Session T08: Boundary Layers: Roughness Elements II

Direct numerical simulations of turbulent boundary layers over calcareous biofouling

It is well established today that biofouling on ships increases the hull roughness, causing increased frictional resistance and fuel consumption, as well as decreased top speed and range.  Today there is a pressing need to develop predictive tools that can assess the impact of various types of fouling and coverage level on the frictional resistance of naval vessels.  Most scaling laws and correlations integrated in the models utilized in such assessments were not developed with sufficient data representative of ship roughness. Surfaces covered by barnacles and/or tubeworms, for example, have much higher skewness (Sk) and lower effective slope (ES) than other surfaces used to develop existing correlations.  The primary goal of this work is to identify geometric parameters on surface roughness topologies found on ships that encapsulate the drag-producing physics.  In particular, we will report Direct Numerical Simulations (DNS) of turbulent boundary layers over biofouled surfaces synthezied using barnacles and/or tubeworms. A highly-efficient, in-house, solver based on an immersed boundary formulation is utilized.  We will report detailed flow statistics for a variety of surfaces while particular emphasis will be placed on the identification/impact of the secondary flow patterns on the flow statistics and outer-layer similarity. 

 

    

Flow channeling on airfoils with rough leading edges

In Kumar et al. (J. Turb., vol. 22(11), 2021, p. 735-760), we studied the flow over an airfoil with leading-edge roughness due to ice depositions. We found stationary spanwise inhomogeneities in the form of alternating regions of fast and slow-moving fluid, which were termed ``flow channels''.  In the present study, we investigate further the channeling phenomenon by performing simulations of a NACA 4412 airfoil at three angles of attack.  Downstream of the roughness zone, the fast regions slow down under the action of hairpin vortices generated by the roughness elements and merge with neighboring slow regions.  The flow channels remain coherent over the entire airfoil and affect the trailing-edge separation.  With an increasing angle of attack, the intensity of flow-channeling can increase or decrease depending on the topology of the leading-edge roughness. Its effect on the trailing-edge separation, however, remains significant. The mean separation line is highly distorted, and the separation length can vary by up to 30% along the span.   

Experimental Investigation of interaction between the flow field and wall deformation in turbulent boundary layers over compliant surfaces

Recent investigations of turbulent boundary layers over compliant surfaces have revealed the dominant effect of flow features in the logarithmic layer on the wall deformation. Two-way coupled interactions occur when the deformation magnitude becomes comparable to the viscous wall unit. The present simultaneous measurements of time-resolved volumetric flow field and spatial distribution of wall deformation are performed using an integrated system involving tomographic PTV for measuring the flow, and Mach Zehnder interferometry for mapping the wall deformation. The measurements are performed in a refractive index matched water tunnel at Re_τ ranging from 3,000 to 9,000, and E/ρU² (E- Young’s modulus) from 1.8 to 22. The unstructured velocity and material acceleration are interpolated onto a structured grid using a physics-based constrained cost minimization method. The pressure field is computed by spatial integration of the material acceleration using a GPU-based omni-directional code. Spectral analysis and conditional statistics are used for characterizing the coupling between flow variables (velocity, vorticity, and pressure) and deformation features, highlighting mechanisms that increase the turbulence level and modify the mean velocity profile near the wall.   

Data driven prediction of roughness-sublayer mean velocity profiles

Most existing roughness-unresolved models of turbulent boundary layers depend on a single roughness length, the equivalent sandgrain height. Though calibration may yield accurate wall shear stress, it does not guarantee accurate prediction of the wall-normal profile of mean velocity below the logarithmic layer, which is important when heat/mass transfer or detailed roughness sublayer (RSL) flow is of interest.

Our earlier work introduced and validated, for a few roughness geometries, an algebraic sublayer velocity profile model (Brereton et al. Phys. Fluids, 33:065121, 2021).

We extend this work to predict RSL velocity as a function of roughness geometrical characteristics, for a wide range of roughness geometries.

Leveraging DNS data of fully developed, fully rough channel flows, deep neural networks, Gaussian process regression, support vector regression are trained to predict the velocity profiles.

These methods are shown to give overall good predictions, though the errors are not small for a few surfaces. Improvement of the predictions may be achieved by integrating additional flow physics. In addition, feature engineering techniques are used to identify roughness features important for the RSL mean flows.   

Commercial Sandpaper and Nikuradse Sandgrain Roughness: Similarities and Differences

Sandpaper is commonly employed as a wall roughness in experiments and even simulations.  This is largely due its widespread availability, range of available roughness heights, and strict manufacturing standards.  Its name often links it to the classic pipe flow experiments of Nikuradse (1933) which used close-packed sand with a narrow grainsize distribution.  Nikuradse’s experiments led to the adoption of the equivalent sand roughness height, k_s, as a hydraulic length scale to compare the drag associated with a given surface roughness.  Recent results reveal that while commercial sandpaper shares a number of similarities with Nikuradse sand, it also displays a number of notable differences.  Similarities include the display of hydraulically-smooth behavior at small but finite roughness Reynolds number and a dip in the skin-friction coefficient in the transitionally-rough regime.  Differences include a k_s that is significantly larger than the median grit size for commercial sandpaper.  This talk will discuss both the similarities and differences as well as the reasons for each.   

Effect of Boundary Layer Thickness on the Estimation of Equivalent Sandgrain Roughness

The equivalent sandgrain roughness, k_s, is routinely extracted from velocity profile data.  To obtain k_s, fully rough conditions should exist, and it is recommended that the ratio of the boundary layer thickness, δ, to k_s should be at least 40. In practice, however, k_s is often found for conditions with δ/k_s<40. Experiments were conducted in boundary layers over a surface with uniform stochastic roughness. Profiles of mean velocity and turbulence quantities were acquired at twelve streamwise locations. The ratio of δ to the rms roughness height varied from 55 to 141, and k_s was approximately 4 times the rms height. In the outer region of the boundary layer the mean velocity and turbulence results were found to be invariant with Reynolds number when scaled using δ and the friction velocity, and exhibited similarity with equivalent smooth-wall boundary layer quantities. The k_s values determined from the profiles were found to vary noticeably and inversely with δ when δ/k_s was less than about 40. This suggests a possible need for a modified correlation to account for the δ/k_s dependence. Such a correlation might prove useful for extracting k_s values from low δ/k_s data, and for predicting the effect of roughness on boundary layers with varying δ/k_s.   

Reynolds number effects on turbulent flow over pyramid roughness with varied solidity

Direct numerical simulations (DNS) of turbulent channel flow over pyramid roughness are performed over a range of friction Reynolds numbers. The rough surfaces are inspired by the experimental work of Schultz and Flack (Phys. Fluids, 21:015104, 2009) and are composed of square pyramids in regular arrangements. Pyramids, unlike uniformly sized cubic roughness elements, allow for independent variation of frontal and plan solidity. Nine different rough surfaces are investigated. The height of the roughness elements is kept constant in all cases, while frontal and plan solidities of the roughness are systematically varied focussing on the 'waviness' regime, i.e., the low frontal solidity range. The results show that the roughness function increases with increase in frontal solidity and decrease in plan solidity. For most surfaces, the mean velocity profiles collapse onto the smooth wall data when plotted in defect form. However, for several cases a clear departure from the outer layer similarity is present, and this departure becomes more prominent at higher Reynolds number. In these cases, the spanwise peak-to-peak distance between pyramid elements is comparable to the channel half-height inducing significant levels of the dispersive stresses well above the roughness canopy.   

Turbulent channel flow response to elliptical high-roughness patches: a "virtual laboratory" for studying the evolution of large-scale motions

The outer layer of the fully-rough wall-sheared turbulent flow consists of uniform momentum zones (UMZs) of momentum excesses and deficits alternating throughout the vertical direction with a 'stair-case' pattern. This outer-layer flow structure was recently revealed as the outcome of the inner-layer interactions (Anderson and Salesky, 2020: J. Fluid Mech. 906, A8-1—13) interpreted from direct numerical simulation (DNS) of fully-rough channel turbulence (Lee & Moser, 2015: J. Fluid Mech. 860, 886–938). In Zheng and Anderson 2022, the origination of the UMZs is further specified as the interaction from roughness sublayer, utilizing conditional sampling from large eddy simulation (LES) of fully-rough turbulent channel flow. To implement the condition that previously virtualized the phase-locked UMZs, the ongoing work leverages the patch method (with high-roughness patch of elliptical shape) for the extraction and revelation of the roughness impacts. Gaussian distribution of the roughness in streamwise and spanwise dimensions is also included as a counterpart for local-stress-based conditional sampling. We speculate this will be substantial proof in addition to the previous discussion of the UMZ origination.   

In search of a universal rough-wall model

Predicting the drag of the flow past a rough surface is a challenging problem but also of great practical use in engineering and geophysics. There are various types of surface roughness from the Gaussian-spectrum-like random surface to the regular cubical roughness array, and their effects on increasing the drag are highly dependent on the detailed geometry, which makes the prediction of the drag using a single universal model extremely difficult. A critical assessment of the existing models is much helpful to provide a prospective direction for future investigations. In this work, we evaluate the performance of 7 existing rough-wall models based on the flow data of 68 rough surfaces. The seven predicting models include two physics-derived models, three correlation-based models and two data-driven machine learning models. The rough surfaces include both random and regular roughness types which cover a wide range of the roughness parameters (the roughness height, coverage density, skewness, the effective slop etc). The results indicate that the effectiveness of the correlation-based model is limited to a small range of roughness parameters, but the physics-based model provides a much better prediction for a broader range, while the accuracy of the data-driven machine learning models are highly dependent on the data that used to train the neural network.   

On the Interaction of a Blasius Boundary Layer with a Roughness Element: A Comparison of Experiments and Simulations for Steady Flow

The interaction of a Blasius boundary layer developing on a flat surface with a cylindrical roughness element of small aspect ratio and a height smaller than the local boundary layer thickness is studied for steady flow. The flow develops a horseshoe-shaped vortical structure around the roughness element as well as a recirculation zone directly downstream of the roughness element. This flow configuration was studied experimentally in a laminar water channel by means of temperature-sensitive paint (TSP) (J. Lemarechal et al., 2018), visualizing the thermal footprint of the flow structure applied to a heated surface. The simulations using Ansys CFD aim to reproduce the previous experiments and to provide additional information inaccessible to surface-based measurement techniques. This contribution will focus on the development and validation of the simulation approach, including the choice of domain size and resolution as well as the heat flow from the surface to the fluid domain. The simulations match the experimental results well both qualitatively and quantitatively. For example, a comparison of the surface temperature map in the roughness element’s wake region yields a correlation coefficient of about 0.85 between the simulations and experiments.

    

On the effect of filament inclination on the different regimes of canopy flows

We have performed high-fidelity simulations of turbulent open-channel flows over submerged rigid canopies made of cylindrical filaments of fixed length h/H = 0.1 with mean spacing of S/H = 0.066 (with ‘H’ being the open channel height). The filaments are flush mounted perpendicular to an impermeable wall. The shape of the canopy was modulated by changing the inclination of the filaments (angle formed by the filaments with the mean streamwise direction) thus modelling the deformation of very soft filaments under the action of a unidirectional mean flow. The inclination, used as a free parameter, dictates the solidity of the canopy, yielding to different flow regimes (sparse or dense). The effect induced by inclining the canopy can also be interpreted as a modulation of the diagonal elements of the permeability tensor the canopy seen as a porous medium. These changing conditions lead to new flow regimes configurations that, so far have not been described in the literature. We have considered six inclinations in the range θ between 0° and 90°, with θ = 0° and θ = 90°, representing normal wall mounted and wall parallel conditions. We find that when the canopy is inclined, the behaviour of the flow (inner and outer) exhibits a drastic changes that cannot be predicted using the notion of solidity as unique parameter that determines the flow behaviour.