[{"type":"article-journal","title":"Numerical simulation of turbulent duct flows with constant power input","issued":{"date-parts":[["2014"]]},"volume":"750","page":"191-209","container-title":"Journal of Fluid Mechanics","DOI":"10.1017\/jfm.2014.269","author":[{"family":"Hasegawa","given":"Yosuke"},{"family":"Quadrio","given":"Maurizio"},{"family":"Frohnapfel","given":"Bettina"}],"ISSN":"0022-1120","abstract":"The numerical simulation of a \ufb02ow through a duct requires an externally speci\ufb01ed forcing that makes the \ufb02uid \ufb02ow against viscous friction. To this end, it is customary to enforce a constant value for either the \ufb02ow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct \ufb02ow before and after a geometrical modi\ufb01cation that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent \ufb02ows, 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 \ufb02ow 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 de\ufb01ning a new power-related Reynolds number, whose velocity scale is the bulk \ufb02ow 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\u2013Iwamoto\u2013Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exempli\ufb01ed in the standard case of a plane turbulent channel \ufb02ow, and then further applied to a \ufb02ow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number \ufb02ow, 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 \ufb02ow rate above the reference case where 100% of the power goes to the pump.","kit-publication-id":"1000047788"}]