**9. References**

254 Computational Simulations and Applications

**8. Nomenclature** 

AB Project area of a bubble, m2

dx Horizontal extreme of a bubble, m dy Vertical extreme of a bubble, m e Coefficient of restitution

g Gravitational acceleration, m/s2 g0 Radial distribution function

J Granular energy transfer, kg/m/s3

q Diffusion of fluctuating energy, kg/s3

 Interphase drag coefficient, kg/m3/s Dissipation of fluctuating energy, kg/m/s3

N Number of bubbles, Eq. 31

u' Fluctuating velocity, m/s

 Granular temperature, m2/s2 Bubble property, Eq. 31 μ Shear viscosity, Pas Bulk viscosity, Pas ρ Density, kg/m3

 Shear stress tensor, N/m2 Angle of internal friction, ° ' Specularity coefficient

KTGF Kinetic Theory of Granular Flow

mf Minimum fluidization

Fr Constant in Johnson et al. (1990) friction model, N/m2

I2D Second invariant of the deviatoric stress tensor, s-2

n Constant in Johnson et al. (1990) friction model p Constant in Johnson et al. (1990) friction model

Cd Drag coefficient d Diameter, m

I Unit tensor

P Pressure, Pa

t Time, s u Velocity, m/s

Greek Letters:

Subscripts:

B Bubble col Collisional f Frictional g Gas phase kin Kinetic

max Maximum

Re Reynolds number

ε Volume fraction

Symbols:


Numerical Simulation of Dense

2701

0098-1354

Gas-Solid Multiphase Flows Using Eulerian-Eulerian Two-Fluid Model 257

Krishna, R.; van Baten J.M.; Urseanu, M.I. & Ellenberger, J. (2000). Rise velocity of single

Kuipers, J.A.M. & van Swaaij W.P.M. (1998). Computational fluid dynamics applied to

Kuipers, J.A.M.; van Duin K.J.; van Beckum, F.P.H. & van Swaaij, W.P.M. (1992). A

Kuipers, J.A.M.; van Duin K.J.; van Beckum, F.P.H. & van Swaaij, W.P.M. (1993). Computer

Kunii, D. & Levenspiel, O. (1991). *Fluidization Engineering, 2nd ed.*, Butterworth-Heineman,

Li, T.; Grace, J.R. & Bi, X. (2010). Study of wall boundary condition in numerical simulations

Lindborg, H.; Lysberg, M. & Jakobsen, H.A. (2007). Practical validation of the two-fluid

flow field. *Journal of Fluid Mechanics*, Vol.140, pp. 223-256, ISSN 0022-1120 Ma, D. & Ahmadi, G. (1986). An equation of state for dense rigid sphere gases. *Journal of* 

Patil, D.J.; van Sint Annaland, M. & Kuipers, J.A.M. (2005). Critical comparison of

Peirano, E.; Delloume, V. & Leckner B. (2001).Two- or three- dimensional simulations of

Schaeffer, D.G. (1987). Instability in the evolution equations describing incompressible

Schmidt, A. & Renz, U. (2005). Numerical prediction of heat transfer between a bubbling

Sinclair, J.L. & Jackson, R. (1989). Gas-particle flow in a vertical pipe with particle-particle

Syamlal, M.; Rogers, W. & O'Brien, T.J. (1993). *MFIX Documentation: Theory guide*. National Technical Information Service, DOE/METC-94/1004, Springfield, USA

*Science*, Vol.62, No.21, (Nove,ber 2007), pp. 5854-5869, ISSN 0009-2509 Lun, C.K.K.; Savage, S.B.; Jeffrey, D.J. & Chepurniy, N. (1984). Kinetic theories for granular

*Chemical Physics*, Vol.84, No.6, pp. 3449-3450, ISSN 0021-9606

56, No. 16, (August 2001), pp. 4787-4799, ISSN 0009-2509

(June 1992), pp. 1913-1924, ISSN 0009-2509

ISBN 978-040-9902-33-4, Boston, USA

447-457, ISSN 0032-5910

73-84, ISSN 0009-2509

50, ISSN 0022-0396

0001-1541

257-270, ISSN 0947-7411

circular-cap bubbles in two-dimensional beds of powders and liquids. *Chemical Engineering and Processing*, Vol.39, No.5, (September 2000), pp. 433-440, ISSN 0255-

chemical reaction engineering. *Advances in Chemical Engineering*, Vol.24, pp. 227-328

numerical model of gas-fluidized beds. *Chemical Engineering Science*, Vol.47, No.8,

simulation of the hydrodynamics of a two-dimensional gas-fluidized bed. *Computers & Chemical Engineering*, Vol.17, No.8, (August 1993), pp. 839-858, ISSN

of bubbling fluidized beds. *Powder Technology*, Vol.203, No.3, (November 2010), pp.

model applied to dense gas–solid flows in fluidized beds. *Chemical Engineering* 

flow: Inelastic particles in couette flow and slightly inelastic particles in a general

hydrodynamic models for gas-solid fluidized beds - Part II: Freely bubbling gassolid fluidized beds. *Chemical Engineering Science*, Vol.60, No.1, (January 2005), pp.

turbulent gas-solid flows applied to fluidization. *Chemical Engineering Science*, Vol.

granular flow. *Journal of Differential Equations*, Vol.66, No.1, (January 1987), pp. 19-

fluidized bed and an immersed tube bundle. *Heat Mass Transfer*, Vol.41, No.3, pp.

interactions. *AIChE Journal*, Vol.35, No.9, September (1989),pp. 1473-1486, ISSN


Ding, J. & Gidaspow, D. (1990). A bubbling fluidization model using kinetic theory of

Enwald, H.; Peirano, E. & Almstedt, A.E. (1996). Eulerian two-phase flow theory applied to

Gamwo, I.K.; Soong, Y. & Lyczkowski, R.W. (1999). Numerical simulation and experimental

Gao, W.M.; Kong, L.X. & Hodgson, P.D. (2007). Computational simulation of gas flow and

Gera, D., Gautam, M., Tsuji, Y., Kawaguchi, T. & Tanaka, T. (1998). Computer simulation of

Gidaspow, D. (1994). *Multiphase flow and fluidization: Continuum and kinetic theory descriptions*,

Gidaspow, D. & Ettehadieh, B. (1983), Fluidization in two-dimensional beds with a jet. 2.

Gustavsson, M. & Almstedt, A.E. (2000). Numerical simulation of fluid dynamics in

Hatano, H.; Khattab, I.A.H.; Nakamura, K. & Ishida, M. (1986). Spatiotemporal

Hoomans, B.P.B.; Kuipers, J.A.M.; Briels, W.J. & van Swaaij, W.P.M. (1996). Discrete particle

Hull, A.S.; Chen, Z.; Fritz, J.W. & Agarwal, P.K. (1999). Influence of horizontal tube banks on

Hulme. I.; Clavelle, E.; van der Lee, L. & Kantzas, A. (2005). CFD modeling and validation of

Jenkins, J.T. & Savage, S.B. (1983). A Theory for the rapid flow of identical, smooth, nearly

Johnson, P.C.; Nott, P. & Jackson, R. (1990). Frictional-collisional equations of motion for

Johnson, P.C. & Jackson, R. (1987). Frictional-collisional constitutive relations for granular

*Technology*, Vol.103, No.3, (July 1999), pp. 230-242, ISSN 0032-5910

*Research*, Vol.44, No.12, (May 2005), pp. 4254-4266, ISSN 0888-5885

1996), pp. 21-66, ISSN 0301-9322

1998), pp. 38-47, ISSN 0032-5910

0021-9592

0022-1120

pp. 99-118, ISSN 0009-2509

pp. 501-535, ISSN 0022-1120

67-93, ISSN 0022-1120

No.2, (Juli 1999), pp. 117-129, ISSN 0032-5910

Academic Press, ISBN 978-012-2824-70-8, Boston, USA

Vol.55, No.4, (February 2000), pp. 857-866, ISSN 0009-2509

No.2, (May 1983), pp. 193-201, ISSN 0196-4313

granular flow. *AIChE Journal*, Vol.36, No.4, (June 1990), pp. 523-538, ISSN 0001-1541

fluidization. *International Journal of Multiphase Flow*, Vol.22, Suppl.1, (December

validation of solids flows in a bubbling fluidized bed. *Powder Technology*, Vol.103,

heat transfer near an immersed object in fluidized beds. *Advances in Engineering Software*, Vol.38,No.11-12, (November-December 2007), pp. 826-834, ISSN 0965-9978

bubbles in large-particle fluidized beds. *Powder Technology*, Vol. 98, No. 1 , (July

hydrodynamic modeling. *Industrial & Engineering Chemistry Fundamentals*, Vol.22,

fluidized beds with horizontal heat exchanger tubes. *Chemical Engineering Science*,

measurement of bubble properties in free-bubbling fluidized beds. *Journal of Chemical Engineering of Japan*, Vol.19, No.5, (September 1986), pp. 425-430, ISSN

simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: A hard-sphere approach. *Chemical Engineering Science*, Vol.51, No.1, (January 1996),

the behavior of bubbling fluidized beds: 1. bubble hydrodynamics. *Powder* 

bubble properties for a bubbling fluidized bed. *Industrial & Engineering Chemistry* 

elastic, spherical particles. *Journal of Fluid Mechanics*, Vol.130, pp. 187-202, ISSN

particulate flows and their application to chutes. *Journal of Fluid Mechanics*, Vol.210,

materials, with application to plane shearing. *Journal of Fluid Mechanics*, Vol.176, pp.


**12** 

*Italy* 

Mirko Baratta and Ezio Spessa

**Numerical Simulation Techniques for the** 

*IC Engines Advanced Laboratory – Politecnico di Torino, Torino* 

**Performance in IC Engines Fuelled by CNG** 

**Prediction of Fluid-Dynamics, Combustion and** 

The design of modern internal combustion (IC) engines requires the understanding and quantification of many physical phenomena, including their impact on engine performance and emissions. In fact, the investigation of thermo-fluid-dynamic processes, combustion, performance and emissions is essential to fulfil the emission regulations, that are becoming more and more severe. Although the experimental analysis of such processes is mandatory to obtain fully quantitative results, the application of numerical simulation techniques is continuously increasing in popularity amongst the research community. This is due, on one hand, to the increased accuracy of specific sub-models, which are dedicated to several physical aspects in IC engines, and, on the other hand, to the availability of computational resources of increasing power. Nowadays, simulation tools can range from zerodimensional analysis tools of the combustion process in the engine chamber, to complete

This chapter is intended as an overview of the state-of-the-art of 1-D computational fluiddynamics (CFD) and thermo-dynamic tools applied to IC engines, with specific reference to compressed natural gas (CNG) fuelling. Moreover, the specific modelling approaches of the

1-D simulation tools are based on the solution of the inviscid form of the conservation laws of mass, momentum and energy (Euler equations). The equations are actually written in a 'generalized' form, in which ad-hoc terms are added, in order to properly simulate the friction and heat-exchange effects at the pipe walls. Furthermore, they are written in a quasi 1-D approach, as the variations of any dependent variable in a direction orthogonal to the flow direction are neglected, and at the same time the changes in the flow cross-section

In the last two decades, several commercial 1-D CFD tools have specifically been developed for engine flow simulation: among others, GT-Power (Gamma Technologies), Wave (Ricardo), Boost (AVL), and AMESim (LSM). Among the different classes of computational models, such tools are often a good compromise between accuracy, the required CPU time,

three-dimensional simulation models of turbulent flows and combustion.

authors are presented, within the 0-D and 1-D frameworks.

and completeness of the engine system that can be analyzed.

**1. Introduction** 

**2. 1-D engine simulation** 

along the pipe axis are accounted for.

