Session A17: Boundary Layers: Roughness Elements I

How are flow structures related to drag forces and equivalent sandgrain height in turbulent flows over rough walls?

The Force Partitioning Method (FPM, Menon and Mittal, JFM 907, A37, 2021) is employed to dissect the hydrodynamic drag over rough walls in a turbulent channel flow. The contributions of distinct flow structures (vortices and straining regions) on the pressure drag are quantified using an auxiliary potential field (Φ), which depends solely on the roughness geometry. Four sources of drag are identified and their relative importance quantified. These are: Q-induced force (Q being the second invariant of the velocity gradient tensor), viscous momentum diffusion induced pressure force, and viscous shear force on the roughness elements and shear force on the base surface. Results indicate that the Q-induced force is the major contributing factor to pressure drag and is mainly produced by the strain-dominated, i.e. Q<0, regions upstream of each roughness element. Based on these insights, we explore characterizing the equivalent sandgrain height k_s for fully rough channel flows using information embedded in the Φ field. An empirical correlation based on several parameters that can be evaluated from  Φ is shown to predict k_s with rms and maximum errors of about 12 and 30 percent, respectively. The comparison used data from a suite of DNS cases (Jouybari et al., JFM, 912, A8, 2021).   

Numerical simulations of oscillating turbulent boundary layer flow over a spherical bed

Erosion, transport and deposition of sediments within a turbulent flow is a key problem which arises in several engineering applications and natural environments, such as fluvial or coastal beds. To date, a complete understanding of the fluid-particle interaction is still lacking, which hinders reliable predictions of the morphological evolution of the sediment bed. The flow dynamics plays a primary role in the initiation of sediment motion and affects the trajectory of suspended particles. In coastal environments, this problem is further compounded by the presence of the oscillating coastal bottom boundary layer generated by sea waves. In this work, we study an oscillating boundary layer over a bed of spherical particles through direct-numerical simulations. Spherical particles are an abstraction for sediments in non-cohesive silica sands encountered in many littoral zones. In the simulations, the sediments are treated with the immersed boundary method, which allows to explicitly resolve frictional and pressure forces due to the flow around the particle. The objective of this study is to investigate the effect of the oscillating boundary layer over the rough bed towards an improved understanding of sediment transport dynamics.   

An experimental investigation of the turbulent boundary layer over 2D roughness with localized blowing

The effects of localized blowing (injection) on the turbulent boundary layer over large-scale 2D k-type roughness was experimentally investigated using planar and volumetric particle image velocimetry. The roughness was composed of identical transverse square bars at a pitch to height ratio p∕h = 11. The experiments were conducted at a Reynolds number of 100,000, based on the boundary layer thickness and the free-stream velocity, and the bars occupied ∼14% of the boundary layer thickness. In addition to a baseline no-injection case, localized blowing through five small spanwise jets was considered for two streamwise locations and at two injection rates. The volumetric flow rate through the jets was below 0.12% of the overall volumetric flow rate, resulting in a small perturbation to the flow field. The results highlight the effects of localized blowing on the time-averaged flow, boundary layer characteristics, and Reynolds stresses. The effects of localized blowing on the boundary layer turbulence structure are also investigated thorough two-point correlations and proper orthogonal decomposition.   

Hydraulic Characterization of Sandpaper Roughness

Sandpaper roughness is often used as a boundary condition for rough wall flows. Friction curves for 220, 320 and 500-grit sandpaper will be presented from the hydraulically smooth to the fully rough flow regimes. The skin friction was determined from pressure drop measurements in a high Reynolds number channel flow facility (300 < Re_τ < 7000). The roughness function for sandpaper will be compared to the close-packed sandgrain surfaces used by Nikuradse, the reference surfaces for the equivalent sandgrain roughness height, k_s. Of interest is the shape of the transitionally rough regime and the roughness Reynolds numbers, k_s⁺, where the flow is no longer hydraulically smooth and becomes fully-rough. Mean flow and Reynolds stresses, obtained using a 2-D LDV system, for the 320-grit sandpaper at a Reynolds number range of 1000 < Re_τ < 6000 will also be presented.   

Direct numerical simulations of turbulent flows over permeable substrates

We conduct direct numerical simulations to fully resolve turbulent flows over and inside isotropic permeable substrates in a channel. The substrates are made up of periodically staggered solid cubes, and the immersed boundary method is employed to impose no-slip conditions on all solid surfaces. Simulation results of mean velocity profiles and turbulent statistics and spectra are presented under a variety of substrate properties, including depth, porosity, and inclusion size. The effects of surface transpiration and surface roughness on the overlying turbulence are analyzed and compared with simulations that include separately either effect.   

Modelling the meandering secondary flow over spanwise periodic roughness

Turbulent flow over heterogeneous roughness is of great importance to many engineering applications. Meandering secondary flows have been observed in experimental studies with spanwise varying roughness (Wangsawijaya et al., JFM, 2020). We seek to shed light on the origin of the meandering behavior by understanding the linear and non-linear interactions that drive this feature. Transpiration boundary conditions (Flores and Jimenez, JFM, 2006) are used to mimic the behavior of spanwise periodic roughness. Direct numerical simulations (DNS) of turbulent channel flow with transpiration at the walls are conducted at friction Reynolds number of 550 and show similar meandering secondary flow as observed in the experiments. The DNS snapshots are also Fourier transformed in time to enable direct comparison with the mode-by-mode analysis of the resolvent framework. The triadic interactions between compatible modes are analyzed and used to inform the construction of a 2D resolvent analysis (Chavarin and Luhar, AIAA Journal, 2020), where the spanwise periodic 2D mean profile is used. The 2D resolvent analysis is able to capture the dominant features of the flow at significantly reduced computation cost compared to the DNS.   

Surface layer response to heterogeneous tree1canopy distributions: roughness regime regulates secondary flow polarity

LES was used to model atmospheric surface layer flow over spanwise-heterogeneous vegetative canopies of elements with height h. Simulations used to study the flow response in the outer later and within the canopy due to spanwise and streamwise heterogeneity in the leaf area density. Synthetic trees were modeled using the well-established canopy drag model, which accounts for forcing due to the presence of trees. Previous experimental and simulation studies have shown the presence of Prandtl’s secondary flows of second kind due to spanwise heterogeneity in the aerodynamic roughness length. However, the role of streamwise gap on the flow dynamics has not been pursued. We took advantage of previous knowledge of the criterion for the presence of the secondary flows (δ-scale distance between the parallel streamwise aligned canopy rows) and varied the streamwise gap to quantify flow response. Results indicated that for δ1/h < 5 (d-type roughness), low momentum pathways (LMP) are present above the canopy row while the high-momentum pathways (HMP) are situated in the valley between the parallel rows. In contrast, for δ1/h > 5 (k-type roughness), the seccondary flow polarity reverses.   

Interaction of wall-bounded turbulence with flexible roughness

Interaction of wall-bounded turbulence with flexible roughness is investigated by direct numerical simulation (DNS) in turbulent channel flow with surface roughness elements consisting of rigid or flexible filamentous structures, uniformly implanted on both channel walls. DNS studies were performed using a lattice Boltzmann, Immersed-Boundary (LB-IB) method, employing a D3Q19, single relaxation time, BKG lattice model. A direct forcing IB scheme, employing reciprocal interpolation-spreading of operators, was adopted for the immersed-boundary scheme. The dynamics of the filaments was tracked by solving the Euler-Bernoulli equation, in which the inertia, tension, bending, and interaction forces were balanced. Simulations were performed in turbulent channel flows at a bulk Reynolds number of Re_b=7,200, corresponding to a friction Reynolds number of Re_τ0≈ 221 in a `base' turbulent channel flow with smooth, no-slip walls. Filamentous structures of height and spacings ranging from 4 to 16 in base flow wall units, with a density ratio of ρ_solid/(ρ_fluid ε_solid)≈100, where ρ_solid and ε_solid are the linear density and hydrodynamic area of the filaments, were investigated for dimensionless bending rigidities of 10^-5 ≤ K_b ≤ 10^-1 and dimensionless stretching coefficients of 0.1 ≤ K_s ≤1. It was found that while at higher bending rigidities the filaments simply act as roughness elements, at lower bending rigidities and for appropriate heights and spacings of the filaments, the filaments can interact with the near-wall vortical turbulence structures to result in a net drag reduction. The mechanism of drag reduction will be discussed   

Global stability analysis and direct numerical simulations of boundary-layer flows past roughness elements

Investigations of roughness-induced transition are conducted for a laminar boundary layer past an isolated cubic roughness element. The ratio between the roughness height and the displacement boundary layer thickness is h/{\delta^*}=2.86. Global linear stability analysis is performed using a time-stepper method in conjunction with the implicitly restarted Arnoldi iteration method. The base flow is computed using the selective frequency damping method. The global stability results using the base flows are compared to those using the mean flows obtained using time-averaging. The critical Reynolds number of global instability based on the roughness height is found to be Re_h=475. The leading unstable global mode exhibits varicose instability. The production terms in the disturbance kinetic energy equation show that the varicose mode extracts most energy from the central low-speed streak and the lateral streaks also make a contribution. The corresponding adjoint mode is located in the upstream vicinity of the cube as well as on top of the element, highlighting the most receptive regions to momentum forcing. The nonlinear evolution downstream of the cube is examined using direct numerical simulations. The effect of the roughness elements are examined in the presence of upstream forcing.