**5. References**

Alkidas, A.C., "Heat Transfer Characteristics of a Spark-Ignition Engine," ASME Trans., Journal of Heat Transfer, Vol. 102, pp.189-193, 1980.

The column on the right in Fig. 9 provides an example of the influence of the main submodels on the results of the overall model. In-cylinder turbulence and heat-transfer submodels are considered, and in addition, the influence of a slight change in the fractal dimension, D, is assessed. The 'reference' series is the same as in the first column, and represents the calibration in (Baratta et al., 2008). The deviation from the 'reference' calibration for each sub-model has been set on the basis of the uncertainty that can be expected in the adopted modelling framework. In particular, a deviation of 40% was considered for the turbulence level at the spark discharge, due to the significant approximations in the K-k model. An error of 30% is reasonable for the heat-transfer, especially if a diagnostic tool is not available for its calibration. Finally, the uncertainty on the fractal dimension D can be even higher than 0.01, since at present there is no agreement on its value (Baratta et al., 2006). As can be seen, for the considered deviation values, an increase in the heat-transfer coefficient has almost the same effect as a decrease in the fractal dimension. Both parameters can influence the model performance to a certain extent. As can be expected, the turbulence level exerts a remarkable influence on the overall model output. In particular, the bell-like shape of the u' profile versus crank angle, although obtained

through empirical formulas, is very important to obtain an acceptable Sb/SL profile.

trends when a design or operation variable is modified.

heat-transfer coefficient and the turbine efficiency multiplier).

Journal of Heat Transfer, Vol. 102, pp.189-193, 1980.

**4. Conclusions** 

**5. References** 

The above discussion confirms that the overall model accuracy depends on each specific sub-model formulation, as well as on the related calibration. A precise model prediction can be obtained by adopting very accurate sub-models, but also when the sub-models error cancel each other. A good predictive combustion model should be formulated and calibrated so as to be able to reproduce the engine indicated cycle with a reasonable accuracy over a wide range of operating conditions, and to capture the engine performance

In the present chapter, the problem of the 1-D simulation the fluid-dynamics, combustion and performance of SI engines has been analyzed in detail. Among the different aspects that have to be faced when approaching this problem, the discussion has been focused on the incylinder pressure evolution versus crank angle, paying specific attention to the closed-valve phase, and on the turbocharger modelling. An accurate model tuning procedure has been outlined for both topics, and indications have been given on how the model could be made predictive, even in the presence of variable coefficients (such as, for example, the in-cylinder

Although quite good results can be obtained adopting of the Wiebe approach for the simulation of combustion, provided lookup tables can be built from combustion experimental data for its coefficients, the reliability of the 1-D approach can be improved to a great extent if a predictive combustion model is used for the heat-release calculations. In this case, the researcher has different options, within the fractal or non-fractal frameworks. Attention has mainly been focused on the authors' combustion model, but acceptable results can also be obtained with any model from the literature. In general, the accuracy of the overall simulation model depends on how the various sub-model results are combined.

Alkidas, A.C., "Heat Transfer Characteristics of a Spark-Ignition Engine," ASME Trans.,


Numerical Simulation Techniques for the

Paper No. 880198; 1988.

1985.

2003.

1979.

1993.

2003.

0996, 2004.

(USA), 1994.

MacMillian, 1982.

Prediction of Fluid-Dynamics, Combustion and Performance in IC Engines Fuelled by CNG 285

Morel, T., and Keribar, R., "A Model for Predicting Spatially and Time Resolved Convective

Morel, T., Rackmil, C., Keribar, R., and Jennings, M.J., "Model for Heat Transfer and

North, G.L., and Santavicca, D.A., "The Fractal Nature of Premixed Turbulent Flames,"

Onorati, A., Ferrari, G., D'Errico, G., and Montenegro, G., "The Prediction of 1D Unsteady

Poulos, S.G., and Heywood, J.B., "The Effect of Chamber Geometry on Spark-Ignition

Sihling , K., and Woschni, G.: "Experimental Investigation of the Instantaneous Heat

Velherst, S., and Sheppard, C.G.W., "Multi-Zone Thermodynamic Modelling of Spark-

Vítek, O., Macek, J., and Polàšek, M., "New Approach to Turbocharger Optimization using

Wahiduzzaman, S., Morel, T., and Sheard, S., "Comparison of Measured and Predicted Com-

Watson, N., and Janota, M.S., "Turbocharging the Internal Combustion Engine",

Westin, F., and Ångström, H.E., "Simulation of a Turbocharged SI-Engine with Two

Westin, F., Rosenqvist, J., and Ångström, H.E., "Heat Losses from the Turbine of a

Westin, F., "Simulation of Turbocharged SI Engines–With Focus on the Turbine", Ph. D.

Wilcox, D.C., "Turbulence Modeling for CFD", DCW Industries Inc., La Canada, California

Winkler, N., and Ångström, H.E., "Study of Measured and Model Based Generated Turbine

Winterbone, D.E., and Pearson, R.J., "Design Techniques for Engine Manifolds",

Dissertation, The Royal Institute of Technology, Sweden, 2005.

During Transient Conditions", SAE Paper No. 2007-01-0491, 2007.

Professional Engineering Publishing, London, 1990.

Combustion Science and Technology, Vol. 72, pp. 215-232, 1990.

Engine Combustion," SAE Paper No. 830334, 1983.

1-D simulation tools", SAE Paper 2006-01-0438, 2006.

Management, Vol. 50, pp. 1326-1335, 2009.

Heat Transfer in Bowl-in-Piston Combustion Chambers," SAE Paper 850204,

Combustion in Spark Ignited Engines and its Comparison with Experiments", SAE

Flows in the Exhaust System of a S.I. Engine Including Chemical Reactions in the Gas and Solid Phase", SAE Transactions, J. Engines, SAE paper 2002-01-0003;

Transfer in the Cylinder of a High Speed Diesel Engine," SAE paper 790833,

Ignition Engine Combustion – An Overview", Energy Conversion and

bustion Characteristics of a Four-Valve SI Engine," SAE Paper No. 930613,

Software and Comparison with Measured Data", SAE Paper No. 2003-01-3124,

Turbocharged SI Engine – Measurements and Simulation", SAE Paper No. 2004-01-

Performance Maps within a 1D Model of a Heavy-Duty Diesel Engine Operated

Propagation Parameters and Nitric Oxide Formation in SI Engines," Comodia '04, Yokohama, Japan, Aug. 2–5, JSME Paper No. 04-202.


D'Errico, G., Ferrari, G., Onorati, A., and Cerri, T., "Modeling the Pollutant Emissions from a

Enomoto Y., and Furuhama, S., "A Study of the Local Heat Transfer Coefficient on the

Galindo, J., Luján, J.M., Serrano, J.R., Dolz, V., and Guilain, S., "Description of a Heat

Galindo, J., Luján, J.M., Serrano, J.R., Dolz, V., and Guilain, S., "Design of an Exhaust

Gamma Technologies Inc., "GT-SUITE Engine Performance Application Manual",

Gülder, Ö.L., and Smallwood, G.J., "Inner Cutoff Scale of Flame Surface Wrinkling in

Gülder, Ö.L., et. al., "Flame Front Surface Characteristics in Turbulent Premixed

Gouldin, F.C., and Miles, P.C., "Chemical Closure and Burning Rates in Premixed Turbulent

Grill, M., Billinger, T., and Bargende, M., "Quasi-Dimensional Modeling of Spark Ignition

Guezennec, Y.G., and Hamada, W., "Two-Zone Heat Release Analysis of Combustion Data

Hattrlel, T., Sheppard, C.G.W., Burluka, A.A., Neumeister, J., and Cairns, "Burn Rate

Heywood, J.B., "Internal Combustion Engine Fundamentals," McGraw-Hill International

Hountalas, D.T., and Pariotis, E.G. "A Simplified Model for the Spatial Distribution of Temperature in a Motored DI Diesel Engine", SAE Paper no. 2001-01-1235; 2001. Lefebvre, A., and Guilain, S., "Modelling and Measurement of the Transient Response of a

Lipatnikov, A.N., and Chomiak, J., "Turbulent Flame Speed and Thickness:

Progress in Energy and Combustion Science, Vol. 28, pp. 1-74, 2002.

Flames", Combustion and Flame, Vol. 100, pp. 202-210, 1995.

2006 World Congress, Detroit, MI, USA, April 3-6, 2006.

Engines", SAE Paper No. 2006-01-1110, 2006.

Yokohama, Japan, Aug. 2–5, JSME Paper No. 04-202.

S.I. Engine," SAE Paper No. 2002-01-0006, 2002.

Journal, Series II, Vol. 32, No. 1, pp.107-114, 1989.

Engineering, Vol.26, pp. 66–76, 2006.

2004.

2009.

1995.

2000.

1999-01-0218, 1999.

Editions, 1988.

0691.

Propagation Parameters and Nitric Oxide Formation in SI Engines," Comodia '04,

Combustion Chamber Walls of a Four-Stroke Gasoline Engine," JSME International

Transfer Model Suitable to Calculate Transient Processes of Turbocharged Diesel Engines With One-Dimensional Gas-Dynamic Codes", Applied Thermal

Manifold To Improve Transient Performance of a High-Speed Turbocharged Diesel Engine", Experimental Thermal and Fluid Science, Vol. 28, pp.863–875,

Turbulent Premixed Flames," Combustion and Flame, Vol. 103, pp. 107-114,

Propane/Air Combustion," Combustion and Flame, Vol. 120, pp. 407-416,

Engine Combustion with Variable Valve Train" SAE Paper No. 2006-01-1107, SAE

and Calibration of Heat Transfer Correlation in an I.C. Engine," SAE Paper No.

Implications of Alternative Knock Reduction Strategies for Turbocharged SI

Turbocharged SI Engine", SAE Paper 2005-01-0691, 2005. DOI 10.4271/2005-01-

Phenomenology, Evaluation, and Application in Multi-Dimensional Simulations",


**13** 

*Japan* 

**Development of Two-Phase Flow Correlation** 

The two-phase fluid mixing phenomena in fuel bundles of BWR plays an important role in the thermal-hydraulic performance of the fuel rod bundle, because it has strong effects on spatial distributions of the void fraction, quality and mass flow rate within it. The subchannel analysis method has been used for the prediction of the macroscopic thermalhydraulic characteristics, such as critical power and pressure loss, of a wide variety of fuel rod bundle designs. This method evaluates the fluid mixing effects using a unique model, known as a "cross flow model". The first successful cross flow model for gas-liquid twophase flow was devised by Lahey and Moody (1993). In their model, cross flow phenomena were decomposed into three components, namely flow diversions caused by transverse pressure gradients, turbulent mixing caused by stochastic pressure and flow fluctuations

Recently, there were studies of cross flow model improvements. Kawahara et al. (1999) presented an improved turbulent mixing model based on RMS (Root Mean Square) values of subchannel-to-subchannel differential pressure fluctuations. One of the advantages of this model was its ability to consider channel gap geometries and scales. Sumida et al.(1995) and Takemoto et al.(1997) supposed that the turbulent mixing and void drift phenomena were only transient components of the diversion cross flow caused by differential pressure fluctuations between the subchannels, and formulated the model known as the "fluctuating pressure model". Although both models appear promising for predicting the fluid mixing phenomena however, their applicability under actual plant operation conditions is presently unclear because it is impossible to simulate differential pressure fluctuations under steamwater high-pressure conditions without relying on experimental data. Although the cross flow model remains the most popular approach today, the mechanics of the third component, the void drift, are still unclear and there is no widely accepted understanding of

In the cross flow model and subchannel analysis, two-phase flow correlations are used to evaluate effects of flow conditions on two-phase flow characteristic easily. To create, modify or confirm these correlations, "actual scale tests" those simulate flow conditions and flow channel of actual fuel bundles are required. In actual BWR, pressure and temperature equals to about 7.2MPa and 560K respectively. Then the actual scale tests take a long time and

and a void drift that is unique to gas-liquid two-phase flow.

**1. Introduction** 

it yet.

**for Fluid Mixing Phenomena** 

**in Boiling Water Reactor** 

*Japan Atomic Energy Agency* 

Hiroyuki Yoshida and Kazuyuki Takase

