Turbulent flow over transitionally rough surfaces with varying roughness densities

Abstract

We investigate rough-wall turbulent flows through direct numerical simulations of flow over three-dimensional transitionally rough sinusoidal surfaces. The roughness Reynolds number is fixed at $k^{+}=10$, where $k$ is the sinusoidal semi-amplitude, and the sinusoidal wavelength is varied, resulting in the roughness solidity $\unicode[STIX]{x1D6EC}$ (frontal area divided by plan area) ranging from 0.05 to 0.54. The high cost of resolving both the flow around the dense roughness elements and the bulk flow is circumvented by the use of the minimal-span channel technique, recently demonstrated by Chung et al. (J. Fluid Mech., vol. 773, 2015, pp. 418–431) to accurately determine the Hama roughness function, $\unicode[STIX]{x0394}U^{+}$. Good agreement of the second-order statistics in the near-wall roughness-affected region between minimal- and full-span rough-wall channels is observed. In the sparse regime of roughness ($\unicode[STIX]{x1D6EC}\lesssim 0.15$) the roughness function increases with increasing solidity, while in the dense regime the roughness function decreases with increasing solidity. It was found that the dense regime begins when $\unicode[STIX]{x1D6EC}\gtrsim 0.15{-}0.18$, in agreement with the literature. A model is proposed for the limit of $\unicode[STIX]{x1D6EC}\rightarrow \infty$, which is a smooth wall located at the crest of the roughness elements. This model assists with interpreting the asymptotic behaviour of the roughness, and the rough-wall data presented in this paper show that the near-wall flow is tending towards this modelled limit. The peak streamwise turbulence intensity, which is associated with the turbulent near-wall cycle, is seen to move further away from the wall with increasing solidity. In the sparse regime, increasing $\unicode[STIX]{x1D6EC}$ reduces the streamwise turbulent energy associated with the near-wall cycle, while increasing $\unicode[STIX]{x1D6EC}$ in the dense regime increases turbulent energy. An analysis of the difference of the integrated mean momentum balance between smooth- and rough-wall flows reveals that the roughness function decreases in the dense regime due to a reduction in the Reynolds shear stress. This is predominantly due to the near-wall cycle being pushed away from the roughness elements, which leads to a reduction in turbulent energy in the region previously occupied by these events.

The minimal-span channel for rough-wall turbulent flows

“…10 1 10 2 10 3 10 0 10 1 10 2 10 3 λ + y z + 10 1 10 2 10 3 10 0 10 1 10 2 regime, which leads to a weakening of the near-wall cycle (MacDonald et al 2016). As it hasn't been destroyed, the buffer-layer streaks and quasi-streamwise vortices are active and so the same trends as the smooth-wall flow are observed.…”

Moving beyond Moody

“…Realistic roughness was studied by Yuan & Piomelli (2011) using LES for roughness replicated from hydraulic turbine blades, with surface features parametrically changed to study the influence of roughness slope on the surface drag. Three-dimensional sinusoidal roughness in the transitionally rough regime was investigated using direct numerical solution (DNS) by Chan et al (2015) and MacDonald et al (2016). It was shown in these studies that the roughness function could be accurately determined using the minimal-span channel technique which allows for low Reynolds number simulations (Re τ = U τ h/ν = 180, where h is the channel half height).…”

Controlling Heat Transport and Flow Structures in Thermal Turbulence Using Ratchet Surfaces

“…Indeed, the study of surface roughness effects in wall-bounded turbulent flows has been an area of intense research (see e.g. some recent work [1][2][3][4][5][6][7][8], the reviews [9,10], and the textbooks [11,12]). Similarly, several studies have been conducted on turbulent thermal convection over rough plates [13][14][15][16][17][18][19][20].…”