LDV measurements of boundary layer velocity profiles on flat plates with different surface roughnesses

Abstract

The dynamics acting upon thin flat plates submerged in a fluid are chiefly governed by the delicate boundary layer enveloping their surfaces. Through a series of experiments, we investigated the impact of surface roughness elements on the boundary layer adjacent to a flat plate across a range of Reynolds numbers. The experiments were performed in the Chungnam National University-Cavitation Tunnel (CNU-CT). Three flat plates, each characterized by distinct surface roughness heights denoted by k, were subjected to scrutiny. One boasted a pristine smoothness, while the others bore the deliberate roughness of sandpaper, each with its own unique texture. With precision instrumentation, including Laser Doppler Velocimetry (LDV), we meticulously documented the axial velocity profile and the RMS (Root Mean Square) velocity at strategic points along the flat plates. Through these measurements, we unveiled the boundary layer's thickness, δ, and momentum thickness, θ, elucidating their variations under differing free-stream velocities. As our exploration deepened, the relationship between the local Reynolds number, Rn_x, and the non-dimensional velocity profiles, u⁺ − y⁺, became apparent. A systematic shift along the log-law line ensued, with both u⁺ and y ⁺ increasing in tandem with the rise in Rn_x. Yet, our inquiry did not conclude with observation alone. Employing empirical rigor, we quantified the drag forces acting upon flat plates of varying roughness heights, deriving them from the measured momentum thickness across a range of local Reynolds numbers, Rn_x.