Frictional Characteristics of Spanwise Circular Trenches in Laminar Microchannel Flow

In microchannel flow, the small scale leads to a high flow resistance and thus a large amount of drag for a specific volumetric flow rate. Applying microtextures to the surfaces of a microchannel to reduce the flow resistance has been an active area of research, and this paper seeks to analyze textured microchannels with circular, spanwise (perpendicular to the flow) trenches of various geometric parameters at several Reynolds numbers in the fully laminar regime to assess changes in the net drag. These circular geometries are defined such that they are analogous to a set of rectangular geometries studied in a previous paper for direct comparison. Ansys Fluent was used to perform direct numerical simulations, assuming steady, 2D flow in a periodic domain. The drag was assessed by computing the Poiseuille number, which quantifies how large a pressure drop is required to achieve a specific flow rate. The Poiseuille number was split into shear and pressure components to demonstrate how geometries can reduce the shear component of drag at the expense of adding a large detrimental pressure component to the total drag. By using the Poiseuille number, the changes in internal volume in the textured microchannel are accounted for through the average hydraulic diameter. This ensures that drag reduction is not found simply by using trenches that increase the total internal volume of the microchannel, which tends to decrease the flow resistance. Several geometries studied had a reduction in the shear Poiseuille number compared to the baseline microchannel, but none had a total Poiseuille number lower than the baseline, so no net drag reduction was found. Compared to the analogous rectangular geometries, the circular geometries tended to have a lower pressure Poiseuille number and a higher shear Poiseuille number with the net effect tending to be a lower total Poiseuille number. Microchannels with small relative roughness values were also investigated and were found to have increases in drag up to 3\%, even though no change in drag would conventionally be expected from surface roughness in the fully laminar regime. This same result was found even with randomly varying dimensions in the microtextures, so it is not simply due to periodic features.