Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization

TL;DR

This paper evaluates various deterministic and stochastic optimization algorithms combined with energy minimization to accurately determine flow fields in ducts and networks for multiple fluid types, confirming the principle's fundamental role in flow dynamics.

Contribution

It introduces a comprehensive comparison of optimization algorithms with energy minimization for diverse fluids, expanding CFD methods for complex flow systems.

Findings

Algorithms agree with analytical solutions across fluid types

Energy minimization is fundamental to flow dynamics

Method enhances CFD capabilities for non-Newtonian fluids

Abstract

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder-Mead, Quasi-Newton, and Global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel-Bulkley, Ellis, Ree-Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of Computational Fluid Dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.