The statistics of power injected in a closed turbulent flow: Constant torque forcing versus constant velocity forcing

Abstract

A confined turbulent flow forced by two counter-rotating stirrers is investigated. Two processes of energy injection are studied. In the first one, called the Ω mode, the forcing devices are driven at constant angular velocity. In the second, called the Γ mode, the forcing devices are driven with a constant torque. For each forcing mode, the power injected and the wall pressure fluctuations are simultaneously measured in the range of Reynolds numbers from 20 000 to 500 000. For each mode, the probability density functions of the injected power are approximately Gaussian with slight reversed skewness between both modes. These asymmetries are due to an excess of low dissipation events compared to high dissipation events. For each mode, the skewness varies as the logarithm of the Reynolds number. On the other hand, the fluctuation rate of the injected power does not depend on the Reynolds number whatever the forcing modes, however, their magnitudes are drastically different. A value of only 5.9% is obtained for the Γ mode against 10.9% for the Ω mode. The local properties of the turbulence at smaller scales, deduced from either hot film anemometry or wall pressure measurements, are identical for both forcing modes. The mean dissipated power remains unchanged as well. It is then deduced that the injected power fluctuations are caused by the turbulence feedback rather than the turbulence production. The difference in the fluctuation rates is a consequence of the natural control of the turbulence feedback that occurs for the Γ mode.