Numerical simulation of turbulent duct flows with constant power input

TL;DR

This paper introduces a method for simulating turbulent duct flows under a constant power input condition, providing a new framework for flow control comparisons and demonstrating its application in drag reduction scenarios.

Contribution

It develops a novel CPI simulation approach, deriving a related Reynolds number and extending existing flow relations to include control power effects.

Findings

CPI simulation method effectively models turbulent flows with constant power input.

Optimal power distribution between pump and control system enhances flow rate.

Application to flow control shows significant drag reduction with power optimization.

Abstract

The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this aim, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches (CFR and CPG) lead to a change of the power input across the comparison. Similarly, when carrying out the (DNS and LES) numerical simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata--Iwamoto--Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of natively including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where the spanwise-oscillating wall is used for skin friction drag reduction. For this low-Reynolds number flow, using 90% of the available power for the pumping system and the remaining 10% for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case, where 100% of the power goes to the pump.