Skip to main content
SpringerLink
Log in

Physical Laws and Model Structure of Simulations

  • Chapter
  • First Online:
Quasi-Dimensional Simulation of Spark Ignition Engines

  • 1194 Accesses

Abstract

In this chapter, we present the Newton’s second law and the first principle of thermodynamics as a set or ordinary differential equations for the pressure and the temperature inside the combustion chamber. The solution of these equations with the appropriate initial conditions in each stroke allows to follow the evolution of the thermodynamic properties of the gas mixture performing the engine cycle. The solution of such equations requires the formulation of some additional submodels for the engine: heat transfer through cylinder walls, frictions, working fluid properties, combustion and chemical reactions, and several others. We present those basic models and how are they engaged in the structure of a computer simulation scheme. Special attention is paid to the use of alternative fuels. Detailed chemical reactions for the combustion of such fuels are presented in Appendix F. We include an up-to-date bibliographic survey on advanced submodels that could help the reader to build a particular advanced simulation scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    A single dot denotes the first derivative with respect to time and two dots the second derivative.

  2. 2.

    The pressure exerted by the oil in the crankcase over the bottom part of the piston in taken as negligible.

  3. 3.

    In this and the following equations, the subscript \(u\) refers to the gas mixture before combustion. It is composed of fresh air and fuel, but also of reaction products from the previous cycle. The subscript \(b\) refers to the gas mixture after combustion, i.e., composed of reaction products. As it will be explained later, both mixtures coexist during combustion in the cylinder. This is one of the main identifying characteristics of two-zone simulations.

  4. 4.

    It is considered that the gas mixture leaving the control volume is essentially formed by burned gases: all the fuel was burned out and the fresh mixture leaving out during the overlap period (see below) is negligible. There are no appreciable temperature changes from inside the cylinder to the exhaust duct, so \(\dot{m}_b(h_\mathrm{ex }-h_b)\simeq 0\).

  5. 5.

    Swirl, as defined by Ferguson [13], is the rotational flow within the cylinder about its axis. It is associated to the existence of a nonzero angular momentum of the incoming flow. It is used in the design of some gasoline engines with the aim to boost a fast burn and in diesel engines to provoke a rapid mixing between fuel and air. Squish is the radial gas motion that takes place at the end of the compression stroke when the piston and the cylinder heads approach each other closely. It is especially associated to direct injection engines.

  6. 6.

    The flame front is considered as the forward boundary of the reacting zone.

  7. 7.

    A cosine burning law is also usual in the literature [6, 15–17]:

    $$\begin{aligned} x_b(\varphi )=\frac{1}{2}\left[ 1-\cos \left( \frac{\pi (\varphi -\varphi _0)}{\varDelta \varphi } \right) \right] . \end{aligned}$$
  8. 8.

    In a turbulent flow, Kolmogorov microscale is the eddy size at which molecular viscosity becomes important.

  9. 9.

    Typical values for the quantities which characterize engine flames can be found in [32].

  10. 10.

    The laminar flame speed, \(S_L\), is defined as the velocity relative to and normal to the flame front, with which unburned gas (locally) moves into the front and is transformed into products under laminar flow conditions [34].

  11. 11.

    To have an approximate idea, for \(t\simeq 3\tau _b\), the term in the brackets in Eq. (2.36) is around \(95\,\%\) of \(u_t+S_L\). Typical characteristic speeds, \(u_t\), are in the interval \(2-6\) m/s (except for hydrogen, which are much faster) [25, 46, 47] and laminar flame speeds, \(S_L\), are around one order of magnitude smaller [34] depending on the fuel type, fuel–air ratio, and several other factors.

  12. 12.

    For practical purposes, in simulations it is usually considered that combustion finishes at the moment the exhaust valve opens, so there could be a small fraction of unburned fuel in the combustion chamber among the residuals.

  13. 13.

    For brevity we shall use the term fue ratio to refer to the ratio between the masses of fuel and air and their stoichiometric counterparts (see Eq. (A.3) in Appendix A) that is usually known as fuel–air equivalence ratio [48].

  14. 14.

    The volumetric efficiency, \(e_v\), is a parameter used to quantify the effectiveness of the intake process. It is the mass that enters the cylinder during intake over the displaced volume \(e_v=m_\mathrm{in }/(\rho _i V_{dt})\). \(\rho _i\) is the density of the mixture evaluated at a reference state; for instance the average conditions on the intake manifold.

  15. 15.

    These particular numerical values are arbitrary but useful for practical reasons.

  16. 16.

    Although abnormal combustion comprises several phenomena, probably the most important are knock and surface ignition [54, 55]. Knock occurs when the mixture appears to ignite and burn ahead of the flame without any external ignition source. There is a rapid release of chemical energy of the gas which provokes pressure waves of considerable amplitude and a particular noise transmitted through the engine structure. Surface ignition is caused by the mixture igniting as consequence of a contact with a hot surface (overheated valve or spark plug) or hot-spot combustion chamber deposits. It may happen before the spark ignites the charge (pre-ignition) or after normal ignition (post-ignition).

  17. 17.

    Very briefly, the main reasons for engine cooling are: to get an elevated volumetric efficiency, to avoid combustion problems, and to guarantee proper mechanical operation and reliability. Advanced cooling systems have been analyzed by Robinson et al. [60] and Yoo et al. [61].

  18. 18.

    As discussed by Heywood [90], friction work for compression ignition engines and spark ignition engines is different. Pumping work for SI engines is larger than that for similar CI engines. Piston-crank assembly friction losses are also different. So the use of the correlation for Chen and Flynn [75, 91] for SI engines in order to get accurate performance results should be carefully examined.

  19. 19.

    Some engines incorporate recycled exhaust as a way to control NO\(_x\) emissions. They are usually called EGR (exhaust gas recirculation) engines.

  20. 20.

    Unless explicitly mentioned, we shall take, \(T_\mathrm ref =298.15\) K.

  21. 21.

    Pressure differences are also substantial, from approximately atmospheric pressure at intake to \(35\) atm at its highest value.

  22. 22.

    In some modern engines, a fraction of recycled exhaust gases are injected into the fresh mixture with the objective of a greater dilution and thus control NO\(_x\) emissions. To quantify the percent of exhaust gas recycled an additional parameter is introduced: EGR\((\%)=(m_\text {EGR}/m_i)\times 100\) where \(m_\text {EGR}\) is the mass of exhaust gas recycled. In this case, the residual gas mass fraction in the fresh mixture is: \(x_r=(m_\text {EGR}+m_r)/m\).

  23. 23.

    This key difference between combustion in both types of engines is more fundamental than the fact that for theoretical purposes a spark ignition engine is associated to an Otto cycle and a compression ignition engine to a Diesel cycle. In reality, combustion never occurs at constant volume in a spark ignition engine, nor does it occur under isobaric conditions in a compression ignition engine.

  24. 24.

    The octane number of a fuel is a measure of its anti-knock properties. It is defined a 0–100 scale assigning \(0\) to n-heptane (a fuel predisposed to knock) and \(100\) to isooctane because of its anti-knock resistance. For instance, a \(95\) octane fuel has anti-knock performance equivalent to a mixture composed of \(95\,\%\) isooctane and \(5\,\%\) n-heptane by volume.

References

  1. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 2, pp. 42–45

    Google Scholar 

  2. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 4, pp. 142–155

    Google Scholar 

  3. C.R. Ferguson, Internal Combustion Engines, Applied Thermosciences (Wiley, 1986), Chap. 1, pp. 1–24

    Google Scholar 

  4. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 6, pp. 206–208

    Google Scholar 

  5. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 6, pp. 293–297

    Google Scholar 

  6. C. Borgnakke, P. Puzinauskas, Y. Xiao, Spark ignition engine simulation models. Technical Report, Department of Mechanical Engineering and Applied Mechanics. University of Michigan. Report No. UM-MEAM-86-35 (1986)

    Google Scholar 

  7. H. Bayraktar, O. Durgun, Energy Sources 25, 439 (2003)

    Google Scholar 

  8. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 3, pp. 78–81

    Google Scholar 

  9. J. Gatowski, J. Heywood, C. Delaplace, Combust. Flame 56, 71 (1984)

    Article  Google Scholar 

  10. J. Tagalian, J. Heywood, Combust. Flame 64, 243 (1986)

    Article  Google Scholar 

  11. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 14, pp. 766–768

    Google Scholar 

  12. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 3, pp. 50–52

    Google Scholar 

  13. C. Ferguson, Internal Combustion Engines, Applied Thermosciences (Wiley, 1986)

    Google Scholar 

  14. A. Alkidas, Energ. Convers Manage. 48, 2751 (2007)

    Article  Google Scholar 

  15. P. Blumberg, J. Kummer, Comb. Sci. Tech. 4, 73 (1971)

    Article  Google Scholar 

  16. P. Blumberg, G. Lavoie, R. Tabaczynski, Prog. Energ. Comb. Sci. 5, 123 (1979)

    Article  Google Scholar 

  17. M. Tazerout, O. Le Corre, Int. J. Appl. Thermodyn. 3(2), 49 (2000)

    Google Scholar 

  18. J. Heywood, J. Higgins, P. Watts, R. Tabaczynski, SAE Paper 790291 (1979)

    Google Scholar 

  19. E. Sher, T. Bar-Kohany, Energy 27, 757 (2002)

    Article  Google Scholar 

  20. H. Bayraktar, O. Durgun, Energ. Convers Manage. 45, 1419 (2004)

    Article  Google Scholar 

  21. S. Sitthiracha, S. Patumsawad, S. Koetniyom, 20th Conference of Mechanical Engineering Network of Thailand (Nakhon Ratchasima, Thailand, 2006)

    Google Scholar 

  22. S. Soylu, J. Gerpen, Energ. Convers Manage. 45, 467 (2004)

    Article  Google Scholar 

  23. A. Fischer, K. Hoffmann, J. Non-Equilib, Thermodyn. 29, 9 (2004)

    MATH  Google Scholar 

  24. J. Keck, in Proceedings of Nineteenth Symposium (International) on Combustion (The Combustion Institute, Pittsburgh, 1982), pp. 1451–66

    Google Scholar 

  25. G. Beretta, M. Rashidi, J. Keck, Combust. Flame 52, 217 (1983)

    Article  Google Scholar 

  26. R.J. Tabaczynski, Prog. Energ. Combust. Sci. 2, 143 (1976)

    Article  Google Scholar 

  27. R.J. Tabaczynski, F.H. Trinker, B.A.S. Shannon, Combust. Flame 39, 111 (1980)

    Article  Google Scholar 

  28. R. Tabaczynski, C. Ferguson, K. Radhakrishnan, SAE Paper 770647 (1977)

    Google Scholar 

  29. H. Bayraktar, Renew. Energ. 32, 758 (2007)

    Article  Google Scholar 

  30. H. Bayraktar, O. Durgun, Energ. Convers Manage. 46, 2317 (2005)

    Article  Google Scholar 

  31. S.R. Turns, An Introduction to Combustion, Concepts and Applications (McGraw Hill, 2012)

    Google Scholar 

  32. J. Heywood, in International Symposium COMODIA 94 (Yokohama, 1994)

    Google Scholar 

  33. S. Poulos, J. Heywood, SAE Paper 830334 (1983)

    Google Scholar 

  34. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 9, pp. 402–406

    Google Scholar 

  35. M. Al-Baghdadi, Turkish J. Eng. Env. Sci. 30, 331 (2006)

    Google Scholar 

  36. S. Hosseini, R. Abdolah, A. Khani, in Proceedings of the World Congress on Engineering Vol II (2008)

    Google Scholar 

  37. M. Al-Baghdadi, H. Al-Janabi, Energ. Convers Manage. 41, 77 (2000)

    Article  Google Scholar 

  38. H. Al-Janabi, M. Al-Baghdadi, Int. J. Hydrogen Energy 24, 363 (1999)

    Article  Google Scholar 

  39. N. Blizard, J. Keck, SAE Paper 740191 (1974)

    Google Scholar 

  40. J. Keck, J. Heywood, G. Noske, SAE Paper 870164 (1987)

    Google Scholar 

  41. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 14, pp. 771–773

    Google Scholar 

  42. G. Andrews, D. Bradley, S. Lwakabamba, Combust. Flame 24, 285 (1975)

    Article  Google Scholar 

  43. S. McAllister, J. Chen, A. Fernandez-Pello, Fundamentals of Combustion Processes (Springer, 2011)

    Google Scholar 

  44. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 8, pp. 361–369

    Google Scholar 

  45. S. Verhelst, C. Sheppard, Energ. Convers Manage. 50, 1326 (2009)

    Article  Google Scholar 

  46. D. Bradley, M. Haq, R. Hicks, T. Kitagawa, M. Lawes, C. Sheppard, R. Woolley, Combust. Flame 133, 415 (2003)

    Article  Google Scholar 

  47. A. Dahoe, J. Loss Prevention Process Ind. 18, 152 (2005)

    Article  Google Scholar 

  48. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 4, pp. 68–72

    Google Scholar 

  49. M. Metghalchi, J. Keck, Combust. Flame 48, 191 (1982)

    Article  Google Scholar 

  50. D. Rhodes, J. Keck, SAE Paper 850047 (1985)

    Google Scholar 

  51. L.O. Gülder, in SAE Paper 841000 (1984)

    Google Scholar 

  52. P. Gülder, Combust. Flame 56, 261 (1984)

    Article  Google Scholar 

  53. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 9, pp. 371–375

    Google Scholar 

  54. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 9, pp. 450–478

    Google Scholar 

  55. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 3, pp. 74–75

    Google Scholar 

  56. A. Ibrahim, S. Bari, Fuel 87, 1824 (2008)

    Article  Google Scholar 

  57. R. Jenkin, E. James, W. Malalasekera, SAE Paper 972877 (1997)

    Google Scholar 

  58. W. Dai, C. Newman, G. Davis, SAE Paper 961962 (1996)

    Google Scholar 

  59. C. Rakopoulos, G. Kosmadakis, A. Dimaratos, E. Pariotis, Appl. Energ. 88, 111 (2011)

    Article  Google Scholar 

  60. K. Robinson, N. Campbell, J. Hawley, D. Tiller, SAE Paper 1999–01-0578 (1999)

    Google Scholar 

  61. I. Yoo, K. Simpson, M. Bell, S. Majkowski, SAE Paper 2000–01-0939 (2000)

    Google Scholar 

  62. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 12, pp. 668–670

    Google Scholar 

  63. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 10, pp. 429–433

    Google Scholar 

  64. G. Borman, K. Nishiwaki, Prog. Energy Comb. Sci. 13, 1 (1987)

    Article  Google Scholar 

  65. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 12, pp. 670–673

    Google Scholar 

  66. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999), Chap. 12, pp. 483–486

    Google Scholar 

  67. S. Khalilarya, M. Javadzadeh, Therm. Sci. 14, 1013 (2010)

    Article  Google Scholar 

  68. O.A. Ozsoysal, Energ. Convers Manage. 47, 1051 (2006)

    Article  Google Scholar 

  69. A. Mohammadi, M. Rashidi, in Proceeding of the 3rd BSME-ASME International Conference on Thermal Engineering (2006)

    Google Scholar 

  70. A. Noori, M. Rashidi, ASME J. Heat Trans. 129, 609 (2007)

    Article  Google Scholar 

  71. G. Woschni, SAE Paper 670931 (1967)

    Google Scholar 

  72. G. Eichelberg, Engineering 148, 463 (1939)

    Google Scholar 

  73. M.I. Karamangil, O. Kaynakli, A. Surmen, Energ. Convers Manage. 47, 800 (2006)

    Article  Google Scholar 

  74. M. Lounici, K. Loubar, M. Balistrou, M. Tazerout, Appl. Therm. Eng. 31, 319 (2011)

    Article  Google Scholar 

  75. R. Stone, Introduction to Internal Combustion Engines (Macmillan Press LTD., 1999)

    Google Scholar 

  76. W. Annand, Proc. I. Mech. E. 177, 973 (1963)

    Article  Google Scholar 

  77. W. Annand, T. Ma, Proc. I. Mech. E. 72, 976 (1985)

    Google Scholar 

  78. N. Watson, J.M.S., Turbocharging the internal combustion engine (Macmillan Press LTD., 1982)

    Google Scholar 

  79. G. Hohenberg, SAE Paper 790825 (1979)

    Google Scholar 

  80. H. Bayraktar, Renew. Energ. 30, 1733 (2005)

    Article  Google Scholar 

  81. H. Özcan, J. Yamin, Energ. Convers Manage. 49, 1193 (2008)

    Article  Google Scholar 

  82. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 12, pp. 694–696

    Google Scholar 

  83. H. Soyhan, H. Yasar, H. Walmsley, B. Head, G. Kalghatgi, C. Sorusbay, Appl. Therm. Eng. 29, 541 (2009)

    Article  Google Scholar 

  84. K.W. Cho, D. Assanis, Z. Filipi, G. Szekely, P. Najt, R. Rask, Proc. Inst. Mech. Eng. Part D-J. Automob. Eng. 222, 2219 (2008)

    Google Scholar 

  85. S. Fiveland, D. Assanis, SAE Paper 2002–01-1757 (2002)

    Google Scholar 

  86. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 13, pp. 712–713

    Google Scholar 

  87. S. Tung, M. McMillan, Tribol Int. 37, 517 (2004)

    Article  Google Scholar 

  88. E. Abu-Nada, I. Al-Hinti, A. Al-Sharki, B. Akash, J. Eng. Gas Turbines Power 130, 022802 (2008)

    Article  Google Scholar 

  89. H.W. Barnes-Moss, A Designer’s Viewpoint in Passenger Car Engines, Conference Proceedings (Institution of Mechanical Engineers, London, 1975), pp. 133–147

    Google Scholar 

  90. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 13, pp. 722–724

    Google Scholar 

  91. S. Chen, P. Flynn, SAE Paper 650733 (1965)

    Google Scholar 

  92. D. Winterbone, The Thermodynamics and Gas Dynamics of Internal Combustion Engines (Oxford University Press, 1986), vol. II, Chap. Transient performance

    Google Scholar 

  93. J. Heywood, Internal Combustion Engine Fundamentals (McGraw-Hill, 1988), Chap. 4, pp. 109–112

    Google Scholar 

  94. NIST-JANAF, Thermochemical Tables, 4th edn. Technical Report, National Institute of Standards and Technology. J. Phys. Chem. Ref. Data (1988)

    Google Scholar 

  95. B. Poling, J. Prausnitz, J. O’Conell, The Properties of Gases and Liquids, 5th edn.(McGraw-Hill, 2001)

    Google Scholar 

  96. NIST Chemistry WebBook. http://webbook.nist.gov/chemistry/

  97. B.J. McBride, G. Sanford, Computer program for calculation of complex chemical equilibrium compositions and applications. Users Manual 1311, National Aeronautics and Space Administration, NASA (1996). http://www.grc.nasa.gov/WWW/CEAWeb/

  98. E. Lemmon, M. Huber, M. McLinden, NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 9.0. Tech. rep., National Institute of Standards and Technology, Standard Reference Data, Program (2010)

    Google Scholar 

  99. C. Taylor, The Internal-Combustion Engine in Theory and Practice, vol. II (MIT Press, 1985), Chap. 4, pp. 128–129

    Google Scholar 

  100. NIST Program on Chemical Kinetics. http://www.nist.gov/srd/chemkin.cfm

  101. CHEMKIN. http://www.reactiondesign.com/products/open/chemkin.html

  102. M. Jelezniak. CHEMKED. http://www.chemked.com/

  103. C. Olikara, G. Borman, SAE Paper 750468 (1975)

    Google Scholar 

  104. C. Ferguson, Internal Combustion Engines (Wiley, 1986), Chap. 3, p. 121

    Google Scholar 

  105. M. Vandevoorde, J. Vierendeels, R. Sierens, E. Dick, R. Baert, J. Eng. Gas Turbines Power 122, 533 (2000)

    Article  Google Scholar 

  106. W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes. The Art of Scientific Computing, 3rd edn. (Cambridge University Press, 2007)

    Google Scholar 

  107. P.L. Curto-Risso, A. Medina, A. Calvo Hernández, J. Appl. Phys. 104, 094911 (2008)

    Article  Google Scholar 

  108. E. Pariotis, G. Kosmadakis, C. Rakopoulos, Energ. Convers Manage. 60, 45 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física Aplicada, Universidad de Salamanca, 37008, Salamanca, Spain

    Alejandro Medina & Antonio Calvo Hernández

  2. Instituto de Ingeniería Mecánica y, Universidad de la República, Montevideo, Uruguay

    Pedro Luis Curto-Risso

  3. Unidad Profesional Interdisciplinaria en, Instituto Politécnico Nacional, Av. IPN 2580, 07340, México D.F., Mexico

    Lev Guzmán-Vargas

  4. Instituto Politécnico Nacional, Edif. 9, 07738, México D.F., Mexico

    Fernando Angulo-Brown

  5. Department of Mathematical Sciences, Richard G. Lugar Centre for Renewable Energy, Indiana University, Indianapolis, 46202, USA

    Asok K Sen

Authors
  1. Alejandro Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pedro Luis Curto-Risso
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonio Calvo Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lev Guzmán-Vargas
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fernando Angulo-Brown
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Asok K Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alejandro Medina .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag London

About this chapter

Cite this chapter

Medina, A., Curto-Risso, P.L., Hernández, A.C., Guzmán-Vargas, L., Angulo-Brown, F., Sen, A.K. (2014). Physical Laws and Model Structure of Simulations. In: Quasi-Dimensional Simulation of Spark Ignition Engines. Springer, London. https://doi.org/10.1007/978-1-4471-5289-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-5289-7_2

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5288-0

  • Online ISBN: 978-1-4471-5289-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation