormal
Received in revised form
combustion. For the engine test of combustion analysis, the piezoelectric transducer
23 February 2020
measures the dynamic cylinder pressure data rather than the absolute one. The traditional
Accepted 1 March 2020
method of absolute cylinder pressure correction is normally based on the polytropic index.
Available online xxx
This paper investigated the polytropic index effects by injection duration, start timing of injection and speed based on a 2.0 L direct-injection hydrogen engine. The experiments
Keywords:
found that, since the injection of large volume hydrogen leads to approximately 0.8 bar
Polytropic index
increase of cylinder pressure in the compression stroke, the traditional correct method is
Direct injection hydrogen engine
not suitable for the DI hydrogen engine. What’s more, the polytropic index drops from 2.2
Combustion analysis
to 1.22 with the changes of the crank angle and is sensitive to the concentration of the
Cylinder pressure correction
hydrogen. The study of the instantaneous polytropic index can not only be used to calculate the accurate heat release rate but also guide the research of the heat transfer of the DI hydrogen engine. The average polytropic index of 1.32 provides a new reference for the absolute cylinder pressure correction of the DI hydrogen engine. © 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Currently, the growing consumption of foil fuels has accelerated the energy crisis. It is necessary to implement alternative
energy sources[1]. Hydrogen, as a prominent selection for the renewable and sustainable energy carrier in the future, has a wide range of sources [2,3]. There are mainly two options to utilize pure hydrogen powering the vehicle, one is by the
* Corresponding author. E-mail address: [email protected] (Q.-H. Luo). https://doi.org/10.1016/j.ijhydene.2020.03.006 0360-3199/© 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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hydrogen fuel cell with high efficiency and zero emissions[4]. The second approach is to apply hydrogen in an internal combustion engine that can utilize the mature industry, achieve high brake thermal efficiency and guarantee high reliability and low price [5]. The characteristics of high heating value, wide flammable range, low ignition energy, and free carbon emissions make hydrogen an ideal fuel [6]. At the same time, these properties make the combustion of hydrogen engines unique from other fueled spark-ignition engines. To investigate and compare this process by quantitative analysis, the combustion diagnosis is implemented. In detail, the cylinder pressure data is used to calculate the heat release rate of combustion, the indicated mean effective pressure, the timing of 50% fuel burned, the energy loss of heat transfer, etc. The basic parameters needed including the geometry of the cylinder, the valve timing, as well as the polytropic index. Therefore, the heat release rate can be obtained by the Rassweiler-Withrow method, as follow:
Qnet ¼
EOC X
Vi þVi1 2
i¼SOC
g pi pi1 VVi1i g1
(1)
where Qnet is the heat release rate; SOC and EOC are the starting and the ending crank angle of combustion separately, V is the cylinder volume calculated by the piston motion and g represents the polytropic index of the compression stroke. Among these parameters, the polytropic index is a variable data determined by the engine working conditions. It is measured by experiment and greatly affects the accuracy of calculation which has been widely investigated by researchers. Lee et al. [7] established a new model with the considering of heat loss to estimate the polytropic index for the real-time application based on a 1.6 L diesel engine. Svete et al. [8] analyzed the polytropic index in the frequency domain and found that the dynamic process of compression can be considered as adiabatic in gasoline engines. Lapuerta et al. [9] studied the factors of heat exchange and the leakage of gases affecting the polytropic index calculation on a reciprocating gasoline SI (Spark Ignition) engine and concluded that polytropic index can also be used to research the heat transfer of the engine according to the equation: dQ Cv P ¼ ðk gÞ dV R
(2)
where, Q is the energy of heat exchange, Cv is the constantpressure special heat, k is the heat specific ratio and g represents the polytropic index. The compression stroke is more adiabatic with a higher polytropic index closing to the heat specific ratio. Hence, the study of the polytropic index can not only improve the accuracy of the combustion analyzer but also reflect the process of heat transfer. However, the former studies are mainly based on the traditional internal combustion engines. The polytropic index is sensitive to the alternative fuels applied since different fuels lead to diverse components of mixed gases in the cylinder of the compression stroke. Luo et al. [10] put forward that the polytropic index of a 2.0 L port fuel injection hydrogen engine ranges from 1.28 to 1.35, which is different from the gasoline engine. Therefore,
the polytropic index of the hydrogen engine is worth being investigated considering the unique physical properties of the gaseous fuel. The study of the hydrogen internal compression engine can be divided into the port fuel injection (PFI) and direct injection (DI) spark-ignited according to the mixture formation types. In terms of the PFI engine, a part load efficiency can be relatively high [11], with a long mixing time of hydrogen-air gases, but low power output [12]. Most researchers pay attention to the DI engine nowadays, which has been demonstrated to offer very high efficiencies, with controllable emissions [13]. It can not only solve the problem of abnormal combustion such as backfire and preignition [14] but also reach a high brake mean effective pressure of approximately 16 MPa [15]. Since the direct injection of hydrogen provides full freedom in injection, the effect and the mechanism of injection strategies have been extensively investigated [16e18]. However, few papers pay attention to the changing of the polytropic index of the compression stroke which is greatly affected by the hydrogen injection. In this paper, the effect of injection, equivalence ratio and engine speed on the polytropic index have been investigated based on the experimental data of a 2.0 L direct-injection engine.
Materials and method Experimental equipment Experiments are implemented on a 2.0 L, four strokes, naturally aspirated direct-injection hydrogen engine. The schematic diagram is described as Fig. 1 with parameters shown in Table 1. A CW250 eddy current dynamometer was equipped to measure the speed and torque of the engine. The H2 volume flow was monitored by CMF010 and CMF025 Coriolis mass flowmeters (measurement deviation: ±0.1%FSa) and the air mass flow was measured by a thermal mass flowmeter (measurement deviation: ±1%FSa). The outward-opening hydrogen injector was placed in the cylinder head, near the valves and injection pressure was adjusted according to the speed and load. A Kistler cylinder pressure transducer 6118 was used to obtain the cylinder pressure and the electric control unit (ECU) was based on the Motohawk system. The data measuring system mainly included temperature (Pt100 and K type thermocouple), the pressure of intake and exhaust pipe (Kistler 4045 A), atmospheric temperature and moisture. The NOx emission and oxygen concentration in the exhaust before and after TWC were measured by the Horiba 7110 and the AVL DiGas 4000 Light.
Measurements of the polytropic index The experiments were conducted after the warm-up of the engine. The temperature of coolant and oil was stabilized at 90 C and 100 C respectively to achieve high efficiency. The appropriate variable valve timing of 2000 rpm was set as the intake vale closing at 140 CA (negative represents the crank angle before the top dead center). For a naturally aspirated DI
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Fig. 1 e Sketch of the direct injection hydrogen engine. (1-Air filter, 2- Air mass flow meter, 3-Throttle valve, 4-Hydrogen pipe, 5-Hydrogen direct injector, 6-spark plug combined with cylinder pressure sensor, 7-Exhaust gas analysis before TWC 8-Exhaust gas analysis after TWC,9-Hydrogen carbon fiber wound bottle, 10-Pressure reducing valve, 11-Hydrogen mass flow meter, 12-Secondary pressure reducing valve, 13-Dynamometer).
hydrogen engine, the controlling strategy of hydrogen injection will be adjusted by the various working conditions. Here the injection pressure is 10 MPa when the engine operates at a lean equivalence ratio, early injection (220 CA) in the intake stroke will promote the formation of the homogeneous hydrogen-air mixing gases. However, the advancing injection of hydrogen takes up the limited space of cylinder, and the fresh air will be pushed back to the intake ports. Therefore, it is wise to inject near the crank angle of the intake valve closing (140 CA). According to the definition, the polytropic index in this paper is calculated by: g¼
dp=p dv=v
(3)
Here the volume of the cylinder is obtained from the law of piston motion, and the pressure is measured by the Kistler combustion analyzer. Considering the large cyclic variation of the hydrogen engine [19], the data come from an average of 200 cycles. However, calculation directly following equation (3) will lead to a wrong result. Because there is a relation between the cylinder pressure data and the polytropic index in the arithmetic of the combustion analyzer. They influence each other and the principle is explained specifically as follows. To avoid the contradiction of the calculation, it is necessary to study the absolute pressure correction of the DI hydrogen engine.
Table 1 e Parameters of the 2.0 L direct-injection hydrogen engine. Engine type
Hydrogen engine
Bore Stroke Cylinders Compression ratio Exhaust valve open Exhaust valve close Inlet valve open Inlet valve close Engine speed
88 mm 82 mm 4 10:1 40 BBDC 4 BTDC 20 ATDC 80 ABDC 1000 rpme6000 rpm
Absolute cylinder pressure correction of the DI hydrogen engine The principle of a cylinder pressure sensor is when the pressure change, the quartz piezoelectric transducer releases the electric charges correspondingly. After the treatment of the charge amplifier, we can obtain the change of pressure by Ref. [20]: pðqÞ ¼
EðqÞ Ebias Ks
(4)
where, pðqÞ is the cylinder pressure of the corresponding crank angle, EðqÞ is the measured voltage, Ebias and Ks refer to the sensor offset voltage and sensor gain. Since the value of Ebias is random and changes cycle by cycle. Hence, it is important to correct the cylinder pressure and find its zero points to gain absolute pressure. There are mainly two measures of zeropoint correction [21], using the pressure of intake manifold or through the calculation by the polytropic index. The first one assumes that the cylinder pressure equals the pressure of intake manifolds when the intake valve closes, and this cannot be applied to a direct injection hydrogen engine. Because if the injector still operates when the intake values close, there is a difference between the cylinder pressure and intake manifolds pressure due to the injection of hydrogen. The second method supposes a part of the pressure curve fits the polytropic process as pVg ¼ const
(5)
Thereby, the pressure offset value is calculated by g p1 Dp ¼ 1
p2 g
V1 V2
(6)
V1 V2
Normally the crank angles of p1 and p2 are recommended as 100 CA and 65 CA. The pressure offset Dp is then subtracted from the cycle pressure values to achieve the absolute pressure, namely the whole cycle pressure data are moved
Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006
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Fig. 2 e Cylinder pressure changes with the crank angle for motoring and different injection pressures.
down by Dp. Hence, according to equation (3) and equation (6), the polytropic index is associated with the cylinder pressure and affect each other. Fig. 2 shows the influence of hydrogen injection on the cylinder pressure in the compression stroke. The DI hydrogen engine was operated at 2000 rpm, throttle wide open condition, the injection pressure of 8 MPa and 10 MPa with an equivalence ratio of 0.4. The spark advanced angle is 10 CA. The start of injection (SOI) timing is adjusted to 160 CA and the injection process lasted 3.4 ms with 10 MPa injection pressure and 4.7 ms with 8 MPa injection pressure. In other words, the injection lasted 61.2 CA and 84.6 CA separately. The motoring data of 2000 rpm was measured simultaneously to guarantee the identical temperature of the coolant and other factors. Therefore, the cylinder pressure was corrected by assuming the pressure of the intake stroke of the motoring is the same as others. As shown in Fig. 2, the cylinder pressure of two working conditions is slightly higher than the motoring one during the period of hydrogen injection. Then the gap of two pressures increases gradually due to the compression of the piston, reaching 4 bar at the timing of the spark. After
ignition, the cylinder pressure of 10 MPa injection pressure rises drastically and reaching a maximum of 36.3 bar, compared to the 21.7 bar of the motoring. The zoom-in Fig. 3 displays the compression stroke in detail. At the timing of the intake valve closing (-140 CA), the cylinder pressure of working conditions is 0.2 bar larger than the pressure of the motoring and the intake manifolds. When the injection finishes at a crank angle of 80 CA, the pressure difference reaches 0.6 bar. Higher injection pressure ends up with a slightly higher pressure of approximately 0.8 bar. The first measure of absolute pressure correction cannot be applied to the DI hydrogen engine. It demonstrates that the injection of hydrogen results in the changing of the cylinder pressure in the compression stroke. Furthermore, this conclusion is only appropriate to the DI hydrogen engine, excluding the PFI hydrogen, gasoline or natural gas engine. Because the issues exist on the gaseous fuel engine are amplified by the extremely low density of hydrogen. As shown in Table 2, although the heat value of hydrogen is twice as large as the one of methane, the volumetric heat value of hydrogen is 10.6 MJ/m3, compared to 32.5 of methane. Therefore, hydrogen accounts for over 29% of the cylinder volume, while methane takes up approximately 10% at the stoichiometric ratio. In terms of the PFI hydrogen engine, the formation of hydrogen-air gases occurs in the manifold in the intake stroke. Thus, the component of mixing gases in the compression stroke of the DI hydrogen engine experiences the most change, and the polytropic index will be different. The second method of absolute cylinder pressure correction cannot be implemented on the DI hydrogen engine. In summary, due to the injection of a large volume of hydrogen in the compression stroke, the traditional method of the cylinder pressure correction is not suitable for the DI hydrogen engine. What’s more, accurate calculation of the polytropic index should base on the absolute cylinder pressure. The polytropic index has to be recalculated, and an appropriate value for cylinder pressure correction needs to be verified.
Results and discussion Effects of the duration of hydrogen injection To investigate the effects of duration of hydrogen injection on the polytropic index of the compression stroke, the experiments test various duration from 4 ms to 6 ms with an engine speed of 2000 rpm, wide-open throttle vale, coolant
Table 2 e Hydrogen properties compared with methane and iso-octane at 300 K and 1 atm. Property
Fig. 3 e Pressure of cylinder and intake manifold changes with the crank angle for motoring and working conditions.
Density (kg/m3) Lower heat value (MJ/kg) Stoichiometric ratio (kg/kg) Volumetric heat value (MJ/m3) Volume fraction at stoichiometric ratio (%)
Hydrogen Methane Iso-octane 0.08 120 34.2 10.6 29%
0.65 50 17.1 32.5 10%
692 44.3 15 e e
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temperature of 90 C. The intake valve of this condition was adjusted to close at-140 CA and the start of injection timing was also set as 140 CA. Therefore, the cylinder pressure can be corrected by the intake manifold pressure and the motoring data in advance. As shown in Fig. 4, the polytropic index of the direct injection hydrogen engine first decreases drastically to approximately 1.37. After a turning point, which corresponding to the crank angle of the end of the injection, it keeps stable for a while, declines gradually and reaches the bottom of approximately 1.22. The range of the compression process is defined as 60 CA to 10 CA considering the ends of the 6 ms injection and the sparking timing. At the beginning of the compression process (-60 CA), the polytropic index of 6 ms duration is slightly higher than the others because adding hydrogen increases the incompressibility of the mixing gases and end up with a high compress pressure. However, it drops to the lowest at 1.23 at the spark angle of 10 CA. The polytropic index of 4 ms durations shows an opposite trend, it reaches 1.35 with a crank angle of 60 CA and decreases to 1.25. This phenomenon can be explained by Newton’s law of heat transfer as follows. Q ¼ a Tg Tw
(7)
where, Q is the heat flux, a is the heat transfer coefficient, Tg and Tw represent the temperature of gas and wall respectively. The thermal conductivity of hydrogen-air gases ascends with the increase of the equivalence ratio [10]. At the same time, there is a positive correlation between the heat transfer coefficient and thermal conductivity. Hence, the heat flux of gases near the top dead center enlarges with the increasing of the duration of injection and results in the decreasing of the polytropic index. In terms of the polytropic index for the absolute cylinder pressure correction, Fig. 5 displays the change of the average value with injection durations for different calculation ranges. The calculation starts from (60 CA), lasting 10 CA, 30 CA, and 50 CA respectively. The mean value of the whole compression stroke (60 CA ~ -10 CA) rises slightly with the increasing of the injection duration, which mainly clusters between 1.32 and 1.33. Without including the crank angle near
Fig. 4 e Polytropic index changes with the crank angle for various injection durations.
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Fig. 5 e Polytropic index changes with injection duration for different average calculation windows.
the top dead center, the average value of short calculation range changes significantly, from 1.35 to 1.38 (60 CA ~ 50 CA). This can be explained by the balance of the effects between the concentration of hydrogen and the effect of heat transfer as mentioned above. Therefore, the polytropic index for the absolute cylinder pressure correction is approximately 1.32 for various injection durations.
Effects of the start timing of hydrogen injection The timing of hydrogen injection is an important factor for the controlling strategy of the direct injection hydrogen engine since it determines the distribution and local equivalence ratio of mixed gases in the cylinder, thereby affect the process of the combustion. In the experiments, when the injection finishes before the intake valve closing, hydrogen will take up the volume of the cylinder and causing the backflow of fresh air in the intake manifolds. Therefore, the conditions can be approximately regarded as the port fuel injection. Fig. 6 displays the polytropic index comparison between the PFI and DI hydrogen
Fig. 6 e Polytropic index comparison between port fuel injection and direct injection hydrogen engine.
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engines. During the compression stroke from the intake valve closing (140 CA) to the spark angle (20 CA), the polytropic index of PFI increases gradually from 1.2 to 1.31. While for direct injection, it first increases dramatically, reaches the peak at 2.2, fluctuates for a moment then declines to a turning point at 90 CA, which is the same crank angle as the end of the injection. Then it drops steadily to approximately 1.28 which displays a different pattern. Hence, the selection of the SOI is crucial and the injection of hydrogen leads to a violent fluctuation of the polytropic index. The following experiments are conducted with the speed of 2000 rpm and the injection duration of 4 ms. The SOI timing was adjusted from 160 CA to 125 CA and the spark advanced angle was fixed at 10 CA. As shown in Fig. 7, the curve mainly shows the same trend as mentioned above. The turning points corresponding to the end of the injection arrange in order. In detail, the polytropic index of SOI-160 CA, 150 CA are larger than the one of SOI-140 CA and 130 CA at the beginning of the compression process. Because the early injection is beneficial to the formation of rich homogeneous hydrogen-air gases that increases the polytropic index. At the spark angle (-10 CA), the polytropic index of the SOI-140 CA is the lowest at 1.23. For the rest of the terms, the polytropic index mainly clusters between 1.25 and 1.27 and the one of SOI -130 CA ranks the first. This can be explained by the mass of hydrogen injected into the cylinder changes with the SOI of injection. As shown in Fig. 8, the flow rate of hydrogen rises steadily and reach the peak at 1.973 kg/h with SOI -140 CA, before declining drastically to 1.928 kg/h with retarded injection. The injection takes place before 140 CA encounters the problem of the backflow of the hydrogen to the intake manifolds. While injection occurs after the closing of the intake valves (-140 CA) will be influenced by the increasing cylinder backpressure with constant duration and injection pressure. As shown in Fig. 9, the average value (60 CA ~ -50 CA) of the polytropic index decreases drastically from 1.385 to 1.34. without the balance of the effect of heat transfer as explained above. However, the average value of (60 CA ~ -10 CA) first declines from 1.34 to 1.32 with the advancing of SOI, touches the bottom at 1.32 with SOI -140 CA and keeps stable after
Fig. 8 e Hydrogen flow rate changes with SOI.
Fig. 9 e Polytropic index changes with SOI for various average calculation windows.
that. Hence, the average polytropic index of early injection is larger than the one of retarded injection. For the injection starts after the closing of the intake valves, the average polytropic index can be set as 1.32.
Effects of engine speed
Fig. 7 e Polytropic index changes with the crank angle for different start timing of injection.
In order to test the effects of engine speed, the throttle valve was set as wide open, injection duration 4 ms, injection SOI140 CA. The speed was adjusted from 1500 rpm to 4000 rpm. As shown in Fig. 10, the curve represents 4000 rpm fluctuate drastically compared with others since fast engine speed accelerates the moving of piston, leading to the fluctuation of cyclic pressure. Besides, the polytropic index rises for high engine speed, and this can be explained in two aspects. For one thing, the mass of leakage gas from the cylinder reduces with the increase of speed and the compression stroke is more similar to an adiabatic process. For another, the temperature of the piston and the cylinder wall rises with the increasing number of working cycles per second. Therefore, the decrease of temperature difference in equation (7) results in the declination of heat flux. Furthermore, according to the Woschni
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a function of the crank angle reflects the extent of heat transfer of the engine. In addition, the average polytropic index can be used to correct pressure and calculate the heat release rate. In this paper, the characteristic of the polytropic index of a 2.0 L DI hydrogen engine effects by the injection duration, the SOI of injection and the engine speed has been investigated. From the above analysis we can get the following conclusions:
Fig. 10 e Polytropic index changes with the crank angle for various engine speeds.
Fig. 11 e Polytropic index changes with the engine speed for different average calculation windows.
heat transfer model [22], the increasing of the piston moving velocity leads to the decreasing heat transfer coefficient. Hence, the polytropic index rises with the increase of engine speeds. The average polytropic index changes with engine speed are displayed in Fig. 11. The average value of 4000 rpm stands out among different speeds, reaching 1.33 with the calculation of 60 CA to 10 CA. Because the injection of 4000 rpm lasts 4 ms and the end of the injection locates at 45 CA. The part of hydrogen injection is included in the calculation leads to the increase of the polytropic index. Considering the large difference of short-range calculation, the average polytropic index for the effects of speed is approximately 1.32 with a range of 60 CA to 10 CA.
Conclusion The polytropic index is an important parameter in the combustion diagnosis. The polytropic index which is measured as
1. There exists a contradiction between the polytropic index and the cylinder pressure. The polytropic index is obtained from the cylinder pressure signal, while the cylinder pressure data is corrected by the polytropic index. Thus, the calculation should base on the pressure data corrected by other methods. 2. The injection of a large volume of hydrogen during the compression stroke results in the change of cylinder pressure and the pressure difference can reach 0.8 bar. Therefore, the traditional absolute pressure correction method is not suitable for the DI hydrogen engine. In this paper, the cylinder pressure data were first corrected by the motoring with the same operating conditions to guarantee the accuracy of the calculation. 3. The injection of hydrogen will lead to a dramatic increase and a violent fluctuation of the polytropic index. After the injection, the polytropic index changes with the crank angle decreases drastically from 2.2 to 1.37, then it declines gradually to approximately 1.22 at the spark angle. 4. The average polytropic index of compression stroke rises with the ascending of the injection duration, the advancing of the SOI timing and the increasing of the engine speed. The calculation range of (60 CA ~ -10 CA) is appropriate for the absolute pressure correction, and the average polytropic index can be approximately set as 1.32. 5. The gas properties have a significant influence on the heat transfer of the hydrogen internal combustion engines. Hence, it is necessary to take the components of mixed hydrogen-air gases into account of the heat transfer model for the DI hydrogen engine.
Acknowledgement The financial support of the works Funded by China Postdoctoral Science Foundation (PFCPSF 2018M641215) is greatly acknowledged.
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Please cite this article as: Bao L-Z et al., Experimental study of the polytropic index of the compression stroke for a direct injection hydrogen engine, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2020.03.006