Analysis of a new analytical law of Heat Release Rate (HRR) for Homogeneous Charge Compression Ignition (HCCI) combustion mode versus analytical parameters

MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT Analysis of a new analytical law of Heat Release Rate (HRR) for Homogeneous Charge Compression Ignition (HCCI) combustion mode versus analytical parameters Miguel Torres Garcia*, Francisco J. Jiménez-Espadafor Aguilar, José A. Becerra Villanueva, Elisa Carvajal Trujillo Thermal Power Group, Department of Energy Engineering, University of Seville Escuela Técnica Superior de Ingenieros de Sevilla, Camino de los Descubrimientos, s/n. 41092 Sevilla, España *Corresponding author. Tel.:+34954486111; fax: +34954487243. E-mail: [email protected] (Miguel Torres García) Abstract Homogeneous charge compression ignition (HCCI) engines produce very low NOx and soot emissions and also improve engine efficiency when compare to conventional spark ignition engines. The combustion process bases on the self-ignition of a homogenous air-fuel mixture without an external ignition source. The gas temperature is very important to initiate the combustion and to promote the appropriate chemical kinetics. As a result, the heat release rate and heat transfer inside the combustion chamber play a significant role in the HCCI combustion mode. The high relevance of gas temperature on this combustion mode means that heat transfer is considered through a dedicated heat transfer model. In this system the forced convection from hot gases to the combustion chamber walls is the dominant heat transfer mechanism. This paper focuses MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT on the relationship between HRR in HCCI combustion mode and the four parameters that are required for an analytical function to model this heat release rate. More specifically, the influences of the fuel-air equivalence ratio, engine speed and EGR on the four parameters that control HRR are examined. The analytical HRR law is validated over a wide range of operating conditions in HCCI combustion mode and shows that these four parameters are directly related to any load condition, including engine speed, fuel rate and EGR. These parameters can therefore be used to characterize this combustion mode. Keywords: HRR (heat release rate); EGR (exhaust gas recirculation); HCCI (homogeneous charge compression ignition). Nomenclature p S Mean piston speed (m/s) Ac Common area of heat transfer a1, a2 Shape factors for HRR ATDC After top dead center BDC Bottom dead center BTDC Before top dead center C1, C2 Constants CFD Computational Fluid Dynamics CO2 Carbon dioxide DI Direct injection EGR Exhaust Gas Recirculation MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT H2O Water hc Heat transfer coefficient HCCI Homogeneous Charge Compression Ignition HRR Heat Release Rate K1, K2 Terms of HRR law LHV Lower Heat Value m & Mass flow (kg/s) Mp, Mpp Shape factors P, p Pressure (bar) Q Heat (J) Qp Heat release in HCCI combustion mode (J) QW Wall heat loss (J) RPM Revolutions per minute SI Spark ignition T Temperature (K) TDC Top dead center Tg Gas temperature (K) TW Cylinder wall temperature (K) V Volume (m3) Vd Displacement W Power (W) Greek letter MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT θ Crankshaft angle (radians) θp Duration of the energy release (radians) Ф fuel/air equivalence ratio ω Angular speed (rad/s) scaling α Scaling factor 1. INTRODUCTION Homogeneous charge compression ignition (HCCI) engines are attracting a great deal of attention as the next generation of internal combustion engine, mainly because of their very low NOx and soot emissions but also due to the improved engine efficiency when compared to conventional spark ignition engines [1-3]. HCCI combustion integrates features of both spark ignition (SI) and compression ignition (CI) engines to give promisingly the high efficiency of a diesel engine with virtually zero NOx and soot emissions[4,5,6 The combustion process is based on the self-ignition of a homogenous air-fuel mixture without an external ignition source. The gas temperature is very important to initiate the combustion and to promote the appropriate the chemical kinetics. For this reason, the heat release rate and heat transfer inside the combustion chamber play a significant role in the HCCI combustion mode. The rate of heat release in HCCI combustion mode is not controlled by the rate of fuel injection (as it is in DI engines) nor by finite turbulent flame propagation (as in SI engines). The absence of an ignition control mechanism has led researchers to explore a range of control strategies. However, performing these explorations solely in the laboratory would be inefficient, expensive and impractical since there are numerous MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT variables that are involved in complex interactions. A great deal of research activity has been carried out on global heat transfer models, e.g. by Annand [7], Woschni [8] and Hohenberg [9], and these have concerned engine conditions that vary significantly from those in HCCI combustion. The dominant heat transfer mechanism in HCCI combustion mode is forced convection from hot gases to the combustion chamber walls. The very low level of soot formation and relatively low bulk gas temperature mean that the radiation effect in this system is very small; a situation in contrast to the case of the conventional diesel combustion mode. For this reason, any HRR analysis for the HCCI combustion mode should be developed through a dedicated heat transfer model. In this paper, the model described by Junseok Chang was considered [10]. A significant amount of research is focused on obtaining an analytical function to model the heat release rate in HCCI combustion mode as this would facilitate combustion analysis and avoid the development of intensive tests and CFD calculus [11, 12]. The HRR for the HCCI process presents a premixed combustion shape while that of the diesel combustion mode includes premixed and diffusive contributions [13, 14]. The work described here involved the analysis of an HRR model developed for the HCCI combustion mode [15]. The influences of the fuel-air equivalence ratio and EGR on the four parameters that control HRR were examined. The development of an analytical HRR law validated over a wide range of operating conditions in HCCI combustion mode represents a significant advance in our understanding of HCCI combustion and also allowed the development of a predictive [15] computational model for this combustion process. 2. ENGINE AND EXPERIMENTAL SETUP MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT The experimental part of this work was based on tests carried out on the DEUTZ FL1 906 engine [16-17]. The original diesel engine was modified to adapt it to HCCI combustion, the injection point was fixed and different operating conditions (e.g., engine speed, air/fuel ratio and intake temperature) were tested. The specifications of the original diesel engine were as follows: cylinder bore 95 mm, stroke 100 mm, displacement 708 cm3, nominal compression ratio 19:1 and rated power of 13 kW at 3000 RPM. Commercial diesel fuel compatible with European Standard EN590 was used in all tests and the fuel properties are shown in Table 1. Systematic tests were carried out with the angle of injection fixed at 45º BTDC. The load was changed from a low load up to the maximum attainable load for the engine in HCCI combustion mode. An increase in the engine load, without EGR, leads to an advance in the start of combustion, an increase in the maximum pressure and also an advance in the crankshaft angle at which maximum pressure is reached. The maximum attainable load was established in order to ensure the mechanical integrity of the engine. The maximum pressure was limited at top dead center to 110 bar, which corresponds roughly to 20 Nm with the engine running without EGR at 1200 RPM, a compression ratio of 19:1 and a charge temperature of 18 ºC. The range of engine speeds studied was from 1200 RPM to 2400 RPM in intervals of 300 RPM. TABLE 1 The recirculated gases (EGR) were cooled in order to control the intake temperature and ensure that this never surpassed the ambient temperature; the effect of inlet temperature on HCCI is well known. The external EGR rate was evaluated by measuring the EGR mass recirculated and the total mass inlet. The formula is as follows: MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT 100)(% ⋅ + = AirEGR EGR mm m massEGR && & (1) where EGR m &and Air m &were measured with a hot wire flow meter. 3. MODEL FOR THE EVALUATION OF THE HRR In this work a thermodynamic zero-dimensional model was used to analyze and evaluate the parameters of an analytical law for HRR by following an iterative optimization process. Equations and simplifications that govern the mathematical model are needed due to the complex interactions between physical and chemical phenomena during combustion and these are described in the following equations [18], where blow by was not considered: • Thermal state equation • Combustion chamber volume • First Principle of Thermodynamics [16] • Heat losses The heat loss model is written as follows: ( ) ω θ 1 Wgcc WTThA d dQ −= (2) A lot of research can be found about heat transfer in internal combustion engines, but almost all of the models have been developed for spark and compression ignition engines. HCCI combustion process is quite different from that of spark or compression ignition engines. In this way the research of Junseok Chang [10] is devoted only to this type of combustion and it has been thoroughly validated in its paper and for these reasons only has been considered this heat losses model. MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT The heat transfer coefficient hc (W/m2 K) is based on the correlation formula given by Junseok Chang [10]. W Q is the wall heat loss, Ac is the area in contact with the gases, Tg(K) is the gas temperature, Tw(K) is the cylinder wall temperature and ω (rad/s) is the average angular speed. The global heat transfer coefficient can be written as: 8.073.08.02.0 )()()()()( tvtTtptLth scalingc −− = α (3) A scaling factor scaling α is used to tune the coefficient to match a specific engine geometry. Combustion-induced gas velocity is a function of the difference between motoring and firing pressure. ( ) motoring rr rd p pp Vp TVC SCtv −+= 6 )( 2 1 (4) The main reason for using this equation is to keep the velocity constant during the nonfiring period of the cycle and to then impose a steep velocity rise once the combustion pressure departs from motoring pressure. The subscript r denotes a reference crank angle, such as the intake valve closing. 4. ANALYTICAL LAW FOR HRR IN HCCI COMBUSTION MODE In this work a newly developed model for HRR has been analyzed. The HRR curves for a constant angular speed of 1200 RPM, inlet temperature of 18 ºC, compression ratio of 19:1 and different injected fuel levels are shown in Figure 1. These curves reveal the very high heat release rate that causes a rapid increase in combustion pressure. As a consequence, combustion is characterized by the sudden steep pressure rise on the cylinder pressure curve and by the peak in the HRR. Once the previously formed flammable mixture has been completely burnt, the HRR decreases until the end of MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT combustion. The HRR showed the same trend for all fuel consumption rates, engine speeds and EGR rates tested in HCCI mode. FIGURE 1 Therefore, combustion is completely controlled by chemical kinetics. The gas cylinder temperature is not sufficiently high and therefore the fuel does not reach pyrolysis conditions, thus almost completely avoiding soot formation and diminishing NOx formation markedly [19, 20]. A model for the HRR that can be adapted efficiently to a combustion process controlled only by chemical kinetics was developed by Wiebe. In this work, this scenario has been analyzed using a modified Wiebe function that allowed the formulation of a new HRR law that fits quite well to the HCCI combustion process [21,22].                 −         += +1 21 exp)1( ppp M p M p p p paM Q a d dQ θ θ θ θ θθ (5) Where a1, a2, Mp, Mpp are shape factors. In order to reproduce the HRR it was necessary to consider the parameter Mp to be different from the parameter Mpp (the opposite of the original Wiebe function), see equation (5). θp is the duration of the energy release and Qp characterizes the heat release in HCCI combustion mode. Defining the terms: ( ) 1 1 11 += +p M p pM Q aK p θ 1 22 1 + =pp M p aK θ (6) It follows that the HRR is: [ ] 1 21 exp + −= ppp MM KK d dQ θθ θ (7) 5. INFLUENCE OF ANALYTICAL LAW PARAMETERS ON THE SHAPE OF HRR MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT combustion rate. The smoke (0.3 vs. 0.7 Bosch number) and exhaust temperature (423ºC vs. 562 ºC) increased as a result of late burning. It can be observed that when the EGR is 20% by mass, NOx emissions remain constant with fuel consumption; without EGR the NOx emissions increase with fuel consumption. Combustion pressure and HRR corresponding to the results in Table 5 are shown in Figure 4, where simulated cylinder pressures are compared with measured ones derived from the experimental study. Quite good agreement between experimental and modeled results can be observed. The modeled cylinder pressures were obtained from the new HRR law for different mass flows and EGR levels. In terms of the area under the pressure curve between IVC and EVO, the maximum error is about 1%. An interesting aspect to highlight is the good reproduction of pressure during the combustion process when an abrupt increase in pressure occurs. FIGURE 4 As can be observed, the new HRR law adapts perfectly to any EGR rate. From the minimum EGR rate (5%), each increment in this parameter has three effects on the HRR: a) A delay in the start of combustion. b) A diminution of the maximum heat release rate. c) An increase in the combustion duration. The increase in torque is due to the diminution of combustion pressure along the compression stroke, which in turn is due to the delay in the start of combustion (effect a). As a result, power increases at the same engine speed and fuel consumption and there is also an improvement in the engine’s specific fuel consumption to weight of effect c, which reduces thermodynamic efficiency [27]. Effect b produces a diminution in the combustion chamber temperature and this will result in a diminution of NOx MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT emissions and exhaust temperature [28]. The parameters for the simulated HRR are shown in Table 6. TABLE 6 The values of the four parameters of the HRR analytical law applied to the cases shown in Figure 4 are presented in Table 6. These parameters for all cases studied at engine speeds of 1200 and 1800 RPM at three fuel rates are presented versus thermal capacity in Figure 5. Parameter K1 shows the same tendency at 1200 and 1800 RPM for all fuel rates and the relationship with thermal capacity is almost linear, see Figures 5 (a1) and 5(b1). At 1200 RPM parameter K1 is always higher for the maximum fuel rate regardless of the m·Cp value. However, at 1800 RPM this behavior changes and for the higher thermal capacity the minimum fuel rate presents the maximum K1. It is also worth noting that the K1 slope changes from positive (1.5e–5 kg/cycle, minimum fuel rate) to negative (2.2 e–5 and 1.5e–5 kg/cycle), with the slope becoming more negative as the fuel rate increases. Plots of K2 versus thermal capacity are shown in Figures 5 (a2) and 5 (b2), with the relationship increasing for all engine speeds and fuel rates in the low thermal capacity range. This reveals that combustion intensity increases as the thermal capacity decreases. However, at 1800 RPM all of the curves present a maximum, which reveals an increase in combustion intensity and combustion duration from this thermal capacity value. This behavior can be explained in terms of the expected increase in charge homogeneity with EGR rate and engine speed. The parameter Mp shows a linear relationship with thermal capacity and this is almost identical at 1200 and 1800 RPM, see Figures 5 (a3) and 5 (b3). However, there is a marked slope change between the different fuel rates and this change from a positive slope at 1.5e–5 kg/cycle to a negative slope for higher fuel rates. Furthermore, the slope MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT becomes more negative as the fuel rate increases. Close to a thermal capacity of 0.5 J/K, Mp is almost constant with respect to m·Cp. The parameter Mpp also shows a linear relationship with thermal capacity and this is again almost the same at 1200 and 1800 RPM, see Figures 5 (a4) and 5 (b4). The slope of the line decreases with injected fuel and is negative for the 2.8e–5 kg/cycle. At 1800 RPM, see Figure 5 (b4), Mpp shows the same behavior for all engine speeds, i.e., with a positive and negative slope, respectively, with the highest value at 1.5e–5 kg/cycle injected fuel and the lowest at 2.8e–5 kg/cycle. FIGURE 5 7. CONCLUSIONS An experimental and simulation study has been carried out that provides a detailed understanding of the HCCI combustion mode through the analysis of HRR. The new HRR law was implemented in an engine model to evaluate performance in comparison to the experimental data obtained in the laboratory. The new HRR law allows the cylinder pressure curve to be predicted with minimum error and shows a very good match to the experimental data. The developed HRR law has shown that four suitable parameters (K1, K2, Mp and Mpp) are sufficient to model the heat release rate. These parameters control the main characteristics of HRR and these are shape, maximum value, maximum angle position and combustion duration. The experimental analysis performed showed that these four parameters are directly related to any load condition, including engine speed, fuel rate and EGR. Research is in progress to develop a sensitive analysis of these parameters on HRR. MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT ACKNOWLEDGMENTS The work described in this paper is a part of the project CTQ2007-68026-CO2-02/PPQ within the I+D+i national plan in the period 2007-2009 and was supported by the Spanish Government (Ministry of Science and Education). The authors are grateful to the Ministry of Science and Education of Spain for their financial support. 1. Thring. R.H. “Homogeneous Charge Compression Ignition (HCCI) Engines.” SAE Paper No.892068. 2. Aceves, S.M., Flowers, D.L., Westbrook, C.K., Smith, J.R., Pitz, W.J., Dibble, R., HCCI combustion and emissions, Paper No 2000-01-0327. 3. Christensen, M., Johanson, B., Ammeus, P., Mauss, F., (1998) Supercharged Homogeneous Charge Compression Ignition, SAE Paper No 980787. 4. Kimura, S. Aoki, O. Ogawa, H. Muranaka, S. Enomoto, Y. New combustion concept for ultra-clean and high-efficiency small DI diesel engines, SAE Paper 1999-01-3681, 1999. 5. 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FIGURES CAPTIONS MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT Figure 1. Combustion Chamber pressure and the HRR in HCCI combustion mode versus crank angle for a constant angular speed of 1200 RPM and inlet temperature of 18 ºC. Compression ratio of 19:1. Analytical HRR versus K1 (a) Analytical HRR versus K2 (b) Analytical HRR versus Mp (c) Analytical HRR versus Mpp (d) MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT Figure 2. Analysis of HRR shape versus different parameters of the functional law. (a1) (b1) (a2) (b2) (a3) (b3) MANUS CRIP T ACCEP TED ACCEPTED MANUSCRIPT (a4) (b4) Figure 3. Analysis of analytical law parameters versus the injected fuel mass for two EGR rate percentages. Figure 4. Measured and predicted cylinder pressure and HRR in HCCI combustion mode (engine speed is 2100 RPM, constant fuel consumption 2.75e–5 kg/cycle, initial Ф = 0.46 and different EGR rates).