The impact of surface roughness on flow through a rectangular microchannel from the laminar to turbulent regimes

Abstract

Modifications of fluid flow within microscale flow passages by internal surface roughness is investigated in the laminar, transitional, and turbulent regimes using pressure-drop measurements and instantaneous velocity fields acquired by microscopic particle-image velocimetry (micro-PIV). The microchannel under study is rectangular in cross-section with an aspect ratio of 1:2 (depth: width) and a hydraulic diameter of $D_{\rm h} =600\,\upmu \hbox{m}.$ Measurements are first performed under smooth-wall conditions to establish the baseline flow characteristics within the microchannel followed by measurements for two different rough-wall cases [with RMS roughness heights of $7.51\,\upmu \hbox{m}$ (0.0125D _h) and $15.1\,\upmu \hbox{m}$ (0.025D _h)]. The roughness patterns under consideration are unique in that they are reminiscent of surface irregularities one might encounter in practical microchannels due to imperfect fabrication methods. The pressure-drop results reveal the onset of transition above $Re_{\rm cr}=1{,}800$ for the smooth-wall case, consistent with the onset of transition at the macroscale, along with deviation from laminar behavior at progressively lower Re with increasing roughness. Mean velocity profiles computed from the micro-PIV ensembles at various Re for each surface condition confirm these trends, meaning $Re_{\rm cr}$ is a strong function of roughness. The ensembles of velocity fields at each Re and surface condition in the transitional regime are subdivided into fields embodying laminar behavior and fields containing disordered motions. This decomposition reveals a clear hastening of the flow toward a turbulent state due both to the roughness dependence of Re _cr and an enhancement in the growth rate of the non-laminar fraction of the flow when the flow is in the early stages of transition. Nevertheless, the range of Re relative to Re _cr over which the flow transitions from a laminar to a turbulent state is found to be essentially the same for all three surface conditions. From a structural viewpoint, instantaneous velocity fields embodying disordered behavior in the transitional regime are found to contain large-scale motions consistent with hairpin-vortex packets irrespective of surface condition. These observations are in accordance with the characteristics of transitional and turbulent flows at the macroscale and therefore indicate that the overall structural paradigm of the flow is relatively insensitive to roughness. From a quantitative viewpoint, however, the intensity of both the velocity fluctuations and structural activity appear to increase substantially with increasing roughness, particularly in the latter stages of transition. These differences are further supported by the trends of single-point statistics of the non-laminar ensembles and quadrant analysis in which an intensification of the velocity fluctuations by surface roughness is noted in the region close to the wall, particularly for the wall-normal fluctuations.