Fast fluid heating by adaptive flow reorientation

Abstract

Transport of scalar quantities such as e.g. heat or chemical species in laminar flows is key to many industrial activities and stirring of the fluid by flow reorientation is a common way to enhance this process. However, “How best to stir?” remains a major challenge. The present study aims to contribute to existing solutions by the development of a dedicated flow-control strategy for the fast heating of a cold fluid via a hot boundary in a representative case study. In-depth analysis of the dynamics of heating in fluid flows serves as foundation for the control strategy and exposes fluid deformation as the “thermal actuator” via which the flow affects the heat transfer. This link is non-trivial, though, in that fluid deformation may both enhance and diminish local heat exchange between fluid parcels and a fundamental “conflict” between local heat transfer and thermal homogenisation tends to restrict the beneficial impact of flow to short-lived episodes. Moreover, the impact of fluid deformation on the global fluid heating is primarily confined to the direct proximity of the moving boundary that drives the flow. These insights imply that incorporation of the thermal behaviour is essential for effective flow-based enhancement strategies and efficient fluid mixing, the conventional approach adopted in industry for this purpose, is potentially sub-optimal. The notion that global heating encompasses two concurrent processes, i.e. increasing energy content (“energising”) and thermal homogenisation, yields the relevant metrics for the global dynamics and thus enables formulation of the control problem as the minimisation of a dedicated cost function. This facilitates step-wise determination of the “best” flow reorientation from predicted future evolutions of actual intermediate states and thereby paves the way to (real-time) regulation of scalar transport by flow control in practical applications. Performance analyses reveal that this “adaptive flow reorientation” significantly accelerates the fluid heating throughout the considered parameter space and thus is superior over conventional periodic schemes (designed for efficient fluid mixing) both in terms of consistency and effectiveness. The controller in fact breaks with conventions by, first, never selecting these periodic schemes and, second, achieving the same superior performance for all flow conditions irrespective of whether said mixing occurs. The controller typically achieves this superiority by thermal plumes that extend from the hot wall into the cold(er) interior and are driven by two alternating and counter-rotating circulations.