Simultaneous optimisation of residence time, heat and mass transfer in laminar duct flows

Suitably designed laminar duct flows admit chaotic advection which, in concert with diffusion, can lead to rapid heat and mass transport and sharpening of the residence time distribution (RTD). Whilst evolution of these distinct scalar fields are strongly related, the exact relationships between these distinct fields is unknown, nor to what extent they can be simultaneously optimised. In this paper we present a unified framework for the simultaneous optimisation of the three scalar fields; RTD, temperature, and mass concentration. This optimisation is performed in terms of the eigenmodes of the advection-diffusion operator, which generalize classical Taylor-Aris axial dispersion. We apply this optimisation framework to a twisted pipe flow (TPF) at Péclet number Pe=105, and find 47- and 237-fold increases in transverse heat and mass transfer respectively over straight tube flow, along with a 2,000-fold suppression of RTD variance growth. We show that generality of the eigenmode decomposition suggests this framework is universal to all duct flows.