Modern vision for critical ﬂow in an egg-shaped section (Part II). (17th August 2022) - Soraya, Bouslah; Lamia, Hachemi-Rachedi; Moussa, Lakehal; Bachir, Achour
Abstract: The main aim of this research was to examine the simultaneous effects of all flow parameters on the critical regime occurrence frequency in an egg-shaped conduit. Furthermore, one may first study the impacts of the conduit's generator diameter, then the influence of the generator diameter/longitudinal slope, and finally the effect of all parameters: the generator diameter, longitudinal slope, roughness and viscosity. It has been concluded that all these parameters, combined, have limit values that can generate a single critical state from which a diagram can be drawn showing different states of the critical flow that can be observed. Notably, this diagram is established according to the following practical ranges: relative roughness 0 ≤ ε / D ≤ 5.10 −2, generator diameter 0.25 m ≤ D ≤ 4 m and Galileo number 2.10 5 ≤ ≤ 4.10 7 . This revealed that the critical regime can develop smooth, rough and transition domains. Critical flow is very unstable; therefore, it is to be avoided in practice, which means that the dimensions and the slope of the conduit must be such that they do not cause such a state of flow. This explains why knowledge of the characteristics of the critical flow, including the frequency of its occurrence for a given installation, is essential. HIGHLIGHTS: Definition of frequency occurrence of a critical regime. Deduce nature of flow regime from the pair slope/generator diameter. General diagram, similar to the Moody diagram, for prediction of critical state frequency occurrence in an egg-shaped conduit using all influencing flow parameters. Critical regime can evolve in the whole turbulent domain. Analytical equation determining the limit slope as a function of the limit generator diameter is proposed. Graphical Abstract