Fluids flow stability in ducts of arbitrary cross-section

Franck Delplace

Abstract

Fluids flow stability is of major importance in both research and engineering. Transition between the laminar and turbulent flow regimes is often characterized by critical Reynolds number value. In this paper, we used experimental results obtained in ducts of several cross-section shape, to analyse the deep link between geometry and flow stability. Experiments clearly showed the influence of geometry on critical Reynolds number values. Considering isoperimetric quotient (IQ), coming from famous isoperimetric theorem, we established and quantified the link between fluids flow stability and IQ. Moreover, we showed that an abacus could be built giving critical Reynolds number values as a function of cross-sections IQ. This abacus could be an interesting and important tool for both research and engineering applications.