A biomimetic analysis is presented in which an expression for the optimum vessel diameter for the design of minimum mass branching or vascular networks in engineering applications is derived. Agreement with constructal theory is shown. A simple design case is illustrated and application to more complex cases with branching networks of several generations discussed. The analysis is also extended into the turbulent flow regime, giving an optimization tool with considerable utility in the design of fluid distribution systems. The distribution of vessel lengths in different generations was also found to be a useful design variable. Integrating a network into a structure is also discussed. Where it is necessary to adopt a non-optimum vessel diameter for structural integration, it has been shown that small deviations from the minimum mass optimum can be tolerated, but large variations could be expected to produce a punitive and rapidly increasing mass penalty.
Self-healing via a vascular network is an active research topic, with several recent publications reporting the application and optimization of these systems. This work represents the first consideration of the probable failure modes of a self-healing system as a driver for network design. The critical failure modes of a proposed self-healing system based on a vascular network were identified via a failure modes, effects and criticality analysis and compared to those of the human circulatory system. A range of engineering and biomimetic design concepts to address these critical failure modes is suggested with minimum system mass the overall design driver for high-performance systems. Plant vasculature has been mimicked to propose a segregated network to address the risk of fluid leakage. This approach could allow a network to be segregated into six separate paths with a system mass penalty of only approximately 25%. Fluid flow interconnections that mimic the anastomoses of animal vasculatures can be used within a segregated network to balance the risk of failure by leakage and blockage. These biomimetic approaches define a design space that considers the existing published literature in the context of system reliability.
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