Modern vision for critical flow in an egg-shaped section (Part II)

Abstract

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 2.105 ≤ ≤ 4.107. 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.