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The Money-vs-Time framework: A modern way for relating pressure drop and flow rate in a duct flow

Prof. Maurizio Quadrio
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano

A conceptual framework, "Money-vs-Time", has been recently proposed (Frohnapfel, Hasegawa & Quadrio, JFM 2012) where the bulk velocity in a duct flow and the energy required to obtain that bulk velocity are simultaneously and explicitly considered. A new plane is introduced that can be viewed as an improved version of the familiar C_f - Re plane, which describes in a dimensionless way how the flow rate and the pressure gradient required to achieve that flow rate are related. In the new plane, an analogous non-dimensional description relates the flow rate and the energy expenditure required to achieve that flow rate, possibly including control energy.

The seminar will introduce the Money-vs-Time approach, and discuss its main implications. Putting energy directly into the scene corresponds to a modern, "green" view that emphasizes the energetic and environmental costs of the technological choices. In designing a particular fluidic application, the choice of the operating conditions requires appreciating the relative importance of energy and flow rate; once this relative importance is formalized into a cost function to be minimized, the Money-vs-Time plane will be shown to be the right tool for a designer to choose the optimal solution. Lastly, different drag-reduction techniques can be easily compared within this framework, where the energetic cost of the control is naturally accounted for.