Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

The use of Lempel-Ziv complexity to analyze turbulence and flow randomness based on velocity fluctuations

Treść / Zawartość
Warianty tytułu
Języki publikacji
One of the mathematical tools to measure the generation rate of new patterns along a sequence of symbols is the Lempel-Ziv complexity (LZ). Under additional assumptions, LZ is an estimator of entropy in the Shannon sense. Since entropy is considered as a measure of randomness, this means that LZ can be treated also as a randomness indicator. In this paper, we used LZ concept to the analysis of different flow regimes in cold flow combustor models. Experimental data for two combustor’s configurations motivated by efficient mixing need were considered. Extensive computer analysis was applied to develop a complexity approach to the analysis of velocity fluctuations recorded with hot-wire anemometry and PIV technique. A natural encoding method to address these velocity fluctuations was proposed. It turned out, that with this encoding the complexity values of the sequences are well correlated with the values obtained by means of RMS method (larger/smaller complexity larger/smaller RMS). However, our calculations pointed out the interesting result that most complex, this means most random, behavior does not overlap with the “most turbulent” point determined by the RMS method, but it is located in the point with maximal average velocity. It seems that complexity method can be particularly useful to analyze turbulent and unsteady flow regimes. Moreover, the complexity can also be used to establish other flow characteristics like its ergodicity or mixing.
Słowa kluczowe
Opis fizyczny
Bibliogr. 30 poz., rys.
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  • Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
  • [1] C. Argyropoulos and N. Markatos, “Recent advances on the numerical modelling of turbulent flows”, Applied Mathematical Modelling 39, 693–732 (2015).
  • [2] M. Gad-El-Hak, “Coherent structures and flow control: genesis and prospect”, Bull. Pol. Ac.: Tech. 67(3), 412–444 (2019).
  • [3] S. Gepner, J. Majewski, and J. Rokicki, “Parallel anisotropic mesh refinement with dynamic load balancing for transonic flow simulations”, Bull. Pol. Ac.: Tech. 65(2), 195–207 (2017).
  • [4] X. Yu and J. Liu “The secondary instability in Goertler flow”, Physics of Fluids A: Fluid Dynamics 3, 1845–1847 (1991).
  • [5] D. Mihailovic, G. Mimic, P. Gualtieri, I. Arsenic, and C. Gual-tieri, “Randomness Representation of Turbulence in Canopy Flows Using Komogorov Complexity Measures”, Entropy 18, e19100519 (2017).
  • [6] K. Gumowski, O. Olszewski, M. Pocwierz, and K. Zielonko-Jung, “Comparative analysis of numerical and experimental studies of the airflow around the sample of urban development”, Bull. Pol. Ac.: Tech. 63(3), 729–737 (2015).
  • [7] E. Akbarian, B. Najafi, M. Jafari, S.F. Ardabili, S. Shamshirband, and K. Chau, “Experimental and computational fluid dynamics-based numerical simulation of using natural gas in a dual-fueled diesel engine”, Engineering Applications of Computational Fluid Mechanics 12(1), 517–534 (2018).
  • [8] F. Nieuwstadt, B. Boersma, and J. Westerweel, Turbulence: Introduction to theory and applications of turbulent f lows, Springer International Publishing: United States of America, 2016.
  • [9] M. Wojcik and M. Szukiewicz, “A simple method of determination of the degree of gas mixing by numerical Laplace inversion and Maple”, Bull. Pol. Ac.: Tech. 67(2), 235–240 (2019).
  • [10] Q. Li and Z. Fu, “Permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records”, Physical Review E 89, 012905 (2014).
  • [11] J. Zhan, B.C. Wang, L.H. Yu, Y.S. Li, and L. Tang, “Numerical investigation of flow patterns in different pump intake systems”, Journal of Hydrodynamics 24, 873–882 (2012).
  • [12] O. Cadot, C. Touze, and A. Boudaoud, “Linear versus nonlinear response of a forced wave turbulence system”, Physical Review E 82, 046211 (2010).
  • [13] T. Cover and J. Thomas, Elements of Information Theory; A Wiley-Interscience Publication, New York: United States of America, (1991).
  • [14] T. Bossomaier, L. Barnett, M. Harre, and J. Lizier, An introduction to transfer entropy; Springer-Verlag, New York: United States of America, (2016).
  • [15] Z. Wang, N. Jin, Z. Gao, Y. Zong, and T. Wang, “Nonlinear dynamical analysis of large diameter vertical upward oil-gas-water three-phase flow pattern characteristics”, Chemical Engineering Science 65, 5226–5236 (2010).
  • [16] Q. Zhang, X. Liang, Z. Fang, and C. Xiao, “Complexity analysis of precipitation using the Lempel-Ziv algorithm and a multi-scaling approach: a case study in Jilin province, China”, Stochastic Environmental Research and Risk Assessment 31, 1697–1707 (2017).
  • [17] M. Atlas, S. Hussain, and M. Sagheer, “Entropy generation and squeezing flow past a Riga plate with Cattaneo-Christov heat flux”, Bull. Pol. Ac.: Tech. 66(3), 291–230 (2018).
  • [18] M. Gazzah and H. Belmabrouk, “Directed co-flow effects on local entropy generation in turbulent heated round jets”, Com-puters and Fluids 105, 285–293 (2014).
  • [19] M. Materassi, G. Consolini, N. Smith, and R.D. Marco, “In-formation Theory Analysis of Cascading Process in a Synthetic Model of Fluid Turbulence”, Entropy 16, 1272–1286 (2014).
  • [20] A. Elkaroui, M. Gazzah, N. Said, P. Bournot, and G.L. Palec “Entropy generation concept for a turbulent plane jet with variable density”, Computers and Fluids 168, 328–341 (2018).
  • [21] A. Pregowska, J. Szczepanski, and E.Wajnryb, “Temporal code versus rate code for binary Information Sources”, Neurocomputing 216, 756–762 (2016).
  • [22] A. Pregowska, A. Casti, E. Kaplan, E. Wajnryb, and J. Szczepanski, “Information processing in the LGN: a comparison of neural codes and cell types”, Biological Cybernetics 113, 453–464, (2019).
  • [23] A. Pregowska, E. Kaplan, and J. Szczepanski, “How Far can Neural Correlations Reduce Uncertainty? Comparison of Information Transmission Rates for Markov and Bernoulli Processes”, International Journal of Neural Systems 29(8) (2019).
  • [24] A. Lempel and J. Ziv, “On the complexity of an individual sequence”, IEEE Transactions on Information Theory IT–22, 75‒88 (1976)
  • [25] U. Frisch, Turbulence, Cambridge University Press: Cambridge, United Kingdom, (1995).
  • [26] T. Kowalewski, European Community Project of Fifth Frame-work Programme, FLOXCOM ENK5-CT-2000‒00114.
  • [27] T. Kowalewski, F. Lusseyran, and S. Blonski, “Flow structure identification with PIV and high speed imaging in cold flow combustor model”, The 5th Euromech Fluid Mechanics Conference, Toulouse, France, August 24–28, (2003).
  • [28] J. Szumbarski and S. Blonski, “Destabilization of laminar flow in a rectangular channel by transversely-oriented wall corrugation”, Archives of Mechanics 4, 393–428 (2011).
  • [29] A. Pregowska, K. Proniewska, P. van Dam, and J. Szczepanski, “Using Lempel-Ziv complexity as effective classification tool of the sleep-related breathing disorders”, Computer Methods and Programs in Biomedicine 182 (2019).
  • [30] A. Pregowska, J. Szczepanski, and E.Wajnryb, “Mutual infor-mation against correlations in binary communication channels”, BMC Neuroscience 16, 1–7 (2015).
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.