Skip to main content
SpringerLink
Log in

Determination and evolution of fractal property of n-heptane pool fires caused by depressurization process in an aircraft cargo compartment

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Fractality is one of the inherent characteristics to present the irregularity and self-similarity of an object. In this study, the fractal theory was applied to the fire scene under decreasing pressure in an aircraft cargo compartment, considering that the compartment is usually inaccessible in flight and flame images are a kind of convenient monitoring information compared to other detection methods. A series of n-heptane pool fires were performed under decreasing pressure with four depressurized rates. The flame image was captured by a video camera with fixed aperture and exposure time. The fractal dimension (FD) of flame images was computed via two approaches, i.e., the box-counting (BC) and differential box-counting (DBC) methods. The results show that n-heptane pool fires have a good fractal property for both binary and grayscale images. The FD via BC method shows little sensitivity with decreasing pressure. However, the FD via DBC method presents a significant linear relationship with a slope of 0.0016 in the range from 2.85 to 2.75 during the depressurization. The quantitative correlation was brought into the classical radiation modeling, and the exponential function between FD and MLR of n-heptane was established.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

FD:

Fractal dimension of flame image

r :

Length of boxes

N r :

Number of boxes

g min/max :

Minimum/maximum numbers of boxes

\({\dot{m}}^{{\prime \prime }}\) :

Mass loss rate (MLR) of n-heptane/g s−1 m−2

p :

Environmental pressure/kPa

D :

Pool diameter/m

References

  1. Zhao PX, Zhuo RS, Li SG, Lin HF, Shu CM, Bin LW, Jia YY, Liang S. Fractal characteristics of gas migration channels at different mining heights. Fuel. 2020;271:117479.

    CAS  Google Scholar 

  2. Wang CH, Cheng YP, Yi MH, Hu B, Jiang ZN. Surface energy of coal particles under quasi-static compression and dynamic impact based on fractal theory. Fuel. 2020;264:116835.

    CAS  Google Scholar 

  3. Ai DH, Zhao YC, Xie BJ, Li CW. Experimental study of fracture characterizations of rocks under dynamic tension test with image processing. Shock Vib. 2019;6352609

  4. Mandelbrot B. The fractal geometry of nature/revised and enlarged. New York: W.H. Freeman & Co.; 1983.

    Google Scholar 

  5. Mandelbrot B. How long is the coast of britain? Stat Self-Simil Fract Dimens Sci. 1967;156(3775):636–8.

    CAS  Google Scholar 

  6. Lopes R, Betrouni N. Fractal and multifractal analysis: a review. Med Image Anal. 2009;13(4):634–49.

    CAS  PubMed  Google Scholar 

  7. Russell D, Hanson J, Ott E. Dimension of strange attractors. Phys Rev Lett. 1980;45(14):1175–8.

    Google Scholar 

  8. So GB, So HR, Jin GG. Enhancement of the Box-Counting Algorithm for fractal dimension estimation. Pattern Recogn Lett. 2017;98:53–8.

    Google Scholar 

  9. Chaudhuri B, Sarkar N. Texture segmentation using fractal dimension. IEEE Trans Pattern Anal Mach Intell. 1995;17(1):72–7.

    Google Scholar 

  10. Sarkar N, Chaudhuri B. An efficient differential box-counting approach to compute fractal dimension of image. IEEE Trans Geosci Remote. 1994;32:1096–102.

    Google Scholar 

  11. Pentland A. Fractal-Based Description of Natural Scenes. IEEE Trans Pattern Anal Mach Intell. 1984;6(6):661–74.

    CAS  PubMed  Google Scholar 

  12. Panigrahy C, Seal A, Mahato NK, Bhattacharjee D. Differential box counting methods for estimating fractal dimension of grayscale images: a survey. Chaos Soliton Frac. 2019;126:178–202.

    Google Scholar 

  13. Smallwood GJ, Gülder ÖL, Snelling DR, Deschamps BM, Gökalp I. Characterization of flame front surfaces in turbulent premixed methane/air combustion. Combust Flame. 1995;101(4):461–70.

    CAS  Google Scholar 

  14. Chen YC, Mansour MS. Geometric interpretation of fractal parameters measured in turbulent premixed Bunsen flames. Exp Therm Fluid Sci. 2003;27(4):409–16.

    CAS  Google Scholar 

  15. Wada Y, Kuwana K. A numerical method to predict flame fractal dimension during gas explosion. J Loss Prevent Proc. 2013;26(2):392–5.

    Google Scholar 

  16. Yi Y, Geng L, Jing G. Experimental study on the fractal characteristic of methane explosion flame. Safety Sci. 2012;50(4):679–83.

    Google Scholar 

  17. Mukaiyama K, Shibayama S, Kuwana K. Fractal structures of hydrodynamically unstable and diffusive-thermally unstable flames. Combust Flame. 2013;160(11):2471–5.

    CAS  Google Scholar 

  18. Yenerdag B, Fukushima N, Shimura M, Tanahashi M, Miyauchi T. Turbulence–flame interaction and fractal characteristics of H2–air premixed flame under pressure rising condition. P Combust Inst. 2015;35(2):1277–85.

    CAS  Google Scholar 

  19. Chatakonda O, Hawkes R, Kerstein Aspden J, R, Kolla H, Chen H. On the fractal characteristics of low Damköhler number flames. Combust Flame. 2013;160(11):2422–33.

    CAS  Google Scholar 

  20. Minamoto Y, Yenerdag B, Tanahashi M. Morphology and structure of hydrogen–air turbulent premixed flames. Combust Flame. 2018;192:369–83.

    Google Scholar 

  21. Shim Y, Tanaka S, Tanahashi M, Miyauchi T. Local structure and fractal characteristics of H2–air turbulent premixed flame. Proc Combust Inst. 2011;33(1):1455–62.

    CAS  Google Scholar 

  22. Tejas K, Fabrizio B. Surface morphology and inner fractal cutoff scale of spherical turbulent premixed flames in decaying isotropic turbulence. Proc Combust Inst. 2020. https://doi.org/10.1016/j.proci.2020.06.117.

    Article  Google Scholar 

  23. Amitesh R, Raman IS. Fractal dimension of premixed flames in intermittent turbulence. Combust Flame. 2021;226:412–8.

    Google Scholar 

  24. Le Maoult Y, Sentenac T, Orteu J, Arcens J. Fire detection: a new approach based on a low cost CCD camera in the near infrared. Process Saf Environ. 2007;85(3):193–206.

    Google Scholar 

  25. Liu QY, Ma QJ, Zhang H, Yang R, Wei D, Lin CH. Experimental study on n-heptane pool fire behavior under dynamic pressure in an altitude chamber. J Therm Anal Calorim. 2016;128(2):1151–63.

    Google Scholar 

  26. Ma QJ, Liu QY, Zhang H, Tian RH, Ye JJ, Yang R. Experimental study of the mass burning rate in n-Heptane pool fire under dynamic pressure. Appl Therm Eng. 2017;113:1004–10.

    CAS  Google Scholar 

  27. Li C, Yao YN, Tao ZX, Yang R, Zhang H. Influence of depressurized environment on the fire behaviour in a dynamic pressure cabin. Appl Therm Eng. 2017;125:972–7.

    CAS  Google Scholar 

  28. Otsu N. A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern. 1979;9(1):62–6.

    Google Scholar 

  29. Li Z, Song CL, Song JO, Lv G, Dong SR, Zhao Z. Evolution of the nanostructure, fractal dimension and size of in-cylinder soot during diesel combustion process. Combust Flame. 2011;158(8):1624–30.

    CAS  Google Scholar 

  30. Pretrel H, Audouin L. Periodic puffing instabilities of buoyant large-scale pool fires in a confined compartment. J Fire Sci. 2012;31(3):197–210.

    Google Scholar 

  31. Shi C, Liu W, Hong WJ, Zhong MH, Zhang XK. A modified thermal radiation model with multiple factors for investigating temperature rise around pool fire. J Hazard Mater. 2019;379:120801.

    CAS  PubMed  Google Scholar 

  32. Tang F, Hu LH, Wang Q, Ding ZJ. Flame pulsation frequency of conduction-controlled rectangular hydrocarbon pool fires of different aspect ratios in a sub-atmospheric pressure. Int J Heat Mass Trans. 2014;76:447–51.

    Google Scholar 

  33. Fang J, Wang JW, Guan JF, Zhang YM, Wang JJ. Momentum- and buoyancy-driven laminar methane diffusion flame shapes and radiation characteristics at sub-atmospheric pressures. Fuel. 2016;163:295–303.

    CAS  Google Scholar 

  34. Wan H, Gao ZH, Ji J, Zhang YM, Li KY, Wang LZ. Effects of pool size and spacing on burning rate and flame height of two square heptane pool fires. J Hazard Mater. 2019;369:116–24.

    CAS  PubMed  Google Scholar 

  35. Hu L, Zhang X, Wang Q, Palacios A. Flame size and volumetric heat release rate of turbulent buoyant jet diffusion flames in normal- and a sub-atmospheric pressure. Fuel. 2015;150:278–87.

    CAS  Google Scholar 

  36. Wang Z, Yang H, Li Y, Wang G, Wang J. Thermal runaway and fire behaviors of large-scale lithium ion batteries with different heating methods. J Hazard Mater. 2019;379:120730.

    CAS  PubMed  Google Scholar 

  37. Liu JH, Zhou ZH, Chen MY. Experimental investigation on the effect of ambient pressure on entrainment coefficient of pool fires. Appl Therm Eng. 2019;148:939–43.

    Google Scholar 

  38. Wan HX, Gao ZH, Ji J, Sun JH, Zhang YM, Li KY. Predicting heat fluxes received by horizontal targets from two buoyant turbulent diffusion flames of propane burning in still air. Combust Flame. 2018;190:260–9.

    CAS  Google Scholar 

  39. Liu JH, Chen MY, Lin X, Yuen R, Wang J. Impacts of ceiling height on the combustion behaviors of pool fires beneath a ceiling. J Therm Anal Calorim. 2016;126(2):881–9.

    CAS  Google Scholar 

  40. De Ris J. Fire radiation—a review. Symp Combust. 1979;17(1):1003–16.

    Google Scholar 

  41. De Ris J, Kanury AM, Yuen MC. Pressure modeling of fires. Symp Int Combust. 1973;14(1):1033–44.

    Google Scholar 

  42. De Ris J, Wu PK, Heskestad G. Radiation fire modeling. Proc Combust Inst. 2000;28(2):2751–9.

    Google Scholar 

  43. Orloff L, De Ris J. Froude modeling of pool fires. Symp Int Combust. 1982;19(1):885–95.

    Google Scholar 

Download references

Acknowledgements

This work was partially supported by National Key Research & Development (R&D) Plan (Grant No. 2018YFC0809500), the National Natural Science Foundation of China (Grant No. U2033206), and the Fundamental Research Funds for the Central Universities (Grant No. 2020XJAQ02).

Author information

Authors and Affiliations

  1. School of Emergency Management and Safety Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

    Cong Li & Chengwu Li

  2. China Academy of Electronics and Information Technology, Beijing, 100041, China

    Yina Yao

  3. Department of Engineering Physics, Tsinghua University, Beijing, 100084, China

    Rui Yang & Hui Zhang

Authors
  1. Cong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yina Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chengwu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cong Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, C., Yao, Y., Yang, R. et al. Determination and evolution of fractal property of n-heptane pool fires caused by depressurization process in an aircraft cargo compartment. J Therm Anal Calorim 147, 2405–2415 (2022). https://doi.org/10.1007/s10973-021-10685-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-021-10685-7

Keywords

Search

Navigation