Research Papers

Nonlinear Analysis of Mineral Wool Fiberization Process

[+] Author and Article Information
Benjamin Bizjan

Abelium d.o.o,
Kajuhova 90,
Ljubljana 1000, Slovenia
e-mail: benjamin.bizjan@abelium.eu

Brane Širok

Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia
e-mail: brane.sirok@fs.uni-lj.si

Edvard Govekar

Faculty of Mechanical Engineering,
University of Ljubljana,
Aškerčeva 6,
Ljubljana 1000, Slovenia
e-mail: edvard.govekar@fs.uni-lj.si

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received September 24, 2013; final manuscript received February 11, 2014; published online January 12, 2015. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 10(2), 021005 (Mar 01, 2015) (8 pages) Paper No: CND-13-1226; doi: 10.1115/1.4026842 History: Received September 24, 2013; Revised February 11, 2014; Online January 12, 2015

In this paper, the mineral wool fiberization process on a spinner wheel was studied by means of the nonlinear time series analysis. Melt film velocity time series was calculated using computer-aided visualization of the process images recorded with a high speed camera. The time series was used to reconstruct the state space of the process and was tested for stationarity, determinism, chaos, and recurrent properties. Mineral wool fiberization was determined to be a low-dimensional and nonstationary process. The 0–1 chaos test results suggest that the process is chaotic, while the determinism test indicates weak determinism.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Taylor, G. I., 1950, “The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to Their Planes,” Proc. R. Soc. London, Ser. A, 201(1065), pp. 192–196. [CrossRef]
Eisenklam, P., 1964, “On Ligament Formation From Spinning Discs and Cups,” Chem. Eng. Sci., 19(9), pp. 693–694. [CrossRef]
Hinze, J. O., and Milborn, H., 1950, “Atomization of Liquids by Means of a Rotating Cup,” J. Appl. Mech., 17(2), pp. 145–153.
Kamiya, T., 1972, “Analysis of the Ligament-Type Disintegration of Thin Liquid Film at the Edge of Rotating Disk,” J. Chem. Eng. Jpn., 5(4), pp. 391–396. [CrossRef]
Liu, J., Yu, Q., and Guo, Q., 2012, “Experimental Investigation of Liquid Disintegration by Rotary Cups,” Chem. Eng. Sci., 73, pp. 44–50. [CrossRef]
Westerlund, T., and Hoikka, T., 1989, “On the Modeling of Mineral Fiber Formation,” Comput. Chem. Eng., 13(10), pp. 1153–1163. [CrossRef]
BlagojevićB., Širok, B., and Štremfelj, B., 2004, “Simulation of the Effect of Melt Composition on Mineral Wool Fibre Thickness,” Ceramics - Silikáty, 48(3), pp. 128–134.
Širok, B.Blagojević, B., and Bullen, P., 2008, Mineral Wool: Production and Properties, Woodhead Publishing Limited, Cambridge, UK.
Širok, B., Bizjan, B., Orbanić, A., and Bajcar, T., 2014, “Mineral Wool Melt Fiberization on a Spinner Wheel,” Chem. Eng. Res. Des., 92(1), pp. 80–90. [CrossRef]
Kantz, H., and Schreiber, T., 2004, Nonlinear Time Series Analysis; Cambridge University Press, Cambridge, UK.
Bajcar, T., Širok, B., and Eberlinc, M., 2009, “Quantification of Flow Kinematics Using Computer-Aided Visualization,” J. Mech. Eng., 55(4), pp. 215–223.
Brady, B. J., 1995, Mineral Physics & Crystallography: A Handbook of Physical Constants, American Geophysical Union, Washington, D.C.
Horn, B. K. R., and Schunck, B. G., 1981, “Determining Optical Flow,” Artificial Intelligence, 17(1–3), pp. 185–204. [CrossRef]
Takens, F., 1981, “Detecting Strange Attractors in Turbulence,” Lecture Notes in Mathematics, 898, pp. 366–381. [CrossRef]
Sauer, T., Yorke, J., and Casdagli, M., 1991, “Embedology,” J. Stat. Phys., 65(3), pp. 579–616. [CrossRef]
Fraser, A. M., and Swinney, H. L., 1986, “Independent Coordinates for Strange Attractors From Mutual Information,” Phys. Rev. A, 22(2), pp. 1134–1140. [CrossRef]
Abarbanel, H. D. I., 1996, Analysis of Observed Chaotic Data, Springer-Verlag, New York.
Kennel, M. B., Brown, R., and Abarbanel, H. D. I., 1992, “Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction,” Phys. Rev. A, 45(6), pp. 3403–3411. [CrossRef] [PubMed]
Schreiber, T., 1997, “Detecting and Analyzing Nonstationarity in a Time Series Using Nonlinear Cross Predictions,” Phys. Rev. Lett., 78(5), pp. 843–846. [CrossRef]
Kaplan, D. T., and Glass, L., 1992, “Direct Test for Determinism in a Time Series,” Phys. Rev. Lett., 68(4), pp. 427–430. [CrossRef] [PubMed]
Krese, B., Perc, M., and Govekar, E., 2010, “The Dynamics of Laser Droplet Generation,” Chaos, 20(1), p. 013129. [CrossRef] [PubMed]
Bradley, E., and Mantilla, R., 2002, “Recurrence Plots and Unstable Periodic Orbits,” Chaos, 12(3), pp. 596–600. [CrossRef] [PubMed]
Krese, B., and Govekar, E., 2011, “Recurrence Quantification Analysis of Intermittent Spontaneous to Forced Dripping Transition in Laser Droplet Generation,” Chaos, 44(5), pp. 298–305.
Marwan, N., Romano, M. C., Thiel, M., and Kurths, J., 2007, “Recurrence Plots for the Analysis of Complex Systems,” Phys. Rep., 438(5), pp. 237–329. [CrossRef]
Zbilut, J. P., Zaldivar-Comenges, J.-M., and Strozzi, F., 2002, “Recurrence Quantification Based Lyapunov Exponents for Monitoring Divergence in Experimental Data,” Phys. Lett. A, 297(3–4), pp. 173–181. [CrossRef]
Gottwald, G. A., and Melbourne, I., 2004, “A New Test for Chaos in Deterministic Systems,” Proc. R. Soc. London, Ser. A, 460(2042), pp. 603–611. [CrossRef]
Gottwald, G. A., and Melbourne, I., 2009, “On the Implementation of the 0–1 Test for Chaos,” SIAM J. Appl. Dyn. Syst., 8(1), pp. 129–145. [CrossRef]
Krese, B., and Govekar, E., 2012, “Nonlinear Analysis of Laser Droplet Generation by Means of 0–1 Test for Chaos,” Nonlinear Dyn., 67(3), pp. 2101–2109. [CrossRef]


Grahic Jump Location
Fig. 1

Simplified presentation of a spinner wheel and initial fiber formation

Grahic Jump Location
Fig. 2

Four-wheel industrial spinner for mineral wool production [9]

Grahic Jump Location
Fig. 3

Experimental setup for visualization of the fiberization process

Grahic Jump Location
Fig. 4

Left: window of interest (yellow rectangle) for velocity calculation. Center: chosen coordinate system. Right: region of interest shown for a sequence of four consecutive frames, 400% magnification.

Grahic Jump Location
Fig. 5

Time series of vy before (upper panel) and after the application of the low pass filter at 2 kHz cutoff frequency (lower panel)

Grahic Jump Location
Fig. 6

Power spectrum of the filtered time series

Grahic Jump Location
Fig. 9

Cross prediction errors for the filtered time series

Grahic Jump Location
Fig. 8

Fraction of false nearest neighbors (fnn) with respect to the embedding dimension m, for τ = 19

Grahic Jump Location
Fig. 7

Autocorrelation function and mutual information for the filtered time series of vy

Grahic Jump Location
Fig. 11

Recurrence plot of the filtered time series

Grahic Jump Location
Fig. 10

Determinism test. The left panel features the reconstructed phase space using τ = 19 and m = 4, while the right panel shows the pertaining approximated directional vector field. Determinism factor of the phase space is κ = 0.66.

Grahic Jump Location
Fig. 12

Recurrence quantification analysis plots



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In