Implications of chaos theory for engineering science

Baker, G. P.; McRobie, FA; Thompson, J. M. T.

doi:10.1243/0954406971522105

Cited by 6 publications

(3 citation statements)

References 71 publications

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Order By: Relevance

“…Although the system seems to be random, it is possible to detect the presence of order in a strange attractor, which makes the system deterministic (Gleick, 1987). The Navier-Stokes equations, which describe this situation, are non-linear in many aspects (De Groot, 1951;Baker et al, 1997;Lebon et al, 2008), which introduces the seeds of chaos into the flow. Physics and mathematics gradually move apart.…”

Section: Disturbances In a Sudden Enlargementmentioning

confidence: 99%

Quieting the Flows in Valves Using Kinetic Energy Degraders

Pluviose¹

2013

Int. J. Thermo

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Valves are equipment which throttle a fluid to adjust the flow rate. At the opening of a relief valve, the mass of fluid released has a very large kinetic energy which is dissipated in a complex way in the pipework downstream. The high pressure ratio at valve opening carries the fluid system away from its initial equilibrium. After traveling through some bifurcations and fluctuating zones, this fluid system becomes self-organized. Flows that are thus confronted with energy dissipation and instabilities are dangerous for installations. Current recommended practice consists in installing internal devices which limit the disturbances to acceptable values, by weakening the chaotic phenomena without eliminating them. The kinetic energy degrader presented in this paper is an original device. It makes it possible to avoid chaotic zones and massively degrades the kinetic energy contained in the fluid. As a result, the fluid reaches its final equilibrium much more quickly. Flows in valves are thus quieted and the facilities are therefore protected.

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Section: Disturbances In a Sudden Enlargementmentioning

confidence: 99%

Quieting the Flows in Valves Using Kinetic Energy Degraders

Pluviose¹

2013

Int. J. Thermo

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show abstract

“…As both conditions are ful"lled for the beam system whereas t in equations (6) and (8) can be chosen arbitrarily large, f (t, x), which is piecewise continuous in t, can be proved to satisfy a global Lipschitz condition [19] which results in the fact that there exists a unique solution for…”

Section: Existence Of a 1-periodic Solutionmentioning

confidence: 99%

“…In many mechanical applications, chaotic attractors only exist in a few small regions of the parameter space, whereas damage and wear to such systems can occur in many large regions as a result of large-amplitude periodic vibrations [8]. If no chaotic attractors exist, other control schemes are needed to stabilize one of the coexisting small-amplitude periodic solutions to obtain vibration amplitude reduction [9,10].…”

Section: Introductionmentioning

confidence: 99%