Session J08: Boundary Layers: Flow Control

Assessment of the Darcy-Brinkman model for the characterisation of flows in permeable substrates

In this work we aim to characterise the flow within matrices of parallel fibres, motivated by their potential for turbulent drag reduction (Gomez-de-Segura et al., J. Fluid Mech., vol 875, 2019, pp. 124-172). For this we conduct fully resolved simulations of the microscale flow within the substrate, driven by shear and/or pressure, both along and across the fibres, for pore sizes small enough to assume Stokes flow. As expected, the component of the flow driven by pressure is well characterised by a Darcy description, but we also show that the component driven by shear follows a self-similar, exponentially decaying form, and is thus well characterised by a Brinkman description. This is the case for the longitudinal flow for fibres of any size, and for the transverse flow for fibres of small size. Beyond a threshold size, however, although the flow remains exponential in magnitude, it experiences regions of reversed direction, which a Brinkman description would fail to capture. For structured arrangements of fibres, the macroscopic Darcy-Brinkman description breaks down near interfaces with free-flow regions, and a jump in flow variables, particularly in shear, is observed, which can be traced to the stress exerted on the flow by the last row of fibres. For disorganised arrangements, however, no such discrete row of fibres exists, no jump in flow variables is observed, and therefore a Darcy-Brinkman description characterises well both the flow deep within the substrate and at the interface.   

Laminarizing effect of nonlinearly saturated crossflow vortices sustained by a sinusoidal roughness

Turbulent transition of three-dimensional boundary layer can be delayed by an artificial leading edge roughness that excites a less unstable (or subcritical) crossflow mode. This mode wins the competition against the most linearly-unstable mode and dominantly generates crossflow vortices in its nonlinear saturation phase. The growth of the most unstable mode is then suppressed, because the mean boundary layer flow is nonlinearly modified due to crossflow vortices. However, crossflow vortices tend to decay shortly after the saturation phase and hence the laminarizing effect naturally occurs only in a limited region. In this study, we propose a sinusoidal roughness which can sustain crossflow vortices for a long distance. When the ridge lines of the sinusoidal roughness are aligned to a specific streamline within the boundary layer, crossflow vortices do not decay but continue to be saturated nonlinearly over a wide range of the chord position. The boundary layer is strongly and widely stabilized by them and the crossflow-induced transition can be completely suppressed or significantly delayed.   

Boundary-layer manipulation using shape-programmable materials

Recent advances in materials science open new possibilities for developing programmable surfaces to aid enhanced near-wall flow control capabilities. We propose a novel approach to manipulating boundary layers via a shape morphing programmable system that exploits liquid metal microfluidic networks embedded in an elastomer surface. The system can achieve a unique set of properties with electromagnetic forms of actuation induced by the distributed Lorentz force. The structure can quickly morph into a diverse group of continuous complex 3D geometry from a 2D planar configuration at highly controllable changes in amplitude and frequency. The interaction between programmable systems and various flow types is experimentally quantified using high-speed digital image correlation and particle image velocimetry. Different low-order decompositions tools are used to extract energetic coherent responses in the form of single and multi-scale perturbations. This multidisciplinary work aims to provide engineering and fundamental foundations for applications in future vehicles.

    

Assessment of Clauser chart method for determination of drag on superhydrophobic surfaces

Superhydrophobic surfaces (SHS) are patterned hydrophobic surfaces that reduce skin friction drag via the entrapment of air pockets when immersed in water. Experiments of patterned SHS have shown that pressure control can sustain wall-attached air films in turbulent flow. Additionally, the dynamic modulation of air film height can further enhance drag reduction, as measured by the Clauser chart method. In this study, we numerically simulate the impact of air film oscillation on drag reduction in a turbulent channel. We quantify how the Clauser chart method, which assumes a log layer region characteristic of smooth walls, performs on patterned SHS, as compared to direct measurement of wall shear stress. We present potential modifications to the Clauser chart method for SHS, motivated by the modified Clauser chart method proposed for rough walls (Perry and Li, J. Fluid Mech. 2006), and discuss relevant findings on the flow structure over both flat and pressure-modulated superhydrophobic surfaces.   

Turbulent skin friction drag reduction over dynamically rough superhydrophobic surfaces

The presence of dynamic wetting conditions on superhydrophic (SH) surfaces can lead to dynamically rough superhydrophobic surfaces. The dynamics of turbulence in the presence of such rough SH surfaces is investigated by direct numerical simulation (DNS) using free-energy lattice Boltzmann (FELB) methods in turbulent channel flows with arrays of SH longitudinal microgrooes on both walls. Simulations were performed in channel flows at a bulk Reynolds number of Re_b = 7200 (Re_τ0 ≈222), with SH longitudinal micrgrooves of groove width 15 ≤ g⁺⁰ ≤ 64 in base-flow wall-units, at nominal solid fractions of φ_s,n = 1/2 and 1/16, and groove aspect ratios of d/g = 1, with a viscosity ratio of N = μ_liq/μ_vap≈55, Weber number of We_τ0 = ρ_liq u_τ0 ν_liq/σ ≈ 3:65x10^-3, and advancing and receding contact angles of θ_adv = 112^o & θ_rec = 106^o. It is observed that dynamic surface roughness can result in drops of ~ 3 - 17% and ~ 11 - 35% in the magnitude of drag reduction (DR) at φ_s,n=1/2 and φ_s,n=1/16, respectively, compared to the drag reductions obtained with smooth, shear-free, superhydrophobic interfaces. These drops in DR arise primarily from dynamic contact line motion, through (i) an increase in the effective solid fraction, from the nominal solid fraction, φ_s,n, to a wetted solid fraction, φ_s,w > φ_s,n, which the fluid is exposed to, and (ii) the formation of streamwise corner vortices due to the motion of the interface and the contact line, which can act as surface roughness. The former leads to drops of 10% - 35% in the effective streamwise slip velocity, whereas the latter leads to enhancements of up to 200% in the effective spanwise slip. The scaling laws for DR, streamwise slip and spanwise slip, as well as the detailed turbulence statistics in the presence of dynamic rough SH surfaces will be discussed.   

Numerical Study of Turbulent Characteristics behind a Novel Vortex Generator

A microstructure consisting of three control surfaces: two sidewalls and a top one, is proposed for flow control. The structure is expected to act as a microscale filter for turbulent motions of certain scales and a generator of specific vortical structures. The angle of attack can be adjusted for each control surface to modify the internal passage of the structure and eddies shed from the three surfaces. DNS of this type of structures in a zero-pressure-gradient turbulent boundary layer at Reynolds number $Re_\delta = U_\infty \delta /\nu = $11,000 were performed. Depending on the angle of attack of the control surfaces, the flow forms separating shear layers either around the outside of the structures or within their internal passage. The mean separation is highly three-dimensional, especially along the two side walls due to the mean velocity gradient in the wall-normal direction. The results show that complex interactions occur between the leading- and trailing-edge shear layers of each control surface, as well as at the structure-wall junction. The Reynolds stresses and TKE budgets will be discussed by comparing them with conventional vortex generators and solid cubical objects.

The authors acknowledge support from NSF Grant CBET-2039433.   

Analysis of underlying physics of drag alteration by riblets using Restricted nonlinear simulations

Riblets (micro-grooves) have been shown capable of altering skin-friction drag in wall-bounded turbulence. Although much is known about the mechanisms underlying drag reduction and its breakdown, the physics associated with the full range of behaviors across a variety of geometries needs further characterization. To this end we exploit the computational advantages of the Restricted nonlinear (RNL) framework to perform simulations over a range of riblet geometries. This reduced order model has been shown to accurately predict salient features such as the roughness function and secondary flow structures.  We use the resulting data to analyze stresses and other statistical quantities of the flow field in the vicinity of the riblets in order to investigate the flow structures.  We also consider these flows at higher Reynolds numbers via an augmented RNL (ARNL) that captures a wider range of scale interactions than the traditional RNL model through the addition of nonlinear interactions at intermediate streamwise scales. The resulting simulated flow fields are compared against direct numerical simulations of flow over riblets at moderate and high Reynolds numbers. 

    

The influence of frontal solidity on fully rough heat transfer modeled through an exposed and sheltered flow dichotomy

The challenge of predicting rough-wall heat transfer is embodied by the many factors which must be considered: the working fluid dependence (Prandtl number Pr), the flow regime (roughness Reynolds number k⁺), and further parameters required to characterize any given roughness. Here, we will focus on one particular geometric parameter in the frontal solidity, Λ. With direct numerical simulation data, we will show that in the fully rough regime (high-k⁺), the local heat transfer can be meaningfully decomposed into two distinct regions: exposed regions following a Reynolds Analogy behaviour and sheltered regions where the heat transfer is spatially-uniform. The total heat transfer follows as a sum of these mechanisms, with their contributions weighted by Λ. We will present a model for the total heat transfer by considering different heat transfer laws in exposed and sheltered regions.   

Model for turbulent drag reduction of superhydrophobic surfaces in large Reynolds number flows

Superhydrophobic surfaces (SHS) can reduce drag for flows over surfaces owing to a gas layer trapped in the SHS texture. Drag reduction (DR) by SHS could significantly reduce energy consumption and carbon emissions in industrial and naval applications such as maritime shipping, which accounts globally for 2% CO2 and 13% NOx and SOx emissions. Current models predict that DR increases relatively rapidly with friction Reynolds number (Re_τ) with DR -> 100% as Re_τ -> ∞. This has been questioned in light of recent numerical and experimental data showing a departure from this trend, with possible saturation in DR, and a regime transition at large Re_τ when the SHS texture size is of the order of P⁺ ~ 10 (in wall units). For P⁺ >> 10, we model the flow over parallel SHS ridges in a plane channel of height  using a turbulent heterogeneous layer near the SHS, together with a turbulent homogeneous layer with a shifted log law in the bulk. Using conservation of mass, momentum and continuity of velocity, we predict DR as a function of all input parameters. In the limit parallel SHS ridges in a plane channel of height 2H using a turbulent heterogeneous layer near the SHS and a turbulent homogeneous layer as a shifted log law in the bulk. Using conservation of mass, momentum and continuity of velocity, we predict DR as a function of all input parameters. In the limit P/H<<1, which corresponds to most applications, our model predicts a DR that asymptotically approaches the gas fraction, with a logarithmic dependence on P/H and Re_τ.  Our prediction agrees with all available numerical data, where the DR shows a logarithmic increase towards the gas fraction as P⁺, Re_τ->∞.  Our model provides the physical mechanisms for this distinct regime of SHS DR at large Reynolds numbers, and testable predictions for the design and optimisation of SHS.   

A systematic numerical investigation of turbulent channel flow over hydrophobic bottom wall: an analogue of rough wall turbulent boundary layer

Hydrophobic surfaces (HSs) can reduce the surface drag because air bubbles trapped inside their micro-grooves form shear-reduced or shear-free regions when water passes over. The corresponding drag reduction mechanism is affected by turbulence, slippery effects, and the so-called “roughness” effects because of the heterogeneity due to the existence of the hydrophobic region. To systematically study the roles of those effects, we carry out direct numerical simulations (DNSs) on turbulent channel flows over various micro-ridge structured HSs at the bottom wall. We explore slippery effects in both the streamwise and spanwise directions by comparing the results with those where only streamwise slip exists on bubble surfaces. To discover the roles of turbulence, spatial heterogeneity, and slippery effects on drag reduction, an equation relating the modified roughness function to Reynolds, dispersive, and wall shear stresses is derived and analyzed based on DNSs at different ridge-groove widths of HSs and Reynolds numbers. Although we neglect three-dimensional effects such as curvature of air-water interface, results reveal that it is proper to treat turbulent boundary layers over HSs as strip-type rough wall turbulent boundary layers where the drag reduction is quantified via a modified roughness function, 

    

Mass Transfer at Topologically Singular Points

We study the convective deposition of mass onto the leading edge of a substrate, a problem analogous to the transport of momentum onto the leading edge of an airfoil. Mass deposition at the leading edge region has a significant influence on the morphology of the deposit, at a region many times ignored in classical electrodeposition morphological stability analysis. The deposition leading edge region spatially precedes the Leveque-type concentration boundary layer downstream, and encompasses a topological transition between an inert wall and a reactive electrode.

 

We consider two representative leading edge transition geometries: a flat transition between an inert wall and an active electrode; and step transition between the inert wall and the electrode, representing a corner leading edge geometry.

In both geometries, the rate of mass deposition is inversely proportional to the length scale of the leading edge region, controlled by the Peclet number and the inert wall to reactive electrode topological transition length. Larger Peclet numbers and shorter transition lengths demonstrate less morphological stability. The ion flux obtains a local maximum at the leading edge of the electrode and decays in magnitude further downstream to match the Leveque concentration boundary layer.