Session G23: Boundary Layers: Roughness Elements I

Secondary motions in stratified flows

A simple model for secondary motions over heterogenous surfaces in stably-stratified turbulent flows is presented. The model is an extension to the Meyers et al. (2019) model which considers the neutral case only. Starting from the RANS equations that include buoyancy, the homogenous background is separated from the dispersive secondary motions. The dispersive equations are linearized, and the superposition principle is used to express solutions per wavenumber. The new model is validated against DNS simulations of a stable channel flow with heterogenous surface temperatures (Bon & Meyers, 2022). Including buoyancy improves the model predictions for weak secondary motions and strong secondary motions away from the surface. However, the model fails to predict the strong secondary motions near to the surface if zero background shear is assumed. Allowing the shear to be non-zero enhances the model predictions. The non-zero shear terms lead to a two-way coupling between vertical velocity and temperature, and a one-way coupling between vertical velocity and vorticity, which seem necessary for strong secondary motions.

Meyers J, Ganapathisubramani B & Cal RB 2019 On the decay of dispersive motions in the outer region of rough-wall boundary layers. J Fluid Mech 862.

Bon T & Meyers J 2022 Stable channel flow with spanwise heterogeneous surface temperature. J Fluid Mech 933.   

Periodic reversal of mean flow within the transitional roughness regime in atmospheric surface layer flow

Large-eddy simulation is used to model turbulent channel flow where the channel bottom is mounted with arrangements of tree canopy elements. These elements are arranged in rows such that rows are parallel to the mean flow direction with a domain scale spanwise gap, $\delta_2/\delta$, where $\delta$ is the channel height. Further, canopies in individual rows are separated by a streamwise gap, $\delta_1/h$, where h is the canopy height, which regulates the streamwise roughness regimes, d-type, and k-type. Such an arrangement of canopy elements results in a spanwise heterogeneity in the aerodynamic roughness length and introduces undulations in the mean flow along the transverse direction. In the present work, we used a set of simulations with a scaled spanwise gap of 1.25, and 1.65 and attempted to understand concurrent effect by varying $\delta_1/h$ on the mean and secondary flows. We collected evidence of a periodic reversal in the mean flow followed by secondary flow reversal. We noticed a periodic sign reversal in the streamwise velocity fluctuations along with reversal in secondary cells. By that, we mean a temporal periodic upwelling and downwelling of low and high momentum fluid packets respectively.   

Restricted Nonlinear Large Eddy Simulations of Turbulent Flow over Spanwise Heterogeneous Strip Roughness

Turbulent flow over heterogeneous rough surfaces arise in a wide range of natural and engineering applications ranging from atmospheric boundary layer flow over a forest or crop fields and flow over bio-fouled ship hulls to engineered herringbone riblets to induce turbulent drag reduction. This range of applications hampers a full understanding of the phenomena due to the difficulty in simulating the vast range of phenomena of configurations which roughness topographies can take. Recently, the Restricted Nonlinear Large Eddy Simulation (RNL-LES) framework has been applied to study flow over spanwise heterogeneous strip roughness at arbitrarily high Reynolds numbers [1]. In this work, we take advantage of the computational tractability of the RNL-LES to perform an extensive parametric study of flow over spanwise heterogeneous strip roughness, varying number of repeating roughness units and strip widths. We highlight the importance of circulation in this flow and use the data from the parametric sweep to characterize the influence of intensified secondary flow mixing has on turbulent statistics and momentum transfer. We then use these results to inform a parametric model to predict secondary flow circulation for a given roughness topography.   

Reynolds number effects on secondary flows over ridge-type surfaces

Secondary flows can be generated by imposing spatial shear stress anisotropy using spanwise heterogeneous surfaces, commonly divided into ridge-type surfaces (spanwise variation in height) and strip-type surfaces (spanwise variation in skin friction). Several studies have looked into the flow structure that determine the nature and strength of the generated secondary currents over both of these surface types. However, information on the variation of global friction as well as the nature of these secondary flows across a range of Reynolds numbers is scarce.

In this study we investigate secondary flows generated by a ridge-type surface in a L ≈ 130H long water channel facility with a rectangular cross-section W/H ≈ 8. The ridge width Wp ≈ 0.8δ, the spanwise centre-to-centre spacing S ≈ 1.6δ, and the ridge height h/δ ≈ 0.1, where δ = H/2 is the channel half-height. The channel centerline pressure gradient is measured starting from L ≈ 65H to the channel outlet. Stereoscopic PIV in a spanwise—wall-normal plane L ≈ 110H downstream of the channel inlet is used to obtain the three-component velocity field. In this talk we present results of skin-friction against bulk Reynolds number and explore the structure of the produced secondary flows over a range of bulk Reynolds numbers.   

Scale Interactions in Flow Overlying Spanwise-, Streamwise-, and Obliquely-Varying Surface Roughness

Flow overlying streamwise-elongated ridge-type (spanwise heterogeneous) roughness features the formation of turbulent secondary flow of streamwise aligned counter rotating vortex cells flanking and centering on individual ridges. This flow phenomenon alters the momentum transfer and turbulence production relative to smooth-wall turbulence. In practical applications, the predominant direction of roughness variability can change relative to the oncoming flow direction. In the extreme case, when the flow orientation is perpendicular to the ridges, the flow is dominated by streamwise repeating wakes tripped by the ridges when the spacing of the ridges is fully separated and the height of the ridges is not very small relative to the boundary layer thickness. In more scenarios, the flow is likely to orientate in an oblique angle to the ridge-type roughness, and it is observed that in this case the flow reflects a mixture of pure secondary flow and wake shedding from upstream ridges. In this work, high-frame-rate stereo PIV data and high-frame-rate dual-camera big/small field of view planar PIV data are used to study the scale interactions in turbulent flow overlying spanwise-, streamwise-, and oblique-ridge-type roughness, and to investigate how orientation angle influences the dominant flow characteristics. A pointwise method of modulation analysis is used to quantify the degree of interaction between inner and outer scales. The spatio-temporal nature of PIV data further enables a conditional average method to extract scale interactions in a spatio-temporal sense.