Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, accurate methods for drag prediction rely on experiments or numerical simulations which are costly and time consuming. Data-driven regression methods have the potential to provide a prediction that is accurate and fast. We assess the performance and limitations of linear regression, kernel methods and neural networks for drag prediction using a database of 1000 homogeneous rough surfaces. Model performance is evaluated using the roughness function obtained at a friction Reynolds number $Re_\tau$ of 500. With two trainable parameters, the kernel method can fully account for nonlinear relations between the roughness function $\Delta U<^>+$ and surface statistics (roughness height, effective slope, skewness, etc.). In contrast, linear regression cannot account for nonlinear correlations and displays large errors and high uncertainty. Multilayer perceptron and convolutional neural networks demonstrate performance on par with the kernel method but have orders of magnitude more trainable parameters. For the current database size, the networks' capacity cannot be fully exploited, resulting in reduced generalizability and reliability. Our study provides insight into the appropriateness of different regression models for drag prediction. We also discuss the remaining steps before data-driven methods emerge as useful tools in applications.

Understanding the influence of surface roughness on drag forces remains a significant challenge in fluid dynamics. This paper presents a convolutional neural network (CNN) that predicts drag solely by the topography of rough surfaces and is capable of discovering spatial patterns linked to drag-inducing structures. A CNN model was developed to analyze spatial information from the topography of a rough surface and predict the roughness function, Δ U + , obtained from direct numerical simulation. This model enables the prediction of drag from rough surface data alone, which was not possible with previous methods owing to the large number of surface-derived parameters. Additionally, the retention of spatial information by the model enables the creation of a feature map that accentuates critical areas for drag prediction on rough surfaces. By interpreting the feature maps, we show that the developed CNN model is able to discover spatial patterns associated with drag distributions across rough surfaces, even without a direct training on drag distribution data. The analysis of the feature map indicates that, even without flow field information, the CNN model extracts the importance of the flow-directional slope and height of roughness elements as key factors in inducing pressure drag. This study demonstrates that CNN-based drag prediction is grounded in physical principles of fluid dynamics, underscoring the utility of CNNs in both predicting and understanding drag on rough surfaces.

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

This thesis investigates how in wall-bounded turbulent flows changes to the wall can induce changes in the flow. To this end, we investigate the use of wall boundary conditions meant to mimic the effect of textured surfaces. We also study the effect of porous walls on their overlying bulk turbulent flow and the consequences of these effects for heat transfer.

Textured surfaces can alter near-wall turbulence in subtle to dramatic ways. Vanishingly small surface textures of the order of the viscous sublayer thickness cause the displacement of the near-wall turbulence-generating flow structures by either restricting or permitting transpiration from taking place close to the surface. The former leads to drag reduction and the latter to its increase. As the textures increase in size and become comparable to the turbulence scales, they alter the near-wall dynamics and cause structural changes to occur in the flow. These effects are emulated using slip and transpiration boundary conditions called the Transpiration-Resistance model (TRM). Its utility in acting as an effective model for wall roughness is assessed. It captures the effect of vanishingly small roughness well, and to a limited extent larger roughness which protrude into the buffer layer. The TRM also helps to shed light on which near-wall structures play an essential role in the near-wall cycle of turbulence.

Porous walls permit the exchange of mass, momentum and energy with the overlying turbulence. Their permeable structure quickly causes the turbulence to depart from its canonical smooth-wall-like structure, and induce a Kelvin-Helmholtz-like instability which leads to the emergence of spanwise rollers. These rollers efficiently redistribute momentum and turbulent kinetic energy into the porous wall. This pronounced interaction between the wall and bulk flow regions is detrimental for drag but beneficial for the transport of heat. The potential of porous walls for enhancing heat transfer exceeds that of other passive wall structures such as roughness.

As an elementary study of the type of fluid-fluid-solid interactions which can take place on the microscale within porous media, the stability of a cylinder-wrapping corner film is investigated. It is shown that linear stability analysis (LSA) can predict the number of primary droplets when the film breaks up. The film morphology, however, exhibits complexities which cannot be predicted using LSA. A disjoining-pressure model (DPM) demonstrates that smaller secondary droplets may emerge during the film breakup process. Additionally, Volume of Fluid (VoF) simulations show that two initially emerging primary droplets may eventually coalesce into one, highlighting the non-linear mechanisms involved in the film morphology evolution.

I detta arbete, undersöker vi hur turbulenta flöden påverkas av ytmodifieringar. För detta ändamål undersöker vi randvilkor som är avsedda att efterlikna effekten av ojämna ytor. Vi studerar också hur porösa ytor påverkar den överliggande turbulenta flödet.

Ytstrukturer kan påverka turbulens på ett subtilt sätt. Mycket små ytojämnheter (i storleksordningen av det viskösa skiktets tjocklek) orsakar en förskjutning av de turbulensgenererande flödesstrukturerna nära väggen genom att antingen begränsa eller tillåta transpiration att äga rum nära ytan. Det förra leder till minskning av luft/vattenmotståndet och det senare till dess ökning. När ytojämnheterna ökar i storlek och blir mer synliga för turbulensen, förändrar de dynamiken nära väggen och orsakar strukturella förändringar i flödet. Dessa effekter modelleras med hjälp av glid- och transpirationsrandvilkor som kallas ”Transpiration-Resistance Model”. Användbarheten av dessa randvilkor för att fungera som en effektiv modell för ytråhet har analyserats. Det visar sig att randvilkoren är en bra modell av små ytojämnheter, och i begränsad utsträckning större ojämnheter (som penetrerar buffertskiktet). TRM ökar vår förståelse kring vilka strukturer som är viktiga i turbulenscykeln när ytor.

Porösa väggar tillåter utbyte av massa, rörelsemängd och energi med den överliggande turbulensen. Deras permeabla struktur gör att turbulensen utvecklar en Kelvin-Helmholtz-liknande instabilitet som orsakar stora virvlar. Dessa virvlar omfördelar rörelsemängden och den turbulenta kinetiska energin i den porösa väggen. Denna överföring av energi bort från bulkflödet ökar motståndet men är fördelaktigt för transporten av värme. Vi visar att potentialen hos porösa väggar för förbättring av värmeöverföring är större jämfört med andra passiva väggstrukturer.

Vi har även utfört en studie av ett flerflassystem vid ytor. Flerfasinteraktioner äger oftast rum på en mikroskala i porösa medier. Vi har undersökt stabiliteten av tunn vätskehinna runt en cylinder. Teoretiska analyser från linjär stabilitetsanalys (LSA) kan prediktera antalet primära droppar som filmen kan bryta upp i. Filmmorfologin uppvisar emellertid komplexiteter som LSA inte tar hänsyn till. En mer komplex icke-linjär modell  visar att mindre sekundära droppar kan uppstå under filmuppbrytningsprocessen. Numeriska simuleringar baserade på .”Volume-of-Fluid (VoF)” visar att två initialt primära droppar så småningom kan gå ihop till en, vilket framhäver de icke-linjära mekanismerna som är involverade i processen.

Turbulent flows over porous lattices consisting of rectangular cuboid pores are investigated using scale-resolving direct numerical simulations. Beyond a certain threshold which is primarily determined by the wall-normal Darcy permeability, K_y, near-wall turbulence transitions from its canonical regime, marked by the presence of streak-like structures, to another marked by the presence of Kelvin-Helmholtz-like (K-H-like) spanwise-coherent structures. The threshold agrees well with that previously established in studies where permeable-wall boundary conditions had been used as surrogates for a porous substrate. In the smooth-wall-like regime, none of the investigated substrates demonstrate any reduction in drag relative to a smooth-wall flow. At the permeable surface, a notable component of the flow is that which adheres to the pore geometry and undergoes modulation by the turbulent scales of motions due to the interaction mechanism described by Abderrahaman-Elena et al. (2019). Its resulting effect can be quantified in terms of an amplitude modulation (AM) using the approach of Mathis et al. (2009). This pore-coherent flow component persists throughout the porous substrate, highlighting the importance of a given substrate's microstructure in the presence of an overlying turbulent flow. This geometry-related aspect of the flow is not accounted for when continuum-based models for a porous medium or effective representations of them such as wall boundary conditions are used. The intensity of the AM effect is enhanced in the K-H-like regime and becomes strengthened with larger permeability. As a result, structured porous materials may be designed to exploit or mitigate these flow features depending upon the intended application.

A set of boundary conditions called the transpiration-resistance model (TRM) is investigated in altering near-wall turbulence. The TRM was proposed by Lacis et al. (J. Fluid Mech., vol. 884, 2020, p. A21) as a means of representing the net effect of surface micro-textures on their overlying bulk flows. It encompasses conventional Navier-slip boundary conditions relating the streamwise and spanwise velocities to their respective shears through the slip lengths and . In addition, it features a transpiration condition accounting for the changes induced in the wall-normal velocity by expressing it in terms of variations of the wall-parallel velocity shears through the transpiration lengths and . Greater levels of drag increase occur when more transpiration takes place at the boundary plane, with turbulent transpiration being predominately coupled to the spanwise shear component for canonical near-wall turbulence. The TRM reproduces the effect of a homogeneous and structured roughness up to , encompassing the regime of smooth-wall-like turbulence described using virtual origins (Luchini, 1996 Reducing the turbulent skin friction. In Computational Methods in Applied Sciences' 96 (Paris, 9-13 Sept. 1996), pp. 465-470. Wiley; Ibrahim et al., J. Fluid Mech., vol. 915, 2021, p. A56) and slightly beyond it. The transpiration factor is defined as the product of the slip and transpiration lengths, i.e. . This factor contains the compound effect of the wall-parallel velocity occurring at the boundary plane and increased permeability, both of which lead to the transport of momentum in the wall-normal direction. A linear relation between the transpiration factor and the roughness function is observed for regularly textured surfaces in the transitionally rough regime of turbulence. This shows that such effective flow quantities can be suitable measures for characterizing rough surfaces in this flow regime.

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where for wettability, θ₁ ∈ [75°, 95°] and θ₂ ∈ [15°, 45°]; for film size, r_w/r₁ ∈ [0.12, 0.30]. The film stability, which depends on the film size and the wall wettability, is firstly predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and post\nobreakdash-instability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and Volume-of-Fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighboring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighboring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Results of direct numerical simulations (DNS) of open channel incompressible turbulent flows over porous lattices are reported in this work. Heat transfer is included as a passive temperature scalar field which is advected by the velocity field but does not affect it. The evolution of the temperature field in both fluid and solid phases is considered, thus solving for the conjugate problem of heat transfer. The fluid-solid combination considered here is that of air and aluminum, which is common to practical cooling applications. Similar to Rouhi et al. (2022), the thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, St, and the fractional increases in the skin-friction coefficient, C_f, relative to a baseline smooth-wall case. The breakdown is in general unfavorable over the porous substrates, similar to rough walls. Unlike rough walls however, a limit in heat transfer is not reached over the porous substrates for a similar amount of fractional increase in C_f. How much of a maximum gain in heat transfer can be achieved however remains to be determined. The unfavorable breakdown in Reynolds analogy is attributable to growing dissimilarities between momentum and heat transport in the vicinity of a substrate's surface as it becomes more permeable. Turbulent sweep and ejection type events contribute much more to the momentum transport across the permeable surface than they do to heat. Additionally, the change in heat transfer over the porous substrates is not monotonic. The total heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial porous-wall regime, the near-wall flow is canonical in structure and the heat transfer is dominated by molecular diffusion. As such, a reduction of the more favorably conducting solid material diminishes the overall heat transfer performance. Beyond a certain level of permeability however, where the near-wall flow transitions to the K-H-like regime marked by the presence of cross-stream rollers, the heat flux undergoes an increasing trend and eventually surpasses that of the smooth-wall case. Therefore, depending upon the cooling configuration being considered, an assessment must first be made as to whether or not the heat transfer influence of the solid phase can be neglected. Otherwise, failing to take into account the thermal behavior of the solid material can result in overestimations of any gains in heat transfer.