Model-Based Calibration of the Reaction-Based Diesel Combustion Dynamics*

Transcription

1 2017 American Control Conference Sheraton Seattle Hotel May 24 26, 2017, Seattle, USA Model-Based Calibration of the Reaction-Based Diesel Combustion Dynamics* Yifan Men 1, Ibrahim Haskara 2, Yue-Yun Wang 2, Chen-Fang Chang 2, and Guoming G. Zhu 1 Abstract A control-oriented reaction-based combustion model is implemented and used to simulate the combustion process in a diesel engine. The model integrates a homogeneous thermodynamic system with a two-step chemical reaction mechanism that consists of six species. The accuracy of the model is evaluated by comparing with experimental data from a GM 6.6L, 8 cylinder Duramax engine. The model is calibrated for different key points over the entire engine map as well as various injection timings and exhaust gas recirculation EGR) ratio using an automated calibration algorithm. The reactionbased model is shown to provide accurate predictions of incylinder pressure, temperature, mass-fraction-burned and heat release rate. As an alternative to Wiebe-based method, this approach could lead to a better model with less calibration effort. The improvement is due to the fact that the burn rate is online calculated based upon the dominated fuel chemical components and combustion chamber properties, such as temperature, oxygen and burned gas concentration, etc. I. INTRODUCTION Modern internal combustion IC) engines are equipped with sophisticated systems to monitor and control various aspects of engine performance during ongoing operation to meet operator demands for performance including torque and fuel economy) and to satisfy government regulations related to emissions, safety, and fuel economy. Engine systems operable at lean air-to-fuel ratios AFR) including diesel and homogeneous-charge gasoline engines) are effective to achieve operator demands. Such engine systems utilize exhaust aftertreatment systems comprising diesel particulate filters DPF), lean NO x traps LNT), NO x absorbers, and selective catalyst reduction SCR) devices, either alone or in combination. To enable model-based engine control, physics-based control-oriented engine models [1-4]) are often developed to simulate the engine behavior in real-time. However, the engine combustion model is traditionally based upon the so-called Wiebe function [5] that models the mass-fractionburned MFB) with pre-calibrated combustion parameters. The main disadvantage of this approach is that the combustion model is based on a set of pre-assumed engine control parameters, such as fuel injection timing and intake charge properties charge oxygen, pressure, temperature, etc.), and it cannot be altered when the control parameters are outside *This work was supported by General Motors Company. 1 Y. Men and G. Zhu are with the Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA menyifan@egr.msu.edu; zhug@egr.msu.edu) 2 I. Haskara, Y.-Y. Wang and C.-F. Chang are with General Motors, Warren, MI 48090, USA ibrahim.haskara@gm.com; yue-yun.wang@gm.com; chen-fang.chang@gm.com) the modeled operational range. A Wiebe-based combustion model is capable of modeling the combustion process accurately under normal operational conditions with proper calibrations for diesel engines. However, under the regenerative operations, in order to maintain the engine exhaust AFR close to stoichiometry, an after injection is normally used to achieve the desired AFR and its injection timing is often significantly retarded. As a result, incomplete combustion could occur and in order to model this process, the Wiebe function should be modified thus more complexities and calibrations are introduced. Therefore, a new method to model the combustion process, especially under regenerative operations, are needed. Reaction-based combustion modeling technique has been used for off-line simulations in the past. Autoignition behavior with different diesel blends was modeled in references [6] and [7], where a reaction-based combustion model was used for predicting the autoignition. A reduced chemical kinetic model was developed in [8] to simulate the IC engine combustion process with primary reference fuels and the model was fairly complicated and cannot be used for real-time simulations. A multistage combustion model for diesel engines is presented in [9], where three combustion stages, autoignition, premixed and diffusion combustion are considered in the combustion process for a typical medium speed diesel engine. Also, a significant improvement on incylinder pressure and temperature prediction is achieved. A control-oriented two zone thermo-kinetic model for a single cylinder HCCI engine is presented in [10], where the combustion process was modeled using the first law of thermodynamics and mixture concentration inhomogeneity. The two-zone model improved the accuracy of cylinder pressure, exhaust gas temperature, emission concentrations and start of combustion SOC), compared to the single-zone model. The Arrhenius integral was used to predict the start of combustion. However, only the state at the beginning and end of combustion was predicted and the heat release rate was calculated based on a pre-assumed combustion duration. A reaction-based control-oriented HCCI combustion model was developed to predict the combustion phase of C 3 H 8 oxidation, using a two-step chemical mechanism [11]. The model was based on the assumption that the in-cylinder mixture properties are homogeneous. The two-step chemical mechanism was used to calculate the crank-based heat release rate for the complete engine cycle, thus there was no need to develop a separate model for the SOC prediction. The model showed fairly good agreement with test data for different valve timings. However, the model was not validated under /$ AACC 4735

2 different operating conditions such as engine speed, load, exhaust gas recirculation EGR) level, etc. As a summary, reaction-based and thermal-kinetic combustion models have been developed in the past. However, the detailed chemical kinetic model is too complex to be used for real-time simulations; and the simple thermo-kinetic model may not provide the accuracy needed for model-based control. A single-zone two-step reaction-based combustion model has been developed to predict the in-cylinder pressure. The main feature of this combustion model is that the burn rate is online calculated based upon the dominated fuel chemical components and combustion chamber properties such as pressure, temperature, oxygen and burned gas concentration, etc. This makes the combustion model accurately reflect the fuel injection property, leading to accurate pressure and torque predictions. In this paper, the single-zone two-step reaction-based model has been modified specifically for application on diesel combustion. The resulting model was calibrated for different key operational conditions over the entire engine map as well as various injection timings and EGR levels. The calibration parameters showed a strong correlation to the physical quantities such as injection timing, EGR, etc. It was shown that the model is simple enough for control purpose while giving accurate predictions under different control inputs. II. MODEL DESCRIPTION The reaction-based model is based upon the first law thermodynamic analysis of an open system, with pre-defined fuel injection into the cylinder. For simplicity, the gas exchange process is avoided by restricting the simulation duration from intake valve closing IVC) to exhaust valve opening EVO). This restriction reduces the error introduced by the valve flow model and the purpose of the study is not affected. Eight states are included into this model and they are the cylinder volume V ), the temperature T ), the concentrations of diesel fuel [C 10.8 H 18.7 ]), oxygen [O 2 ]), carbon dioxide [CO 2 ]), water [H 2 O]), nitrogen [N 2 ]), and carbon monoxide [CO]). A. Volume and Volume Rate Equations The instant volume is dependent on current crank angle and the geometry of the cylinder and can be calculated as V θ) = V c + πb2 ) l + a acosθ l 4 2 a 2 sin 2 θ, 1) where V c is the clearance volume; B is the bore; l is the connecting rod length; a is the crank radius half stroke); and θ is the crank angle. The volume rate equation is derived by taking derivative on volume with respect to crank angle: ) dv dθ = πb2 a sinθ acosθ l 2 a 2 sin 2 θ. 2) Equations 1) and 2) can also be expressed in time domain by applying the following transformation: θ = π RPM t, 3) 30 where RPM is the engine speed in revolution per minute. B. Concentration Rate Equations In a chemical kinetic system, the molecular concentration of species i is defined as [X i ] = N i V, 4) where N i = m i /MW i is the number of moles of species i. m i is the mass and MW i is the molecular weight. The rate of change of molar concentration of species i is defined as [X i ] = d ) Ni = Ṅi V V V N i V 2 = w i V V [X i], 5) where w i Ṅ i /V is the concentration production, which can be further separated into two parts: w i = w rxn,i + w f low,i, 6) where w rxn,i is the concentration production due to chemical reactions and it is calculated by the chemical kinetic mechanism; and w f low,i is the concentration change due to mass flow into and out of the control volume. In this specific model, w f low,i only consists of fuel injection rate, i.e. w f low,i = w f low, f uel = ṁ in j V MW f uel, 7) where ṁ in j is the fuel injection rate. The concentration rate equations are essentially the conservation of mass. C. Temperature Rate Equation From the first law of thermodynamics, we have du = Q Ẇ + ṁ j h j 8) where U is the internal energy of the system; Q is the net heat transfer rate into the system; Ẇ is the net rate of work done by the system; and ṁ j h j is the energy change due to mass flow. In this specific model, the mass flow includes only the fuel injection, i.e. ṁ j h j = ṁ in j h f uel = ṁin j MW f uel h f uel, 9) where h f uel is the specific enthalpy of the fuel and h f uel is the molar enthalpy. The rate of work done is defined as Ẇ = p V. 10) The relation between internal energy U and enthalpy H is H = U + pv. 11) Then by re-arranging and differentiating with respect to time the left hand side of 8) becomes du = dh pv ) = dh ṗv p V. 12) 4736

3 By substitution, 8) can be re-arranged as dh = Q + ṗv + ṁ j h j. 13) The extensive property H can be expressed as a sum of weighted molar enthalpies of all species Thus, LHS of 13) becomes LHS = dh H = N i h i = V [X i ] h i. 14) = V [X i ] h i +V [X i ] h i +V [X i ] h i, 15) where h i = c p,i Ṫ. Note that c p,i is the constant-pressure specific heat of species i. The state equations of ideal gas in terms of concentrations are given as and p = [X i ]R u T, 16) ṗ = R u T [X i ] + R u Ṫ [X i ], 17) where R u = 8314 J/kmol K) is the universal gas constant. By substitution, the right hand side RHS) of 13) becomes RHS = Q + R u TV [X i ] + R u ṪV [X i ] + ṁ j h j. 18) Equating 15) and 18) and re-arranging the equation gives the formula for the temperature rate: Q V Ṫ = + R ut [X i ] [X i ] h i V V [X i ] h i + ṁ jh j V. 19) [X i ] c p,i R u ) D. Heat Loss Rate Equation The heat transfer rate Q can be expressed as Q = A c h c T T w ), 20) where A c is the effective contact area between gas and cylinder wall; h c is the heat transfer coefficient; and T w is the cylinder wall temperature. The heat transfer coefficient is calculated by Woschni s correlation [12] h c = αb 0.2 p 0.8 T S p ) 0.8, 21) where S p is the mean piston speed; and α is the calibration parameter. E. Chemical Kinetic Model The two-step chemical reaction [13] of C 10.8 H 18.7 oxidation can be expressed as C 10.8 H O CO H 2 O, CO + 0.5O 2 CO 2. 22a) 22b) The reaction rates for C 10.8 H 18.7 and CO oxidation are given by Arrhenius functions w C10.8 H 18.7 = A 1 exp E ) A,1 [C 10.8 H 18.7 ] m 1 [O 2 ] n 1, 23a) R u T w COox = A 2 exp E ) A,2 [CO] m 2 [O 2 ] n 2 [H 2 O] k 1 R u T + A 3 exp E ) A,2 [CO 2 ] k 2, 23b) R u T where A 1, A 2, A 3, E A,1, E A,2, m 1, m 2, n 1, n 2, k 1 and k 2 are the coefficients to be calibrated. By inspecting 22a) and 22b), the rest of the reaction rates are as follows w O2 = w C10.8 H w COox, w CO2 = w COox, w H2 O = 9.35w C10.8 H 18.7, w CO = 10.8w C10.8 H w COox. 24a) 24b) 24c) 24d) Note that the second step is a reversible reaction where the reverse reaction decomposes CO 2 molecules into CO and O 2. III. MODEL CALIBRATION A. Overview of The experimental data to be used for calibration is from a 6.6L, 8 cylinder Duramax engine. The specifications of the engine is summarized in Table I. The engine was tested at steady-state under various speed and load conditions. The recorded test data includes in-cylinder pressure traces and other engine control inputs, along with post-processed heatrelease traces, air and EGR variables, pressure metrics such as IMEP indicated mean effective pressure) and NMEP net mean effective pressure). TABLE I. Engine Specifications Parameter Model Value bore 103mm stroke 99.05mm connecting rod length 163mm compression ratio 16.4:1 intake valve duration 148 crank degree exhaust valve duration 244 crank degree TABLE II. Summary of the OPs BMEP q in j SOI main EGR kpa mm 3 btdc % Engine map 16 OPs) Max Min TDC RPM 9 OPs) Max Min TDC RPM 9 OPs) Max Min RPM 10 OPs) Max Min RPM 9 OPs) Max Min RPM 45 OPs) Max Min OPs: operational points BEMP: brake mean effective pressure q in j : quantity of fuel injected per cycle SOI main : main injection timing in CAD before TDC EGR: exhaust gas recirculation ratio in % The available test data is summarized in Table II with three test data sets described as follows. Test Set #1: Engine map 16 operational points OP) over the speed-load map. 4737

4 Engine operated as calibrated at each OP with combustion inputs fuel injection timings, EGR, air-fuel ratio, etc.) from speed-fuel maps and varied based on OP. main injection used for most key points and post injection used at certain high-load OPs. Test Set #2: SOI sweeps at fixed speed and load 4 speed-load pairs: 680 RPM, 1 bar; 1400 RPM, 2.5 bar; 1400 RPM, 5 bar; 2000 RPM, 7 bar. Main injection only for 680 RPM and 1400 RPM and additional post injection included at 2000 RPM. Fixed EGR level for each speed-load pair. Test Set #3: SOI sweeps with constant fuel quantity Constant mass of fuel injected at 1400 RPM. Different EGR levels. B. Sensitivity analysis In this study, there are 11 candidates A 1, A 2, A 3, E A,1, E A,2, m 1, m 2, n 1, n 2, k 1 and k 2 ) for calibration. The one-ata-time method of sensitivity analysis is used. Conceptually, this method is to repeat the process of varying one parameter at a time and holding the others fixed for each parameter. Suppose there are n parameters, the sensitivity coefficient of system response η i to parameter β j can be approximated as s i, j = β j η i β j β j η i β 1,...,1 + δ)β j,...,β n ) η i β 1,...,β j,...,β n ) 1 + δ)β j β j = η i 1 + δ)β j ) η i β j ) δ 25) where δ is the relative perturbation and in this study its value is chosen as The sensitivity coefficients of all the parameters are calculated for a variety of engine operating conditions. It turns out that the set of the most significant and sensitive) parameters remain the same for all the tested points. The sensitivity ranking is shown in Table III. Note that the parameters with percentage less than 2% is not listed. The system response chosen in this study is the cylinder pressure because it is directly measured in the test data. The sensitivity in the table is the averaged value over the entire tested cycle. The percentage of the sensitivity coefficients with respect to the mean value of nominal cylinder pressure, which is not perturbed, is calculated to evaluate the relative significance of each parameter. Consequently, the parameters to be comprehensively calibrated are E A,1 and E A,2. TABLE III. Sensitivity ranking of parameters at 680 RPM Parameter Sensitivity Percentage coefficient %) E A, E A, n m C. Calibration Process The nonlinear Least-Squares [14] solver minimizes the 2- norm f x) 2 2 of a vector-valued cost function f x). f x) = W 0.5 IMEP ) WP 0.5 P Pexp P 0 ) WT 0.5 T Texp T 0 ) IMEP IMEPexp IMEP 0 W 0.5 MFB MFB MFB exp), 26) where P exp, T exp, IMEP exp and MFB exp are crank-based time series in column vector from experimental data. P 0, T 0 and IMEP 0 are normalizing factors. W P, W T, W IMEP and W MFB are weighting factors. The reason for choosing this cost function is to achieve an IMEP error within 5%, while keeping errors of combustion metrics, such as pressure, temperature and heat release rate, as small as possible. As an example, Fig. 1 shows the predicted in-cylinder pressure compared to experimental data at 1400 RPM, 2.5 bar. The model succeessfully predicts the combustion phasing, pressure rise, peak pressure and pressure drop. However, there is a difference in pressure near the onset of combustion. Since the two-step mechanism does not account for the dissociation of large hydrocarbon molecules into small hydrocarbon molecules, the heat absorption due to the dissociation was not modeled, resulting in higher pressure rise around the start of combustion. In-cylinder Pressure bar) Fig. 1: Predicted in-cylinder pressure vs. experimental data at 1400 RPM, 2.5 bar The corresponding temperature Fig. 2), mass-fractionburned Fig. 3) and heat release rate Fig. 4) are shown in the following. The overall shape of the predicted temperature is in good agreement with experimental data, although there is a discrepancy in the compression stroke near top dead center, peak temperature and exhaust gas temperature. The large temperature drop at the end of combustion is due to the overestimated heat release rate as shown in Fig. 4. The first peak in the heat release rate refers to the first step of the chemical reaction. The model predicted an earlier start of heat release but a delayed and steep rising. After a short duration, the first step terminated and the second step 4738

5 Injection Profile scaled) In-cylinder Temperature K) Heat Release Rate kj/s) Fig. 2: Predicted in-cylinder temperature vs. experimental data at 1400 RPM, 2.5 bar Fig. 4: Predicted heat release rate vs. experimental data at 1400 RPM, 2.5 bar initiated. The heat release rate of the second step was also over-predicted since there is a peak in the predicted curve while the experimental data shows a dip. In the MFB plot Fig. 3), it can be noted that the model accurately predicted the combustion incompleteness, where the MFB does not reach 1 at the end of combustion. Note that a standard Wiebe-based combustion model is not able to predict this phenomenon. It also shows an earlier completion of the combustion compared to the experimental data. 1 As shown in Fig. 5, E A,1 is small for very advanced injection and rises as the injection timing gets more retarded. For injection at 5 to 10 degree before TDC, E A,1 reaches its peak. As the injection is further retarded, E A,1 decreases. Although the correlation between E A,1 and SOI is not linearlike, a clear trend of E A,1 increasing as load getting higher is shown. The maximum relative variation of E A,1 is 14.7% RPM,1bar 1400RPM,2.5bar 1400RPM,5bar 2000RPM,7bar Mass-Fraction-Burned E A, Start of injection Degree btdc) Fig. 5: Calibrated E A,1 vs. SOI for different speed-load pairs Fig. 3: Predicted mass-fraction-burned vs. experimental data at 1400 RPM, 2.5 bar The IMEP error was kept within 5% throughout the calibration process. It can be confirmed that the two-step reaction-based model is capable of capturing the main combustion features while being simple enough for real-time model-based control. D. SOI Sweep Cases of fixed speed-load pairs were studied by calibrating the same set of coefficients. In spite of several outliers, the coefficients are shown to be correlated with SOI and engine operating conditions. Fig. 6 shows the variation of E A,2 with respect to SOI. A more linear-like correlation has been observed. However, at 1400 RPM with 5 bar load, E A,2 is lower than expected in general, especially when the injection is extremely advanced. The coefficients were also calibrated at the 1400 RPM with constant quantity of fuel injection. In this case, there were 4 EGR levels: 5%, 40%, 50% and 65%. Only main injection was considered. The results are shown in Fig. 7 and Fig. 8. For E A,1, the 5% EGR level is away from its counterparts, where the data is fluctuating around However, the maximum variation is only 5%. For higher EGR levels the trend is much more linear and no large variations are observed for different EGR levels. For E A,2, an even better trend is observed. The coefficient is almost linearly correlated with SOI for each EGR level. 4739

6 RPM,1bar 1400RPM,2.5bar 1400RPM,5bar 2000RPM,7bar % EGR 40% EGR 50% EGR 65% EGR E A,2 2.6 E A, Start of injection Degree btdc) Start of injection Degree btdc) Fig. 6: Calibrated E A,2 vs. SOI for different speed-load pairs Fig. 8: Calibrated E A,2 vs. SOI for different EGR levels at 1400 RPM E A, % EGR 40% EGR 50% EGR 65% EGR Start of injection Degree btdc) Fig. 7: Calibrated E A,1 vs. SOI for different EGR levels at 1400 RPM Although the trend with respect to EGR level is not clear because of the lower values for 65% EGR case, The scattered points are generally close. The maximum variation is 6%. IV. CONCLUSIONS A reaction-based control-oriented combustion model was developed based on a two-step chemical kinetic mechanism. The model was simulated and calibrated by comparing to experimental results. The model was under the assumption of one-zone homogeneous condition and the combustion rate was determined by Arrhenius functions related to incylinder temperature and species concentrations. From the sensitivity analysis, only two coefficients were selected to be calibrated. The results showed good agreement with experimental data. And the coefficients were strongly related to engine operating conditions and control variables, such as speed, load, injection timing and EGR ratio. It is possible to calculate the coefficients as functions of engine operating conditions and control variables in order to reduce the effort for model-based control calibrations. The future work will be developing a multi-zone model accounting for in-cylinder gas inhomogeneity. REFERENCES [1] X. Yang, and G. G. Zhu, A mixed mean-value and crank-based model of a dual-stage turbocharged SI engine for hardware-in-theloop simulation, in Proc Am. Control. Conf., Baltimore, 2010, pp [2] X. Yang and G. G. Zhu, A control-oriented hybrid combustion model of a homogeneous charge compression ignition capable spark ignition engine, Proc. Inst. Mech. Eng. D J. Automob. Eng., pp , February [3] S. Zhang, G. Zhu, and Z. Sun, A control-oriented charge mixing and two-zone HCCI combustion model, IEEE Trans. Veh. Technol., vol. 63, no. 3, pp , March [4] Y. Yoon, Z. Sun, S. Zhang, G. Zhu, A control-oriented two-zone charge mixing model for HCCI engines with experimental validation using an optical engine, J. Dyn. Syst. Meas. Control, vol. 136, no. 4, pp , July [5] J. I. Ghojel, Review of the development and applications of the Wiebe function: a tribute to the contribution of Ivan Wiebe to engine research, Int. J. Engine Res., vol. 11, no. 4, pp , May [6] E. Toulson, C. M. Allen, D. J. Miller, J. McFarlane, H. J. Schock and T. Lee, Modeling the autoignition of fuel blends with a multistep model, Energy Fuels, vol. 25, no. 2, pp , January [7] E. Toulson, C. M. Allen, D. Miller and T. Lee, Modeling the autoignition of oxygenated fuels using a multistep model, Energy Fuels, vol. 24, no. 2, pp , December [8] Y. Ra and R. D. Reitz, A reduced chemical kinetic model for IC engine combustion simulations with primary reference fuels, Combust. Flame, vol. 155, no. 4, pp , May [9] G. J. Micklow and W. Gong. A multistage combustion model and soot formation model for direct-injection diesel engines, Proc. Inst. Mech. Eng. D J. Automob. Eng., vol. 216, no. 6, pp , March [10] V. Tandra and N. Srivastava, A control-oriented two zone thermokinetic model of a single cylinder HCCI engine, ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Brooklin, 2008, DETC [11] G. M. Shaver, J. C. Gerdes, P. Jain, P. A. Caton, C. F. Edwards, Modeling for control of HCCI engines, in Proc Am. Control. Conf., Denver, 2003, pp [12] G. Woschni, A universally applicable equation for the instantaneous heat transfer coefficient in the internal combustion engine, SAE Technical paper, No , [13] C. K., Westbrook and F. L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combust. Sci. Technol., vol. 27, no. 1-2, pp , July [14] T. F. Coleman and Y. Li, An interior trust region approach for nonlinear minimization subject to bounds, SIAM J. Optimiz., vol. 6, no. 2, pp , May