Skip to main content
SpringerLink
Log in

Prediction of the Rate of Heat Release of Mixing-Controlled Combustion in a Common-Rail Engine with Pilot and Post Injections

  • Chapter
  • First Online:
Modelling Diesel Combustion

Part of the book series: Mechanical Engineering Series ((MES))

Abstract

A one-dimensional model for the prediction of the rate of heat release (ROHR) in common-rail direct injection diesel engines with the pilot, main, and post-injections is developed. The model is an improvement on the previously developed mixing-controlled combustion model extended by including the effect of the wall jet. The decay of the ROHR curve has been improved in the second regime of combustion. It was observed that the input kinetic energy of the wall–spray is retarded only after the growth of spray along the bowl wall exceeds the diameter of the spray cone. It is shown that this model can be extended for engines with multiple injections, i.e. pilot, main, and post-injections. The ROHR was modelled as a function of the turbulence kinetic energy of the fuel mass and the dissipation rate of this energy in different stages of spray propagation. The inputs required for the model are the nozzle discharge coefficient, the injection pressure, the injection timing, and the injected fuel quantity for each injection stage that are readily controlled in common-rail engines. The predicted heat release histories corresponding to the pilot injection, the main injection, and the post-injection were found to agree with the experiments.

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 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

Abbreviations

A h :

Area of the nozzle hole (m2)

C d :

Nozzle discharge coefficient (–)

C diss :

Constant for dissipation of the turbulence energy = 0.01 (s−1)

C model :

Model constant = 1000 (kJ/kg)

C rate :

Constant for the rate of mixing = 0.002 (s)

C turb :

Efficiency of conversion of the kinetic energy to the turbulence energy (–)

C wall :

Ratio of the kinetic energy of the spray along the wall to the kinetic energy of the free spray (–)

(dQ/dh) MI :

Quantity of heat released during the main injection for the corresponding crank angle of the post-injection (kJ/deg)

d :

Diameter of the nozzle hole (m)

d e :

Effective diameter of the nozzle hole (m)

d scone :

Radius of the spray cone on the piston-bowl wall (m)

E diss :

Dissipation turbulence kinetic energy (J)

E k, i :

Input kinetic energy of the jet (J)

E t, k, i :

Turbulence kinetic energy of the jet (J)

E total :

Total turbulence kinetic energy (J)

f 1 :

Function representing the availability of fuel for combustion (–)

f 2 :

Function representing the rate of mixing of the fuel (–)

k :

Density of the turbulence kinetic energy (J/kg)

l impg :

Impingement distance, the minimum distance between the nozzle hole and the bowl wall (m)

LCV :

Lower calorific value of the fuel (kJ/kg)

M a :

Mass of charge air per cylinder per stroke (kg)

M f :

Cumulative mass of fuel injected up to a given crank angle (kg)

n h :

Number of injector holes (–)

N :

Engine speeda (r/min)

P c :

Combustion pressure (bar)

P r :

Rail pressure (bar)

Q :

Cumulative heat release (J)

s :

Penetration distance of the spray jet (m)

s wall :

Growth of the wall spray (m)

t impg :

Time after the start of spray impingement on the wall (s)

t inj :

Time after the start of injection (s)

T surr :

Temperature of the mixture in the combustion chamber(K)

T 0 :

Reference temperature = 294 (K)

V :

Instantaneous cylinder volume (m3)

V free :

Velocity of the spray jet through the charged air in the combustion chamber (m/s)

V j :

Velocity of the spray jet (m/s)

V wall :

Velocity of the spray jet along the combustion bowl wall (m/s)

θ :

Crank angle (deg)

θ cone :

Cone angle of the spray cone (deg)

ε :

Rate of dissipation of the turbulence kinetic energy (s−1)

k :

Polytropic coefficient, the ratio of specific heats (–)

λ :

Excess air ratio

r f :

Density of the diesel fuel (kg/m3)

r g :

Density of charge air inside the cylinder (kg/m3)

References

  1. Aghav YV, Lakshminarayanan PA, Babu MKG (2008) Validating the phenomenological smoke model at different operating conditions of DI diesel engines. Trans ASME J Eng Gas Turbines Power 130(1):012803

    Google Scholar 

  2. AVLB (2008) User’s guide, version 5.1, 2008 (AVL List GmbH, Graz)

    Google Scholar 

  3. Chang CT, Farrell PV (1998) Spray characteristics and near injector tip effects of injection pressure and ambient density. In: Proceedings of the fourth international symposium on the diagnostics and modeling of combustion in internal combustion engines (COMODIA ’98), Kyoto, Japan, 20–23 July 1998, Japan Society of Mechanical Engineers, Tokyo, pp 465–470

    Google Scholar 

  4. Chmela FG, Orthaber GC (1999) Rate of heat release prediction for direct injection diesel engines based on purely mixing controlled combustion. SAE paper 1999–01–0186

    Google Scholar 

  5. Dronniou N, Lejeune M, Balloul I, Higelin P (2005) Combination of high EGR rates and multiple injection strategies to reduce pollutant emissions. SAE paper 2005–01–3726

    Google Scholar 

  6. ETAS (2010) INCA software products, ETAS Group, Stuttgart. Available from http://www.etas.com/en/products/inca_software_products.php

  7. Heywood JB (1988) In: Internal combustion engine fundamentals, McGraw-Hill, New York

    Google Scholar 

  8. Hohenberg GH (1979) Advance approach for heat transfer calculation. SAE paper 790825

    Google Scholar 

  9. Jaipuria A, Lakshminarayanan PA (2011) Prediction of the rate of heat release of mixing-controlled combustion in a common-rail engine with pilot and post injections. Proc Instit Mech Eng Part D: J Automobile Eng 225(2):246–259. https://doi.org/10.1243/09544070JAUTO1615

  10. Lakshminarayanan PA, Aghav YV (2010) Modelling diesel combustion. Springer Science + Business Media, Dordrecht, pp 213–254

    Google Scholar 

  11. Lakshminarayanan PA, Dent JC (1983) Interferometric studies on vaporizing and combusting spray. SAE paper 830244

    Google Scholar 

  12. Lakshminarayanan PA, Aghav YV, Dani AD, Mehta PS (2002) Accurate prediction of the rate of heat release in a modern direct injection diesel engine. Proc IMechE, Part D: J Automobile Eng 216(8):663–675

    Google Scholar 

  13. Marek SJ (1996) Thermodynamic determination of T.D.C. in piston combustion engines. SAE paper 960610

    Google Scholar 

  14. Nilsson Y, Eriksson L (2004) Determining TDC position using symmetry and other methods. SAE paper 2004–01–1458

    Google Scholar 

  15. Ranz WE (1958) Some experiments on orifice sprays. Can J Chem Eng 36(4):175–181

    Article  Google Scholar 

  16. Tatschi R, Pachler K, Fuchs H (1995) Multidimensional simulation of diesel engine combustion process—modeling and experimental validation. In: Proceedings of the fifth symposium on the working process of the internal combustion engine, Graz, Austria, September, Technische Universitat Graz, Graz

    Google Scholar 

  17. Tazerout M, Le Corre O, Rousseau S (1999) TDC determination in IC engines based on the thermodynamic analysis of the temperature–entropy diagram. SAE paper 1999–01–1489

    Google Scholar 

  18. Vibe II (1970) Brennverlauf und Kreisprozess von Verbennungsmotoren, VEB Verlag Technik, Berlin

    Google Scholar 

  19. Woschni G (1967) A universally applicable equation for the instantaneous heat transfer coefficient in the internal combustion engine. SAE paper 670931

    Google Scholar 

  20. Woschni G (1991) Einfluß von Rußablagerungen auf den Wa¨rmeu¨bergang zwischen Arbeitsgas und Wand im Dieselmotor. In 3. Tagung Der Arbeitsprozess des Verbrennungsmotors, Mitteilungen des Instituts fur Verbrennungskraftmaschinen und Thermodynamik, Graz, Austria, 20–21 September 1991, (Instituts fur Verbrennungskraftmaschinen und Thermodynamik, Graz), pp 149–169

    Google Scholar 

  21. Zinner K (1978) Supercharging of internal combustion engines—fundamental; calculations; examples. Springer, Berlin

    Google Scholar 

Download references

Acknowledgements

The authors thank Mr Prasann Deshpande and the testing team of Engine R&D, Ashok Leyland, Hosur, Tamil Nadu, India, for their help to write the computer program and analyzing the data.

This chapter is based on the paper, “Prediction of the Rate of Heat Release of Mixing-Controlled Combustion in a Common-Rail Engine with Pilot and Post Injections” published in the Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 225, no. 2 (February 2011): 246–59. https://doi.org/10.1243/09544070JAUTO1615 by the authors as permitted by SAGE Publishing under “SAGE’s Author Archiving and Re-Use Guidelines”: https://in.sagepub.com/en-in/sas/journal-author-archiving-policies-and-re-use.

Author information

Authors and Affiliations

  1. Formerly with Ashok Leyland, Chennai, India

    Anirudh Jaipuria

  2. IIT Kanpur, Kanpur, India

    P. A. Lakshminarayanan

Authors
  1. Anirudh Jaipuria
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. A. Lakshminarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. A. Lakshminarayanan .

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Jaipuria, A., Lakshminarayanan, P.A. (2022). Prediction of the Rate of Heat Release of Mixing-Controlled Combustion in a Common-Rail Engine with Pilot and Post Injections. In: Modelling Diesel Combustion. Mechanical Engineering Series. Springer, Singapore. https://doi.org/10.1007/978-981-16-6742-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-6742-8_10

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-6741-1

  • Online ISBN: 978-981-16-6742-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation