Fluids, Volume 9, Issue 1 (January 2024) – 30 articles

This work studies how the sliding-gate valve (SGV) modifies the features and the dynamic behavior of the outlet jets for flat-bottom and well-bottom bifurcated submerged entry nozzles (SENs) used in continuous casting machines. Three conditions for the SGV were studied: no obstruction, moderate obstruction, and severe obstruction. The experimental study used a scaled model, employing cold water as the working fluid. A high-frequency analysis of the flow inside the SEN’s bore arriving at the outlet ports was performed by employing the particle image velocimetry (PIV) technique. Low-frequency measurements of the volumetric flow at the exit port were obtained by splitting the exit jet into four quadrants and employing digital flowmeters. It was observed that reducing the SGV clearance increases the turbulence of the flow inside the SEN bore, but the flow displays ordered rather than erratic fluctuations. Flowmeter measurements showed that, regardless of the level of obstruction in the SGV, the outlet jets on flat-bottom and the well-bottom SENs have dynamic behaviors and features with significant differences. This finding is relevant because the flow distribution inside the outlet ports is directly related to the jet’s wideness, affecting the recirculation pattern inside the mold and, therefore, the quality of the finished steel slab. Full article

We present an analysis of the effect of particle inertia and thermal inertia on the heat transfer in a turbulent shearless flow, where an inhomogeneous passive temperature field is advected along with inertial point particles by a homogeneous isotropic velocity field. Eulerian–Lagrangian direct numerical simulations are carried out in both one- and two-way coupling regimes and analyzed through single-point statistics. The role of particle inertia and thermal inertia is discussed by introducing a new decomposition of particle second-order moments in terms of correlations involving Lagrangian acceleration and time derivative of particles. We present how particle relaxation times mediate the level of particle velocity–temperature correlation, which gives particle contribution to the overall heat transfer. For each thermal Stokes number, a critical Stokes number is individuated. The effect of particle feedback on the attenuation or enhancement of fluid temperature variance is presented. We show that particle feedback enhances fluid temperature variance for Stokes numbers less than one and damps is for larger than one Stokes number, regardless of the thermal Stokes number, even if this effect is amplified by an increasing thermal inertia. Full article

The understanding of the boundary layer flame flashback (BLF) has considerably improved in recent decades, driven by the increasing focus on clean energy and the need to address the operational issues associated with flashback. This study investigates the influence of the Lewis number (Le) on symmetric flame shapes under the critical conditions for a laminar boundary layer flashback in cylindrical tubes. It has been found that the transformation of the flame shape from a mushroom to a tulip happens in a tube of a given radius, as the thermal expansion coefficient and Le are modified. A smaller Lewis number results in a local increase in the burning rate at the flame tip, with the flame being able to propagate closer to the wall, which significantly increases the flashback propensity, in line with previous findings. In cases with a Lewis number smaller than unity, a higher thermal expansion results in a flame propagation happening closer to the wall, thus facing a weaker oncoming flow and, consequently, becoming more prone to flashback. For Le > 1, the effect of the increase in the thermal expansion coefficient on the flashback tendency is much less pronounced. Full article

The treatment for asthma and chronic obstructive pulmonary disease relies on forced inhalation of drug particles. Their distribution is essential for maximizing the outcomes. Patient-specific computational fluid dynamics (CFD) simulations can be used to optimize these therapies. In this regard, this study focuses on creating a parametric model of the human respiratory tract from which synthetic anatomies for particle deposition analysis through CFD simulation could be derived. A baseline geometry up to the fourth generation of bronchioles was extracted from a CT dataset. Radial basis function (RBF) mesh morphing acting on a dedicated tree structure was used to modify this baseline mesh, extracting 1000 synthetic anatomies. A total of 26 geometrical parameters affecting branch lengths, angles, and diameters were controlled. Morphed models underwent CFD simulations to analyze airflow and particle dynamics. Mesh morphing was crucial in generating high-quality computational grids, with 96% of the synthetic database being immediately suitable for accurate CFD simulations. Variations in wall shear stress, particle accretion rate, and turbulent kinetic energy across different anatomies highlighted the impact of the anatomical shape on drug delivery and deposition. The study successfully demonstrates the potential of tree-structure-based RBF mesh morphing in generating parametric airways for drug delivery studies. Full article

The article explores flow behavior around thick airfoils at low Reynolds numbers and the potential application of energy methods to manipulate the flow field for increased lift and reduced drag. The study relies on a set of propulsion airfoils calculated using a combined approach of solving the inverse problem of aerodynamics and applying stochastic global optimization methods. The calculations consider the transition from laminar to turbulent flow regimes, which significantly affects lift and airfoil drag. The suitability of different turbulence models for airfoil modeling in low Reynolds numbers is discussed, and numerical simulation results determine the lift coefficient dependence on angle of attack and the optimal air flow rate taken from the airfoil surface for each angle of attack. The accuracy of different turbulence models is analyzed by comparing numerical simulation results to physical experiment data. Full article

Our ability to reliably and efficiently predict complex high-Reynolds-number ($Re$) turbulent flows is essential for dealing with a large variety of problems of practical relevance. However, experiments as well as computational methods such as direct numerical simulation (DNS) and large eddy simulation (LES) face serious questions regarding their applicability to high $Re$ turbulent flows. The most promising option to create reliable guidelines for experimental and computational studies is the use of analytical conclusions. An essential criterion for the reliability of such analytical conclusions is the inclusion of a physically plausible explanation of the asymptotic turbulence regime at infinite $Re$ in consistency with observed physical requirements. Corresponding analytical results are reported here for three canonical wall-bounded turbulent flows: channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer. The asymptotic structure of the mean velocity and characteristic turbulence velocity, length, and time scales is analytically determined. In outer scaling, a stable asymptotic mean velocity distribution is found corresponding to a linear probability density function of mean velocities along the wall-normal direction, which is modified through wake effects. Turbulence tends to decay in this regime. In inner scaling, the mean velocity is governed by a universal log-law. Turbulence does survive in an infinitesimally thin layer very close to the wall. Full article

The aim of this article is to investigate the parameter sensitivity of the (Non-Linear) Unsteady Vortex Lattice Method-Vortex Particle Method [(NL-)UVLM-VPM] with Particle Strength Exchange-Large Eddy Simulations (PSE-LES) method on a lower Reynolds number rotor. The previous work detailed the method, but introduced parameters whose influence were not investigated. Most importantly, the Vreman model coefficient was chosen arbitrarily and was not suitable to ensure stability for this lower Reynolds number rotor simulation. In addition, the previous work presented a consistency study where geometry and time discretization were refined simultaneously. The present article starts with a comparative literature review of potential methods used to solve the aerodynamics of an isolated hovering rotor. This review highlights the differences in modeling, discretizations, sensitivity analysis, validation cases, and the results chosen by the different studies. Then, a transparent and thorough parametric study of the method is presented alongside discussions of the observed results and their physical interpretation regarding the flow. The sensitivity analysis is performed for the three free parameters of UVLM, namely Vatistas core size, the geometry and the temporal discretizations, and then for the three additional parameters introduced by UVLM-VPM, which are the Vreman model coefficient, the particle spacing, and the conversion time. The effect of different databases in the non-linear coupling is also shown. The method is shown to be consistent with both geometry and temporal refinements. It is also consistent with the expected behavior of the different parameters change, including the numerical stability that depends on the strength of the LES diffusion controlled by the Vreman model coefficient. The effect of discretization refinement presented here not only shows the integrated coefficients where different errors can cancel each other, but also looks at their convergence and where relevant, the distributed loads and tip singularity position. Finally, the aerodynamics results of the method are compared for different databases and with higher fidelity Unsteady Reynolds Averaged Navier–Stokes (URANS) 3D results on a lower Reynolds number rotor. Full article

Some non-Newtonian fluids have time-dependent rheological properties like a shear stress that depends on the shear history or a stress overshoot that is a function of the resting time, when fluid movement is started. The rheological properties of such complex fluids may not stay constant while they are used in an industrial process, and it is therefore desirable to measure these properties frequently and with a simple and robust device like a pipe rheometer. This paper investigated how the time-dependent rheological properties of a thixotropic and viscoelastic shear-thinning fluid can be extracted from differential pressure measurements obtained at different flowrates along a circular pipe section. The method consists in modeling the flow of a thixotropic version of a Quemada fluid and solving the inverse problem in order to find the model parameters using the measurements made in steady-state conditions. Also, a Maxwell linear viscoelastic model was used to reproduce the stress overshoot observed when starting circulation after a resting period. The pipe rheometer was designed to have the proper features necessary to exhibit the thixotropic and viscoelastic effects that were needed to calibrate the rheological model parameters. The accuracy of rheological measurements depends on understanding the effects that can influence the observations and on a proper design that takes advantage of these side effects instead of attempting to eliminate them. Full article

The usual concept of simulation methods for turbulent flows is to impose a certain (partial) flow resolution. This concept becomes problematic away from limit regimes of no or an almost complete flow resolution: discrepancies between the imposed and actual flow resolution may imply an unreliable model behavior and high computational cost to compensate for simulation deficiencies. An exact mathematical approach based on variational analysis provides a solution to these problems. Minimal error continuous eddy simulation (CES) designed in this way enables simulations in which the model actively responds to variations in flow resolution by increasing or decreasing its contribution to the simulation as required. This paper presents the first application of CES methods to a moderately complex, relatively high Reynolds number turbulent flow simulation: the NASA wall-mounted hump flow. It is shown that CES performs equally well or better than almost resolving simulation methods at a little fraction of computational cost. Significant computational cost and performance advantages are reported in comparison to popular partially resolving simulation methods including detached eddy simulation and wall-modeled large eddy simulation. Characteristic features of the asymptotic flow structure are identified on the basis of CES simulations. Full article

The continuous casting tundish is non-isothermal due to heat losses and temperature variation from the inlet stream, which generate relevant convection forces. This condition is commonly avoided through qualitative fluid dynamic analysis only. This work searches to establish the conditions for which non-isothermal simulations are mandatory or for which isothermal simulations are enough to accurately describe the fluid dynamics inside the tundish by quantifying the buoyant and inertial forces. The mathematical model, simulated by CFD software, considers the Navier-Stokes equations, the realizable k-ε model for solving the turbulence, and the Lagrangian discrete phase to track the inclusion trajectories. The results show that temperature does not significantly impact the volume fraction percentages or the mean residence time results; nevertheless, bigger velocity magnitudes under non-isothermal conditions than in isothermal conditions and noticeable changes in the fluid dynamics between isothermal and non-isothermal cases in all the zones where buoyancy forces dominate over inertial forces were observed. Because of the results, it is concluded that isothermal simulations can accurately describe the flow behavior in tundishes when the flow control devices control the fluid dynamics, but simulations without control devices or with a weak fluid dynamic dependence on the control devices require non-isothermal simulations. Full article

The use of nanofluids in heat transfer applications has significantly increased in recent times due to their enhanced thermal properties. It is therefore important to investigate the flow behavior and, thus, the rheology of different nanosuspensions to improve heat transfer performance. In this study, the viscosity of a BN-diamond/thermal oil hybrid nanofluid is predicted using four machine learning (ML) algorithms, i.e., random forest (RF), gradient boosting regression (GBR), Gaussian regression (GR) and artificial neural network (ANN), as a function of temperature (25–65 °C), particle concentration (0.2–0.6 wt.%), and shear rate (1–2000 s⁻¹). Six different error matrices were employed to evaluate the performance of these models by providing a comparative analysis. The data were randomly divided into training and testing data. The algorithms were optimized for better prediction of 700 experimental data points. While all ML algorithms produced R² values greater than 0.99, the most accurate predictions, with minimum error, were obtained by GBR. This study indicates that ML algorithms are highly accurate and reliable for the rheological predictions of nanofluids. Full article

Throughout many decades, the Schlieren visualization method has been mainly used as means to visualize transparent flows in a qualitative manner. The images recorded provide data regarding the existence of the flow, or illustrate predicted flow geometries and details. The colored Schlieren method has been developed in the late 1890s and has always had the intent to provide quantitative data rather than qualitative pictures of the studied phenomena. This paper centers on applying a quantitative color Schlieren method to help determine the gasodynamic parameters of an H₂–O₂ exhaust jet, developing in air. A comparison between the parameters obtained through calibrating the color filter for the Schlieren method and the results from a CFD simulation is performed to assess the range of the CS (color Schlieren) measurement. This paper’s findings address the issues of calibrated color filter Schlieren encounter during its implementation and discusses possible errors appearing when the method is applied to a 3D flow. While the qualitative Schlieren images are still impressive to observe, the quantitative Schlieren presents challenges and a low measurement accuracy (75%) when applied to 3D flows and compared to 2D cases found in the literature (97–98%). Full article

The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/$hp$ stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/$hp$ framework. We introduce revised stabilization parameters, ${\tau }_{supg}$, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, $\delta$: the first is described with entropy variables, and the other is the $YZ\beta$ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both $L^1$ and $L^2$ norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of $3.0$ and numerically validate the shock standoff distance with results obtained from NASA Overflow $2.2$ code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries. Full article

This study proposes a computational model to define the wind velocity of the environment on the photovoltaic (PV) module via heat transfer concepts. The effect of the wind velocity and PV module is mostly considered a cooling effect. However, cooling and controlling the PV module temperature leads to the capability to optimize the PV module efficiency. The present study applied a nominal operating cell temperature (NOCT) condition of the PV module as a reference condition to determine the wind velocity and PV module temperature. The obtained model has been examined in contrast to the experimental heat transfer equation and outdoor PV module performance. The results display a remarkable matching of the model with experiments. The model’s novelty defines the PV module temperature in relation to the wind speed, PV module size, and various ambient temperatures that were not included in previous studies. The suggested model could be used in PV module test specification and provide analytical evaluation. Full article

The numerical study of relativistic magnetohydrodynamics (MHD) plays a crucial role in high-energy astrophysics but unfortunately is computationally demanding, given the complex physics involved (high Lorentz factor flows, extreme magnetization, and curved spacetimes near compact objects) and the large variety of spatial scales needed to resolve turbulent motions. A great benefit comes from the porting of existing codes running on standard processors to GPU-based platforms. However, this usually requires a drastic rewriting of the original code, the use of specific languages like CUDA, and a complex analysis of data management and optimization of parallel processes. Here, we describe the porting of the ECHO code for special and general relativistic MHD to accelerated devices, simply based on native Fortran language built-in constructs, especially do concurrent loops, few OpenACC directives, and straightforward data management provided by the Unified Memory option of NVIDIA compilers. Thanks to these very minor modifications to the original code, the new version of ECHO runs at least 16 times faster on GPU platforms as compared to CPU-based ones. The chosen benchmark is the 3D propagation of a relativistic MHD Alfvén wave, for which strong and weak scaling tests performed on the LEONARDO pre-exascale supercomputer at CINECA are provided (using up to 256 nodes corresponding to 1024 GPUs, and over 14 billion cells). Finally, an example of high-resolution relativistic MHD Alfvénic turbulence simulation is shown, demonstrating the potential for astrophysical plasmas of the new GPU-based version of ECHO. Full article

The article presents a summarised history of the equations governing fluid motion, known as the Navier–Stokes equations. It starts with the work of Castelli, who established the continuity equation in 1628. The determination of fluid flow resistance was a topic that involved the brightest minds of the 17th and 18th centuries. Navier’s contribution consisted of the incorporation of molecular attraction effects into Euler’s equation, giving rise to an additional term associated with resistance. However, his analysis was not the only one. This continued until 1850, when Stokes firmly established the boundary conditions that must be applied to the differential equations of motion, specifically stating the non-slip condition of the fluid in contact with a solid surface. With this article, the author wants to commemorate the bicentennial of the publication of “Sur les Lois du Mouvement des Fluides” by Navier in the Mémoires de l’Académie Royale des Sciences de l’Institut de France. Full article

In pursuit of advancing the development of more electric aircraft, the present research explores the forefront capabilities of electro-hydrostatic actuators (EHAs) as potential replacements for conventional hydraulic flight control systems. EHAs are currently used primarily as backup options due to their limited durability. As of now, the high dynamic axial piston pump is the main cause of the limited longevity of the EHA, due to strong tribological wear. The primary objective of this investigation is the identification of parameters and pump behavior to determine the current wear of the pump, as well as providing valuable insights into run-ins, temperature dependencies, and wear-related efficiency losses for future pump improvements. In the scope of this paper, the design of EHAs is explained in detail and the impact of challenging working conditions on the health status of the pump by comprehensive analysis of load-holding modes is examined. The experimental data for analysis is conducted on a longevity test bench with test profiles specifically designed to simulate real-world operational scenarios. Full article

Drilled shafts are cylindrical, cast-in-place concrete deep foundation elements. During construction, anomalies in drilled shafts can occur due to the kinematics of concrete, flowing radially from the center of the shaft to the concrete cover region at the peripheral edge. This radial component of concrete flow develops veins or creases of poorly cemented or high water-cement ratio material, as the concrete flows around the reinforcement cage of rebars and ties, jeopardizing the shaft integrity. This manuscript presents a three-dimensional computational fluid dynamics (CFD) model of the non-Newtonian concrete flow in drilled shaft construction developed using the finite volume method with interface tracking based on the volume of fluid (VOF) method. The non-Newtonian behavior of the concrete is represented via the Carreau constitutive model. The model results are encouraging as the flow obtained from the simulations shows patterns of both horizontal and vertical creases in the concrete cover region, consistent with previously reported field and laboratory experiments. Moreover, the flow exhibits the concrete head differential developed between the inside and the outside of the reinforcement cage, as exhibited in the physical experiments. This head differential induces the radial component of the concrete flow responsible for the creases that develop in the concrete cover region. Results show that the head differential depends on the flowability of the concrete, consistent with field observations. Less viscous concrete tends to reduce the head differential and the formation of creases of poorly cemented material. The model is unique, making use of state-of-the-art numerical techniques and demonstrating the capability of CFD to model industrially relevant concrete flows. Full article

Thermal transpiration flow, a flow from cold to hot, driven by a temperature gradient along a wall under a high Knudsen number condition, was studied using the molecular dynamics method with a two-dimensional channel consisting of infinite parallel plates with nanoscale clearance based on our previous study. To accelerate the numerical analysis, a dense gas was employed in our previous study. In this study, the influence of the number density of gas was investigated by varying the height of the channel while keeping the number of molecules to achieve the flow ranging from dense to dilute gas while maintaining a constant Knudsen number. From the flow velocity profile compared to the number density profile, the thermal transpiration flow was observed for all number density conditions from dense to dilute gas. A similar flow structure was exhibited regardless of the number density. Thus, the numerical analysis in a dense gas condition is considered to be valid and useful for analyzing the thermal transpiration flow. Full article

Ladle metallurgy serves as a crucial component of the steelmaking industry, where it plays a pivotal role in manipulating the molten steel to exercise precise control over its composition and properties. Turbulence in ladle metallurgy influences various important aspects of the steelmaking process, including mixing and distribution of additives, alongside the transport and removal of inclusions within the ladle. Consequently, gaining a clear understanding of the stirred flow field holds the potential of optimizing ladle design, improving control strategies, and enhancing the overall efficiency and steel quality. In this project, an advanced Particle-Tracking-Velocimetry system known as “Shake-the-Box” is implemented on a cylindrical water ladle model while compressed air injections through two circular plugs positioned at the bottom of the model are employed to actively stir the flow. To mitigate the particle images distortion caused by the cylindrical plexi-glass walls, the method of refractive matching is utilized with an outer polygon tank filled with a sodium iodide solution. The volumetric flow measurement is achieved on a 6 × 6 × 2 cm domain between the two plugs inside the cylindrical container while the flow rate of gas injection is set from 0.1 to 0.4 L per minute. The volumetric flow field result suggests double gas injection at low flow rate (0.1 L per minute) produce the least disturbed flow while highly disturbed and turbulent flow can be created at higher flow rate of gas injection. Full article

Elevated face temperature due to mask wearing can cause discomfort and skin irritation, making mask mandates challenging. When thermal discomfort becomes intolerable, individuals instinctively or unknowingly loosen or remove their facemasks, compromising the mask’s protective efficacy. The objective of this study was to numerically quantify the microclimate under the mask and facial thermoregulation when wearing a surgical mask with different levels of misfit. An integrated ambient–mask–face–airway computational model was developed with gaps of varying sizes and locations and was validated against complementary experiments. The low Reynolds number (LRN) k-ω turbulence model with porous media was used to simulate transient respiratory flows. Both skin convective heat transfer and tissue heat generation were considered in thermoregulation under the facemask, besides the warm air exhaled from the body and the cool air inhaled from the ambient. The results of this study showed that when wearing a surgical mask with a perfect fit under normal breathing, the temperature at the philtrum increased by 4.3 °C compared to not wearing a mask. A small gap measuring 0.51 cm² (gap A) at the nose top resulted in 5.6% leakage but reduced the warming effect by 28% compared to zero gap. Meanwhile, a gap of 4.3 cm² (R1L1) caused 42% leakage and a 62% reduction in the warming effect. Unique temporospatial temperature profiles were observed at various sampling points and for different gap sizes, which correlated reasonably with the corresponding flow dynamics, particularly close to the gaps. The temperature change rate also exhibited patterns unique to the gap site and sampling point, with distinctive peaks occurring during the inspiratory–expiratory flow transitions. These results have the significant implications that by using the temporospatial temperature profiles at several landmark points, the gap location can potentially be pinpointed, and the gap size and leakage fractions can be quantified. Full article

Laminar flow aircraft may potentially save fuel and reduce the emission of pollutants and greenhouse gases. However, laminar flow aircraft face challenges caused by contaminations on the wings, such as insect impact residue. To study insect residue on an aircraft airfoil, a new setup was developed that used rotary wings and shot an insect toward the leading edge. This setup kept insects intact before impact while airflow was maintained throughout the experiment. Additionally, the setup enabled the long-term observation of the impact residue while the test speed was adjusted. Two experiments were carried out to investigate inconsistencies from past studies about insect rupture velocity and the effect of airflow on residue. Drosophila Hydei was the insect used, and aluminum was used as the baseline substrate, which was also coated with polyurethane, acrylic, and two superhydrophobic coatings. Instead of a threshold velocity for the minimum rupture velocity of the insect, a range from initial insect rupture to the velocity at which insects ruptured in all instances was determined (i.e., 17–30 m/s). Furthermore, the presence of a coating (polyurethane) on the airfoil did not affect the minimum rupture velocity. It was observed that airflow, which has been previously mentioned as a mitigation method, did not change the residue amount after coagulation for all coatings. Full article

This research explores the two-phase flow behavior involved in enhanced dense phase carbon dioxide inactivation of E. coli DH5α, which has been shown to possess a high microbial reduction efficiency of up to 3.7 ± 0.4 log. We present an experiment in which the liquid sample was pressurized with liquid carbon dioxide to 8.2 MPa and, after saturation, was forced to flow through a mini tube. An experimental setup was developed to visualize the flow patterns (plug, slug and churn flows) occurring in the mini tube by means of high-speed imaging. The values of the wall shear stress were estimated within the mini tube with the help of the gas slug velocities (8–9 m/s) and were compared with threshold shear stress values reported for the disruption of fresh E. coli cells. The results suggest that the preliminary pressurization phase may cause a substantial destabilization of the cell wall of E. coli DH5α. Full article

In this article, we report on numerical simulations of laminar Rayleigh–Bénard convection of air in cuboids. We provide numerical evidence of the existence of multiple steady states when the aspect ratio of the cuboid is sufficiently large. In our simulations, the Rayleigh number is fixed at $Ra=1.7\times {10}^4$. The gas in the cube is initially at rest but subject to random small-amplitude velocity perturbations and an adverse temperature gradient. When the flow domain is a cube, i.e., the aspect ratio is equal to unity, there is only one steady state. This state is characterized by the development of a single convective roll and by a symmetric normalized temperature profile with respect to the mid-height. On the contrary, when the aspect ratio is equal to 2, there are five different steady states. Only one of them exhibits a symmetric temperature profile and flow structure. The other four steady states are characterized by two-roll configurations and asymmetric temperature profiles. Full article

We investigate the dynamics and instabilities of a droplet that floats on a liquid substrate. The substrate is cooled from below. In the framework of the slender droplet approximation and the precursor model, the problem is studied numerically. Oscillatory and stationary regimes of thermocapillary convection have been observed. The influence of a two-dimensional spatial inhomogeneity of temperature on the droplet dynamics is investigated. The two-dimensional spatial temperature inhomogeneity can suppress oscillations, changing the droplet’s shape. In a definite region of parameters, the two-dimensional spatial modulation can lead to the excitation of periodic oscillations. The influence of the Biot number on the shape of the droplets is studied. Full article

Many problems in fluid mechanics describe the change in the flow under the effect of electromagnetic forces. The present study explores the behaviour of an electric conducting, Newtonian fluid flow applying the magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) principles. The physical problems for such flows are formulated by the Navier–Stokes equations with the conservation of mass and energy equations, which constitute a coupled non-linear system of partial differential equations subject to analogous boundary conditions. The numerical solution of such physical problems is not a trivial task due to the electromagnetic forces which may cause severe disturbances in the flow field. In the present study, a numerical algorithm based on a finite volume method is developed for the solution of such problems. The basic characteristics of the method are, the set of equations is solved using a simultaneous direct approach, the discretization is achieved using the finite volume method, and the solution is attained solving an implicit non-linear system of algebraic equations with intense source terms created by the non-uniform magnetic field. For the validation of the overall algorithm, comparisons are made with previously published results concerning MHD and FHD flows. The advantages of the proposed methodology are that it is direct and the governing equations are not manipulated like other methods such as the stream function vorticity formulation. Moreover, it is relatively easily extended for the study of three-dimensional problems. This study examines the Hartmann flow and the fluid flow with FHD principles, that formulate MHD and FHD flows, respectively. The major component of the Hartmann flow is the Hartmann number, which increases in value the stronger the Lorentz forces are, thus the fluid decelerates. In the case of FHD fluid flow, the major finding is the creation of vortices close to the external magnetic field source, and the stronger the magnetic field of the source, the larger the vortices are. Full article

In this work, we present a lower-dimensional model for flow and transport problems in thin domains with rough walls. The full-order model is given for a fully resolved geometry, wherein we consider Stokes flow and a time-dependent diffusion–convection equation with inlet and outlet boundary conditions and zero-flux boundary conditions for both the flow and transport problems on domain walls. Generally, discretizations of a full-order model by classical numerical schemes result in very large discrete problems, which are computationally expensive given that sufficiently fine grids are needed for the approximation. To construct a computationally efficient numerical method, we propose a model-order-reduction numerical technique to reduce the full-order model to a lower-dimensional model. The construction of the lower-dimensional model for the flow and the transport problem is based on the finite volume method and the concept of numerical averaging. Numerical results are presented for three test geometries with varying roughness of walls and thickness of the two-dimensional domain to show the accuracy and applicability of the proposed scheme. In our numerical simulations, we use solutions obtained from the finite element method on a fine grid that can resolve the complex geometry at the grid level as the reference solution to the problem. Full article

The acoustic properties of real liquids are largely related to the phase inclusions contained in them, of which gas bubbles are the most common. The aim of the work was to find the relationship between the nonlinear acoustic parameter and the cavitation strength of the liquid with the distribution of bubbles in the liquid, which has so far been poorly studied. The theoretical studies of the parameter of acoustic nonlinearity and the cavitation strength of a liquid with bubbles were carried out within the framework of the homogeneous approximation of a micro-homogeneous liquid; the relationship of these parameters with the bubble distribution function was established, and the typical values of these parameters for different concentrations of bubbles were calculated. Experimental measurements of the parameter of acoustic nonlinearity and the cavitation strength in the upper layer of seawater were carried out; these measurements were consistent with the theoretical estimates. A connection was established between the thresholds of acoustic and optical cavitation—the optical breakdown of a liquid by laser radiation. The results obtained can find practical application in the measurement of the cavitation strength of seawater at great depths in the sea, and the use of an optoacoustic method associated with the use of optical cavitation is proposed. Full article

Metachrony is defined as coordinated asynchronous movement throughout multiple appendages, such as the cilia of cells and swimmerets of crustaceans. Used by species of crustaceans and microscopic cells to move through fluid, the process of metachronal propulsion was investigated. A rigid crustacean model with paddles moving in symmetric strokes was created to simulate metachronal movement. Coupled with the surrounding fluid domain, the immersed boundary method was employed to analyze the fluid–structure interactions. To explore the effect of a nonlinear morphology on the efficiency of metachronal propulsion, a range of crustacean body shapes was generated and simulated, from upward curves to downward curves. The highest propulsion velocity was found to be achieved when the crustacean model morphology was a downward curve, specifically a parabola of leading coefficient k = −0.4. This curved morphology resulted in a 4.5% higher velocity when compared to the linear model. As k deviated from −0.4, the propulsion velocity decreased with increasing magnitude, forming a concave downward trend. The impact of body shape on propulsion velocity is shown by how the optimal velocity with k = −0.4 is 71.5% larger than the velocity at k = 1. Overall, this study suggests that morphology has a significant impact on metachronal propulsion. Full article

Hemodynamic simulations are increasingly used to study vascular diseases such as Intracranial Aneurysms (IA) and to further develop treatment options. However, due to limited data, certain aspects must rely on heuristics, especially at the simulation’s distal ends. In the literature, Murray’s Law is often used to model the outflow split based on vessel cross-section area; however, this poses challenges for the communicating arteries in the Circle of Willis (CoW). In this study, we contribute by assessing the impact of Murray’s Law in patient-specific geometries featuring IA at the posterior communication. We simulate different domain extensions representing common modelling choices and establish Full CoW simulations as a baseline to evaluate the effect of these modelling assumptions on hemodynamic indicators, focusing on IA growth and rupture-related factors such as the Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI). Our findings reveal qualitative alterations in hemodynamics when not modeling posterior communication. Comparisons between computing the anterior circulation and computing the whole Circle of Willis reveal that quantitative changes in WSS may reach up to 80%, highlighting the significance of modelling choices in assessing IA risks and treatment strategies. Full article