Engine model for onboard marine engine failure simulation


The primary source of the power for marine industry comes from large two-stroke low-speed marine diesel engines. The more severe emission regulations are forcing the ship owners to use more efficient engines. The electronically controlled engines were introduced which comply with the needs. The electronically controlled engine requires more calibration effort and is mostly based on calibration from the testbed with some environmental condition corrections. In this paper, the physical engine model was introduced including AVL multi-zone combustion model and self-developed models for turbocharger, charge air cooler, injector and rail model. Typical engine failures were simulated. The demonstrated engine model was based on six-cylinder large two-stroke low-speed marine diesel engine and verified with the measurements from the engine testbed. The model calibration was done for the pressure traces and available mean value measurement for 40%, 60% and 100% of engine load. The results show 2–7% of relative deviation of the BMEP, 1–2% relative deviation for in-cylinder peak pressure and almost no deviation in scavenged air pressure. The model showed representative engine behavior and was used for studies on engine failure simulation. The presented engine model can be used for optimization and diagnostic purposes.

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\(A_{\text{NH}}\) :

Area of the nozzle hole (m2)

\(A_{\text{NS}}\) :

Area of needle seat (m2)

\(A_{\text{i}}\) :

Zone surface calculated from the zone volume with assumption of its spherical shape (m2)

\(a_{\text{p}}\) :

Model parameter

\(A_{\text{trans}}\) :

Heat transfer surface (m2)

\(b_{{{\text{O}}_{2} }}\) :

Model parameter

\(c_{\text{arrh}}\) :

Model parameter

\(c_{\text{D}}\) :

Injector nozzle discharge coefficient

\(C_{\text{Entrain}}\) :

Model parameter

\(C_{\text{eth}}\) :

Parameter to control the heat up of the droplet

\(C_{\text{Evap}}\) :

Parameter for controlling the evaporation rate

\(C_{\text{IgnDel}}\) :

Ignition delay parameter

\(C_{\text{IgnExp}}\) :

Ignition delay exponent

\(c_{\text{p}}\) :

Specific heat capacity (J kg−1 K−1)

\(C_{\text{rad}}\) :

Model parameter

\(C_{1}\), \(C_{2}\), \(C_{3}\) :

Model parameters

\(D_{\text{hyd}}\) :

Hydraulic diameter (m)

\(d_{\text{inj}}\) :

Injector nozzle diameter (m)

\(\frac{{{\text{d}}m_{\text{inj}} }}{{{\text{d}}t}}\) :

Mass flow through injector

\(\frac{{{\text{d}}m_{\text{inj}} }}{{{\text{d}}t}}\) :

Injected fuel mass flow

\(\frac{{{\text{d}}m_{\text{pump}} }}{{{\text{d}}t}}\) :

Mass flow through pump

\(\frac{{{\text{d}}x_{\text{fb}} }}{{{\text{d}}t}}\) :

The fuel burning rate

\(E\) :

The bulk modulus for the working fluid

\(f_{\text{ax}}\) :

Correction functions to account for axial position in the spray

\(F_{\text{fr}}\) :

Friction force

\(F_{\text{HT}}\) :

Heat transfer multiplier

\(f_{\text{rad}}\) :

Correction functions to account for radial position in the spray

\(F_{\text{target}}\) :

Factor used to evaluate target pressure drop or target efficiency

\(\dot{H}_{\text{i}}\) :

Are heat fluxes

\(h_{03}\) :

Total enthalpy at the turbine inlet (J kg−1)

\(h_{04}\) :

Total enthalpy at the turbine outlet (J kg−1)

\(h_{1}\) :

Enthalpy at the inlet of the compressor (J kg−1)

\(h_{2}\) :

Enthalpy at the outlet of the compressor (J kg−1)

\(i_{{{\text{ax}},{ \hbox{max} }}}\) :

Number of all axial zones

\(i_{\text{ax}}\) :

Index of axial zones

\(i_{\text{rad}}\) :

Radial position of the package in the spray

\(I_{\text{TC}}\) :

Turbocharger wheel inertia

\(K_{\text{b}}\) :

Chemical reaction parameter

\(L\) :

Length (m)

\(m\) :

Solid wall mass

\(\dot{m}\) :

Mass flow rate

\(\dot{m}_{\text{c}}\) :

Mass flow rate in the compressor

\(\dot{m}_{\text{t}}\) :

Mass flow rate in the turbine

\(m_{\text{i}}\) :

Zone mass at t

\(m_{\text{inj}}\) :

Injected package fuel mass

\(P_{\text{C}}\) :

Compressor power consumption (W)

\(p_{\text{cyl}}\) :

Pressure inside cylinder (Pa)

\(p_{\text{pipe}}\) :

Pressure inside pipe (Pa)

\(p_{\text{s}}\) :

Saturation pressure

\(P_{\text{t}}\) :

Turbine power (W)

\(\frac{{p_{02} }}{{p_{01} }}\) :

Total-to-total compressor pressure ratio

\(\frac{{p_{4} }}{{p_{03} }}\) :

Turbine expansion ratio, total to static

\(t\) :

Time (s)

\(T_{\text{ch}}\) :

Charge temperature (K)

\(T_{\text{i}}\) :

Temperature of zone (K)

\(T_{\text{inlet}}\) :

Inlet fluid temperature (K)

\(T_{\text{IgnDel}}\) :

Temperature for ignition delay calculation and it represents mean spray temperature (K)

\(T_{\text{l}}\) :

Temperature of liquid (K)

\(T_{\text{s}}\) :

Temperature of the solid (K)

\(T_{\text{w}}\) :

Wall temperature (K)

\(T_{03}\) :

Total turbine inlet temperature (K)

\(T_{1}\) :

Compressor inlet temperature (K)

\(V_{\text{rail}}\) :

Rail volume

\(\alpha\) :

Heat transfer coefficient (W m−2 K−1)

\(\alpha_{\text{ht}}\) :

Heat transfer coefficient (W m−2 K−1)

\(\Delta p\) :

Pressure drop (Pa)

\(\Delta t_{\text{inj}}\) :

Number of radial zones

\(\zeta\) :

Friction factor which is a function of the Reynolds number

\(\zeta_{\text{NH}}\) :

Nozzle hole flow coefficient

\(\zeta_{\text{NS}}\) :

Needle seat flow coefficient

\(\eta_{{{\text{s}},{\text{t}}}}\) :

Isentropic turbine efficiency

\(\eta_{{{\text{s}},{\text{C}}}}\) :

Isentropic efficiency of the compressor

\(\kappa\) :

Ratio of the heat capacity at a constant pressure to the heat capacity at constant volume

\(\lambda_{\text{m}}\) :

Thermal conductivity (W m−1 K−1)

\(\nu\) :

Kinematic viscosity (m2 s−1)

\(\rho\) :

Density (kg m−3)

\(\rho_{\text{ch}}\) :

Charge density (kg m−3)

\(\rho_{ch}\) :

Charge density (kg m−3)

\(\rho_{\text{fuel}}\) :

Density of the fuel (kg m−3)

\(\rho_{\text{rail}}\) :

Density of the fluid inside rail (kg m−3)

\(\sigma_{\text{fuel}}\) :

Surface tension of the fuel

\(\tau\) :

Characteristic ignition delay time

\(\omega_{\text{TC}}\) :

Turbocharger wheel speed


Sauter mean diameter

\({\text{Nu}}\) :

Nusselt number

\({\text{Sh}}\) :

Sherwood’s number


  1. 1.

    Buhaug Ø, Corbett JJ, Endresen Ø, Eyring V, Faber J, Hanayama S, Lee DS, Lee D, Lindstad H, Markowska AZ, Mjelde A, Nelissen D, Nilsen J, Pålsson C, Winebrake JJ, Wu W, Yoshida K. Second IMO GHG study. London: International Maritime Organization (IMO); 2009. p. 240.

    Google Scholar 

  2. 2.

    Matulić N, Radica G, Nižetić S. Thermodynamic analysis of active modular internal combustion engine concept: targeting efficiency increase and carbon dioxide emissions reduction of gasoline engines. Int J Energy Res. 2018;42(9):3017–29.

    Article  Google Scholar 

  3. 3.

    Wärtsilä Condition based maintenance. https://cdn.wartsila.com/docs/default-source/Service-catalogue-files/Genius-Services/condition-based-maintenance.pdf?sfvrsn=2. Accessed on 11 June 2019.

  4. 4.

    Caterpillar: Dicare—system for diesel engine diagnostic and predictive maintenance. https://www.cat.com/en_ZA/support/operations/technologydicare.html. Accessed on 11 June 2019.

  5. 5.

    El Gohary MM, Abdou KM. Computer based selection and performance analysis of marine diesel engine. Alex Eng J. 2011;50(1):1–11.

    Article  Google Scholar 

  6. 6.

    Radica G, Radovan A, Račić N. Engine working cycle analysis for diagnostic and optimisation purposes. Brodogradnja. 2009;60:378–88.

    Google Scholar 

  7. 7.

    Radica G. Expert system for diagnosis and optimisation of marine diesel engines. Strojarstvo. 2008;50(2):105–16.

    CAS  Google Scholar 

  8. 8.

    Murphy AJ, Norman AJ, Pazouki K, Trodden DG. Thermodynamic simulation for the investigation of marine diesel engines. Ocean Eng. 2008;102:117–28.

    Article  Google Scholar 

  9. 9.

    Lamaris VT, Hountalas DT. A general purpose diagnostic technique for marine diesel engines—application on the main propulsion and auxiliary diesel units of a marine vessel. Energy Convers Manag. 2010;51:740–53.

    Article  Google Scholar 

  10. 10.

    Pagán JA, Vera-García RF, Graub JH, Cámara JM, Hernandez DA. Marine diesel engine failure simulator based on thermodynamic model. Appl Therm Eng. 2005;144:982–95.

    Article  Google Scholar 

  11. 11.

    Delvecchioa S, Bonfiglio P, Pompolib P. Vibro-acoustic condition monitoring of internal combustion engines: a critical review of existing techniques. Mechnical Syst Signal Process. 2018;99:661–83.

    Article  Google Scholar 

  12. 12.

    Zhixiong L, Xinping Y, Zhiwei G, Yuelei Z, Chengqing Y. Condition monitoring and fault diagnosis for marine diesel engines using information fusion techniques. Electron Electr Eng -Kaunas Technol. 2012;7(123):109–12.

    Google Scholar 

  13. 13.

    Ali YA, Rahman RA, Hamzah RI. Acoustic emission signal analysis and artificial intelligence techniques in machine condition monitoring and fault diagnosis: a review. J Teknol Malays. 2014;69(269:2):121–6. https://doi.org/10.11113/jt.v69.3121.

    Article  Google Scholar 

  14. 14.

    AVL, Cruise M Manual, 2015.

  15. 15.

    Wartsila, Technology Review. http://engine.od.ua/ufiles/Wartsila-20121.pdf. Accessed date 16 June 2019.

  16. 16.

    Hiroyasu H, Kadota T, Arai M. Development and use of a spray combustion modeling to predict diesel engine efficiency and pollutant emissions, part I: combustion modeling. Bull JSME. 1983;26:569–75.

    Article  Google Scholar 

  17. 17.

    Poetsch C, Ofner H, Schutting E, Assessment of a multi zone combustion model for analysis and prediction C0I engine combustion and emissions. SAE 2011-01-1439, SAE world congress, Detroit, USA, 2011.

  18. 18.

    Reinhardt H, Modellierung des Zuendverzuges bei Mehrfacheinspritzungen aufgeladener Dieselmotoren mit Direkteinspritzung innerhalb der thermodynamischen Prozessrechnung. Abschlussbericht. FVV Heft 870, 2008.

  19. 19.

    Jung D, Assanis DN, Multi-zone DI diesel spray combustion model for cycle simulation studies of engine performance and emissions. SAE 2001-0-1246, SAE world congress, Detroit, USA, 2001.

  20. 20.

    Pattas K, Haefner G. Stickoxidbildung bei der ottomotorischen Verbrennung. MTZ Nr. 1973;12:397–404.

    Google Scholar 

  21. 21.

    Zeldovich YB. The oxidation of nitrogen in combustion and explosions. Acta Physiochim. 1946;21:577–628.

    CAS  Google Scholar 

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Correspondence to Gojmir Radica.

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Matulić, N., Radica, G. & Nižetić, S. Engine model for onboard marine engine failure simulation. J Therm Anal Calorim 141, 119–130 (2020). https://doi.org/10.1007/s10973-019-09118-3

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  • Large marine diesel engine
  • Failure simulation
  • Diagnostic
  • Emissions