Why the turbulent buoyant plumes evolve to round cross sections? A 'Constructal' view

The turbulent buoyant plumes are fundamental turbulent structures that are responsible for the heat transfer by convection in numerous complex systems. Many of these plumes have an elliptic cross section near the source and evolve to round cross sections in the far-field. In this work, we study the convective flow of turbulent buoyant plumes with an elliptic cross section to see if an explanation for their transition to round cross sections can be given by the 'Constructal Law'. We consider the mixing length theory in order to obtain an ener-gy-consistent plume model for the elliptic turbulent plumes. We study the dependency of the flow, buoyancy and entrainment on the eccentricity of the plume using both the self-similar solutions, and the numerical solutions of our integral model. We show that the vertical (longitudinal) flow is optimized for round cross sections in both unstratisfied and unstable environments, which suggests that indeed the 'Constructal Law' might be able to explain the transition. In addition, we study the entropy generation of the turbulent plumes and show that an explanation based on a principal of minimisation/maximisation of entropy generation cannot be given for the evolution of the plumes to round cross sections.

Automated summary

In this study, the convective flow of turbulent buoyant plumes with an elliptic cross section is investigated to determine if the transition to round cross sections can be explained by the 'Constructal Law'. The mixing length theory is used to obtain an energy-consistent plume model, and both self-similar and numerical solutions are used to study the dependence of flow, buoyancy, and entrainment on the eccentricity of the plume. The results show that the vertical flow is optimized for round cross sections, suggesting that the 'Constructal Law' may provide an explanation for the transition. However, the entropy generation of the plumes does not support a minimization/maximization principle for the evolution to round cross sections.