Analysis of the different sources of stress acting in fully rough turbulent flows over geometrical roughness elements

Abstract

The discrete element roughness method is considered in this article for the prediction of turbulent flows over rough walls. This approach is derived by ensemble- and volume-averaging the Navier–Stokes equations, providing double-averaged Navier–Stokes equations, and yielding three unknown terms in the momentum equation: the Reynolds stress and dispersive stress tensors and the average drag force acting on the roughness elements. This work aims at analyzing these different terms, quantifying their respective contributions to the near-wall momentum budget, and providing guidance for their modeling. For this purpose, relevant data of turbulent flows are required. Roughness-resolved Reynolds-averaged Navier–Stokes simulations of transitionally and fully rough channel flows over academic roughness configurations are performed at high friction Reynolds numbers ranging from 3500 to 8000. Comparisons with existing and new velocity measurements performed in rough-wall turbulent boundary layers provide support to the simulation results, a particular emphasis being given on the validity of the numerical results in the wake of the roughness elements. These numerical results highlight the influence of roughness elements geometry and density on the roughness drag coefficient and the dispersive stress. It is particularly suggested that the standard roughness drag closure model should be revisited for double-averaged flows. Furthermore, the dispersive stress is shown to mainly originate from the wake of the roughness elements, an observation that could be leveraged for its modeling. However, since this stress contributes only marginally to the global stress and to the skin friction coefficient, such a modeling may not be critical at first order.

Experimental Investigations of the Turbulent Boundary Layer for Biomimetic Protrusive Surfaces Inspired by Pufferfish Skin: Effects of Spinal Density and Diameter

“…Compared with a smooth surface, a significant upward shift of the logarithmic region in the surfaces of sample B and sample G is observed over two bulk Reynold numbers Re b . This is in agreement with the experimental result of Toussaint et al , The offset distance is denoted by −Δ U + . The detailed surface properties are summarized in Table ; when −Δ U + is negative, the velocity distribution shifts downward, and the drag is greater than the corresponding smooth wall.…”

“…Not only are tiny spines scattered on the surface of the pufferfish, but the stout rounded bodies of the fish are discovered to be also covered with small spines. 13 Toussaint et al 14 utilized numerical simulation to analyze the roughness elements (hemisphere, cylinder, and truncated cone) in the turbulent flow and found that the virtual origin of the rough surface of the cone shape (the height of the average roughness drag) is lower than the others. Chen and Martinuzzi 15 and Taylor and Martinuzzi 16 presented statistics on the speed around the cone in the open wind tunnel, observed the vortex shedding period in the cone, and proposed that the counter-rotating base vortices that were stretched repeatedly appeared behind the cone.…”

Investigation of the Turbulent Boundary Layer Structure over a Sparsely Spaced Biomimetic Spine-Covered Protrusion Surface

“…Normalized number u + = u / u τ and y + = y ′ u * /ν where y ′ is corrected with the roughness offset y 0 . κ is the Kármán constant (κ = 0.4), B is the smooth-wall intercept ( B = 5.5), ν is kinematic viscosity (ν = 1.011 × 10 –6 at a water temperature of 20 °C), and Δ U + is the roughness function which is variable-dependent on the wall situation. For the smooth wall, Δ U + and y 0 is zero and the log-law region is described by equation u / u * = 2.55 ln ( yu τ /ν) + 5.5.…”

Focus on Bioinspired Textured Surfaces toward Fluid Drag Reduction: Recent Progresses and Challenges

“…[ 191 ] Toussaint et al used a two‐component LDV system to measure the velocity components of the flow direction and wall normal. [ 192 ] Flack et al explored the influence of surface roughness skewness on fluid drag by two‐component LDV. The results showed that the surface friction drag tends to increase with increasing deflection.…”