Chaotic Analysis of the Velocity Signal in Impinging Stream Mixer

Abstract:

The velocity signal of the flow field in Impinging Stream Mixer (ISM) was measured with Laser Doppler Anemometer. A de-noising method for velocity signal in ISM based on wavelet threshold was used. It is obtained that the attractor of the system possess infinite self-similar nested structure by comparing the strange attractor before and after de-noising, which is based on phase space reconstruction theory. It is shown that K entropy and the largest Lypunov exponents have the similar tendency in spatial distribution through scientific computation, however, the stratification of K entropy is more obvious. The value of K entropy and the largest Lypunov exponents are both positive, proving that the system is chaotic. The results indicate that K entropy and Lyapunov exponents can be increased by improving the rotating speed, the disorder and unpredictability of chaos system will increase homogeneously, so as to promote the micro-mixing and improve work efficiency

• Periodical: Applied Mechanics and Materials (Volume 187)
• Pages: 122-129
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.187.122
• Online since: June 2012
• Authors: Jian Wei Zhang, Yan Fang Song
• Keywords: Chaotic Analysis, Correlation Dimension, Impinging Stream, Kolmogorov Entropy, Lyapunov Exponent, Scientific Computation

References

[1] Elprein I.T. Heat and mass transfer in opposing currents, ．Engng．Physics，vol. 6, pp.62-68, (1961).

[2] Tamir A. Impinging stream reactor - theory and application. Wu Yuan translation. Beijing: Chemical Industry Press, (1996).

[3] Brauer H．Staustrahlmischer，German patent，2900083, pp.7-23, (1980).

[4] Perry R H，Green D．Chemical Engineer'Handbook，6th ed. New York: Mc-Graw-Hill， (1984).

[5] Packard N．H ．et al．Geometry from a time series, ．Phys．Rev Letters，vol. 45, pp.712-716, (1980).

[6] P．Grassberger，I．Procaccia． Characterization of Strange Attractors, ．Phys．Rev Lett，vol. 50, pp.346-349, (1983).

[7] Duan Wenfeng. Chaotic Analysis Method and its Application to Pressure Fluctuation in Gas-Solid Fluidized Beds, Si Chuan: Si Chuan University(China)，(2001).

[8] P. Grassberger and I. Procaccia，Estimation of the Kolmogorov entropy from a chaotic signal,. Phys. Rev. A，vol. 28, pp.2591-2593, (1983).

DOI: 10.1103/physreva.28.2591

[9] Rosenstein M T, Collins J, and De luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets,. Physica D, vol. 65, pp.117-134, (1993).

DOI: 10.1016/0167-2789(93)90009-p

[10] D．L．Donoho, De-noising by soft-thresholding, ．IEEE Trans．Inform Theory，vol. 41, pp.613-627, (1995).

[11] Zhang Jianwei , Wang Yang , Tang Huihua , Jiao Li, Chaotic analysis of pressure fluctuation in impinging region of SCISR, Journal of Chemical Industry and Engineering(China), vol. 12, pp.2309-2314, (2005).