Large-eddy estimate of the turbulent dissipation rate using PIV

Abstract

The result of a particle image velocimetry (PIV) measurement is a velocity field averaged over interrogation windows. This severely affects the measurement of small-scale turbulence quantities when the interrogation window size is much larger than the smallest length-scale in turbulence, the Kolmogorov length. In particular, a direct measurement of the dissipation rate demands the measurement of gradients of the velocity field, which are now underestimated because the small-scale motion is not resolved. A popular procedure is to relate the statistical properties of the measured, but underresolved gradients to those of the true ones, invoking a large-eddy argument (Sheng et al. in Chem Eng Sci 55(20):4423–4434, 2000 ). We argue that the used proportionality constant, the Smagorinsky constant, should depend on the window overlap, on the used elements of the strain tensor, and on the way in which derivatives are approximated. Using an analytic description, PIV measurements of velocity fields from a kinematic simulation and experiments in a synthetic jet-driven turbulent flow with zero mean velocity, we propose new values for this constant.