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.

Issue Section:
Research Papers
Keywords:
mineral wool, melt fiberization, nonlinear analysis, time series, visualization method
Topics:
Mineral wool, Time series, Wheels

References

1.
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
.10.1098/rspa.1950.0052
2.
Eisenklam
,
P.
,
1964
, “
On Ligament Formation From Spinning Discs and Cups
,”
Chem. Eng. Sci.
,
19
(
9
), pp.
693
–
694
.10.1016/0009-2509(64)85056-9
3.
Hinze
,
J. O.
, and
Milborn
,
H.
,
1950
, “
Atomization of Liquids by Means of a Rotating Cup
,”
J. Appl. Mech.
,
17
(
2
), pp.
145
–
153
.
4.
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
.10.1252/jcej.5.391
5.
Liu
,
J.
,
Yu
,
Q.
, and
Guo
,
Q.
,
2012
, “
Experimental Investigation of Liquid Disintegration by Rotary Cups
,”
Chem. Eng. Sci.
,
73
, pp.
44
–
50
.10.1016/j.ces.2012.01.010
6.
Westerlund
,
T.
, and
Hoikka
,
T.
,
1989
, “
On the Modeling of Mineral Fiber Formation
,”
Comput. Chem. Eng.
,
13
(
10
), pp.
1153
–
1163
.10.1016/0098-1354(89)87018-8
7.
Blagojević
B.
,
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
.
8.
Širok
,
B.
Blagojević
,
B.
, and
Bullen
,
P.
,
2008
,
Mineral Wool: Production and Properties
,
Woodhead Publishing Limited
,
Cambridge, UK
.
9.
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
.10.1016/j.cherd.2013.06.014
10.
Kantz
,
H.
, and
Schreiber
,
T.
,
2004
,
Nonlinear Time Series Analysis;
Cambridge University Press
,
Cambridge, UK
.
11.
Bajcar
,
T.
,
Širok
,
B.
, and
Eberlinc
,
M.
,
2009
, “
Quantification of Flow Kinematics Using Computer-Aided Visualization
,”
J. Mech. Eng.
,
55
(
4
), pp.
215
–
223
.
12.
Brady
,
B. J.
,
1995
,
Mineral Physics & Crystallography: A Handbook of Physical Constants
,
American Geophysical Union
,
Washington, D.C
.
13.
Horn
,
B. K. R.
, and
Schunck
,
B. G.
,
1981
, “
Determining Optical Flow
,”
Artificial Intelligence
,
17
(
1–3
), pp.
185
–
204
.10.1016/0004-3702(81)90024-2
14.
Takens
,
F.
,
1981
, “
Detecting Strange Attractors in Turbulence
,”
Lecture Notes in Mathematics
,
898
, pp.
366
–
381
.10.1007/BFb0091903
15.
Sauer
,
T.
,
Yorke
,
J.
, and
Casdagli
,
M.
,
1991
, “
Embedology
,”
J. Stat. Phys.
,
65
(
3
), pp.
579
–
616
.10.1007/BF01053745
16.
Fraser
,
A. M.
, and
Swinney
,
H. L.
,
1986
, “
Independent Coordinates for Strange Attractors From Mutual Information
,”
Phys. Rev. A
,
22
(
2
), pp.
1134
–
1140
.10.1103/PhysRevA.33.1134
17.
Abarbanel
,
H. D. I.
,
1996
,
Analysis of Observed Chaotic Data
,
Springer-Verlag
,
New York
.
18.
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
.10.1103/PhysRevA.45.3403
19.
Schreiber
,
T.
,
1997
, “
Detecting and Analyzing Nonstationarity in a Time Series Using Nonlinear Cross Predictions
,”
Phys. Rev. Lett.
,
78
(
5
), pp.
843
–
846
.10.1103/PhysRevLett.78.843
20.
Kaplan
,
D. T.
, and
Glass
,
L.
,
1992
, “
Direct Test for Determinism in a Time Series
,”
Phys. Rev. Lett.
,
68
(
4
), pp.
427
–
430
.10.1103/PhysRevLett.68.427
21.
Krese
,
B.
,
Perc
,
M.
, and
Govekar
,
E.
,
2010
, “
The Dynamics of Laser Droplet Generation
,”
Chaos
,
20
(
1
), p.
013129
.10.1063/1.3367772
22.
Bradley
,
E.
, and
Mantilla
,
R.
,
2002
, “
Recurrence Plots and Unstable Periodic Orbits
,”
Chaos
,
12
(
3
), pp.
596
–
600
.10.1063/1.1488255
23.
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
.
24.
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
.10.1016/j.physrep.2006.11.001
25.
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
.10.1016/S0375-9601(02)00436-X
26.
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
.10.1098/rspa.2003.1183
27.
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
.10.1137/080718851
28.
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
.10.1007/s11071-011-0132-1
Copyright © 2015 by ASME
You do not currently have access to this content.