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Research Papers: Gas Turbines: Combustion, Fuels, and Emissions

A Linear Least-Squares Algorithm for Double-Wiebe Functions Applied to Spark-Assisted Compression Ignition

[+] Author and Article Information
Erik Hellström

University of Michigan,
Ann Arbor, MI 48109
e-mail: erikhe@umich.edu

Anna Stefanopoulou

University of Michigan,
Ann Arbor, MI 48109
e-mail: annastef@umich.edu

Li Jiang

Robert Bosch LLC,
Farmington Hills, MI 48331
e-mail: li.jiang@us.bosch.com

The solution is obtained by differentiating the criterion in Eq. (3) with respect to p, setting the result to zero, and solve for p.

Contributed by the Combustion and Fuels Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received February 15, 2014; final manuscript received February 16, 2014; published online May 5, 2014. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(9), 091514 (May 05, 2014) (7 pages) Paper No: GTP-14-1096; doi: 10.1115/1.4027277 History: Received February 15, 2014; Revised February 16, 2014

An algorithm for determining the four tuning parameters in a double-Wiebe description of the combustion process in spark-assisted compression ignition engines is presented where the novelty is that the tuning problem is posed as a weighted linear least-squares problem. The approach is applied and shown to describe well an extensive data set from a light-duty gasoline engine for various engine speeds and loads. Correlations are suggested for the four parameters based on the results, which illustrates how the double-Wiebe approach can also be utilized in a predictive simulation. The effectiveness of the methodology is quantified by the accuracy for describing and predicting the heat release rate and predicting the cylinder pressure. The root-mean square errors between the measured and predicted cylinder pressures are 1bar or less, which corresponds to 2% or less of the peak cylinder pressure.

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References

Najt, P. M. and Foster, D. E., 1983, “Compression-Ignited Homogeneous Charge Combustion,” SAE Technical Paper 830264. [CrossRef]
Willand, J., Nieberding, R.-G., Vent, G., and Enderle, C., 1998, “The Knocking Syndrome—Its Cure and Its Potential,” SAE Technical Paper 982483. [CrossRef]
Thring, R. H., 1989, “Homogeneous Charge Compression Ignition (HCCI) Engines,” SAE Technical Paper 892068. [CrossRef]
Hyvönen, J., Haraldsson, G., and Johansson, B., 2005, “Operating Conditions Using Spark Assisted HCCI Combustion During Combustion Mode Transfer to SI in a Multi-Cylinder VCR-HCCI Engine,” SAE Technical Paper 2005-01-0109. [CrossRef]
Kalian, N., Standing, R., and Zhao, H., 2005, “Effects of Ignition Timing on CAI Combustion in a Multi-Cylinder DI Gasoline Engine,” SAE Technical Paper 2005-01-3720. [CrossRef]
Urushihara, T., Yamaguchi, K., Yoshizawa, K., and Itoh, T., 2005, “A Study of a Gasoline-Fueled Compression Ignition Engine—Expansion of HCCI Operation Range Using SI Combustion as a Trigger of Compression Ignition,” SAE Technical Paper 2005-01-0180. [CrossRef]
Bunting, B. G., 2006, “Combustion, Control, and Fuel Effects in a Spark Assisted HCCI Engine Equipped With Variable Valve Timing,” SAE Technical Paper 2006-01-0872. [CrossRef]
Wagner, R. M., Edwards, K. D., Daw, C. S., Green, J. B., Jr., and Bunting, B. G., 2006, “On the Nature of Cyclic Dispersion in Spark Assisted HCCI Combustion,” SAE Technical Paper 2006-01-0418. [CrossRef]
Manofsky, L., Vavra, J., Assanis, D., and Babajimopoulos, A., 2011, “Bridging the Gap Between HCCI and SI: Spark-Assisted Compression Ignition,” SAE Technical Paper 2011-01-1179. [CrossRef]
Ghojel, J. I., 2010, “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., 11(4), pp. 297–312. [CrossRef]
Yang, X. and Zhu, G. G., 2012, “A Control-Oriented Hybrid Combustion Model of a Homogeneous Charge Compression Ignition Capable Spark Ignition Engine,” Proc. Inst. Mech. Eng., Part D: J. Automob. Eng., 226(10), pp. 1380–1395. [CrossRef]
Ghojel, J. I., 1982, “A Study of Combustion Chamber Arrangements and Heat Release in D.I. Diesel Engines,” SAE Technical Paper 821034. [CrossRef]
Miyamoto, N., Chikahisa, T., Murayama, T., and Sawyer, R., 1985, “Description and Analysis of Diesel Engine Rate of Combustion and Performance Using Wiebe's Functions,” SAE Technical Paper 850107. [CrossRef]
Witt, H., Hassenforder, M., and Gissinger, G. L., 1995, “Modelling and Identification of a Diesel Combustion Process With the Downhill Gradient Search Method,” SAE Technical Paper 950854. [CrossRef]
Yasar, H., Soyhan, H. S., Walmsley, H., Head, B., and Sorusbay, C., 2008, “Double-Wiebe Function: An Approach for Single-Zone HCCI Engine Modeling,” Appl. Therm. Eng., 28(11–12), pp. 1284–1290. [CrossRef]
Glewen, W. J., Wagner, R. M., Edwards, K. D., and Daw, C. S., 2009, “Analysis of Cyclic Variability in Spark-Assisted HCCI Combustion Using a Double Wiebe Function,” Proc. Combust. Inst., 32(2), pp. 2885–2892. [CrossRef]
Martz, J. B., Lavoie, G. A., Hong, H.I., Middleton, R. J., Babajimopoulos, A., and Assanis, D. N., 2012, “The Propagation of a Laminar Reaction Front During End-Gas Auto-Ignition,” Combust. Flame, 159(6), pp. 2077–2086. [CrossRef]
Persson, H., Hultqvist, A., Johansson, B., and Remon, A., 2007, “Investigation of the Early Flame Development in Spark Assisted HCCI Combustion Using High Speed Chemiluminescense Imaging,” SAE Technical Paper 2007-01-0212. [CrossRef]
Hellström, E., Stefanopoulou, A. G., Vávra, J., Babajimopoulos, A., Assanis, D., Jiang, L., and Yilmaz, H., 2012, “Understanding the Dynamic Evolution of Cyclic Variability at the Operating Limits of HCCI Engines With Negative Valve Overlap,” SAE Int. J. Engines, 5(3), pp. 995–1008. [CrossRef]
Lavoie, G. A., Martz, J. B., Wooldridge, M., and Assanis, D., 2010, “A Multi-Mode Combustion Diagram for Spark Assisted Compression Ignition,” Combust. Flame, 157(6), pp. 1106–1110. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

SACI combustion heat release data transformed using Eq. (2) to show the linear regions

Grahic Jump Location
Fig. 2

The heat release rate Q' (top panel) and the first three derivatives of the burn fraction xb (bottom panel). The transition angle θ1 is defined at the peak value of xb''' between θ0 and θx, the peak of xb'.

Grahic Jump Location
Fig. 3

Using Eq. (2) to determine the parameters for the flame propagation (FP) Wiebe function x0 and the autoignition (AI) Wiebe function x1, respectively

Grahic Jump Location
Fig. 4

Construction of the composite Wiebe function from Eqs. (11) and (14), by smoothly joining the two Wiebe functions

Grahic Jump Location
Fig. 5

Sweep of the eEGR at 5 bar BMEP and 2000 rpm. Data are shown with gray thick lines and fits with thin black lines. The dots mark the locations of θ0, θ1, and θ2.

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Fig. 6

Simultaneous sweep of the spark and eEGR at 5 bar BMEP and 2000 rpm. Data are shown with thick gray lines and fits with thin black lines. The dots mark the locations of θ0, θ1, and θ2.

Grahic Jump Location
Fig. 7

Double-Wiebe function fits for a grid of engine speed, in krpm, and load, BMEP in bar. The different combustion characteristics at each operating point correspond to a multitude of conditions for various actuator settings (eEGR valve, start of injection, intake and exhaust cam timing, and spark timing) based on the chosen design of experiments. The root-mean-square (rms err) and maximum (max err) errors between the fitted curves (thin black lines) and measured data (thick gray lines) are computed for the interval (θsoc, θeoc).

Grahic Jump Location
Fig. 8

Predicted heat release rate (top three rows) and predicted cylinder pressure (bottom three rows) are compared with data for varying engine speed, in krpm, and load, BMEP in bar. The root-mean-square (rms err) and maximum (max err) errors between the predicted curves (thin black lines) and measured data (thick gray lines) are computed for the interval (θsoc, θeoc). The coefficients for the Wiebe functions are calculated from the regressors in Table 1 and the pressures are then simulated using the predicted heat release rate.

Tables

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