A procedure for computing the spot production rate in transitional boundary layers, Large field Digital Image Plane Holography with a double cavity high speed laser

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The present work describes a method for the computation of the nucleation rate of turbulent spots in transitional boundary layers from particle image velocimetry (PIV) measurements. Different detection functions for turbulent events recognition were first tested and validated using data from direct numerical simulation, and this latter describes a flat-plate boundary layer under zero pressure gradient. The comparison with a previously defined function adopted in the literature, which is based on the local spanwise wall-shear stress, clearly highlights the possibility of accurately predicting the statistical evolution of transition even when the near-wall velocity field is not directly available from the measurements. The present procedure was systematically applied to PIV data collected in a wall-parallel measuring plane located inside a flat plate boundary layer evolving under variable Reynolds number, adverse pressure gradient (APG) and free-stream turbulence. The results presented in this work show that the present method allows capturing the statistical response of the transition process to the modification of the inlet flow conditions. The location of the maximum spot nucleation is shown to move upstream when increasing all the main flow parameters. Additionally, the transition region becomes shorter for higher Re and APG, whereas the turbulence level variation gives the opposite trend. The effects of the main flow parameters on the coefficients defining the analytic distribution of the nucleation rate and their link to the momentum thickness Reynolds number at the point of transition are discussed in the paper. The three velocity components in a fluid plane can be measured by applying Digital Image Plane Holography. This technique is limited by the laser coherence length, which reduces its application with high speed lasers that, generally, have a very short coherence length. In addition, the use of a double cavity can also imply a small wavelength difference between the two laser beams. In this work, we present an improved Optical Path Length Enlarging Device that allows the velocity measurement, in a 2D field whose width is four times larger than the laser coherence length. The optical set-up and the procedure for measuring in a larger field (ten times the laser coherence length) were optimized, and the issues derived from the laser spatial and temporal coherence and wavelength changes were analyzed and solved. Digital Image Plane Holography with the Optical Path Length Enlarging Device and Particle Image Velocimetry were applied for measuring the whole velocity field in the central plane of a cylindrical cavity with a rotating lid, for two Reynolds numbers (800 and 2000), showing both of them a very good agreement with the numerical simulations.