Macroscopic Flow Behavior Research Articles

Recent Advances in Additive Friction Stir Deposition: A Critical Review.

Additive friction stir deposition (AFSD) is a novel solid-state additive manufacturing method developed on the principle of stirring friction. Benefits from its solid-phase properties, compared with traditional additive manufacturing based on melting-solidification cycles, AFSD solves the problems of porosity, cracks, and residual stress caused by the melting-solidification process, and has a significant improvement in efficiency. In AFSD, the interaction between feedstocks and high-speed rotating print heads suffers severe plastic deformation at high temperatures below the melting point, ending up in fine, equiaxed recrystallized grains. The above characteristics make components by AFSD show similar mechanical behaviors to the forged ones. This article reviews the development of AFSD technology, elaborates on the basic principles, compares the macroscopic formability and material flow behavior of AFSD processes using different types of feedstocks, summarizes the microstructure and mechanical properties obtained from the AFSD of alloys with different compositions, and finally provides an outlook on the development trends, opportunities, and challenges to the researchers and industrial fields concerning AFSD.

Innovative centrifugal airflow upgrading for coal gasification fine slag based on experiment and CFD-DEM approach

In this work, an innovative process combining centrifugal airflow upgrading and sieving was proposed to achieve enrichment of residual carbon. The separation mechanism and macroscopic flow behavior in centrifugal air classifier were explained and predicted by constructing a coupled CFD-DEM model considering particle contact parameters. Compared the grinding, dry sieving pre-treatment had a better promotion effect on the enrichment of residual carbon. The general flow pattern was composed of an upward swirling flow and a horizontal rotation flow, facilitating dispersion and secondary elution of carbon. However, the tangential inlet and horizontally mounted rotor cage were the main cause of secondary vortex formation, leading to severe particle entrainment. Increasing inlet gas velocity at appropriate rotor speed was conducive to obtaining higher carbon content and carbon yield. By regulating the inlet gas velocity and rotor speed, higher carbon content and yield could be achieved at particle size fractions of 78–160 μm.

Computational study of momentum interactions between fluid and a static particle under the impact of anisotropic Stefan flow

The microscale gas–particle interaction is the determining process for the macroscopic flow behaviors of gas–particle systems. Anisotropic Stefan flow is often manifested at the surface of the biomass particle when thermally decomposed. However, the influence of the anisotropic Stefan flow on the gas–particle interactions is not well understood. To this end, particle-resolved direct numerical simulations were carried out in this research to explore the momentum interactions between the gas flow and a static particle emitting mass flux at its surface. A signed distance function based immersed boundary method is first extended to account for the Stefan flow at the gas–particle interface and successfully validated by comparing with literature results in the case of no Stefan flow or uniform Stefan flow. It is found that the presence of the outward uniform Stefan flow leads to an expanded wake formation and the intensity of the vortex (Re ≥ 40) is enhanced as result of the Stefan flow. Subject to the impact of anisotropic Stefan flow parallel to the main flow, the low-speed region in the front and rear of the particle is reduced when the Stefan flow goes inwards, resulting in the increase in the drag coefficient. As the Stefan flow is outward, the low-speed region in the front of the particle is pushed forward by the emitting gas and the velocity magnitude in the wake region is increased, which behaves like an enlargement of the gas cushion and leads to a significant reduction of the drag coefficient comparing with a uniform Stefan flow. In contrast, the impact of anisotropic Stefan flow with the direction perpendicular to the main flow on the fluid–particle drag interaction is less significant due to the fact that the flow structure in the front and rear regions is not significantly disturbed.

Effect of Microscopic Properties on Flow Behavior of Industrial Cohesive Powder

The characteristics of powders on a bulk scale are heavily influenced by both the material properties and the size of their primary particles. Throughout the stages of storage and transportation in the powder processing industry, various forms of deformation and stress, such as pressure and shear, impact these materials. Recognizing the point at which a powder undergoes yielding becomes particularly significant in numerous applications. There are also times when the level of stress needed to maintain it must be understood. The measurement of powder yield and flow properties remains a challenge and is addressed in this study. As part of the European collaborative project, a number of shear experiments were performed using two shearing devices: the Schulze ring shearing device and the Anton Paar Powder Cell (APCC). These experiments have three purposes: (i) test reproducibility/consistency between two shear devices and test protocols; (ii) relate bulk behavior to microscopic particle properties, focusing on bulk density and thus the effect of cohesion between particles; and (iii) investigate the influence of the temperature of heated powders on the powder’s flow properties, which is important for industrial reactors. Interestingly, for samples with small particle sizes, bulk cohesion increases slightly, but bulk friction increases significantly because of particle interaction effects. The experimental data not only provide useful insight into the role of microscopically attractive van der Waals gravitational and/or compressive forces on the macroscopic flow behavior of bulk powders but also have industrial relevance. We also provide robust data of cohesive and attritional fine powder for silo design used for calibration and validation of silos, models, and computer simulations.

Thermo-mechanical effects and microstructural evolution-coupled numerical simulation on the hot forming processes of superalloy turbine disk

Abstract Macroscopic deformation and microstructural evolution simultaneously exist in the hot forming processes of superalloy. In order to effectively and accurately study the hot forming processes of superalloy turbine disk with the numerical simulation method, a multi-scale finite element model of GH4065 superalloy turbine disk involving macroscopic and microscopic aspects was established by defining macro- and micromaterial model of superalloy, hot forming processing parameters, and boundary conditions. Via the numerical simulations of superalloy turbine disk, the macroscopic material flow and microstructural evolution behaviors in the hot forming processes of superalloy turbine disk were studied. Besides, the macroscopic deformation and microstructure distribution states after the hot forming processes were revealed and analyzed. A corresponding hot forming physical test of superalloy turbine disk was conducted to verify the results of the numerical simulation. Via the qualitative and quantitative analyses, it was concluded that the macroscopic deformation and microstructural evolution in the hot forming processes of superalloy turbine disk can be accurately predicted by the numerical simulation method.

In-situ 3D measurements of water films on the natural grain surface of porous rocks

During fluid displacement, e.g. in aquifers or other fluid reservoirs such as CO2 or H2 storage sites or hydrocarbon reservoirs, water films are expected to form along the internal pore surface due to its wetting properties and capillarity. Near connate water saturation, these water films would dominate the macroscopic multiphase flow behaviour when e.g. water penetrates the porous medium. We use Atomic Force Microscopy (AFM) to study the sub-pore scale configuration of microscale water films on the rough pore surface of Ketton and Estaillades rocks, after drainage of the medium with decane. Then, we compare the results with a numerical simulation and use a film flow model to estimate the relative permeability through these films, which can be potentially used to link the water film configuration to pore- and core-scale responses. We find that the surface coverage and connectivity of the water films varies substantially with capillary pressure. This can affect the permeability of the films up to several orders of magnitude and thus potentially dictate the displacement efficiency at the onset of imbibition, when the brine phase re-enters the pore space. The novel experimental workflow proposed in this study may help future digital assessment of multiphase flow behaviour near connate saturation.

Rate dependence in adhesive particle–particle contacts affect ceramic suspension bulk flow behavior

Particle–fluid mixtures are known for displaying a wide variety of interesting flow mechanisms, such as thickening and thinning under shear. It is now becoming increasingly evident that even molecular scale effects are relevant for this macroscopic flow behavior of suspensions. Here we show that even 50μm ceramic beads in a non-density matched solvent are affected by the pH of the solvent. We trace the origin of the pH dependence to the contact mechanics using colloidal probe atomic force microscopy (CP-AFM). The gel-like structure of the pH 3 samples suggests that adhesion effects play a major role, but which adhesion timescale competes with shear rate to affect the rheology is not obvious. We test here two time scales in the contact mechanics: total contact time tc and contact retraction speed vr. We observe that contact time is the most important variable to correlate with rheology. The ceramic particle suspension so serves as a model system to help understand which adhesive mechanism affects flow behavior in the suspension.

Foam formation during drainage of a surfactant solution in a microfluidic porous medium model

Foam has been shown to have great potential to significantly improve sweep efficiency during gas injection in oil recovery, remediation of contaminated sites, gas storage, and acidification processes. The gas mobility reduction largely depends on the generation and stability of lamellae in the pore space that traps the gas phase. Most available analyses focus on foam formation during the co-injection of gas and liquid phases at different fractional flow (foam quality) or flow of foam formed before being injected in the porous media. During surfactant-alternating-gas (SAG) injection, foam is formed as the aqueous phase is displaced by the gas slug that follows. The dynamics of lamellae formation and their stability are different from that of a co-injection process, since the amount of surfactant available to stabilize the gas-liquid interfaces is fixed as fresh surfactant solution is not injected together with the gas phase. This work studies foam formation during the drainage of a surfactant solution by gas injection at a fixed flow rate. A transparent microfluidic model of a porous medium is used in order to enable the correlation of pore-scale phenomena and macroscopic flow behavior. The results show that the maximum number of lamellae increases with surfactant concentration, even much above the critical micelle concentration (CMC). The availability of surfactant molecules needed to stabilize newly formed gas-liquid interfaces rises with concentration. The higher number of lamellae formed at higher surfactant concentration leads to stronger mobility reduction of the gas phase and longer time needed for the gas to percolate through the porous medium.

Microstructure change characteristic and fracture mechanism of Ti-47.5Al-2.5V-1.0Cr-0.2Zr alloy during high temperature tensile deformation

Changes in the microstructure characteristics and fracture mechanism of Ti-47.5Al-2.5 V-1.0Cr-0.2Zr alloy during tensile deformation were studied by high temperature tensile tests at 750–900 °C and strain rate of 10−5–10−3 s−1. The experimental results indicate that when the tensile temperature increases or the strain rate decreases, the number of small dimples in the tensile fracture structure increases, the proportion of cross-layer fracture decreases, the dimples have torn edges, and the plastic deformation resistance increases. The higher tensile temperature corresponds to a higher dynamic recrystallization (DRX) ratio, and the number of dislocations near the DRX structure is reduced, which shows that the rheological softening effect is significantly enhanced. A lower strain rate corresponds to a higher proportion of DRX and a smaller proportion of lamellar microstructure. Dislocation slip is the main deformation mode; stacking faults can be observed in DRX grains. The changes in the hot deformation microstructure directly reflect decrease of high temperature tensile strength in macroscopic flow behavior. Under the action of tensile stress, holes usually form at the lamellar grain boundary, and the aggregation of multiple micro-holes will merge and connect to form micro-cracks. Cracks are generated and propagated between layers, and the tendency of holes or cracks generated at lower deformation temperatures or higher strain rates is greater. When the stress concentration reaches a certain critical value, the specimen will eventually fracture.

Experimental Investigation of Fluid Flow through Zinc Open-Cell Foams Produced by the Excess Salt Replication Process and Suitable as a Catalyst in Wastewater Treatment

The “excess salt replication process” is a new simple method of fabrication of open-cell metal foam based on the commonly known salt replication method. Porous materials with porosity between 46% and 66% result when the employed alloy is 25% antimonial lead alloy and when it is 58% to 65% zamak 5. These foams are proposed as structured catalysts instead of packed beds in the treatment of wastewater. The local regimes influencing macroscopic air flow behaviour through these foams are delimited and boundaries are analysed in terms of sample length. Most of the experimental tests in this work exhibited a general trend of air flow in ESR foams dominated by the “strong inertia regime”. It was established that the law governing the unidirectional air flow through these foams was the full cubic law. The permeability and inertia coefficient of five samples with a cell diameter between 2.5 and 4.5 mm were calculated, and an empirical correlation was fitted. The irregular cuboid shape of salt grains used in the ESR foam was the origin of the special cell form of ESR foams leading to an anisotropic ordered porous media. This can explain the macroscopic turbulence of air flow because there were many dead zones present in the corner of each cubic cell, thus causing kinetic energy loss starting at earlier regimes.

RheologyNet: A physics-informed neural network solution to evaluate the thixotropic properties of cementitious materials

Thixotropic behaviors can be predicted by rheological partial differential equations (PDEs) of cementitious materials. The ability to solve the rheological PDEs of viscous fluids accurately and efficiently has become an emerging interest in research. However, due to the growing number of parameters in rheological constitutive equations and the non-ideal behavior of materials from experiments, solving the rheological PDEs becomes computationally costive and error-prone. We propose a physics-informed neural network (PINN)-based framework, RheologyNet, as a surrogate solution to predict the general thixotropic behavior of cementitious materials. The complex PDEs are embedded in the well-designed RheologyNet architecture to link macroscopic viscous flow behaviors and microstructural changes. Numerical experiments suggested that RheologyNet can accurately and efficiently predict the rheological properties of cementitious materials compared to the traditional Fully-connected Neural Network (FNN) and mechanistic Finite Element Analysis (FEA). Particularly, RheologyNet demonstrated great promise for simulating history-dependent thixotropic behaviors.

Rock-on-a-chip: "Seeing" the association/disassociation of an adaptive polymer in solutions flowing through porous media.

The flow and transport of polymer solutions through porous media are ubiquitous in myriad scientific and engineering applications. With escalating interest in adaptive polymers, understanding the flow dynamics of their solutions is indispensable (yet lacking). Here, the hydrophobic-effect-driven reversible associations in a self-adaptive polymer (SAP) solution and its flow characteristics in a microfluidic-based "rock-on-a-chip" device have been analyzed. The hydrophobic aggregates were fluorescent labeled; this enabled a direct visualization of the in situ association/disassociation of the polymer supramolecular assemblies in pore spaces and throats. Furthermore, the influence of this adaptation on the macroscopic flow behavior of the SAP solution was analyzed by comparing its flow with that of two partially-hydrolyzed polyacrylamide (the molecular weight (MW)-equivalent HPAM-1 and ultrahigh-MW HPAM-2) solutions in the semi-dilute regime with similar initial viscosities. At low flow rates (with shear predominance), the SAP solution showed a low shear viscosity compared to HPAM-1, indicating a higher shear susceptibility for association than chain entanglement. Although the SAP exhibited the same elastic instability as the non-adaptive polymers above a threshold flow rate, the adaptable structure of the former advanced the onset of its viscoelastic-governed flow, providing a stronger flow resistance, possibly through an extension resistance. Furthermore, 3D-media analysis indicated that the reversible association/disassociation of SAP increased the accessible pore space during nonaqueous-liquid displacement, facilitating oil production.

In‐Situ Capillary Pressure and Its Interrelationships With Flow Characteristics During Steady‐State Three‐Phase Flow in Water‐Wet Berea Sandstone

AbstractWe present a detailed multi‐level investigation of steady‐state three‐phase flow processes in a water‐wet Berea sandstone sample. We use high‐resolution micro‐computed tomography images acquired during micro‐scale core‐flooding experiments which include successive gas injection, waterflooding, and nonspreading oil flooding steps. We develop and employ robust techniques to comprehensively characterize and probe the complex interrelationships between the pore‐scale three‐phase capillary pressures, fluid occupancy, displacement events, and the macroscopic flow behavior. The results demonstrate that the local capillary pressures involving the invading phase rise or drop in compliance with the changes in the macroscopic flow ratios. For instance, the gas‐oil capillary pressures were at their highest levels during the gas injection process (highest gas/oil fractional flow) and dropped during the subsequent processes. More importantly, the oil‐water capillary pressure is found to sharply rise during the gas injection process, implying that the gas‐displacing‐oil‐displacing‐water double displacements are the dominant double displacement mechanism during this experiment. For the waterflooding test, the local gas‐oil capillary pressures consistently decrease due to water‐displacing‐oil‐displacing‐gas double displacement events. Moreover, the results show that the variations in the gas‐liquid capillary pressures are more significant than those in the oil‐water capillary pressures. Also, the variations in all capillary pressures during gas injection are higher than in the subsequent processes. The higher variations in capillary pressure values are attributed to more localized and less uniform pore‐scale events across the medium. Finally, the capillary pressure gradients along the flow direction are incorporated in the three‐phase relative permeability measurements.

On non-Darcian flow behavior in a rough-walled fracture filled with a porous medium

Fluid flow through filled rock fractures is relevant to numerous engineering applications and geophysical processes. However, a proper understanding of the flow behaviors in filled fractures is still far from being completed. To investigate the fluid flow in a rough-walled fracture filled with a porous medium, we systematically compare the micro- and macroscopic flow behaviors within filled fractures and corresponding open fractures and porous media based on a series of pore-scale simulation results. We find that the filling medium has a dual role in altering the flow regime, as the filling particles can not only cut the flow domain into several pore channels and thus limit the generation of large-span eddies, but also force the fluid to flow around them and promote the generation of local eddies. Compared with porous media, the fluid flow within filled fractures is confined by fracture walls, which greatly alters the media permeability and the flow nonlinearity therein. By introducing the hydraulic radius and Darcy-Weisbach equation, we develop a new semi-empirical model to estimate the fluid flow through filled fractures using phenomenological coefficients of corresponding open fractures and porous media. The proposed model, satisfying dimensional consistency, shows high fidelity in predicting water flow through filled fractures. More importantly, this model can be successfully reduced to the typical form of the Forchheimer equation applied to open fractures and porous media. The results and findings are expected to be useful in predicting and evaluating the fluid flow in complex geological setting.

Slag Flow in the Packed Bed With Varied Properties and Bed Conditions: Numerical Investigation

Molten slag, which is primarily generated in the blast furnace (BF) cohesive zone, trickles down through the coke packed bed in the form of films, rivulets, or droplets in the lower zone of the BF. During its downward flow, there are significant interactions occurring between slag and other phases such as gas, coke particles, hot metal, and fine powders. In terms of these interactions, slag flow behavior can greatly affect BF productivity and be associated with furnace irregularities such as channeling, hanging, and slipping. Hence, understanding the interactions between phases is useful to maximizing BF efficiency in terms of operating cost, reliability, and production capacity. In the current study, a Volume of Fluid (VOF) modeling technique was applied to track the movement of individual slag droplets in the packed bed at a mesoscopic level, considering various bed permeabilities, more wide-ranging slag properties, and different wettability between slag and packing particles. Results demonstrate the significant role of modeling at a mesoscopic level in understanding macroscopic slag flow behavior. Modeling work helps to visualize the trickling behavior of slag droplets in more realistic and complex conditions representing a BF, and clarify the mechanisms of the different flow patterns generated for variations in operating conditions. Transient flow characteristics such as localized slag accumulation and droplet morphology were identified and analyzed in relation to complex condition changes. The current modeling proved to be a valuable tool to provide a foundation for better understanding the slag flow behavior and its interactions with other phases in the BF lower zone.

Viscoelastic behavior of dilute polyelectrolyte solutions in complex geometries

In this work, we develop a theoretical model describing the viscoelastic behavior of dilute polyelectrolyte (PE) solutions using Onsager’s variational principle, with the effect of the polyelectrolyte charge and solvent salinity accounted for. The PE molecules are described as finitely extensible charged dumbbells suspended in a solvent containing ionic species which screen the charged sites on the macromolecules. The performance of the model was examined and compared against experimental data in simple flows, accounting for the magnitude of charge on the PE molecules and counterion screening effects. Numerical simulations of the flow past a single cylinder and an idealized porous medium with multiple cylinders were carried out and compared to flow of uncharged polymers in the same geometries to explore the effect of intramolecular electrostatic repulsion on the flow behavior. The extra rigidity offered by the repulsion between the charged monomeric units of the PE, and screening of these charged sites by the ionic species in the solvent led to significantly different behavior in complex flows when compared to that of uncharged polymers. The normal stresses generated in a complex flow show an increase with the polyelectrolyte molecule charge density, whereas enhanced screening of the charged sites by counterions suppresses this effect, showing behavior closer to that of uncharged polymers. Drag on a cylinder placed in the flow and pressure drop across the porous geometry increased with charge density of the molecules, exhibiting rheological behavior in complex geometries not shown by their uncharged counterparts. The results show the effects of the degree of hydrolysis and solvent salinity on the flow behavior of dilute PE solutions in complex geometries and has implications for biological systems in which PE species are commonly encountered, as well as operation of industrial processes such as enhanced oil recovery, which frequently involve the flow of dilute polyelectrolyte solutions in porous media. • Macroscopic flow behavior of dilute polyelectrolyte solutions is investigated. • Onsager’s Variational Principle used for developing model from first principles. • Reformulation of charged dumbbell model for simulating flows in complex geometries. • Polyelectrolyte charge density and solvent salinity influence flow behavior. • Drag coefficients and normal stresses increase with charged nature of molecules.

Determining meso-parameters of hot mix asphalt with reclaimed asphalt pavement based on workability

The flowability and compaction behaviors of hot mix asphalt (HMA) are critical for the mechanical performance and durability of HMA. When reclaimed asphalt pavement (RAP) is incorporated into HMA, the flowability and compaction would be significantly affected. Since the recycled asphalt mixture consists of virgin aggregate, virgin asphalt, aged asphalt, and RAP, the contact parameters and the related contact relations cannot be directly defined during discrete element modeling. Therefore, this study employed the slump test to measure the flowability of two types of HMAs, HMA with 0 % and 100 % RAP. The angle of repose (AoR) was used to characterize the macroscopic flowability and to determine the mesoscopic parameters used in the discrete element modeling (DEM). The contact parameters inside the asphalt mixture were determined by comparing the actual AoR with the virtual AoR at different asphalt contents. The results of the study showed that the contact relations between particles in the mixtures were directly affected by the RAP and the asphalt content, which leads to the variation of flow behaviors of the uncompacted asphalt mixtures. The macroscopic flow behaviors could be qualitatively explained as a coupling effect of friction and bonding. The friction between particles and the bonding provided by asphalt binder were determined when different binder content was added. By trial calculation, the friction coefficient of the RAP surface was 0.37, which was lower than that of the virgin aggregate. When AoRs reached the maximum values, the bond strength inside the HMA without RAP was 7.5 × 104 Pa. Due to the compatibility of the aged and virgin asphalt, the bond strength inside the HMA with 100 % RAP was only 6.2 × 104 Pa. Then, virtual compaction tests were conducted for HMAs with 0 % and 100 % RAP. Under the same compaction effort, HMA with 100 % RAP presented larger porosity, which was consistent with the actual situation, indicating the parameter calibration method is feasible to characterize the flowability of HMA with or without RAP. In conclusion, this study indirectly realizes the calibration of internal parameters in recycled asphalt mixtures based on the flowability and provide a microscopic mechanism to explain the macroscopic performance variations of recycled asphalt mixtures.

Thermodynamically‐consistent flash calculation in energy industry: From iterative schemes to a unified thermodynamics‐informed neural network

Multicomponent multiphase fluid flows are commonly seen in the engineering practice of hydrocarbon production and transportation; thus, the phase-wise heat and mass transfer mechanisms underneath the macroscopic flow and transport behaviors are essentially needed for better understanding of the physical phenomena and optimization of the industrial processes. Flash calculation, as the main approach computing phase equilibrium conditions, has arisen increasing interests to establish the thermodynamic foundations of multiphase flow simulation, as well as to determine whether two-phase model is needed. In this paper, the general thermodynamically-consistent flash calculation scheme will be developed, and the general adaptability to various special mechanisms will be analyzed. A unified framework of thermodynamics-informed neural network will also be designed to accelerate conventional iterative flash calculation schemes that will be applied in various engineering scenarios to provide certain suggestions to the energy industry based on the predictions and analysis. Novelty Statement A thermodynamically-consistent flash calculation scheme incorporating various special mechanisms that are often met in energy industry. A unified thermodynamics-informed neural network structure for various engineering demands in the energy industry. Suggestions to the energy industry to optimize the productions based on the phase transition predictions and analysis.

Simulation of Water Flow in a Nanochannel with a Sudden Contraction or Expansion.

Water flow in a nanoscale channel is known to be affected by strong water-wall interactions; as a result, the flow considerably deviates from the conventional continuum flow. Nanochannel with a sudden contraction or expansion is the most fundamental morphological nanostructure in many nanoporous systems such as shale matrix, mudrock, membrane, etc. However, the nanoconfinement effects of water flow in nanoporous systems and its effect on macroscopic flow behavior are still evolving research topics. In this work, our recently developed pore-scale lattice Boltzmann method (LBM) considering the nanoscale effects is extended to directly simulate water flow in nanoporous systems. The results show that the flow rate is dramatically decreased in hydrophobic nanopores because of additional flow resistances at the contraction and expansion junctions. This indicates that the bundle of capillary models or the permeability averaging method overestimates the water flow rate in nanoporous media if the contraction/expansion effects between different nanopores are ignored. This work highlights the importance of wettability of the nanochannel in the determination of dynamic water flow behaviors in the contraction/expansion nanosystem. Other important aspects, including velocity distribution, flow patterns, and vortex characteristics as well as pressure variation along the flow direction, are for the first time revealed and quantified. Large differences can be found comparing gas or larger-scale water flows through the same system. A new type of pressure variation curve along the axis of flow direction is found in the hydrophobic nanochannel with a sudden contraction/expansion. This work provides the fundamental understanding of water transport through the nanoscale system with contraction and expansion effects, giving implications to a wide range of industry applications.

A homogenization approach for buoyancy-induced flows over micro-textured vertical surfaces

Asymptotic homogenization is employed to formulate upscaled effective boundary conditions at a smooth virtual surface for a natural-convection flow over a periodically roughened vertical wall, to bypass the expensive numerical resolution of flow and temperature fields near and within wall corrugations. Microscale problems are found by expanding near-wall variables in terms of a small parameter $\epsilon$ , the ratio between the microscopic and the macroscopic length scales. The expressions of the upscaled velocity and temperature boundary conditions are provided up to second-order accuracy in $\epsilon$ . The case of transverse square ribs is considered as a representative example. The classical Navier-slip condition for the streamwise and the spanwise velocity components is modified at second order by the gradient of the normal stress and the time derivative of the shear stress. The streamwise slip velocity is additionally corrected by a buoyancy term at first order and a temperature-gradient term at second order. The normal velocity at the virtual surface appears only as a second-order transpiration condition. A Robin-like condition for the temperature is found, where the wall temperature is corrected with a temperature-gradient term representing thermal slip. The accuracy levels and the applicability range of the effective conditions to mimic the macroscopic flow behaviour are investigated under laminar flow conditions, in comparison with results of full feature-resolving simulations. A formal validity limit for the approximation is sought in terms of a single accuracy criterion ( $C$ ), which combines the effects of the Grashof number and the ribs’ density. The introduced model is further tested on different rib geometries.