Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms

In this paper, a bottom-up approach is used to construct random rough bottom walls for trapezoidal silicon microchannels with hydraulic diameters $Dh$ from $47μm$ to $241μm$⁠. The top and side walls are set to be smooth. A computational fluid dynamics solver is used to solve the 3D Navier–Stokes equations for the water flow through the rough trapezoidal microchannels. No-slip and periodic boundary conditions are applied to achieve the fully developed flow characteristics. The effects of Reynolds number Re (75–600), relative roughness height $H/Dh$ (1.66–5.39%), aspect ratio $β$ (0.13–1), and base angle $θ$ (30–90 deg) on the Poiseuille number Po are investigated. It is found that the roughness strongly affects the flow near the bottom wall but does not have significant effect on the center flow. The Po number in the developing flow region increases with the Re number and in the fully developed region tends to be independent of the Re number. The entrance length $Le$ is found to be smaller than that in smooth channels because the roughness reduces hydraulic diameter $Dh$ of the microchannel. It is also observed that with a certain $H/Dh$⁠, the Po number has a larger deviation from the theoretical value with a smaller $β$⁠, and with the same $H/Dh$ and $β$⁠, $θ$ can also change the Po number, especially at small base angles.