Inception of Turbulence in the Stokes Boundary Layer Over a Transpiring Wall

In this work, the onset of turbulence inside a rectangular chamber is investigated, with and without side-wall injection, in the presence of an oscillatory pressure gradient. Two techniques are used to define the transition from laminar to turbulent regimes: statistical analysis and flow visualization. Calibrated hot film anemometry and a computer data acquisition system are used to record and analyze acoustical flow data. Four classifications of flow regimes are reported: (a) laminar, (b) distorted laminar, (c) weakly turbulent, and (d) conditionally turbulent. Despite numerous attempts to promote turbulence, a fully turbulent flow does not develop at any of the driving frequencies tested. Statistical measurements reveal that a periodic drop in standard deviation of axial velocity fluctuations always occurs, indicating relaminarization within each cycle. Transition between flow regimes is assessed from the standard deviation of velocity data correlated as a function of the acoustic Reynolds number $ReA.$ Under predominantly laminar conditions, the standard deviation is found to vary approximately with the square of the acoustic Reynolds number. Under turbulent conditions, the standard deviation becomes almost directly proportional to the acoustic Reynolds number. Inception of turbulence in the oscillatory flow with side-wall injection is found to be reproducible at the same critical value of $ReA≅200.$