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Research Papers

Chaotic and Hyperchaotic Dynamics of Smart Valves System Subject to a Sudden Contraction

[+] Author and Article Information
Peiman Naseradinmousavi

Assistant Professor
Dynamic Systems and Control Laboratory,
Department of Mechanical Engineering,
San Diego State University,
San Diego, CA 92115
e-mails: pnaseradinmousavi@mail.sdsu.edu;
peiman.n.mousavi@gmail.com

David B. Segala

Naval Undersea Warfare Center,
1176 Howell Street,
Newport, RI 02841
e-mail: david.segala@navy.mil

C. Nataraj

Mr. & Mrs. Robert F. Moritz
Senior Endowed Chair
Professor in Engineered Systems
The Villanova Center for Analytics of Dynamic Systems (VCADS),
Villanova University,
Villanova, PA 19085
e-mail: nataraj@villanova.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 9, 2016; final manuscript received April 29, 2016; published online June 2, 2016. Assoc. Editor: Stefano Lenci.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Nonlinear Dynam 11(5), 051025 (Jun 02, 2016) (9 pages) Paper No: CND-16-1123; doi: 10.1115/1.4033610 History: Received March 09, 2016; Revised April 29, 2016

In this paper, we focus on determining the safe operational domain of a coupled actuator–valve configuration. The so-called “smart valves” system has increasingly been used in critical applications and missions including municipal piping networks, oil and gas fields, petrochemical plants, and more importantly, the U.S. Navy ships. A comprehensive dynamic analysis is hence needed to be carried out for capturing dangerous behaviors observed repeatedly in practice. Using some powerful tools of nonlinear dynamic analysis including Lyapunov exponents and Poincaré map, a comprehensive stability map is provided in order to determine the safe operational domain of the network in addition to characterizing the responses obtained. Coupled chaotic and hyperchaotic dynamics of two coupled solenoid-actuated butterfly valves are captured by running the network for some critical values through interconnected flow loads affected by the coupled actuators' variables. The significant effect of an unstable configuration of the valve–actuator on another set is thoroughly investigated to discuss the expected stability issues of a remote set due to others and vice versa.

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References

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Figures

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Fig. 1

(a) A schematic configuration of two solenoid-actuated butterfly valves subject to sudden contraction and (b) a coupled model of two butterfly valves in series without actuation

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Fig. 2

A comparison between the experimental and analytical total torques

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Fig. 3

The interconnected sets' stability map; 10−8≤bdi=μi≤9×10−2 and 10−1≤bdi=μi≤3×10−1 stand for unstable and stable domains, respectively

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Fig. 4

(a) The coupled sets' phase portraits for Initial1 and (b) the coupled sets' phase portraits for Initial2

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Fig. 5

(a) The Lyapunov exponents for Initial1 and (b) the positive Lyapunov exponents for Initial2 versus different approach angles (θ)

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Fig. 6

(a) The poincaré map for Initial1 of the upstream set and (b) the poincaré map for Initial1 of the downstream set

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Fig. 7

(a) The Poincaré map for Initial2 of the upstream set and (b) the Poincaré map for Initial2 of the downstream set

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Fig. 8

(a) The sum of flow loads versus magnetic force of both the upstream and downstream sets for Initial1 and (b) the sum of flow loads versus magnetic force of both the upstream and downstream sets for Initial2

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Fig. 9

A broad spectrum of Lyapunov exponents versus the equivalent beqi's and μi's revealing transition from chaos to hyperchaos

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Fig. 10

(a) The bifurcation diagram versus the equivalent beqi's and μi's for the upstream valve revealing transition from chaos to hyperchaos and (b) the bifurcation diagram versus the equivalent beqi's and μi's for the downstream valve revealing transition from chaos to hyperchaos

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Fig. 11

(a) The phase portrait of the upstream set for Initial2 and (b) the phase portrait of the downstream set for Initial2

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Fig. 12

(a) The poincaré map of the upstream set for Initial2 and (b) the poincaré map of the downstream set for Initial2

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