ASME - JSME - KSME Joint Fluids Engineering Conference 2019, California, United States Of America, 28 July - 01 August 2019
Flows inside microchannels have been studied both experimentally and numerically for many years, but still there are debatable points. The critical question that needs to be answered is whether the friction factor and the Nusselt number deviates from the conventional theory or not. And if a deviation is seen, further questions arise such as the amount and the cause of it, how it scales with the Reynolds number, how is it affected by the channel geometry and the surface roughness, how it affects the transition to turbulence, etc. It is possible to find conflicting answers and explanations to these questions in the literature.
Experimental studies are very valuable to clarify this and there are a vast number of them. Unfortunately, many of them, while trying to shed light to the problem, also bring their own confusion mainly due to the lack of provided data. There are studies in which information such as the geometrical dimensions, surface roughness details, entrance effects and how they are included in the calculations, measurement uncertainties, etc. are missing.
At this point, numerical studies become helpful. Many of the microchannel applications involve laminar flow. Without being worried about transition and turbulence modeling issues, these low Reynolds number flows inside simple geometries with no separation can be simulated very accurately. As far as the surface roughness effects in microchannel flows is considered, almost all numerical studies in the literature are two-dimensional and make use of artificial roughness elements. Among the limited number of three-dimensional ones, only two consider somewhat realistic rough surfaces with Gaussian distributions.
With the aim to bring clarity to the confusion described above, laminar flows inside microchannels is investigated numerically in this study. The effect of the surface roughness on the friction factor is the focus point. To form a base, Natrajan & Christensen's (2010) experimental study, which was concerned with the same problem, is chosen. A rectangular channel of length 144 mm, width 900 µm, height 450 µm with hydraulic diameter 600 µm is considered. Reynolds number is varied between 100 and 2100. Side walls of the channel are considered to be rough with root mean square roughness (RMS) height ranging between 0 and 5%. To have realistic rough surfaces, sinusoidal waves of random sampling are used, which results in more realistic surfaces than those used in the previous studies. Simulations are performed using OpenFOAM with meshes ranging between 1.5 and 45 million cells, with the most challenging case taking less than 15 hours on a typical workstation with 28 cores.
Results of smooth and rough channels with RMS roughness height of 1.25% shows perfect agreement with the experimental data and the conventional theory. However, results of RMS roughness height of 2.5% shows discrepancy with both experimental data and the theory. Although the results are not matching with those of the reference paper, they are in agreement with the review made by Dai, Li, & Ma (2014), which states that the effect of roughness is seen above average roughness height of 1%. It is believed that carefully done numerical studies with realistic rough surfaces are of critical importance to clarify the debated issues in the microchannel flow research. We also believe that one of the reasons behind the confusion in the literature is due to the lack of information in describing the surface roughness. In most studies only, the average or RMS roughness height is given, which may not be enough. Therefore, it is important to consider other surface aspects such as skewness and kurtosis of the roughness. It is possible to perform extensive controlled studies of these parameters with the proposed numerical approach.