Automotive and Engine Technology

, Volume 3, Issue 1–2, pp 45–60 | Cite as

CFD–CHT calculation method using Buckingham Pi-Theorem for complex fluid–solid heat transfer problems with scattering boundary conditions

  • Peter Hölz
  • Thomas Böhlke
  • Thomas Krämer
Original Paper


A three-dimensional CFD–CHT simulation method is presented and validated with a turbocharged single cylinder SI engine. Various ignition time and lambda strategies as well as variations of boost pressure are investigated with regard to cycle averaged component temperatures. This complements existing published works which experimentally studied crank angle resolved heat fluxes or temperature swings rather than averaged temperatures. Cyclical fluctuations in the pressure curves were measured and processed statistically using probability density functions for the heat transfer coefficient and the cylinder gas temperature. The corresponding joint probability density function considers their strong correlation. The interpretation as random variables enables a time-scale separation with a low-pass filter function. The thermomechanical problem of heat transfer is addressed with simplified models according to Woschni, Eichelberg, and Hohenberg. Previous investigations primarily focused on their predictive quality of instantaneous in-cylinder heat fluxes. In this paper, their effect on cycle averaged component temperatures is investigated and the corresponding different sensitivities to specific engine settings are presented and compared with measurements. It is shown that, by choosing the right model, the suggested simulation approach is an alternative to prevailing experimental methods in temperature analysis: all thermodynamic variations examined are in good agreement with theoretical predictions.


Similarity mechanics Buckingham Pi-Theorem Conjugate heat transfer Engine heat transfer Scattering boundary conditions 



P. Hölz would like to thank Tobias Möllenhof and Christian Eifrig, both Porsche Motorsport, for their experimental support.


  1. 1.
    Yokomori, T.: Super-lean burn technology for high thermal efficiency SI engines in FVV 2017 Autumn Conf. Leipzig (2017)Google Scholar
  2. 2.
    Liu, L., Li, Z., Liu, S., Shen, B.: Effect of exhaust gases of Exhaust Gas Recirculation (EGR) coupling lean-burn gasoline engine on NOx purification of Lean NOx trap (LNT). Mech. Syst. Signal Process. 87, 195–213(2017).
  3. 3.
    Robinson, J.S., Cudd, R.L., Evans, J.T.: Creep resistant aluminium alloys and their applications. Mater. Sci. Technol. 19(2), 143–155 (2003).
  4. 4.
    Golloch, R.: Downsizing bei Verbrennungsmotoren, 1st edn. Springer-Verlag, Berlin Heidelberg (2005)Google Scholar
  5. 5.
    Warnatz, J., Maas, U., Dibble, R.W.: Combustion, 4th edn. Springer, Berlin, Heidelberg, New York (2006)zbMATHGoogle Scholar
  6. 6.
    Eichelberg, G.: Engineering, Some investigations on old combustion-engine problems. Parts I and II. 148, 463 (1939)Google Scholar
  7. 7.
    Woschni, G.: In A Universally Applicable Equation for the Instantaneous Heat Transfer Coefficient in the Internal Combustion Engine. SAE Tech. Pap. 670931 (1967).
  8. 8.
    Hohenberg, G.F.: Advance approaches for heat transfer calculation. In: SAE Tech. Pap. 790825 (1979).
  9. 9.
    Bargende, M.: Ein Gleichungsansatz zur Berechnung der instationären Wandwärmeverluste im Hochdruckteil von Ottomotoren. Ph.D. thesis, Technical University Darmstadt (1991)Google Scholar
  10. 10.
    Schubert, C., Wimmer, A., Chmela, F.: Advanced Heat Transfer Model for CI Engines. In: SAE Tech. Pap. 2005–01-0695. SAE International (2005).
  11. 11.
    Lee, T.K., Filipi, Z.S.: Improving the Predictiveness of the Quasi-D Combustion Model for Spark Ignition Engines with Flexibles Intake Systems. Int. J. Automot. Technol. 12(1), 1–9 (2011).
  12. 12.
    Payri, F., Margot, X., Gil, A., Martin, J.: Computational Study of Heat Transfer to the Walls of a DI Diesel Engine. In: SAE Tech. Pap. 2005–01-0210. SAE International (2005).
  13. 13.
    Mohammadi, A., Yaghoubi, M., Rashidi, M.: Analysis of local convective heat transfer in a spark ignition engine. Int. Commun. Heat Mass Transf. 35(2), 215–224 (2008).
  14. 14.
    Mohammadi, A., Yaghoubi, M.: Estimation of instantaneous local heat transfer coefficient in spark-ignition engines. Int. J. Therm. Sci. 49(7), 1309–1317 (2010).
  15. 15.
    Chiodi, M., Bargende, M.: Improvement of engine heat transfer calculation in the three-dimensional simulation using a phenomenological heat transfer model. In: SAE Tech. Pap. 2001–01-3601. SAE International (2001).
  16. 16.
    Broekaert, S., Cuyper, T.D., Paepe, M.D., Verhelst, S.: Evaluation of empirical heat transfer models for HCCI combustion in a CFR engine. Appl. Energy 205, 1141–1150 (2017).
  17. 17.
    Soyhan, H.S., Yasar, H., Walmsley, H., Head, B., Kalghatgi, G.T., Sorusbay, C.: Evaluation of heat transfer correlations for HCCI engine modeling. Appl. Therm. Eng. 29(2–3), 541–549 (2009).
  18. 18.
    Chang, J., Güralp, O., Filipi, Z., Assanis, D.N., Kuo, T.W., Najt, P., Rask, R.: New Heat Transfer Correlation for an HCCI Engine Derived from Measurements of Instantaneous Surface Heat Flux, in SAE Tech. Pap. 2004–01-2996. SAE International (2004).
  19. 19.
    Michl, J., Neumann, J., Rottengruber, H., Wensing, M.: Derivation and validation of a heat transfer model in a hydrogen combustion engine. Appl. Therm. Eng. 98, 502–512 (2016).
  20. 20.
    Demuynck, J., Paepe, M.D., Huisseune, H., Sierens, R., Vancoillie, J., Verhelst, S.: Investigation of the in fluence of engine settings on the heat flux in a hydrogen- and methane-fueled spark ignition engine. Appl. Therm. Eng. 31, 1220–1228 (2011).
  21. 21.
    Shudo, T., Nakajima, Y., Futakuchi, T.: Thermal efficiency analysis in a hydrogen premixed combustion engine. JSAE Rev. 21(2), 177–182 (2000).
  22. 22.
    Broekaert, S., Demuynck, J., Cuyper, T.D., Paepe, M.D., Verhelst, S.: Heat transfer in premixed spark ignition engines part I : Identification of the factors influencing heat transfer. Energy 116, 380–391 (2016).
  23. 23.
    Cuyper, T.D., Demuynck, J., Broekaert, S., Paepe, M.D., Verhelst, S.: Heat transfer in premixed spark ignition engines part II: Systematic analysis of the heat transfer phenomena. Energy 116, 851–860 (2016).
  24. 24.
    LeFeuvre, T., Myers, P.S., Uyehara, O.A.: Experimental instantaneous heat fluxes in a diesel engine and their correlation. In: SAE Tech. Pap. 690464. SAE International (1969).
  25. 25.
    Gilaber, P., Pinchon, P.: Measurements and multidimensional modeling of gas-wall heat transfer in a S.I. Engine. In: SAE Int. Congr. Expo. SAE International (1988).
  26. 26.
    Wimmer, A., Pivec, R., Sams, T.: Heat Transfer to the Combustion Chamber and Port Walls of IC Engines-measurement and prediction. SAE Tech. Pap. 2000-01-0568. SAE International (2000).
  27. 27.
    Sanli, A., Ozsezen, A.N., Kilicaslan, I., Canekci, M.: The influence of engine speed and load on the heat transfer between gases and in-cylinder walls at fired and motored conditions of an IDI diesel engine. Appl. Therm. Eng. 28, 1395–1404 (2008).
  28. 28.
    Sanli, A., Sayin, C., Gumus, M., Kilicaslan, I., Canakci, M.: Numerical evaluation by models of load and spark timing effects on the in-cylinder heat transfer of a SI engine. Numer. Heat Transf. Part A Appl. 56(5), 444–458 (2009).
  29. 29.
    Sharief, A., Chandrashekar, T.K., Antony, A.J., Samaga, B.S.: Study on heat transfer correlation in IC engines. In: SAE Tech. Pap. 2008–01-1816. SAE International (2008).
  30. 30.
    Wang, X., Price, P., Stone, C.R., Richardson, D.: Heat release and heat flux in a spray-guided direct-injection gasoline engine. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 221, 1441–1452 (2007).
  31. 31.
    Enomoto, Y., Furuhama, S.: Study on thin film thermocouple for measuring instantaneous temperature on surface of combustion chamber wall in internal combustion engine. Bull. JSME 28(235), 108–116 (1985).
  32. 32.
    Enomoto, Y., Furuhama, S.: Study on thin film thermocouple measuring instantaneous temperature on surface of combustion chamber wall in internal combustion engine—2nd report, study on thin film thermocouples embedded in combustion chamber wall. Bull. JSME 29(256), 3434–3441 (1986).
  33. 33.
    Enomoto, Y., Furuhama, S.: A study of the local heat transfer coefficient on the combustion chamber walls of a four-stroke gasoline engine. JSME Int. Journal. Ser. 2 32(1), 107–114 (1989).
  34. 34.
    Luo, X., Yu, X., Jansons, M.: Simultaneous in-cylinder surface temperature measurements with thermocouple, laser-induced phosphorescence, and dual wavelength infrared diagnostic techniques in an optical engine. In: SAE Tech. Pap. 2005–01-1658. SAE International (2015).
  35. 35.
    Kenningley, S., Morgenstern, R.: Thermal and mechanical loading in the combustion bowl region of light vehicle diesel AlSiCuNiMg pistons; reviewed with emphasis on advanced finite element analysis and instrumented engine testing techniques. In SAE Tech. Pap. 2012–01-1330. SAE International (2012).
  36. 36.
    Sugihara, T., Suzuki, Y., Shimano, K., Enomoto, Y., Emi, M.: Direct heat loss to combustion chamber walls in a D.I. Diesel Engine. In SAE Tech. Pap. 2007–24-0006. SAE International (2007).
  37. 37.
    Choi, G.H., Choi, K.H., Lee, J.T., Song, Y.S., Ryu, Y., Cho, J.W.: Analysis of combustion chamber temperature and heat flux in a DOHC engine. In: SAE Tech. Pap. 970895. SAE International (1997).
  38. 38.
    Tillock, B.R., Martin, J.K.: Measurement and modeling of thermal flows in an air-cooled engine. In: SAE Tech. Pap. 961731. SAE International (1996).
  39. 39.
    Caton, J., Heywood, J.: An experimental and analytical study of heat transfer in an engine exhaust port. Int. J. Heat Mass Transf. 24(4), 581–595 (1981).
  40. 40.
    Yang, L.C., Hamada, A., Ohtsubo, K.: Engine valve temperature simulation system. In: SAE Tech. Pap. 2000–01-0564. SAE International (2000).
  41. 41.
    Fieberg, C., Korthäuer, M.: Forschungsvereinigung Verbrennungskraftmaschinen, Kontaktwärmeübergang—Vorhaben Nr. 828, Kontaktdruckabhängiger Wärmeübergang im motorischen Umfeld, vol. 821 (2006)Google Scholar
  42. 42.
    Shojaefard, M.H., Noorpoor, A.R., Bozchaloe, D.A., Ghaffarpour, M.: Transient thermal analysis of engine exhaust valve. Numer. Heat Transf. Part A Appl. 48(7), 627–644 (2005).
  43. 43.
    Menter, F.R.: Two-equation Eddy-viscosity turbulence models for engineering applications. AIAA J. 32(8), 1598–1605 (1994).
  44. 44.
    Siemens: STAR-CCM+ User Manual, v11.06 (2018)Google Scholar
  45. 45.
    Finol, C.A., Robinson, K.: Thermal modelling of modern engines: a review of empirical correlations to estimate the in-cylinder heat transfer coefficient. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 220(12), 1765–1781 (2006).
  46. 46.
    Adair, R.P., Qvale, E.B., Pearson, J.T.: Instantaneous heat transfer to cylinder wall in reciprocating compressors. Int. Compress. Eng. Conf, pp. 521–526 (1972)Google Scholar
  47. 47.
    Kleinschmidt, W.: Zur Theorie und Berechnung der instationären Wärmeübertragung in Verbrennungsmotoren. In: 4. Tagung “Der Arbeitsprozess des Verbrennungsmotors”. Graz (1993)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Porsche AGPorsche MotorsportWeissachGermany
  2. 2.Chair for Continuum MechanicsInstitute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT)KarlsruheGermany

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