On The Effects of Roughness Parameters on Turbulent Boundary Layer Flows

Abstract

Turbulent boundary layers (TBLs) are a well-known phenomenon in fluid dynamics and are observed in various transport, such as ships and aeroplanes. The majority of wall-bounded flows in engineering applications possess a rough surface, such as the growth of bio-fouling on ship hulls or surface erosion of wind turbine blades. The existence of surface roughness significantly influences the boundary layer flow and affects the heat and momentum transfer. The increase in drag caused by roughness leads to greater fuel consumption and emissions in transportation. Therefore, comprehending the impact of roughness on boundary layer flows is vital for enhancing energy efficiency and decreasing environmental impact across multiple industries. One of the principal objectives of rough wall fluid dynamics research is to determine the drag penalty of surfaces exclusively based on their topographical characteristics. Nevertheless, there is no consensus regarding the most important length scale or roughness parameter that accurately describes a surface in relation to friction drag, and several studies have attempted to identify it. This study investigates the impact of various two-dimensional (2D) and three-dimensional (3D) roughness geometries on turbulence statistics and drag coefficient (Cf ) in a zero pressure gradient (ZPG) turbulent boundary layer (TBL), using single hotwire anemometry (HWA). The research involves the use of three types of 2D roughness elements, namely circular rods, 3D printed triangular ribs, and computerised numerical control (CNC) machined sinewave surfaces with different heights and streamwise spacings. Additionally, three types of 3D sinewave rough- ness are examined, including isotropic 3D sinewave surfaces with equal streamwise and spanwise wavelengths, anisotropic 3D sinewave surfaces with different streamwise and spanwise wave- lengths, and isotropic 3D sinewave surfaces with different roughness skewness values (positive, negative, and zero). The turbulence statistics and drag coefficient are evaluated to determine the effects of the various 2D and 3D roughness geometries in the ZPG-TBL flows. In the fully rough regime, the friction Reynolds number (Reτ ) no longer affects Cf . Compared to smooth wall profiles, all types of roughness cause a downward shift in the wall- unit normalised streamwise mean velocity profile. When the roughness height and streamwise spacing are the same, 2D roughness has higher Cf and roughness functions (∆U +) than 3D roughness. This is due to the larger blockage area imposed by 2D roughness, which forces the fluid to flow over the roughness elements. Conversely, the fluid can flow around and above the roughness elements of 3D roughness. As TBL develops from a transitionally to a fully rough regime, the inner peak of turbulence intensity profiles for 2D surface roughness gradually reduces with increasing Reynolds number. However, the inner peak disappears entirely in the fully rough regime, and the profiles only exhibit an outer peak, located at a wall-normal location of approx- imately y δ ≈ 0.06 where δ represents the boundary layer thickness. These findings suggest that Townsend’s similarity hypothesis for 2D surface roughness is relatively well approximated in the outer region of the flow, as evidenced by the collapse of velocity defect, turbulence intensity, skewness, and flatness distributions when scaled with δ, The streamwise spacing to height ratio (s k) has a greater impact on ∆U + and C than the spanwise spacing to height ratio (sz k) for 3D sinewave roughness. However, sz k substantially affects streamwise turbulence intensities in the log and outer layer. Surfaces with positive roughness skewness (ksk) exhibit higher drag, resulting in a more significant downward shift compared with zero and negative roughness skewness. Cf decreases as ksk decreases. The increase in the percentage of Cf and ∆U + is significantly higher when moving from negative to zero roughness skewness than when moving from zero to positive roughness skewness. The shape factor (H) was identified as a suitable scaling parameter for improving the data collapse of the diagnostic plot for both 2D and 3D roughness. Numerous studies have been conducted to determine the most significant surface pa- rameter in wall-bounded turbulence. The concept of equivalent sand-grain roughness (ks) was introduced by Nikuradse (1933) to standardise different types of roughness and serve as an in- put parameter for predictions of ∆U +. A chronological compilation of roughness correlations is presented, providing details on the parameter ranges and types of roughness used during their development. The research findings indicate that in the fully rough regime, for 2D roughness, the roughness skewness ksk and the streamwise effective slope ESx are significant parameters that influence the drag coefficient Cf . These parameters have been incorporated into a new expression for ks that is normalised with the maximum peak to valley roughness height (kt). Similarly, for 3D roughness in the fully rough regime, a correlation has been developed based on ksk and ESx to predict ks normalised with the root mean square roughness height kq . Despite the fact that this correlation is restricted to 3D surface roughness, which is a more realistic representation, the model demonstrated a high level of accuracy in predicting ks for over 120 distinct rough surfaces, with a coefficient of determination (R2) of 0.96, The R2 value, is a statistical measure that represents the proportion of the variance in the dependent variable that is explained by the independent variable(s) in a regression model. It is a measure of how well the regression line fits the data.