Abstract
The variation of transitional flow features past a micro-ramp is investigated when the Reynolds number is decreased approaching the critical regime. Experiments are conducted in the incompressible flow spanning from supercritical to subcritical roughness-height-based Reynolds number ($Re_{h}=1170$, 730, 460 and 320) with tomographic particle image velocimetry. The effect of $Re_{h}$ on three-dimensional flow behaviour is analysed in a domain encompassing 73 ramp heights in the streamwise direction. Above the critical $Re_{h}$, the primary vortex pair and induced central low-speed region in the mean flow field are active over longer range when decreasing $Re_{h}$. In the instantaneous flow, at $Re_{h}<1000$, the hairpin vortices induced by Kelvin–Helmholtz (K–H) instability progress gradually from close to the micro-ramp into the region where the overall shear layer is destabilized, indicating the correlation between the K–H instability and the onset of transition. The breakdown of K–H vortices as observed at $Re_{h}=1170$, does not occur at lower $Re_{h}$. Decreasing $Re_{h}$, the secondary vortex structures make their first appearance significantly downstream, postponing the formation of sideward disturbances, which destabilize the local shear layer by ejection events. Two major types of eigenmodes with symmetric and asymmetric spatial distribution of velocity fluctuations in the near wake are clearly identified by proper orthogonal decomposition. The symmetric and asymmetric modes correspond to the presence of vortex shedding and a sinuous wiggling motion respectively. It is found that $Re_{h}$ is the key factor determining the importance of the symmetric mode. At $Re_{h}=1170$, the disturbance energy of the symmetric mode decays before the onset of transition, suggesting that it is relatively insignificant in the process. However, decreasing $Re_{h}$ to 730 and 460, the symmetric mode produces continuous growth of high level disturbance energy, leading to transition.
Highlights
The role of surface roughness in boundary layer transition is significant due to its impact in aerodynamic and aero-thermodynamic problems
For a two-dimensional roughness element without spanwise variation, the natural transition process is promoted by amplification of Tollmien–Schlichting (TS) waves at the downstream separation and recovery region of the roughness (Klebanoff & Tidstrom 1972)
For three-dimensional distributed or isolated roughness, the transition process cannot be explained by the enhancement of TS waves, as three-dimensional roughness introduces a localized spanwise deflection of the streamlines without strong downstream flow separation
Summary
The role of surface roughness in boundary layer transition is significant due to its impact in aerodynamic and aero-thermodynamic problems. Studied, the presence of high velocity fluctuations located at the inflection point of the velocity profile indicates a possible effect of Kelvin–Helmholtz (K–H) instability on transition They found the exponential growth rate of the unsteady disturbances increases rapidly with increasing Reh. At supercritical Reh, the unsteady disturbances undergo transient growth and spread laterally across the wake, leading to transition to turbulence. In order to understand the instability mechanism behind roughness elements, Cherubini et al (2013) searched for the perturbations inducing the largest disturbance energy growth in the wake of a three-dimensional smooth bump by performing linear optimization analysis. Schrijer & Scarano (2016a,b) measured the three-dimensional vortical structures in the wake of isolated roughness elements having different geometries (cylinder, square, hemisphere and micro-ramp) at supercritical Reh using tomographic particle image velocimetry (PIV). The low-order model consisting of selected POD modes highlights the development of secondary vortex structures, giving rise to the spanwise spreading of perturbations
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