Natural constructal emergence of vascular design with turbulent flow

Here, we show that vascular design emerges naturally when a volume is bathed by a single stream in turbulent flow. The stream enters the volume, spreads itself to bathe the volume, and then reconstitutes itself as a single stream before it exits the volume. We show that in the pursuit of a smaller global flow resistance and larger volumes, the flow architecture changes stepwise from a stack of identical elements bathed in parallel flow (like a deck of cards) to progressively more complex structures configured as trees matched canopy to canopy. The transition from one architecture to the next occurs at a precise volume size, which is identified. Each transition marks a decrease in the rate at which the global flow resistance increases with the volume size. This decrease accelerates as the volume size increases. The emergence of such vasculatures for turbulent flow is compared with the corresponding phenomenon when the flow is laminar. To predict this design generation phenomenon is essential to being able to scale up the designs of complex flow structures, from small scale models to life size models. The constructal law is a bridge between the principles of physics and biology.