Laminar to turbulent transitions of pipe flows by resonances of natural frequencies of components of test sections

Abstract

This investigation analyses special papers and doctoral theses that treat transitions of pipe flows as a resonance phenomenon of wave frequencies. These frequencies are natural frequencies of pipe flows, of components of the test section and of vortex ring formations. Resonance conditions are derived that show how the critical Reynolds number, Re_c, depends on the volume of the plenum chamber, the pipe diameter, the pipe length, etc. The derived resonance relations were verified experimentally using the experimental data of the third author, yielding $R{e}_c\sim 1/\sqrt{V_{\mathrm{ple}}}$, $R{e}_c\sim 1/\left(\sqrt{L}D\right)$ and other interesting results. These findings suggest that the laminar-to-turbulent transition has various modes and transitive dependences. To understand this fully, it is necessary to take all components of the test section involved into account. The test section considered in this paper consists of a mass flow controller to supply the airflow and a plenum chamber, followed by the actual pipe of interest. It is shown that all the components can contribute to the measured value of the critical Reynolds number of pipe flow transition.

KEYWORDS:

• Pipe flow
• laminar
• turbulent
• transition
• Helmholtz resonator

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

One of us (G.B.) acknowledges support from the JC Bose National Fellowship of Science and Engineering Research Board (SERB), India [grant number JBR/2020/000042].