Experiments in Fluids

, 55:1837 | Cite as

Cluster-based analysis of cycle-to-cycle variations: application to internal combustion engines

  • Yujun Cao
  • Eurika Kaiser
  • Jacques Borée
  • Bernd R. Noack
  • Lionel Thomas
  • Stéphane Guilain
Research Article


We define and illustrate a cluster-based analysis of cycle-to-cycle variations (CCV). The methodology is applied to engine flow but can clearly be valuable for any periodically driven fluid flow at large Reynolds numbers. High-speed particle image velocimetry data acquired during the compression stroke for 161 consecutive engine cycles are used. Clustering is applied to the velocity fields normalised by their kinetic energy. From a phase-averaged analysis of the statistics of cluster content and inter-cluster transitions, we show that CCV can be associated with different sets of trajectories during the second half of the compression phase. Conditional statistics are computed for flow data of each cluster. In particular, we identify a particular subset associated with a loss of large-scale coherence, a very low kinetic energy of the mean flow and a higher fluctuating kinetic energy. This is interpreted as a good indicator of the breakdown of the large-scale coherent tumbling motion. For this particular subset, the cluster analysis confirms the idea of a gradual destabilisation of the in-cylinder flow during the final phase of the compression. Moreover, inter-cycle statistics show that the flow states near TDC and in the measurement zone are statistically independent for consecutive engine cycles. It is important to point out that this approach is generally applicable to very large sets of data, e.g. generated by PIV or LES, and independent of the considered type of information (velocity, concentration, etc.).


Proper Orthogonal Decomposition Proper Orthogonal Decomposition Mode Engine Cycle Compression Stroke Crank Angle Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The PhD grant of Y. CAO is financed by Renault. The work is partially funded by the ANR Chair of Excellence TUCOROM. E. Kaiser acknowledges additional funding from region Poitou–Charentes, France, ANR Project “SePaCoDe” (Étude de la Physique du Décollement et Réalisation de son Contrôle) and NSF PIRE Grant OISE-0968313.


  1. Arcoumanis C, Hu Z, Whitelaw JH (1990) Tumbling motion: a mechanism for turbulence enhancement in spark-ignition engines. SAE paper 900060Google Scholar
  2. Bishop CM (2006) Pattern recognition and machine learning (information science and statistics). Springer, New YorkGoogle Scholar
  3. Bizon K, Continillo G, Mancaruso E, Merola SS, Vaglieco BM (2010) POD-based analysis of combustion images in optically accessible engines. Comb Flame 157:632–640CrossRefGoogle Scholar
  4. Borée J, Miles P (2014) In-cylinder flow. In: Crolla D, Foster DE, Kobayashi T, Vaughan N (eds) Encyclopedia of automotive engineering. Wiley, ChichesterGoogle Scholar
  5. Borg I, Groenen PJ (2005) Modern multidimensional scaling: theory and applications. Springer, BerlinGoogle Scholar
  6. Chen H, Reuss DL, Sick V (2012) On the use and interpretation of proper orthogonal decomposition of in-cylinder flows. Meas Sci Technol 23(8):1–14Google Scholar
  7. Chen H, Hung DLS, Xu M, Zhuang H, Yang J (2014) Proper Orthogonal decomposition analysis of fuel spray structure variation in a spark-ignition direct-injection optical engine. Exp Fluids 55:1703–1715CrossRefGoogle Scholar
  8. Cosadia I, Borée J, Charnay G, Dumont P (2006) Cyclic variations of the swirling flow in a Diesel transparent engine. Exp Fluids 41(1):115–134CrossRefGoogle Scholar
  9. Du Q, Gunzburger MD (2003) Centroidal Voronoi tessellation based proper orthogonal decomposition analysis. In: Desch W, Kappel F, Kunisch K (eds) Control and estimation of distributed parameter systems. Birkhäuser, Basel, pp 137–150Google Scholar
  10. Fogleman MA (2005) Low dimensionnal models of internal combustion engine flows using the proper orthogonal decomposition, PhD Thesis, Cornell UniversityGoogle Scholar
  11. Fogleman M, Lumley JL, Rempfer D, Haworth D (2004) Application of the proper orthogonal decomposition to datasets of internal combustion engine flows. J Turbul 5:1–18CrossRefGoogle Scholar
  12. Gosman AD (1986) Flow processes in cylinders. Thermodynamics and gas dynamics of internal combustion engines, vol 2. Oxford University Press, Oxford, pp 616–772Google Scholar
  13. Hasse C, Sohm V, Durst B (2010) Numerical investigation of cyclic variations in gasoline engines using a hybrid URANS/LES modeling approach. Comput Fluids 39:25–48CrossRefzbMATHGoogle Scholar
  14. Heywood JB (1988) Internal combustion engines fundamentals. McGRAW Hill Company, New YorkGoogle Scholar
  15. Hill PG, Zhang D (1994) The effects of swirl and tumble on combustion in spark-ignition engines. Prog Energy Combust Sci 20:373–429CrossRefGoogle Scholar
  16. Holmes P, Lumley JL, Berkooz G, Rowley CW (2012) Turbulence, coherent structures, dynamical systems and symmetry, 2nd edn. Cambridge University Press, CambridgeCrossRefzbMATHGoogle Scholar
  17. Kaiser E, Noack BR, Cordier L, Spohn A, Segond M, Abel M, Daviller G, Östh J, Krajnovic S, Niven RK (2014) Cluster-based reduced-order modelling of a mixing layer. J Fluid Mech 754:365–414CrossRefGoogle Scholar
  18. Kapitsa L, Imberdis O, Bensler HP, Willand J, Thévenin D (2010) An experimental analysis of the turbulent structures generated by the intake port of a DISI-engine. Exp Fluids 48:265–280CrossRefGoogle Scholar
  19. Keromnes A, Dujol C, Guibert P (2010) Aerodynamic control inside an internal combustion engine. Meas Sci Technol 21:125–404Google Scholar
  20. Liu K, Haworth D (2011) Development and assessment of POD for analysis of turbulent flow in piston engines. SAE Technical paper 2011-01-0830Google Scholar
  21. Lloyd SP (1957) “Least square quantization in PCM”. Bell Telephone Laboratories Paper. Published: Lloyd., S. P. (1982). “Least squares quantization in PCM”. IEEE Trans Inf Theory 28(2):129–137. doi: 10.1109/TIT.1982.1056489
  22. Lumley JL (1967) The structure of inhomogeneous turbulence. In: Yaglom AM, Tatarski VI (eds) Atmospheric turbulence and wave propagation. Nauka, Moscow, pp 166–178Google Scholar
  23. Lumley JL (1999) Engines. An introduction. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  24. Lundgren TS, Mansour NN (1996) Transition to turbulence in an elliptic vortex. J Fluid Mech 307:43–62CrossRefzbMATHMathSciNetGoogle Scholar
  25. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability 1:281–297Google Scholar
  26. Schneider TM, Eckhardt B, Vollmer J (2007) Statistical analysis of coherent structures in transitional pipe flow. Phys Rev E 75(6):066313CrossRefMathSciNetGoogle Scholar
  27. Voisine M, Thomas L, Borée J, Rey P (2011) Spatio-temporal structure and cycle-to-cycle variations of an in-cylinder tumbling flow. Exp Fluids 50(5):1393–1407CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yujun Cao
    • 1
    • 2
  • Eurika Kaiser
    • 1
  • Jacques Borée
    • 1
  • Bernd R. Noack
    • 1
  • Lionel Thomas
    • 1
  • Stéphane Guilain
    • 2
  1. 1.Institut PPRIME CNRS - Université de Poitiers - ENSMA, UPR3346PoitiersFrance
  2. 2.Powertrain Engineering and Technologies DepartmentRENAULT s.a.s.LardyFrance

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