Correlations for the Prediction of Intermittency and Turbulent Spot Production Rate in Separated Flows

Abstract

Experimental data describing laminar separation bubbles developing under strong adverse pressure gradients, typical of ultra-high-lift turbine blades, have been analyzed to define empirical correlations able to predict the main features of the separated flow transition. Tests have been performed for three different Reynolds numbers and three different free-stream turbulence intensity levels. For each condition, around 4000 particle image velocimetry (PIV) snapshots have been acquired. A wavelet-based intermittency detection technique, able to identify the large scale vortices shed as a consequence of the separation, has been applied to the large amount of data to efficiently compute the intermittency function for the different conditions. The transition onset and end positions, as well as the turbulent spot production rate, are evaluated. Thanks to the recent advancements in the understanding on the role played by Reynolds number and free-stream turbulence intensity on the dynamics leading to transition in separated flows, guest functions are proposed in the paper to fit the data. The proposed functions are able to mimic the effects of Reynolds number and free-stream turbulence intensity level on the receptivity process of the boundary layer in the attached part, on the disturbance exponential growth rate observed in the linear stability region of the separated shear layer, as well as on the nonlinear later stage of completing transition. Once identified the structure of the correlation functions, a fitting process with own and literature data allowed us to calibrate the unknown constants. Results reported in the paper show the ability of the proposed correlations to adequately predict the transition process in the case of separated flows. The correlation for the spot production rate here proposed extends the correlations proposed in literature for attached (by-pass like) transition process, and could be used in γ–Reϑ codes, where the spot production rate appears as a source term in the intermittency function transport equation.

An Extended Version of an Algebraic Intermittency Model for Prediction of Separation-Induced Transition at Elevated Free-Stream Turbulence Level

“…This means that the size of the separation bubble scales with the thickness of the boundary layer at separation under a varying adverse pressure gradient. This scaling effect is clear from the correlations constructed by Dellacasagrande et al [2,3] for the distance between the position of separation and the start of breakdown and for the distance between the start of breakdown and the position of reattachment. These correlations, in the form of a distance Reynolds number as a function of the momentum thickness Reynolds number and the free-stream turbulence level at the point of separation, do not contain the magnitude of the adverse pressure gradient.…”

“…From the correlations determined by Dellacasagrande et al [2,3], the scaling effects can be seen. For the distances between separation and start of transition (ST) and transition to reattachment (TR), the correlations are Re ST = 44.5Re 0.65 θs /Tu 0.5 and Re TR = 146Re 0.9 θs , and these correlations express similar tendencies as earlier constructed ones.…”

“…The effect of the adverse pressure gradient is less clear from the research cited up to now, because the pressure gradient was not varied in any of the research studies. More insight comes from the recently composed experimental data base by Simoni et al [16], on boundary layer flows on a flat plate, with four turbulence levels, four adverse pressure gradient levels and three Reynolds numbers and the interpretation of the effects by Dellacasagrande et al [2,3].…”

“…In a free stream with a low turbulence level, the inherent instability of the separated layer leads to transition after separation. The transition is accelerated in the presence of elevated free-stream turbulence, due to perturbations by fluctuations from the free stream [2,3].…”

Experimental investigation of the effect of active flow control on the wake of a wind turbine blade

“…Thus, identification of the entire process from LSB formation and growth up to the point where laminar separation flutter occurs, would be a key for flow control operations, especially for the wind turbine blades. 12,13 There exist primarily two types of flow control devices; namely passive and active, where both methods essentially replace the flow pattern in wall bounded or free shear flows. These devices postpone or discourage separation around obstacles and they may even delay the onset of transition to turbulent flow.…”