Title: A thermodynamic explanation of the function of bifurcated structures in nature and in engineered artefacts

Authors: Enrico Sciubba

Addresses: Department of Mechanical and Aerospace Engineering, University Roma Sapienza, Italy

Abstract: Why do bifurcated structures appear? In living and non-living systems, the construction of a bifurcation requires some energy input, and the 'economic principle' of nature suggests that this be justified by a compensating gain for the resulting structure. If the purpose of bifurcations is to transport material and immaterial flows, what underlying principle governs the radius ratio between branches, the diameter/length ratio, and the splitting angle? Do the prevailing boundary conditions influence their onset? This paper presents a novel thermodynamic model based on the assumption that the driving force behind the emergence of a bifurcation is its exergy cost. This is an extension and a completion of the Hess-Murray law: extension, because it measures the advantage of branched structures with respect to their non-branched counterparts in terms of exergy; completion, because it includes the 'formation exergy' neglected by previous theories. The model leads to a quantification of this primary exergy cost.

Keywords: exergy analysis; entropy-based optimisation; CFD of turbomachinery; ultra-micro gas turbines; energy systems analysis; bifurcated flows; exergy cost; exergy footprint; Hess-Murray law; constructal theory.

DOI: 10.1504/IJEX.2021.115087

International Journal of Exergy, 2021 Vol.35 No.1, pp.84 - 99

Received: 04 Dec 2019
Accepted: 30 Jun 2020

Published online: 06 May 2021 *

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