Influence of a Combustion Parametric Model on the Cyclic Angular

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Influence of a Combustion Parametric Model on the Cyclic Angular Speed of Internal Combustion Engines. Part I: Setup for Sensitivity Analysis Fernando Cruz-Peragon,*,† Francisco J. Jimenez-Espadafor,‡ Jose M. Palomar,† and M. Pilar Dorado§ Department of Mechanics and Mining Engineering, EPS de Jaen, UniVersidad de Jaen, Campus Las Lagunillas s/n, 23071 Jaen, Spain, Department of Energetic Engineering, ESI, UniVersidad de SeVilla, Camino de los Descubrimientos s/n, Isla de la Cartuja, 41092 SeVilla, Spain, and Department of Chemistry Physics and Applied Thermodynamics, EPS, Edif. Leonardo da Vinci, Campus de Rabanales, UniVersidad de Cordoba, 14071 Cordoba, Spain ReceiVed February 5, 2009. ReVised Manuscript ReceiVed April 13, 2009

Combustion parameters evaluation presents an important application to engines failures diagnosis. The most extended parametric procedure to describe combustion processes in internal combustion engines is based on the Wiebe’s function and depends on the rate of heat release of the fuel (ROHR) and several input parameters. When a combustion model is used for indirect identification and optimization processes, the simulation of both profiles, cyclic pressure and speed, must guarantee an accurate estimation of ROHR through convenient curves estimation. However, in case some input parameters of the combustion model are unknown, several solutions will show up. To fix this problem, a combustion parametric model is proposed. In this work, the necessity of establishing the correlation between the combustion model input parameters, the engine dynamic response (cyclic angular speed), and the interrelation between them, has been demonstrated. This correlation is considered the starting point that will allow the performance of a further sensitivity analysis of the response in terms of combustion, thus optimizing the combustion model in search of unique solutions. The study has been carried out in both a single-cylinder direct-injection (DI) compression ignition engine (CIE) and a threecylinder spark ignition engine (SIE). Data associated to the angular speed profile have been adopted as output parameters of the engine, while combustion-related ones have been considered input parameters. Results showed that, for further sensitivity analysis and model optimization, evaluation of the influence of combustion parameters over the engine angular speed is extremely important, if indirect modeling is applied. The best way to assess the relation between input and output variables is by a sensitivity analysis through a previous design of experiments.

1. Introduction To guarantee an optimized combustion engine design, the influence of design parameters over engine performance must be defined. In this sense, cylinder pressure, which is directly related to exhaust emissions, vibration, noise, engine performance, and dynamics, provides useful information about engine behavior. Thus, it is sometimes used for engine design, control, diagnosis, and combustion analysis. Depending on the target, pressure cycle modeling could be required. As an example, it actually plays an important role in new biofuels engine testing. Although biodiesel properties are very similar to fossil fuels, combustion processes are slightly different, resulting in different pressure, power, and emissions curves.1-6 * Corresponding author. Phone: +34 953 212367. Fax: +34 953 212870. E-mail: [email protected]. † Universidad de Jaen. ‡ Universidad de Sevilla. § Universidad de Cordoba. (1) Szybist, J. P.; Boehman, A. L.; Taylor, J. D.; McCormick, R. L. Fuel Process. Technol. 2005, 86, 1109–1126. (2) Szybist, J. P.; Song, J.; Alam, M.; Boehman, A. L. Fuel Process. Technol. 2007, 88, 679–691. (3) Hribernik, A.; Kegl, B. Energy Fuels 2007, 21, 1760–1767. (4) Kegl, B.; Pehan, S. Thermal Sci. 2008, 12, 171–182.

Although experimental design strategies aid laboratory experimentation, modeling strategies help designers to analyze experimentation results. In this sense, there are two kinds of procedures to model the cylinder pressure profile: stochastic modeling and empirical parametric procedures. Stochastic modeling is widely used to model the cyclic pressure profile. The pressure curve may be modeled joining a deterministic mean pressure waveform and a Gaussian process, which is related to a particular combustion region, but unrelated to other combustion processes.7-9 The conventional approach is to focus on the statistical variability of a few key parameters, namely, maximum pressure, maximum pressure angle, and the indicated mean effective pressure (Imep).10-12 Recently, a very (5) Dorado, M. P.; Ballesteros, E.; Arnal, J. M.; Go´mez, J.; Lo´pez, F. J. Fuel 2003, 82, 1311–1315. (6) Dorado, M. P.; Ballesteros, E.; Arnal, J. M.; Go´mez, J.; Lo´pez, F. J. Energy Fuels 2003, 17, 1560–1565. (7) Connolly, F. T.; Yagle, A. E. J. Eng. Gas Turbines Power 1993, 115, 801–809. (8) Connolly, F. T.; Yagle, A. E. Mech. Syst. Signal Process. 1994, 8, 1–19. (9) Bonnier, J.; Tromp, C.; Klein, J. Decoding Torsional Vibration Recordings for Cylinder Process Monitoring. In 22nd CIMAC Congress: 1998; pp 639-649. (10) Jacob, P. J.; Gu, F.; Ball, A. D. Proc. Inst. Mech. Eng. Part D 1999, 213, 73–81.

10.1021/ef900109h CCC: $40.75  2009 American Chemical Society Published on Web 05/05/2009

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Figure 1. Combustion indicators from the ROHR profile: (a) SIE and (b) DI CIE.

Figure 2. Combustion indicators from the MBF profile: (a) SIE and (b) DI CIE. Table 1. Input Parameters of the Combustion Sub-Model engine

input parameters

SIE CIE

φ, θi, θC, A, m φ, θj, θp, θd, mp, md, qp

useful application that simulates the cylinder pressure data, based on the concept of a dimensionless pressure curve in the frequency domain, has been proposed.13 The main drawback of this approach is that little information is drawn from the simulated curves. Although diagnosis is another possible application,8 the nature of malfunctions is difficult to predict, that is, malfunctions related to combustion process. Furthermore, a postprocessing procedure is needed. On the other hand, parametric models include the combustion influence on the pressure curve. Main parametric models are the Wiebe model and the Logistical models, besides general recursive procedures, providing a fuel mass-burned fraction (MBF) profile that depends on the crank angle degree (CAD).14 Although there are other expressions such as the models from Chmela et al. and Barba et al.,15,16 the widely used Wiebe model provides a good agreement between measured and calculated in-cylinder pressure.17-22 Different analyses predict correlations between some of these parameters.14,23 Engines are mechanical systems where pressures are considered to be the input forces, and the response of a given torque is the instantaneous angular speed. In this sense, in many failure diagnosis applications, the pressure cyclic curve is determined from the angular speed analysis.10,11,22 Although the pressure profile is approached accurately, results from the analysis of combustion parameters through parametric models differ from real values, with the exception of two parameters (fuel equivalence ratio and injection

timing), that can be fairly estimated, thus demonstrating the relation between input and output parameters is not unique.20,21 The goal of this work is to evaluate the relationship between the input parameters of the combustion model (via Wiebe function) and the system response (instantaneous angular speed) through indirect modeling, to further perform a sensitivity analysis. The interaction among combustion parameters and on the system performance is showed. First, input-output indicators related to the system performance must be selected, as shown in this paper. Second, a design of experiments (DoE) that provides the different operating conditions of the tested engine, considering the minimum number of tests and a wide working conditions range, must be proposed. Then, a sensitivity analysis through a stochastic assessment and model optimization must be done. These last two features will be proposed and discussed in a further work. 2. Background 2.1. Parametric Combustion Submodel. The combustion process of an internal combustion engine can be evaluated by (11) Gu, F.; Jacob, P. J.; Ball, A. D. Proc. Inst. Mech. Eng. Part D 1999, 213, 135–143. (12) Johnsson, R. Mech. Syst. Signal Process. 2006, 20, 1923–1940. (13) Zeng, P.; Assanis, D. N. Cylinder Pressure Reconstruction and Its Application to Heat Transfer Analysis, SAE Paper No. 2004-01-0922; SAE World Congress: Detroit, MI, March 8-11, 2004. (14) Roberts, J. B.; Peyton Jones, J. C.; Lansboroguh, K. J. Mech. Syst. Signal Process. 2001, 15, 419–438. (15) Barba, C.; Burkhardt, C.; Boulouchos, K.; Bargende, M. Motortech. Z. 1999, 60 (4), 262–270. (16) Chmela, F. G.; Orthaber, G. C. Rate of Heat Release Prediction for Direct Injection Diesel Engines Based on Purely Mixing Controlled Combustion, SAE Paper 1999-01-0186; 1999.

A Combustion Parametric Model

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Figure 3. Results from pressure and dynamic models varying randomly combustion parameters in a single-cylinder CIE (Case 1: φ ) 0.68; θi ) 5°, θp ) 40°; θd ) 110°; mp) 2; md ) 0.5; qp ) 0.25; Case 2: φ ) 0.68; θi ) 0°, θp ) 20°; θd ) 110°; mp) 2; md ) 0.5; qp ) 0.05; Case 3: φ ) 0.68; θi ) 0°, θp ) 20°; θd ) 70°; mp ) 2; md ) 0.5; qp ) 0.05).

means of the fuel rate of heat release (ROHR, kJ/CAD), indicating the instantaneous contribution of the fuel combustion in the gas evolution. It can be directly obtained from the first Law of Thermodynamics applied to the cylinder along one cycle, on the assumption of uniform pressure and temperature over the instantaneous volume.24 The area of this curve along the rotation represents the energy fuel release in the evaluated condition, that is, the accumulated ROHR (AROHR, kJ/cycle). The ROHR profile provides certain information about the combustion process, establishing angular positions related to the top dead centre (TDC) of the piston into the cylinder:

(i) In a SIE (see Figure 1a25), the starting point of the combustion (θi) denotes the ignition timing, where the spark discharges. Difference between this point and the end of the ROHR curve provides the duration of combustion or overall burning angle (θC). In a SIE, there are three main parts of the combustion: first, a flame-development angle (θ1), with a laminar combustion nature, taking place nearly in 10% (although it could reach also values from 1 to 5%) of the whole combustion process. Here, a small but significant fraction of the cylinder mass is burned. Second, a rapid-burning angle (θ2), with a turbulence combustion nature, giving rise to the flame propagation rate. It takes place in about 80-85% of the combustion process. The third phase is another laminar combustion period (θ3), carrying out the flame termination. In any case, the ROHR fails to clearly establishing the three parts of the whole combustion process. (ii) For a CIE (see Figure 1b26), the starting point of the curve represents the injection timing (θj). The first period of the curve represents the ignition delay angle (or time) (θD), where combustion does not already exist. At this time, there are physical and chemical phenomena where fuel drops are formed and vaporized. The negative value of the curve is due to the fuel vaporization that makes the mixture with the cylinder gases cool down. When the curve reaches a positive value, the combustion starts, and the crank position corresponds to the ignition timing (θi). At this point, a fast combustion phase starts, where the fuel that is vaporized and mixed with air is burned quickly. In this period the pressure gradient is increased, as well as the pressure increment. This period is also called premixed phase with a duration of θp degrees. Finally, the third combustion phase, or diffusion phase, is the period where the remaining fuel is burned off until the flame extinction (θd). The division between these two phases varies considerably with both, combustion chamber design and engine operating conditions,

Figure 4. Scheme of the engine test bench. Table 2. Main Characteristics of the Engine Test Bench parameters stroke (mm) bore (mm) compression ratio maximum torque (Nm) maximum power (kW) Imep at max. power (MPa) pulse sensor type (in flywheel) pulse per revolution (ppr) or No. of teeth pressure transducer type

Deutz Dieter LKRS-A

Maruti 800

single-cylinder CIE three-cylinder SIE 100.0 72.0 85.0 68.5 17.5:1 9.5:1 34 (at 2400 rpm) 61.7 (at 3000 rpm) 9.5 (at 3000 rpm) 33 (at 6000 rpm) 0.83 0.995 Peper + Fuchs, NJO 8-4, 5-N, max. frequency ) 10 kHz 148 96 Kistler 6061B piezoelectric cooled Kistler 6117B piezoelectric in spark plug

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Figure 5. Direct method (DM) to identify the combustion submodel parameters (direct problem).

that is, EGR (exhaust gasses recirculation) rate, use or not of one or two pilot combustions before principal injection, inlet temperature and pressure, etc. The overall burning angle (θC) is also derived from the difference between the ignition timing and the end of the ROHR curve. Again, the ROHR clearly fails to defin the three parts of the whole combustion process. Figure 1b shows the relative difference between the profiles of the two main parts on which it is divided, corresponding to both combustion periods (premixed and diffusion), for a DI CIE.27,28 Nevertheless, these two parts could suffer certain modifications. In a premixed CIE, the diffusion period reaches a higher maximum value than that in a non-premixed one.18,29 Even in homogeneous charge compression ignition (HCCI) engines, under similar CIE conditions, an additional period is attached previously to the others and after the ignition delay (θD), corresponding to a cool flame period.30 In this work, up to two combustion periods models have been analyzed. Though the different combustion phases are visible in the instantaneous ROHR diagram (Figure 1), it is difficult to determine both the limits between them and the starting and ending points of the combustion period. To clearly distinguish between the different combustion phases, the ROHR profile must be integrated, providing the MBF curve that usually follows an exponential law. The form factors associated to this new curve provide the previously mentioned angles (see Figure 2a, in case of SIE, and Figure 2b, for CIE). Figure 2b depicts a more complex MBF profile for CIE that can be approached, at least, by two exponential laws multiplied by a proportional factor. With these considerations, the combustion process is evaluated through the Wiebe function. The MBF law depends on the CAD (θ) and the type of engine (SIE or CIE), as showed in eqs 1.a and 1.b, respectively.

[ ( ) ] ( ( ) )] [ ( ( ) )]

MBFSIE ) 1 - exp -A

[

MBFCIE ) qp 1 - exp -6, 9

θ - θi θp

θ - θi θc mp+1

qd 1 - exp -6, 9

m+1

(1.a)

+

θ - θi θd

md+1

(1.b)

Figure 6. Indirect method (IMP) to identify the combustion parameters from pressure measurements.

Figure 7. Indirect method (IMV) to identify the combustion parameters from engine speed measurements.

where A and m are form factors (dimensionless). Considering CIE, subindexes p and d denote premixed and diffusion phase, respectively. The diffusion phase period (θd) corresponds to the difference between the duration of combustion (θC and θp), that is, θC ) θp + θd. For CIE, the function varies between 0 and 1, as depicted in Figure 2b. So, the addition of both curves must incorporate two proportionality factors, allowing the MBFCIE profile to follow the tendency depicted in Figure 2b. They are denoted by the specific energy released during the premixed phase (qp), and the diffusion phase (qd), being qp+ qd ) 1. The ROHR curve corresponds to the derivative of the MBF curve, considering the fuel consumption, Mf (kg/cycle) (related to the equivalence ratio,31 φ) and the fuel low heating value, LHV (kJ/kg), following the expressions shown in eq 2.a.


ROHRSIE )


( ) [ ( ) ]

dQf (m + 1) θ - θi ) LHVMf(φ)A dθ θc θc θ - θi exp -A θc

m

×

m+1

(2.a)

( )

θ - θi mp dQf qp ) LHVMf(φ)6.9 (mp + 1) × dθ θp θp θ - θi mp+1 qd + LHVMf(φ)6.9 (md + 1) exp -6.9 θp θd θ - θi md × θd θ - θi md+1 exp -6.9 (2.b) θd

ROHRDE )

[ ( ) ] ( )

[ ( ) ]

Another important CIE attribute considers the ignition delay (θD) from the start of the injection (θj), as follows: θi ) θj θD. To simulate the ignition delay there are different approaches, such as the Sitkei correlation shown in eq 3, depending on pressure, temperature, and fuel characteristics, such as cetane number (CN).32,33 These equations are obtained from experiments with constant temperature (T) and pressure (p) environments. An iterative procedure provides the value of θD.26 θD ) f(p, T, CN)

(3)

Table 1 summarizes the input parameters to be considered in a general combustion submodel, depending on the engine. ˆ. These parameters compose the input vector of the system, W 2.2. Cylinder Gas Evolution and Models. The pressure evolution in the cylinder can be drawn through the first Law of Thermodynamics, considering the combustion chamber as an (17) Miyamoto, N.; Chikahisa, T.; Murayama, T.; Sawyer, R. SAE International Congress and Exposition, Detroit, Michigan, March, 8-11, 1985; Paper no. 850107. (18) Arregle, J.; Lopez, J. J.; Garcia, J. M.; Fenollosa, C. Appl. Therm. Eng. 2003, 23, 1301–1317. (19) Arregle, J.; Lopez, J. J.; Garcia, J. M.; Fenollosa, C. Appl. Therm. Eng. 2003, 23, 1319–1331. (20) Cruz-Peragon, F.; Jimenez-Espadafor, F. J. Energy Fuels 2007, 21, 2600–2607. (21) Cruz-Peragon, F.; Jimenez-Espadafor, F. J. Energy Fuels 2007, 21, 2627–2636. (22) Cruz-Peragoń, F.; Jimenez-Espadafor, F.; Palomar, J. M.; Dorado, M. P. Energy Fuels 2008, 22, 2972–2980. (23) Cruz-Peragon, F.; Jimenez-Espadafor, F. J. Anal. Ingen. Mecań. 2004, 15, 1891–1896. (24) Desantes, J. M.; Pastor, J. V.; Arregle, J.; Molina, S. A. J. Eng. Gas Turbines Power 2002, 124, 636–644. (25) Ferguson, C. R. Internal Combustion Engines: Applied Thermosciences; John Wiley & Sons: New York, 1985. (26) Challen, B.; Baranescu, R. Diesel Engine Reference Book, 2nd ed.; Elsevier: Oxford, UK, 1999. (27) Cruz-Peragon, F. Ana´lisis de metodologıás de optimizacioń inteligentes para la determinacioń de la presioń en ca´mara de combustioń para motores alternativos de combustioń interna por me´todos no intrusivos; PhD Thesis, University of Seville: Spain, Seville, 2005. (28) Ali, Y.; Hanna, M. A.; Borg, J. E. Trans. ASAE 1996, 39, 407– 414. (29) Wakisaka, T.; Kato, N.; Nguyen, T. T.; Okude, K.; Takeuchi, S.; Isshiki, Y. Numerical prediction of mixture and combustion processes in premixed compression ignition engines. In 5th International Symposium on diagnosis and modelling of combustion in internal combustion engines; COMODIA 2001: Nagoya, Japan, July 1-4, 2001; pp 426-433. (30) Fayoux, A.; Dupre´, S.; Scouflaire, P.; Houille, S.; Pajot, O.; Rolon, J. C. OH and HCHO LIF Measurements in HCCI Engine. In Proceedings of the 12th International Symposium Applications of Laser Techniques to Fluid Mechanics: Lisbon, Portugal, July 12-152004; pp 1-11. (31) Heywood, J. B. Internal Combustion Engine Fundamentals; McGraw Hill: New York, 1988. (32) Sitkei, G. Kraftstoffaufbereitung und Verbrennung bei Dieselmotoren; Springer-Verlag: Berlin, Germany, 1964. (33) Hardenberg, H. D.; Hase, F. W. SAE Transactions, SAE Paper No. 790493; 1979; p 88.

open system (see eq 4). The simplest model for diagnosis applications considers the combustion chamber a single homogeneous zone, with a continuous mixture of ideal gases. The instantaneous state of the mixture can be described by its pressure (p), volume (V), temperature (T), and equivalence ratio (φ). dQL dQf dV -p + dt dt dt

∑ m˙ h

i i

i

)

dU dt

(4)

where m ˙ i and hi are the mass flow rate and enthalpy, respectively, at location i, (i corresponds to the inlet and outlet valves and the ring loss) p(dV/dt) is the work transfer rate, and U is the internal energy of the gas inside the system boundaries. To model the combustion process for cycle simulation purposes, the key parameter is the variation of MBF over time, once ignition has started, dQf/dt (ROHR), as well as the heat losses dQL/dt through the wall. In this sense, eq 1.a can be assessed in the time domain or, for more convenience, in the crank angle domain.8 In addition to the heat release rate submodel, the overall model incorporates the following criteria:31,34 (i) Wall heat transfer losses, through a validated correlation. (ii) Gasses leakage. Flow of gases through the rings has been modeled considering an isentropic and quasi-stationary flow. The temperature of the gas between the rings is the same as that of the engine wall, because the high surface-volume ratio and its composition are the same than those of the material inside the combustion chamber. A small effective flow area has been chosen to ensure the values given by the model match those measured in the tested engine. (iii) Thermodynamic properties change with pressure and temperature. (iv) Exhaust of burned gases and simultaneous charging of the cylinder. The purpose of the exhaust and inlet processes (or scavenging process for two-stroke engines) is to remove the burned gases at the end of the power stroke, thus filling the cylinder with fresh charge ready for the next cycle to start. The volumetric efficiency is an overall parameter related to this process that depends on manifolds, valves, ports, and engine operating conditions. Both quasistatic and dynamic effects are usually significant. 2.3. Modeling Engine Dynamic Behavior. In the engine dynamics subsystem, the input parameter is the cylinder’s pressure, related to both angular speed and load values. In this sense, to analyze the relation between input and output parameters, research has been carried out. Experimental results have showed that some parameters, such as brake-specific fuel consumption BSFC (g/kWh) and exhaust emissions (sucha s NOx or soot), depend on combustion parameters, such as ignition timing or ROHR.1,35 Moreover, geometric and mechanical characteristics of engines produce different angular speed values along the rotation evolution in an engine cycle. This cyclic instantaneous angular speed can be calculated by solving a torque balance numerical equation,8,36 such as eq 5, assuming the complete knowledge of dynamic and geometric characteristics included in vector uˆ: (34) Cruz-Peragoń, F.; Carvajal, E.; Cantador, J.; Castillo, A.; JimeńezEspaldafor, F.; Munõz, A.; Sańchez, T. DeVelopment of a Non IntrusiVe Method for the Diagnosis of the Combustion System of a Small Direct Injection Diesel Engine, SAE Paper No. 2001 01 1790/4212; Proceedings of the 7th SETC Small Engine Technology Conference and Exhibition: Pisa, Italy, 2001; pp 665-673. (35) Willmann, M.; Qpalinski, A.; Wislocki, K. J. KONES Int. Combust. Engines 2002, 1-2, 275–282. (36) Geveci, M.; Osburn, A. W.; Franchek, M. A. Mech. Syst. Signal Process. 2005, 19, 1107–1134.

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Figure 8. Measured data in engines: (a) three-cylinder SIE, 3300 rpm and 14 N m; (b) single-cylinder CIE, at 1800 rpm and 16.7 N m.

Ti(Pji(θj), θj, uˆ) + TMI(θj, ωj, uˆ, Rj) + Tf ) TL

(5)

where Ti is the global indicated torque, TMI corresponds to the global inertia torque of the moving parts (both rotating and reciprocating elements), Tf denotes the mechanical losses torque, that applies to an additional submodel,37 and TL is the load. These terms vary while the cycle evolves, depending on the instantaneous chamber pressure into each cylinder j, Pji(θ), angle, θ, speed, ω and acceleration, R. The last parameters can be summarized in a single one, since angular speed and acceleration are derived from the crank angle position along the time. Thus, given a pressure profile and load value for each cylinder, through eq 5, the instantaneous angular speed curve along one engine cycle is provided. It reproduces the real response of the engine dynamic elements when input parameters (pressures) are considered.27 To analyze the relation between input and output parameters or functions of the whole system, the set of eqs 2.a-5 are used. As an example, Figure 3 shows how the speed profile varies with pressure variations. Pressure profile could be changed, altering randomly some combustion parameters into the model (see eqs 2.a-4). 3. Methodology 3.1. Selection of the System for Models Identification and Validation. To validate the proposed mathematical models and procedures that will help to identify the combustion parameters, two different engines have been analyzed. Table 2 shows the main characteristics of both systems. The engine test bench included an electric dynamometer attached to the tested engine (see Figure 4). A pressure transducer was mounted in each cylinder, and the signal passed through a charge amplifier. For the SIE, inductive winding around the spark wire in cylinder 1 provided a reference signal of the ignition starting point at cylinder No. 1. To indicate the angular position along the time, a magnetic pulse sensor was located in the flywheel. From this signal, the angular speed was calculated. All the measurements have been done in the time domain. Since the angular sensors (37) Rezeka, S. F.; Henein, N. H. SAE Paper No. 840179; 1985.

provide the crankshaft position, results can be later presented in the angle domain. 3.2. Parameter Identification Procedures. Equation 4 allows a direct determination of the ROHR (direct method, DM) once the pressure curve is depicted. This curve must be integrated (providing MBF) and analyzed to define the combustion submodel components. To identify those parameters, a Newton method-based iterative process38 is used and is summarized in Figure 5. This method is widely used to analyze combustion properties and emissions of new biofuels.1-4,24,39 Parametric relations or fitting equations between engine operating conditions (such as average speed and load), emissions (NOx, particulate matter, etc.), and particular points of the ROHR curve (such as angular positions related to the combustion process, maximum gradient, maximum value of RHOR, etc.) can be acquired through experimental research. Results can be used to optimize engine performance under different working conditions, improving the injected fuel mass and the ignition/injection timing, to reach a compromise between emissions and engine efficiency.1,2 Application of DM by eq 4 results in a ROHR curve that incorporates noise or inadequate profile, including a MBF value that does not follow the tendencies depicted in Figure 2. This can be explained considering two main error sources: (i) The pressure curve could incorporate some irregularities, derived from the measuring and conditioning equipment of the original signal.27,40 Typical sensing errors include mismatch between true pressure variation and pressure sensed by a transducer at the end of the connecting passage, failure to give a true average value of a fluctuating quantity, and time lag under transient conditions. In any case, it can be minimized by conveniently filtering the original pressure signal. (ii) Although geometric properties and other parameters are usually difficult to estimate accurately, they are crucial to define additional submodels in eq 4, such as the wall heat losses, gas (38) Gill, P. E.; Murray, W.; Wright, M. H. Practical Optimization, 11th ed.; Academic Press: London, 1997. (39) Hong, S.; Assanis, D. N.; Wooldridge, M. S.; Im, H. G. SAE Paper No. 04P-273; 2004. (40) Plint, M.; Martyr, A. Engine Testing: Theory and Practice, 2nd ed.; Butterworth-Heinemann: UK, 1999.



Figure 9. Combustion model results from cylinder No.1 (three-cylinder SIE), at 3300 rpm and 14 N m.

exchange process, and gases leakage. The complexity of heat transfer is highly responsible of this problem, since the relevant phenomena are transient, three-dimensional, and depending on rapid swings in cylinder gas pressure and temperatures, mainly in CIE.41 On the other hand, the dynamic effects over the gas exchange process produce a complex model, thus the overall definition of geometric data in ports and ducts is needed.31 Pumping losses are significant in SIE. Finally, pressures into CIE cylinders are responsible of mass gas passing through the rings, thus the use of the gas leakage submodel to correctly validate the pressure model is needed.27 As a result of these considerations, angles and combustion periods could be poorly estimated in some cases. Furthermore, to fix this problem, another identification procedure consisting on initially established combustion parameters values is required. Then, the combustion submodel is developed considering eq 4, providing the pressure curve, temperature, and mass evolution.26,31 Next, to fit both, measured and modeled chamber pressures, a Newton method-based iterative process will help to identify the parameters that define MBF.38 Finally, results will ensure that both, ROHR and MBF profiles, follow the tendencies depicted in Figures 1 and 2. It must be noticed that other terms associated to the different submodels (such as residuals, discharge coefficients, etc.) besides the combustion parameters must be also determined. Figure 6 shows a scheme that describes the process to determine the combustion submodel parameters by the proposed indirect method (IMP). For diagnosis applications, some researchers have proposed to indirectly estimate the pressure profile by measuring the instantaneous angular speed (IMV).42,43 In fact, several new techniques, such as genetic algorithms (GA) and artificial neural networks (ANN), besides the Newton method, have been adopted.10-12,20-22 In this case, there is no experimental pressure curve to test the feasibility of the proposed combustion model. However, the indirect identification procedure allows the comparison between modeled and real angular speed. The use of the dynamic model explained before is crucial and results in an identification procedure, as showed in Figure 7.27 (41) Rakopoulos, C. D.; Mavropoulos, G. C.; Hountalas, D. T. Int. J. Energy Res. 2000, 24, 587–604. (42) El-Ghamry, M.; Steel, J. A.; Reuben, R. L.; Fog, T. L. Mech. Syst. Signal Process. 2005, 19, 751–765. (43) Moro, D.; Cavina, N.; Ponti, F. J. Eng. Gas Turbines PowerTrans. ASME 2002, 124, 220–225.

3.3. Application Examples. As an example, these procedures have been evaluated under a single operating condition, considering each analyzed engine (see Table 2). Figure 8 shows the cyclic pressure profile and dynamic response (instantaneous angular speed) of this case study. The TDC has been approached by the “motored method.”26 As a result, Figures 9 and 10 show the ROHR and MBF profiles, considering the parameter values from Tables 3 and 4, under the three proposed methods. The direct method (DM) provides the ROHR curve through the combustion model. Nevertheless, it must be mentioned that the ROHR profile may adopt inadequate values in the proximities of the combustion period. This method considers the cyclic pressure curve profile, the ignition timing (θi, in SIE, and injection timing θj, in CIE), and fuel equivalence ratio (φ) as input parameters. Though the ignition, θi, in SIE is wellknown, the ignition in CIE needs to be inferred from the model described before, according to eq 3. θi values will be considered the starting points in their respective combustion periods. On the other hand, integration of the ROHR provides the MBF curve. The angle where this curve reaches a value equal to one is considered the end of the combustion period. Also, the optimum parameters values that provide both profiles (ROHR and MBF) have been searched by an identification procedure. In any case, it is the faster and more reliable way to identify the combustion parameters by a direct method. The other two mentioned indirect procedures provide θi, θj, φ, as well as the remaining parameters values. The indirect method IMP provides the combustion parameters values comparing the pressure curves (real and modeled), whereas the method IMV evaluates those parameters comparing angular speeds (real and modeled). In both methods, the ROHR profiles derived from identified parameters ensure a very good accuracy between both modeled and measured pressure curves, wth IMP showing the best accuracy. IMV presents estimation errors increase because a perfect fitting between both modeled and measured angular speed curves is very difficult, due to the associated system dynamic model, which is difficult to fit. Although results could be acceptable (pressure and angular speed profiles), several solutions could appear concerning the ˆ . In this case, the accuracy of the estimation of input vector W those parameters depends on their weight into both, pressure and dynamic models, and on the interrelation between them. In

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Figure 10. Combustion model results from a single-cylinder DI CIE, at 1800 rpm and 16.7 N m. ˆ in Cylinder No. 1 of the Three-cylinder SIE (see Figure 9) Table 3. Identified Values of the Input Vector W parameter

direct method (DM)

φ (dimensionless) θi (CAD) θC (CAD) m (dimensionless) A (dimensionless)

0.28 (measured) 19 (measured) 31 0.57 1.83

indirect method comparing pressures (IMP) 0.29 (3% error) 19.2 (0.2 CAD error) 32 0.55 1.87

indirect method comparing angular speeds (IMV) 0.26 (dimensionless) (8% error) 20 (1 CAD error) 33 0.6 1.79

ˆ in the Single-cylinder DI CIE (see Figure 10) Table 4. Identified Values of the Input Vector W parameter

direct method (DM)

φ (dimensionless) θj (CAD) θp (CAD) θd (CAD) mp (dimensionless) md (dimensionless) qp (dimensionless)

0.684 (measured) 11° (measured) (5° start ignition) 21° 49° 1.16 1.73 0.58

indirect method comparing pressures (IMP) 0.65 (5% error) 10.3° (0.7 CAD error) 22° 53° 1.11 1.74 0.56

summary, indirect method procedures allow a good estimation of the input parameters through the combustion submodel, for diagnosis applications. Nevertheless, several solutions are depicted, making evident the necessity of decreasing the number ˆ . For this purpose, the first step must of parameters in vector W be to analyze the relations between parameters and their weight into the engine system behavior.

indirect method comparing angular speeds (IMV) 0.66 (dimensionless) (3% error) 12.5° (1.5 CAD error) 22° 54° 1.12 1.72 0.57

speed profile. They correspond to the output variables of the engine system, besides the average angular speed and load. Table 5 summarizes the output variables to be analyzed. The best way to assess the relation between input and output variables is by a sensitivity analysis. Sensitivity Sij of an ith variable Yi (corresponding to angular speed) related to a particular model coefficient or parameter Wj (from the combustion submodel) is defined by eq 6.

4. Input-Output Parameters Relationship. Justification of a Sensitivity Analysis Figure 3 shows the relation between input and output parameters for the overall engine behavior. In these relations, the input parameters of the engine system will be used as the characteristic terms of the combustion submodel. It is worth noticing that the model response is not a single value or a few parameters vector, but a cyclic speed profile (see Figure 3). To reduce the complexity of output data they will be parametrized, thus some indicators associated to that curve will be defined. In the speed profile there are some special points such as maxima, minimums, inflection points, etc., usually considered for engine behavior characterization.43,44 These points provide the starting point to establish a set of output indicators of the curve. For many operating conditions, it can be observed that, independently of the mean angular speed value, differences in the variable term of the angular speed between maximum and minimum values, next to derivatives in different points into the speed profile must also be considered. As a result of this analysis, Figure 11 shows the main indicators associated to the

Figure 11. Output parameters of the cyclic speed profile of the engine (TL ) 27.4 N m; n ) 1800 rpm).


Sij ) ∂Yi /∂Wj


(6)

This expression is used when the purpose is to evaluate the variation of one coefficient or parameter over other coefficients, keeping their original values.45 The major drawbacks of this approach are as follows: (a) the comparison between multiple outputs is difficult; (b) it is not possible to evaluate the interaction between parameters; and (c) a global sensitivity analysis could only be inferred from linear models. Alternatively, statistical analysis approaches can be used to elucidate the effect of parameters combination.46 Then, another way to evaluate sensitivity via statistical methods is established. Previously, a DoE must be performed. Some issues related to the equivalence ratio and injection/ ignition timing that must be taken into consideration as follow: if the characteristics of the fuel injection system (FIS) are wellknown, it could be possible to optimize the injected fuel mass along the cycle and the start of injection (CIE)/start of combustion (SIE).47-50 In this case, different approaches can be defined: 4.1. Fuel consumption. (i) In case fuel mass injected (Mf,FIS) is known, though fuel burned (Mf) is unknown: φ must be identified at each evaluated condition. The main advantage of this consideration is that the combustion efficiency, ηcomb (dimensionless), could be evaluated following eq 7.31 ηcomb )

AROHR Mf,FISLHV

Table 5. Indicators of the System Response Speed (see Figure 11) output parameter

definition

∆ω1 ∆ω2 dωd1/dt dωd2/dt dωu1/dt dωu2/dt n TL

angular speed increment before TDC (s-1) angular speed increment after TDC (s-1) derivative of the first deceleration section (s-2) derivative of the second deceleration section (s-2) derivative of the first acceleration section (s-2) derivative of the second acceleration section (s-2) average angular speed (rpm) load torque (Nm)

identification process, whereas the injection timing (θj) must be identified. From these data, the ignition delay (θD) could be directly determined. On the other hand, when the injection timing is unknown, the parameter to identify will be θj, providing θi by considering the ignition delay (θD) approaches. 4.3. Start of Combustion (SIE). (i) In case ignition timing (θi) is known: if FIS is known, this parameter does not need to be identified. (ii) In case ignition timing (θi) is unknown: this parameter must be identified. Anyway, increasing the number of unknown parameters enlarges the difficulty of the evaluation. So, the probability of several solutions coexistence is high and needs to be assessed. Other situations could be better evaluated after removing some error sources.

(7)

(ii) In case injected fuel mass is known, considering Mf,FIS ) Mf, the equivalence ratio is considered as an input datum and do not need to be evaluated. The combustion efficiency will be considered as 100%. (iii) In case fuel mass injected is unknown, considering Mf,FIS ) Mf, the equivalence ratio must be evaluated. As a result of the identification process, it is considered that Mf,FIS ) Mf. The combustion efficiency will be also considered to be 100%. 4.2. Start of Injection (CIE). (i) Direct evaluations: the ROHR profile provides both the injection timing (θi) and ignition time (θi). The first point will be the start of the ROHR profile, while the second one represents the position where the ROHR takes a positive value. The ignition delay time (θD) can be directly determined. In any case, the limits could not be clear, so a little deviation could take place. (ii) Indirect evaluations (identification). If the FIS is wellknown, the injection timing will be an input datum to the (44) Yang, J. G.; Pu, L. J.; Wang, Z. H.; Zhou, Y. C.; Yan, X. P. Mech. Syst. Signal Process. 2001, 15, 549–564. (45) Wu, C. W. U.; Hamada, M. Experiments: Planning, Analysis, and Parameter Design Optimization; John Wiley & Sons: New York, 2000. (46) Edwards, S. P.; Grove, D. M.; Wynn, H. P. Statistics for Engine Optimization; Professional Engineering Publishing Ltd.: London, UK, 2000. (47) Kegl, B. J. Mech. Des. 1996, 118, 490–493. (48) Kegl, B. J. Mech. Des. 1999, 121, 159–165. (49) Palomar, J. M.; Cruz-Peragoń, F.; Jimenez-Espadafor, F. J.; Dorado, M. P. Energy Fuels 2007, 21, 110–120. (50) Yamene, K.; Shimamoto, Y. J. Eng. Gas Turbines Power 2002, 124, 660–667.

Conclusions This manuscript demonstrates the necessity of evaluating the influence of combustion parameters in the engine response (angular speed), to achieve unique solutions in their identification procedures, when indirect methods are applied. To add a parametric form, certain indicators related to the angular speed curve profile must be adopted. Combustion parameters evaluation can be applied to engines failures diagnosis. In the second part of this work, it can be concluded that the best way to assess the relation between input and output variables is by a sensitivity analysis. In this sense, DoE allows the performance of a sensitivity analysis to correlate the engine response to the combustion input parameters. In the present work, the relationship between the instantaneous ROHR profile and the instantaneous angular speed, in the case of a unique injection during the cycle, has been shown. However, in future works concerning modern CI engines, provided that the injection event is mostly split into various injections (for instance, one or two pilot injections, one or two main injections, and sometimes one or two post injections), it should be taken into consideration. Acknowledgment. Authors gratefully acknowledge support for this research from the Spanish Ministry of Education and Science (ENE2007-65490/ALT and Integrated Actions Program, HI20080229) and from “Junta de Andalucıá”, Spain (Grupo PAI TEP 169, BIOSAHE). EF900109H

Influence of a Combustion Parametric Model on the Cyclic Angular

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