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This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficient techniques such as adsorption on granulated active carbon filters and micro-, nano-, or ultrafiltration. To have these processes under better control and to assure the transfer from small- to large-scale treatment stations, specific mathematical models are necessary. Starting from Navier–Stokes equations and imposing proper boundary conditions, some mathematical physics problems are obtained for which adequate solving methods via variational methods and surjectivity results are proposed. The importance of these solution characterizations consists in their continuation in adequate numerical methods and the possibility to visualize the result by using a CFD program. [ABSTRACT FROM AUTHOR]

The inviscid, nonlinear shallow water model developed by Sun was applied to study the inverse of equatorial Rossby solitons, which can be represented by the Korteweg–De Vries equation (KdV equation). The model was integrated forward in time, then the results were used as initial conditions for backward integration by just changing time step from positive to negative. The detailed structure, secondary circulation, and propagating speed of waves from both integrations are in good agreement with analytic solutions. The total mass, energy, and enstrophy are also well conserved. The procedure is much simpler and the results are more accurate than other backward integrations of 2D nonlinear models, which require significant modification of the model and can be contaminated by unwanted diffusion in forward–backward integrations or time-consuming iterative methods. This paper is also different from the numerical method for solving the inverse of the KdV equation. [ABSTRACT FROM AUTHOR]

Miller (Arch. Rational Mech. Anal., 2020) posed the question of whether it is possible to prove the Navier–Stokes regularity criterion using only one entry of the strain tensor S i j . Although this paper does not fully address this question, we do establish several scaling-invariant Serrin-type criteria based on one row of the strain tensor. [ABSTRACT FROM AUTHOR]

Background/Objectives: Arteriovenous (AV) graft is a procedure for hemodialysis performed in the arm. Optimizing AV graft design is vital to enhance haemodialytic efficiency in patients with kidney disease. Despite being a standard procedure, making it work optimally is still difficult due to various graft diameters and anastomosis configurations, which have limited studies. This research aims to find the ideal AV graft tube diameter on blood flow and pressure gradients and the ideal body site for AV graft implantation and to study their angles for dialysate flow. Methods: Nine models were designed in Autodesk Fusion 360 with 40°, 50°, and 60° angles each having 2 mm, 5.1 mm, and 14.5 mm diameters, all following specific equations on continuity, momentum (Navier-Stokes Equation)), and the Reynolds Stress Model (RSM). The CFD simulation of these models was performed in ANSYS Fluent with an established parameter of 0.3 m/s inlet velocity and stiff/no-slip graft and artery wall boundary condition. Results: As a result, the design with a diameter of 14.5 mm and a 40° angle was overall the most ideal in terms of minimal wall shear stress and turbulence. Conclusions: Thus the brachiocephalic area or the forearm is calculated to be the most optimal implantation site. Additionally, varying angles do affect dialysate flow, as smaller values cause less stress. [ABSTRACT FROM AUTHOR]

Natural rock fractures often exhibit non-matching characteristics at certain scales, leading to uneven aperture distributions that significantly affect fluid flow. This study investigates the impact of the mismatch between the upper and lower surfaces on the flow through three-dimensional rough fractures. By applying fractal theory, a rough upper surface of the fracture is generated, and different degrees of mismatch are introduced by adding random noise to this surface. This approach enables the construction of a variety of three-dimensional rough fracture flow models. Numerical simulations, which involve directly solving the Navier-Stokes equations, are used to simulate flow through a rough single fracture, assessing the effects of various degrees of mismatch between the surfaces. The study also examines how the inclusion of the matrix alters flow characteristics. The results demonstrate that the Forchheimer equation accurately describes the nonlinear flow behavior in fractures with different degrees of mismatch. The increased mismatch intensifies the uneven distribution of fracture apertures, causing the flow velocity to shift from uniform to discrete and the streamlines to become increasingly curved. The overall tortuosity of the flow path increases and the formation of 'concave' and 'convex' areas leads to vortex zones, promoting nonlinear seepage. The correlation between both viscous and inertial permeability with the degree of mismatch is negative, whereas the impact of matrix permeability on the flow capacity of the fracture shows a positive correlation with a mismatch. [ABSTRACT FROM AUTHOR]

During tunnel development in metal mines, there are situations where a zone of contact between the ore and the surrounding rock is reached. Nevertheless, there is a notable disparity in the mechanical characteristics between the ore and the surrounding rock, leading to a specific response of grouting in the contact area between the ore and rock. This response differs from the typical diffusion and curtain formation effects observed when using grouting slurry. This study investigates the effects of grouting curtain creation when implementing highly advanced curtain grouting in a water-rich highway, utilizing the engineering conditions of Zhongjiu Iron Mine as a reference. At first, Darcy's law and the Navier-Stokes equation are used to control the flow of fluid in the area where the ore-rock meets the rock around it. COMSOL, a multi-physical field coupled analysis software, is employed for the numerical simulation of slurry plane diffusion, single-hole, and group-hole curtain grouting. Two optimization strategies for group-hole grouting parameters are subsequently suggested and proven using numerical simulation. Finally, the project implements the research to assess the influence of curtain grouting by employing the water influx of the exploratory apertures as the standard of comparison before and after grouting; the results demonstrate that the slurry forms a highly efficient grouting curtain, effectively impeding water infiltration. The findings indicate that slurry diffusion in the contact zone between the ore and rock follows a spherical motion pattern, resulting in a considerable decrease in the flow rate compared to the previous stage. The force of gravity visibly affects the spreading of the slurry in the area where the ore and rock come into contact, causing the slurry to mostly spread downwards. This inclination intensifies as the rate of grouting is elevated. To successfully address the inadequate distribution of the slurry, one can either increase the rate at which grouting is performed or decrease the distance between the grouting holes. [ABSTRACT FROM AUTHOR]

Creating a high-quality aircraft engine is closely connected to the problem of obtaining the jet flow characteristics that appear while an aircraft's engine is in operation. As natural experiments are costly, studying turbulent jets by numerical simulation appears practical and acute. Biconic nozzle supersonic jet flow is the research subject of this article. A compression and expansion train of waves called barrels were formed in the jet flow at preset conditions. The simulation was performed on an unstructured numerical grid. In order to enhance the calculation accuracy in the shock-wave domain, a hybrid gradient computation scheme and numerical grid static adaptation method were applied in the regions of gas-dynamic values' significant differential. This approach resulted in a description of nozzle supersonic gas flow structure. It was shown that building local refinement when using a static adaptation numerical grid contributed to improving the accuracy of determining shock waves' fronts. In addition, this approach facilitated the identification of the Mach disk in the flow when using an unstructured grid, allowing for calculation schemes not higher than a second-order of accuracy. [ABSTRACT FROM AUTHOR]

This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the original boundary value problem. The model under consideration consists of the Navier–Stokes equations, the Maxwell equations without displacement currents, the generalized Ohm's law for a moving medium and the convection-diffusion equation for temperature. These relations are nonlinearly connected via the Lorentz force, buoyancy force in the Boussinesq approximation and convective heat transfer. Results concerning the existence and uniqueness of the solution of the original boundary value problem and of its generalized linear analog are presented. The global solvability of the control problem under study is proved and the optimality system is derived. Sufficient conditions on the data are established which ensure local uniqueness and stability of solutions of the control problems under study with respect to small perturbations of the cost functional to be minimized and one of the given functions. We stress that the unique stability estimates obtained in the paper have a clear mathematical structure and intrinsic beauty. [ABSTRACT FROM AUTHOR]

We consider evolution (non-stationary) spatially-periodic solutions to the n-dimensional non-linear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in spatial coordinates and time and satisfying the relaxed ellipticity condition. Employing the Galerkin algorithm with the basis constituted by the eigenfunctions of the periodic Bessel-potential operator, we prove the existence of a global weak solution. [ABSTRACT FROM AUTHOR]

This paper presents a study on the magnetic and thermal behaviors of a planar toroidal transformer, comprising two planar toroidal coils. In our configuration, the primary coil consists of twenty turns, while the secondary coil consists of ten turns. This design combines the advantages of both toroidal and planar transformers: it employs flat coils, akin to those utilized in planar transformers, while retaining a toroidal shape for its magnetic core. This combination enables leveraging the distinctive characteristics of both transformer types. This study delves into electromagnetic and thermal behaviors. Electromagnetic behavior is elucidated through Maxwell's equations, offering insights into the distribution of magnetic fields, potentials, and electric current densities. Fluid flow is modeled via the Navier–Stokes equations. By coupling these equation sets, a more comprehensive and accurate portrayal of the thermal phenomena surrounding electrical equipment is attained. Such research is invaluable in the design and optimization of electrical systems, empowering engineers to forecast and manage thermal effects more efficiently. Consequently, this aids in enhancing the reliability, durability, and performance optimization of electrical equipment. The mathematical model was solved using the finite element method integrated into the COMSOL Multiphysics software v. 6.0. The COMSOL Multiphysics simulation showed correct behavior of potential, electric field, current density, and uniformly distributed temperature. In addition, this planar toroidal coil transformer model offers many advantages, such as small dimensions, high resonance frequency, and high operating reliability. This study made it possible to identify the range of its optimal functioning. [ABSTRACT FROM AUTHOR]

Creating time-marching unsteady governing equations for a steady state in high-speed flows is not a trivial task. Residue convergence in time cannot be achieved when using most low- and high-order spatial discretization schemes. Recently, high-order, weighted, essentially non-oscillatory schemes have been specially designed for steady-state simulations. They have been shown to be capable of achieving machine precision residues when simulating the Euler equations under canonical coordinates. In the present work, we review these schemes and show that they can also achieve machine residues when simulating the Navier–Stokes equations under generalized coordinates. This is carried out by considering three supersonic flows of perfect fluids, namely the flow upstream a cylinder, the flow over a blunt wedge, and the flow over a compression ramp. [ABSTRACT FROM AUTHOR]

This work is devoted to the study of gas-dynamic processes in the operation of climate control systems in the cabins of vehicles (HVAC), focusing on pressure values. This research examines the issue of assessing the required values of air overpressure inside the locomotive cabin, which is necessary to prevent gas exchange between the interior of the cabin and the outside air through leaks in the cabin, including protection against the penetration of harmful substances. The pressure boost in the cabin depends, among other things, on the external air pressure on the locomotive body, the power of the climate system fan, and the ratio of the input and output deflectors. To determine the external air pressure, the problem of train movement in a wind tunnel is considered, the internal and external fluids domain is considered, and the air pressure on the cabin skin is determined using numerical methods CFD based on the Navier–Stokes equations, depending on the speed of movement. The finite-volume modeling package Ansys CFD (Fluent) was used as an implementation. The values of excess internal pressure, which ensures the operation of the climate system under different operating modes, were studied numerically and on the basis of an approximate applied formula. In particular, studies were carried out depending on the speed and movement of transport, on the airflow of the climate system, and on the ratio of the areas of input and output parameters. During a numerical experiment, it was found that for a train speed of 100 km/h, the required excess pressure is 560 kPa, and the most energy-efficient way to increase pressure is to regulate the area of the outlet valves. [ABSTRACT FROM AUTHOR]

Numerical modeling of wave transformation, hydrodynamics, and morphodynamics in coastal regions holds paramount significance for combating coastal erosion by evaluating and optimizing various coastal protection structures. This study aims to present an integration of numerical models to accurately simulate the coastal processes with the presence of coastal and harbor structures. Specifically, integrated modeling employs an advanced mild slope model as the main driver, which is capable of describing all the wave transformation phenomena, including wave reflection. This model provides radiation stresses as inputs to a hydrodynamic model based on Reynolds-averaged Navier–Stokes equations to simulate nearshore currents. Ultimately, these models feed an additional model that can simulate longshore sediment transport and bed level changes. The models are validated against experimental measurements, including energy dissipation due to bottom friction and wave breaking; combined refraction, diffraction, and breaking over a submerged shoal; wave transformation and wave-generated currents over submerged breakwaters; and wave, currents, and sediment transport fields over a varying bathymetry. The models exhibit satisfactory performance in simulating all considered cases, establishing them as efficient and reliable integrated tools for engineering applications in real coastal areas. Moreover, leveraging the validated models, a numerical investigation is undertaken to assess the effects of wave reflection on a seawall on coastal processes for two ideal beach configurations—one with a steeper slope of 1:10 and another with a milder slope of 1:50. The numerical investigation reveals that the presence of reflected waves, particularly in milder bed slopes, significantly influences sediment transport, emphasizing the importance of employing a wave model that takes into account wave reflection as the primary driver for integrated modeling of coastal processes. [ABSTRACT FROM AUTHOR]

The semi-circular breakwater (SBW) has been implemented at numerous global locations due to its outstanding wave dissipation effectiveness and high structural performance. This study extends prior research by investigating the seabed dynamic response and hydrodynamic response characteristics around perforated SBWs. A coupled numerical model is developed to integrate waves, a semi-circular breakwater, and a sandy seabed. Wave behavior is simulated using Reynolds-averaged Navier–Stokes equations with a k-ε turbulence closure scheme, and the seabed response is numerically simulated using Biot's full-dynamic (u-w) equations. After verifying computational accuracy, a series of tests is conducted to explore the effects of marine environments and SBW characteristics. Test results reveal a positive correlation between seabed response and wave height, wave period, and perforation number, while showing a negative correlation between seabed response and water depth and perforation rate. The basic perforation type is more effective than front and rear perforation types in maintaining a stable flow field and seabed response. These findings provide insights for designing SBWs for effective wave dissipation and seabed stability in complex marine environments, offering valuable recommendations for future designs. [ABSTRACT FROM AUTHOR]

A reliable initiation of oblique detonation is critical in oblique detonation engines, especially for oblique detonation engines under extreme conditions such as a high altitude and low Mach number, which may lead to excessive length of the induction zone and even the phenomenon of extinction. In this paper, surface ignition was applied to the initiation of oblique detonation, and a high-temperature region was set on the wedge to simulate the presence of a hot-spot induced by the laser heating. The two-dimensional multi-component Navier–Stokes equations considering a detailed H2 combustion mechanism are solved, and the oblique detonation wave accelerated by a hot-spot is studied. In this paper, hot-spots in the induction zone on the wedge, are introduced to explore the possibility of hot-spot initiation, providing a potential method for initiation control. Results show that these methods can effectively promote the accelerated initiation of the oblique detonation. Furthermore, the hot-spot temperature, size and position are varied to analyze their effects on the initiation position. Increasing the temperature and size of the hot-spot both can accelerate initiation, but from the perspective of energy consumption, a small hot-spot at a high temperature is preferable for accelerating ODW initiation than a large hot-spot at a low temperature. The initiated position of the oblique detonation is sensitive to the position of the hot-spots; if a 2000 K hotspot is at the beginning of the wedge, then the ODW's initiation distance will be reduced to about 30% of that without hotspot acceleration. [ABSTRACT FROM AUTHOR]

Aircraft cabin noise poses a health risk for regular passengers and crew, being connected to a heightened risk of cardiovascular disease, hearing loss, and sleep deprivation. At cruise conditions, its most significant cause is random pressure fluctuations in the turbulent boundary layer of aircraft, and as such the derivation of an accurate model to predict the power spectral density of these fluctuations remains an important ongoing research topic. Early models (such as those by Lowson and Robertson) were derived by simplifying the governing equations, the Reynolds-averaged Navier Stokes equations, and solving for fluctuating pressure. Most subsequent equations were derived either by applying statistical and mathematical techniques to simplify the Robertson and Lowson models or by making modifications to address apparent shortcomings. Overall, these models have had varying success—most are accurate near the Mach and Reynolds numbers they were designed for, but less accurate under other conditions. In response to this shortcoming, Dominique demonstrated that a novel technique (machine learning, specifically artificial neural networking) could produce a model that is accurate under most flight conditions. This paper extends this research further by applying a different machine learning technique (nonlinear least squares regression analysis) and dimensional analysis to produce a new model. The resulting equation proved accurate under its design conditions of low airspeed (approximately 11 m/s) and low turbulent Reynolds number (approximately 850,000). However, a larger dataset with more diverse flight conditions would be required to make the model more generally applicable. [ABSTRACT FROM AUTHOR]

Due to their complex aerodynamics, helicopters may enter different dangerous aerodynamic conditions under certain adverse circumstances. In this paper, we examine one such phenomenon—the Vortex Ring State (VRS). We present a simulation of the formation and evolution of a vortex ring around a helicopter's main rotor. The calculations were carried out by solving Navier–Stokes equations using the Ansys CFX code. The simulations modeled a real helicopter using the rotor wing concept, assuming that only the main rotor blade's geometry was modeled. A sensitivity study assessed the impact of the calculation domain and mesh size on main rotor thrust and required moment parameters. Simulations were conducted to determine the VRS region by observing the transition of the helicopter from a level flight, with the main rotor blades held at a fixed pitch position, to a gradual increase in vertical descent. The VRS region was compared with experimental results obtained from other authors, revealing sufficient coincidences. The main characteristics of the identified region were then described. [ABSTRACT FROM AUTHOR]

The twin problems of closure and dissipation have been barriers to the analytical solution of the Navier–Stokes equation for fluid flow by top-down methods for two centuries. Here, the statistical multifractal analysis of airborne observations is used to argue that bottom-up approaches based on the dynamic behaviour of the basic constituent particles are necessary. Contrasts among differing systems will yield scale invariant turbulence, but not with universal analytical solutions to the Navier–Stokes equation. The small number of publications regarding a molecular origin for turbulence are briefly considered. Research approaches using suitable observations are recommended. [ABSTRACT FROM AUTHOR]

Current developments in vehicles have generated great interest in the research and optimization of heating, ventilation, and air conditioning (HVAC) systems as a factor to reduce fuel consumption. One of the key trends for finding solutions is the intensive development of electric transport and, consequently, additional requirements for reducing energy consumption and modifying climate systems. Of particular interest is the optimal functioning of comfort and life support systems during air recirculation, i.e., when there is a complete or partial absence of outside air supply, in particular to reduce energy consumption or when the environment is polluted. This work examines numerical models of airfields (temperature, speed, and humidity) and also focuses on the concentration of carbon dioxide and oxygen in the cabin, which is a critical factor for ensuring the health of the driver and passengers. To build a mathematical model, the Navier–Stokes equations with energy, continuity, and diffusion equations are used to simulate the diffusion of gases and air humidity. In the Ansys Fluent finite volume analysis package, the model is solved numerically using averaged RANS equations and k-ω turbulence models. The cabin of a mainline locomotive with two drivers, taking into account their breathing, is used as a transport model. The problem was solved in a nonstationary formulation for the design scenario of summer and winter, the time of stabilization of the fields was found, and graphs were constructed for different points in time. A comparative analysis of the uniformity of fields along the height of the cabin was carried out with different locations of deflectors, and optimal configurations were found. Energy efficiency values of the climate system operation in recirculation operating modes were obtained. A qualitative assessment of the driver's blowing directions under different circulation and recirculation modes is given from the point of view of the concentration of carbon dioxide in the breathing area. The proposed solution makes it possible to reduce electricity consumption from 3.1 kW to 0.6 kW and in winter mode from 11.6 kW to 3.9 kW and save up to 1.5 L/h of fuel. The conducted research can be used to develop modern energy-efficient and safe systems for providing comfortable climate conditions for drivers and passengers of various types of transport. [ABSTRACT FROM AUTHOR]

An explicit computational scheme is proposed for solving fractal time-dependent partial differential equations (PDEs). The scheme is a three-stage scheme constructed using the fractal Taylor series. The fractal time order of the scheme is three. The scheme also ensures stability. The approach is utilized to model the time-varying boundary layer flow of a non-Newtonian fluid over both stationary and oscillating surfaces, taking into account the influence of heat generation that depends on both space and temperature. The continuity equation of the considered incompressible fluid is discretized by first-order backward difference formulas, whereas the dimensionless Navier–Stokes equation, energy, and equation for nanoparticle volume fraction are discretized by the proposed scheme in fractal time. The effect of different parameters involved in the velocity, temperature, and nanoparticle volume fraction are displayed graphically. The velocity profile rises as the parameter I grows. We primarily apply this computational approach to analyze a non-Newtonian fluid's fractal time-dependent boundary layer flow over flat and oscillatory sheets. Considering spatial and temperature-dependent heat generation is a crucial factor that introduces additional complexity to the analysis. The continuity equation for the incompressible fluid is discretized using first-order backward difference formulas. On the other hand, the dimensionless Navier–Stokes equation, energy equation, and the equation governing nanoparticle volume fraction are discretized using the proposed fractal time-dependent scheme. [ABSTRACT FROM AUTHOR]

Extracting statistics for turbulent flows directly from the Navier–Stokes equations poses a formidable challenge, particularly when dealing with unsteady or inhomogeneous flows. However, embracing Kolmogorov's inertial range spectrum for isotropic turbulence as a dynamic equilibrium provides a conceptual starting point for perturbation theory. We review theoretical results, combining perturbation approaches, and phenomenological turbulence closures, which allow us to gain valuable insights into the statistics of unsteady and inhomogeneous turbulence. Additionally, we extend the ideas to the case of the mixing of a passive scalar. [ABSTRACT FROM AUTHOR]

Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward-facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier–Stokes equations are reduced to the nonlinear boundary region equations (BREs) in a high Reynolds number asymptotic framework, wherein the streamwise wavelength of the disturbances is assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number M ∞ , the shear layer thickness δ , the amplitude of the incoming disturbance A, and the relative velocity difference across the shear layer Δ V on the development of these centrifugal instabilities. Our parametric study shows that, among other things, the kinetic energy of the curved shear layer flow increases with increasing Δ V and A decreases with increasing d e l t a . It was also found that increasing the disturbance amplitude of the incoming disturbance leads to significant growth in the mushroom-like structure's amplitude and renders the secondary instability structures more prominent, indicating increased mixing for all Mach numbers under consideration. [ABSTRACT FROM AUTHOR]

This study proposes a new computational framework for the multi-objective topology optimization of conjugate heat transfer systems using a continuous adjoint approach. It relies on a monolithic solver for the coupled steady-state Navier–Stokes and heat equations, which combines finite elements stabilized by the variational multi-scale method, level set representations of the fluid–solid interfaces and immersed modeling of heterogeneous materials (fluid–solid) to ensure that the proper amount of heat is exchanged to the ambient fluid by solid objects in arbitrary geometry. At each optimization iteration, anisotropic mesh adaptation is applied in near-wall regions automatically captured by the level set. This considerably cuts the computational effort associated with calling the finite element solver, in comparison to traditional topology optimization algorithms operating on isotropic grids with a comparable refinement level. Given that we operate within the constraint of a specified number of nodes in the mesh, this allows not only to improve the accuracy of interface representation and motion but also to retain the high fidelity of the numerical solutions at the grid points just adjacent to the interface. Finally, the remeshing and resolution steps both run within a highly parallel environment, which makes it possible for the proposed algorithm to tackle large-scale problems in three dimensions with several tens of millions of state degrees of freedom. The developed solver is validated first by minimizing dissipation in a flow splitter device, for which the method delivers relevant optimal designs over a wide range of volume constraints and flow rate distributions over the multiple outlet orifices but yields better accuracy compared to reference data from literature obtained using uniform meshes (in the sense that the layouts are more smooth, and the solutions are better resolved). The scheme is then applied to a two-dimensional heat transfer problem, using bi-objective cost functionals combining flow resistance and thermal recoverable power. A comprehensive parametric study reveals a complex arrangement of optimal solutions on the Pareto front, with multiple branches of symmetric and asymmetric designs, some of them previously unreported. Finally, the algorithmic developments are substantiated with several three-dimensional numerical examples tackled under fixed weights for heat transfer and flow resistance, for which we show that the optimal layouts computed at low Reynolds number, that are intrinsically relevant to a broad range of microfluidic application, can also serve as smooth solutions to high-Reynolds-number engineering problems of practical interest. [ABSTRACT FROM AUTHOR]

Coral reefs are effective natural flood barriers that protect adjacent coastal communities. As the need to adapt to rising sea levels, storms, and environmental changes increases, reef restoration may be one of the best tools available to mitigate coastal flooding along tropical coastlines, now and in the future. Reefs act as a barrier to incoming short-wave energy but can amplify low-frequency infragravity waves that, in turn, drive coastal flooding along low-lying tropical coastlines. Here, we investigate whether the spacing of reef restoration elements can be optimized to maximize infragravity wave energy dissipation while minimizing the number of elements—a key factor in the cost of a restoration project. With this goal, we model the hydrodynamics of infragravity wave dissipation over a coral restoration or artificial reef, represented by a canopy of idealized hemispherical roughness elements, using a three-dimensional Navier–Stokes equations solver (OpenFOAM). The results demonstrate that denser canopies of restoration elements produce greater wave dissipation under larger waves with longer periods. Wave dissipation is also frequency-dependent: dense canopies remove wave energy at the predominant wave frequency, whereas sparse canopies remove energy at higher frequencies, and hence are less efficient. We also identify an inflection point in the canopy density–energy dissipation curve that balances optimal energy losses with a minimum number of canopy elements. Through this work, we show that there are an ideal number of restoration elements per across-shore meter of coral reef flat that can be installed to dissipate infragravity wave energy for given incident heights and periods. These results have implications for designing coral reef restoration projects on reef flats that are effective both from a coastal defense and costing standpoint. [ABSTRACT FROM AUTHOR]

In the present study, a passive flow device is considered for drag reduction purposes through implementation in a transonic high-power rocket. The high-power rocket serves as a reference platform that, apart from the operating conditions, enforces several constraints in terms of available volume and placement locations. A step-by-step methodology is suggested, where the unit is initially broken down into an inlet and an outlet component. The flow field is investigated by means of computational modeling (CFD), where the Reynolds-averaged Navier–Stokes equations are solved coupled with turbulence models that vary depending on the design phase and the individual component. In the first design phase, the best alternative configuration is selected for each component by comparing mass flow rates and discharge coefficients. In the second design phase, each component is analyzed in greater detail based on the first phase results. Indicatively, the protruding inlet diffuser-type channel is converted into a protruding inlet nozzle-type channel to avoid choked flow phenomena, and a nozzle geometry is selected as the outlet amongst the other considered scenarios. The two components are eventually integrated into a common base bleed unit and a final assessment is made. The computational results are used to predict the performance and trajectory of the rocket through a well-established trajectory software. The overall methodology is validated against full-scale test flight data. The results show that the base bleed unit developed in the framework of this study yields a drag reduction of approximately 15% at transonic speeds without impacting the rocket mass and stability. [ABSTRACT FROM AUTHOR]

The Phase-Change Heat Exchanger Unit in Layered Porous Media (PCEU-LPM) is obtained through frozen pouring processing, and exhibits characteristics such as high thermal conductivity, high latent heat, and high permeability, making it suitable for dissipating heat in airborne electronic devices. This study numerically investigates the impact of aircraft speed acceleration conditions, which lead to weightlessness or overload, on the performance of the PCHEU-LPM, with a particular focus on the influence of natural convection in the liquid-phase region. Initially, a microscale thermal analysis model is established based on the Navier–Stokes equation scanning electron micrograph to calculate the effective thermal conductivity and permeability of the PCHEU-LPM under different porosities. Subsequently, these parameters are incorporated into a macroscale thermal analysis model based on Darcy's law, employing an average parameter approach. Using the macroscale thermal analysis model, temperature and velocity fields are computed under various porosities, acceleration magnitudes, and directions. The calculation results indicate that as the acceleration increases from α = 0 to α = 10 g, the interface temperature of the PCHTU-LPM decreases by approximately 5.2 K, and the temperature fluctuation decreases by 2.4 K. If the porosity of the PCHTU-LPM is increased from ε = 70% to ε = 85%, the influence of acceleration change on natural convection will be further amplified, resulting in a decrease in the interface temperature of the PCHTU-LPM by approximately 10.2 K and a decrease in temperature fluctuation by 5.8 K. When the acceleration direction is +z, the interface temperature of the PCHTU-LPM is at its lowest, while it is highest when the acceleration direction is −z, with a maximum difference of 15.4 K between the two. When the acceleration direction is ±x and ±y, the interface temperature lies between the former two cases, with the interface temperature slightly higher for ±y compared to ±x, with a maximum difference of 3.9 K between them. [ABSTRACT FROM AUTHOR]

In this paper, a numerical investigation is performed to study the broadband noise of a fan stage with wavy trailing-edge blades. A study of the wavelength and ratio of amplitude to wavelength (H/L) is conducted to better understand the noise reduction effect of wavy trailing-edge blades. A rotor–stator interaction broadband noise prediction method based on the result of a Reynolds-averaged Navier–Stokes equation is used. The results show that all wavy trailing-edge configurations reduce the sound power level of the fan stage. The noise reduction effect of H20L10 is the best among all the wavy trailing-edge configurations, and the sound power level is reduced by 2.4 dB at 1000 Hz. When the H/L remains unchanged, the noise reduction effect of the wavy trailing-edge configuration increases with the increase in wavelength. When the wavelength remains unchanged, the noise reduction effect of the wavy trailing-edge configuration with an H/L of 2 is the best. The use of wavy trailing-edge configurations reduces the turbulent kinetic energy and turbulent integral length scale upstream of the stator by changing the wake of the rotor, thereby reducing the rotor–stator interaction broadband noise of the fan stage. [ABSTRACT FROM AUTHOR]

Metallic zinc (Zn) presents a compelling alternative to conventional electrochemical energy storage systems due to its environmentally friendly nature, abundant availability, high water compatibility, low toxicity, low electrochemical potential (−0.762 V vs. SHE), and cost-effectiveness. While considerable efforts have been devoted to enhancing the physical and chemical properties of zinc-ion battery materials to improve battery efficiency and longevity, research on multi-physics coupled modeling for a deeper understanding of battery performance remains relatively scarce. In this study, we established a comprehensive two-dimensional model for single-flow zinc–nickel redox batteries to investigate electrode reactions, current-potential behaviors, and concentration distributions, leveraging theories such as Nernst–Planck and Butler–Volmer. Additionally, we explored the distribution of the velocity field using the Brinkman theory in porous media and the Navier–Stokes equations in free-flow channels. The validated model, informed by experimental data, not only provides insights into the performance of the battery, but also offers valuable recommendations for advancing single-flow zinc–nickel battery technology. Our findings offer promising avenues for enhancing the design and performance of not only zinc–nickel flow batteries, but also applicable for other flow battery designs. [ABSTRACT FROM AUTHOR]

This paper presents a topology optimization (TopO) method for conjugate heat transfer (CHT), with turbulent flows. Topological changes are controlled by an artificial material distribution field (design variables), defined at the cells of a background grid and used to distinguish a fluid from a solid material. To effectively solve the CHT problem, it is crucial to impose exact boundary conditions at the computed fluid–solid interface (FSI); this is the purpose of introducing the cut-cell method. On the grid, including also cut cells, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model with wall functions, and the temperature equation are solved. The continuous adjoint method computes the derivatives of the objective function(s) and constraints with respect to the material distribution field, starting from the computation of derivatives with respect to the positions of nodes on the FSI and then applying the chain rule of differentiation. In this work, the continuous adjoint PDEs are discretized using schemes that are consistent with the primal discretization, and this will be referred to as the "Think Discrete–Do Continuous" (TDDC) adjoint. The accuracy of the gradient computed by the TDDC adjoint is verified and the proposed method is assessed in the optimization of two 2D cases, both in turbulent flow conditions. The performance of the TopO designs is investigated in terms of the number of required refinement steps per optimization cycle, the Reynolds number of the flow, and the maximum allowed power dissipation. To illustrate the benefits of the proposed method, the first case is also optimized using a density-based TopO that imposes Brinkman penalization terms in solid areas, and comparisons are made. [ABSTRACT FROM AUTHOR]

The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier–Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature's findings. This approach offers an alternative to previously proposed methods for IBM implementation. [ABSTRACT FROM AUTHOR]

Predictions are presented of mean values of statistical variables of large-scale turbulent flow of the widely used basic k- ϵ model, and of a new model, which is based on general statistical descriptions of turbulence. The predictions are verified against published results of direct numerical simulations (DNSs) of Navier–Stokes equations. The verification concerns turbulent channel flow at shear Reynolds numbers of 950, 2000, and 10 4 . The basic k- ϵ model is largely based on empirical formulations accompanied by calibration constants. This contrasts with the new model, where descriptions of leading statistical quantities are based on the general principles of statistical turbulence at a large Reynolds number and stochastic theory. Predicted values of major output variables such as turbulent viscosity, diffusivity of passive admixture, temperature, and fluid velocities compare well with DNS for the new model. Significant differences are seen for the basic k- ϵ model. [ABSTRACT FROM AUTHOR]

Vertical axis wind turbines (VAWTs) are gaining increasing significance in the realm of renewable energy. One notable advantage they possess is their ability to operate efficiently in diverse wind conditions, including low-speed and turbulent winds, which are often prevalent in urban areas. In this study, dimples and pitch angles into the rotor blades are used to enhance the aerodynamic performance of a straight-bladed Darrieus turbine. To simulate the turbine's rotation under transient conditions, computational fluid dynamics calculations are conducted in a two-dimensional setting. The unsteady Navier–Stokes equations are solved, and the k-ω SST turbulence model is employed to represent turbulent flow. The results of the simulation demonstrate that the application of a circular dimple on the pressure side of the blades, positioned at 0.25 of the chord length with a diameter of 0.08 chord length, leads to a 5.18% increase in the power coefficient at λ = 2.7, in comparison to a turbine with plain airfoils. Moreover, when an airfoil with both a dimple and a + 1° pitch angle is utilized, the turbine's performance at λ = 2.7 improved by 7.17% compared to a plain airfoil, and by 1.8% compared to a dimpled airfoil without a pitch angle. Additionally, the impact of a double dimple on both the pressure and suction sides of the airfoil on turbine performance was investigated. It was discovered that the double-dimpled airfoil exhibited lower performance in comparison to a plain airfoil. The study showed that the utilization of both dimples and pitch angles for airfoils of a Darrieus turbine blade increases the power generated by the turbine. [ABSTRACT FROM AUTHOR]

A three-dimensional Navier–Stokes and continuity equation model is employed to numerically predict the resonant modes of sessile droplets on horizontally vibrating substrates. A dynamic contact angle model is implemented to simulate the contact angle variations during vibrations. The four resonant modes (n = 1, 2, 3 and 4) of a droplet under horizontal vibrations are investigated. Simulations are compared to experimental results for validation. Excellent agreement is observed between predicted results and experiments. The model is used to simulate the internal flow patterns within the droplet under resonant modes. It is found that the flow in all four resonant modes can be divided into the Stokes region, the gas–liquid interface region, and the transition region located in between. Numerical simulations show that the average velocity within the droplet increases with the increase in frequency, while the fluctuations in average velocity after reaching the steady state show different trends with the increase in frequency. It is also found that with an increase in the order of resonant modes, the contact angle difference between the two sides of the droplet increases, and the contact angle difference of the droplet is maximized when the applied frequency is the resonant frequency of the specified mode. [ABSTRACT FROM AUTHOR]

Fluid migration in a fracture network plays an important role in the oil accumulation mechanism and hence is key to oil exploration. In this study, we build a model by combining one-dimensional (1D) Navier–Stokes equations, linear elastic equations, and energy equations, and validate the model by reproducing the thickness profile of a fluid-driven crack measured in an experiment. We employ this model to simulate the upward flow of viscous fluid in a single fracture during hydrocarbon migration. The simulation suggests that the parameters of both the fluid and the surrounding rock matrix, as well as the boundary condition imposed on the fracture outlet, affect the upward flow in the fracture. We then extend our model from the single fracture to the bifurcated fracture and the fracture network by maintaining homogeneous pressure and mass conservation at the connection of the channels. We find that the increase in network complexity leads to an increase in the inlet pressure gradient and inlet speed, and a decrease in the outlet pressure gradient and outlet speed. The effective area where the fluid is driven upward from the inlet to the outlet is offset toward the inlet. More importantly, the main novelty of our model is that it allows us to evaluate the effect of inconsistencies in individual branch parameters, such as matrix stiffness, permeability, temperature, and boundary conditions, on the overall upward flow of viscous fluid. Our results suggest that the heterogeneity enforces the greater impact on the closer branches. [ABSTRACT FROM AUTHOR]

Pressure gain combustion cycles are under the spotlight due to their higher theoretical cycle thermal efficiency compared to conventional machines. Under this prism, a constant-volume combustor (CVC) prototype supplied with a mixture of air and liquid iso–octane was developed. The efforts of the current study were focused on both creating a 1D model of the experimental test rig for the CVC analysis and a 3D numerical simulation of the exhaust system. The goal of the study was to retrieve the total outlet quantities of the combustor, which would otherwise be difficult to assess experimentally, and to investigate the pulsating flow field at the outlet. First, a thorough description of the reduced order model was accompanied with the model's validation using the available experimental data of the chamber. Then, the resulting outlet stagnation properties of the CVC were imposed as spatially averaged transient boundary conditions to the 3D exhaust flow domain. The unsteady Reynolds–averaged Navier–Stokes equations were solved for a sufficient number of periods, and the assessment of the out-take system in terms of losses and attenuation was conducted. In conclusion, the analysis of the combustor's outflow will pave the way for an effective future design of the CVC exhaust system. [ABSTRACT FROM AUTHOR]

Reaction fronts propagating in liquids separate reacted from unreacted fluid. These reactions may release heat, increasing the temperature of the propagating medium. As fronts propagate, they will induce density changes leading to convection. Exothermic fronts that propagate upward increase the temperature of the reacted fluid located underneath the front. For positive expansion coefficients, the warmer fluid will tend to rise due to buoyancy. In the opposite case, for fronts propagating downward with the warmer fluid on top, an unexpected thermally driven instability can also take place. In this work, we carry out a linear stability analysis introducing perturbations of fixed wavelength. We obtain a dispersion relation between the perturbation wave number and its growth rate. For either direction of propagation, we find that the front is stable for very short wavelengths, but is unstable for large enough wavelengths. We carry out a numerical solution of a cubic reaction–diffusion–advection equation coupled to Navier–Stokes hydrodynamics in a two-dimensional rectangular domain. We find transitions between the non-axisymmetric and axisymmetric fronts increasing with the width of the domain. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the solvability of a boundary value problem for a heat and mass transfer model with the spatially averaged Rayleigh function. The considered model describes the 3D steady-state non-isothermal flow of a generalized Newtonian fluid (with shear-dependent viscosity) in a bounded domain with Lipschitz boundary. The main novelty of our work is that we do not neglect the viscous dissipation effect in contrast to the classical Boussinesq approximation, and hence, deal with a system of strongly nonlinear partial differential equations. Using the properties of the averaging operation and d-monotone operators as well as the Leray–Schauder alternative for completely continuous mappings, we prove the existence of weak solutions without any smallness assumptions for model data. Moreover, it is shown that the set of all weak solutions is compact, and each solution from this set satisfies some energy equalities. [ABSTRACT FROM AUTHOR]

This paper presents the experience of using the V Flow high-frame-rate ultrasound vector imaging method to study the pulsatile velocity fields in the area of the proximal anastomosis for femoral popliteal bypass surgery in vitro and in vivo. A representative (average) anastomosis model and the experimental setup designed for in vitro studies covering forward and reverse flow phases throughout the cycle are described. The results of the measurements are presented for areas with a relatively uniform velocity distribution and for areas with pronounced spatial inhomogeneities due to the jet or recirculating nature of the flow. The results of ultrasonic studies of the velocity field of the three-dimensional pulsatile flow in vitro and in vivo are compared with the data of numerical simulations carried out for the average and personalized models based on the Navier–Stokes equations. Acceptable consistency between the results of experimental and numerical studies is demonstrated. [ABSTRACT FROM AUTHOR]

The fluidic pintle nozzle, a new method to control the thrust of a solid rocket motor, has been proposed in recent years by combining the pintle with the aerodynamic throat (fluidic throat). The study of static characteristics has proved that it has a remarkable effect on thrust control. To study the transient characteristics of the fluidic pintle nozzle, 2D transient simulations of a fluidic pintle nozzle propulsion system were conducted, employing dynamic meshing techniques. The Reynolds-averaged Navier–Stokes equations were meticulously solved, implementing a k–ω SST turbulence model. The thrust control principle of the fluid pintle nozzle was studied, and the wave structure was summarized. The transient characteristics of the secondary flow opening, secondary flow closing, pintle moving forward (pressure rise), and pintle moving backward (pressure drop) were obtained, and the effects of the injection angle and injection port position were studied. The response process after injection can be roughly divided into three stages: pressure propagation, pressure oscillation, and equilibrium stability, with time distributions of 0.4%, 5.39%, and 94.21%, respectively. In the process of the pintle moving forward, the rate of combustion chamber pressure increases and thrust decreases gradually because of the arc wall of the nozzle throat upstream, and the process of throats moving backward is just the opposite. Compared with the condition with a maximum throat opening and no secondary flow, the thrust of the condition with a minimum throat opening and a 0.3-flow-ratio secondary flow is increased by 80.95%. Under conditions of constrained flow ratio, the injection angle of the secondary flow ostensibly exerts negligible influence on the dynamic modulation of thrust. Nevertheless, it remains evident that a reduction in throat opening accentuates the impact of reverse injection. Furthermore, the proximity of the injection port to the head of the pintle is directly proportional to the efficacy of thrust control. [ABSTRACT FROM AUTHOR]

Future UHBR (Ultra-High Bypass-Ratio) engines might cause serious 'turbine noise storms' but, at present, turbine noise prediction capability is lacking. The large turning angle of the turbine blade is the first major factor deserving special attention. The RANS (Reynold Averaged Navier–Stokes equation)-informed (here called RI) method and LINSUB (the bound vorticity 2D model LINearized SUBsonic flow in cascade), developed to predict fan broadband noise, coupled with a two-flat-plates (here called TP) assumption for the turbine blade, is applied here, and one autonomous rapid RI-TP model for predicting turbine wake interaction broadband noise has been developed. Firstly, taking the single axial turbine test rig NPU-Turb as the object, both the experimental data and the DDES/AA (delayed Detached Eddy Simulation/Acoustic Analogy) hybrid model have been used to validate the RI-TP model. High consistency in the medium and high frequencies among the three designed and off-designed rotation speeds indicates that the RI-TP model has the ability to predict turbine broadband noise rapidly. And compared with the original RANS-informed method, with one thin-flat-plate assumption on the blade, the RI-TP model can enhance the PWL (sound power level) in almost the whole spectral range below 10 KHz, which, in turn, is closer to the experimental data and the DDES/AA prediction results. The PWL trend with a 'dividing point' position is also studied. The spectrum would move up or down if the location is away from true value. In addition, the extraction location for turbulence as an input for the RI-TP model is negligible. In the future, multi-stage characteristics and the blade thickness effect should be further considered when predicting turbine noise. [ABSTRACT FROM AUTHOR]

Various researchers in the field of engineering have used porous media for many years. The present paper studies heat enhancement using two different types of porous media. In the first type, porous metal foam media was used experimentally and numerically for heat extraction. The porous medium was replaced with a porous structure using the Gyroid model and the triply periodic minimum surfaces technique in the second type. The Darcy–Brinkman model combined with the energy equation was used for the first type, whereas Navier–Stokes equations with the energy equation were implemented for the second type. The uniqueness of this approach was that it treated the Gyroid as a solid structure in the model. The two types were tested for different heat fluxes and different flow rates. A comparison between the experimental measurements and the numerical solution provided a good agreement. By comparing the performance of the two types of structure, the Gyroid structure outperformed the metal foam for heat extraction and uniformity of the temperature distribution. Despite an 18% increase in the pressure drop in the presence of the Gyroid structure, the performance evaluation criteria for the Gyroid are more significant when compared to metal foam. [ABSTRACT FROM AUTHOR]

Land subsidence is a global challenge that enhances the vulnerability of aquifers where climate change and driving forces are occurring simultaneously. To comprehensively analyze this issue, integrated modeling tools are essential. This study advances the simulation of subsidence using Computational Fluid Dynamics (CFD); it assessed the effects of exploitation and recharge of groundwater on the vertical displacement of coarse and fine sands in a laboratory-scale aquifer. A model was developed by integrating the Navier–Stokes equations to study the groundwater flow and Terzaghi's law for the vertical displacement of sands. The boundary conditions used were Dirichlet based on the changes in the hydraulic head over time. The specific storage coefficient was used to calibrate the model. The findings confirmed that subsidence occurs at slower rates in soil with fine sands with average particle diameters of 0.39 mm than in coarse sands with average particle diameters of 0.67 mm. The maximum discrepancy between the experimental and the numerical reaffirms that CFD platforms can be used to simulate subsidence dynamics and potentially allow the simultaneous simulation of other dynamics. Concluding remarks and recommendations are highlighted considering the up-to-date advances and future work to improve the research on subsidence in unconfined aquifers. [ABSTRACT FROM AUTHOR]

This work's goal is to numerically investigate the interactions between two gas bubbles in a fluid flow in a circular cross-section channel, both in the presence and in the absence of gravitational forces, with several Reynolds and Weber numbers. The first bubble is placed at the center of the channel, while the second is near the wall. Their positions are set in such a way that a dynamic interaction is expected to occur due to their velocity differences. A finite element numerical tool is utilized to solve the incompressible Navier–Stokes equations and simulate two-phase flow using an unfitted mesh to represent the fluid interface, akin to the front-tracking method. The results show that the velocity gradient influences bubble shapes near the wall. Moreover, lower viscosity and surface tension force account for more significant interactions, both in the bubble shape and in the trajectory. In this scenario, it can be observed that one bubble is trapped in the other's wake, with the proximity possibly allowing the onset of coalescence. The results obtained contribute to a deeper understanding of two-phase inner flows. [ABSTRACT FROM AUTHOR]

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa. [ABSTRACT FROM AUTHOR]

Submerged Reefs (SRs) are a kind of artificial fish habitat that can protect coasts and maintain ecological biodiversity. In this study, the flow field of the SR is simulated by solving a Reynolds-averaged Navier–Stokes equation closed with the Realizable k-ε model based on the finite volume method. The turbulent characteristics of SRs under different inflow velocities and submergences in the vicinity of the SR are analyzed. The wake vorticities are the primary turbulent pattern within and around the SR. The back wake and vorticity are chosen as critical indicators to quantitatively assess the hydrodynamic characteristics induced by the SR. The results show: (1) as the main flow passes through the SR, the upwelling is produced in front of the SR and a large-scale wake region is formed behind the SR which contains a clockwise vortex; (2) the length of the wake region formed behind the SR is positively and linearly correlated with both the inflow velocity and submergence; (3) the dipole-type vorticity patterns are induced within the compartment of the SR, where the area and average value of high vorticity have a positive correlation with the flow velocity and a negative correlation with the submergence, respectively. [ABSTRACT FROM AUTHOR]

To accurately predict the matching relationships between the various components and the engine performance in the whole aero-engine environment, this study introduces a two-dimensional throughflow simulation method for the whole aero-engine. This method is based on individual throughflow solvers for the turbo-machinery and the combustor. It establishes a throughflow simulation model for the whole engine by integrating with the compressor-turbine co-operating equations and boundary conditions. The turbo-machinery throughflow solver employs a circumferentially averaged form of the time-dependent Navier–Stokes equations (N-S) as the governing equation. The combustor solver uses the Reynolds Average Navier–Stokes (RANS) method to solve flow and chemical reaction processes by constructing turbulence, combustion, and radiation models. The accuracy of the component solver is validated using Pratt and Whitney's three-stage axial compressor (P&W3S1) and General Electric's high-pressure turbine (GE-EEE HPT), and the predicted results are consistent with the experimental data. Finally, the developed throughflow method is applied to simulate the throttling characteristics of the WZ-X turboshaft engine. The results predicted by the throughflow program are consistent with the GasTurb calculations, including the trends of shaft power delivered, specific fuel consumption (SFC), inlet airflow, and total pressure ratio of the compressor. The developed method to perform throughflow simulation of the whole aero-engine eliminates the dependence on a general component map. It can quickly obtain the meridian flow field parameters and overall engine characteristics, which is expected to guide the design and modification of the engine in the future. [ABSTRACT FROM AUTHOR]

The axially symmetric solutions to the Navier–Stokes equations are considered in a bounded cylinder Ω ⊂ R 3 with the axis of symmetry. S 1 is the boundary of the cylinder parallel to the axis of symmetry, and S 2 is perpendicular to it. We have two parts of S 2 . On S 1 and S 2 , we impose vanishing of the normal component of velocity and the angular component of vorticity. Moreover, we assume that the angular component of velocity vanishes on S 1 and the normal derivative of the angular component of velocity vanishes on S 2 . We prove the existence of global regular solutions. To prove this, the coordinate of velocity along the axis of symmetry must vanish on it. We have to emphasize that the technique of weighted spaces applied to the stream function plays a crucial role in the proof of global regular axially symmetric solutions. The paper is a generalization of Part 1, where the periodic boundary conditions are prescribed on S 2 . The transformation is not trivial because it needs to examine many additional boundary terms and derive new estimates. [ABSTRACT FROM AUTHOR]

The article aimed to show the fundamental possibility of constructing a computational digital twin of the acoustic tomograph within the framework of a unified physics–mathematical model based on the Navier–Stokes equations. The authors suggested that the size of the modeling area is quite small, sound waves are waves of "small" disturbance, and given that a person consists of more than 60% water, human organs can be modeled using a liquid model, taking into account their density. During numerical experiments, we obtained the pressure registered in the receivers that are located on the side walls of the tomograph. The differences in pressure values are shown depending on the configuration of inclusions in the mannequin imitating internal organs. The results show that the developed technology can be used to probe the human body in medical acoustic tomographs and determine the acoustic parameters of the human body to detect neoplasms. [ABSTRACT FROM AUTHOR]

With the rapid development of artificial intelligence technology, the physics-informed neural network (PINN) has gradually emerged as an effective and potential method for solving N-S equations. The treatment of constraints is vital to the PINN prediction accuracy. Compared to soft constraints, hard constraints are advantageous for the avoidance of difficulties in guaranteeing definite conditions and determining penalty coefficients. However, the principles on the formulation of hard constraints of PINN currently remain to be formed, which hinders the application of PINN in engineering fields. In this study, hard-constraint-based PINN models are constructed for Couette flow, plate shear flow and stenotic/aneurysmal flow with curved geometries. Particular efforts have been devoted to assessing the impact of the model parameters of hard constraints, i.e., degree and scaling factor, on the prediction accuracy of PINN at different Reynolds numbers. The results show that the degree is the most important factor that influences the prediction accuracy, followed by the scaling factor. As for the N-S equations, the degree of hard constraints should be at least two, while the scaling factor is recommended to be maintained around 1.0. The outcomes of the present work are of reference value for the development of PINN methods in fluid mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we propose algorithms for the real-time simulation of grass deformation and wind flow in complex scenes based on the Navier–Stokes fluid. Grasses play an important role in natural scenes. However, accurately simulating their deformation due to external forces such as the wind can be computationally challenging. We propose algorithms that minimize computational cost while producing visually appealing results. We do this by grouping the grass blades and then applying the same force to the group to reduce the computation time. We also use a quadratic equation to deform the blades affected by the wind force rather than using a complicated spline technique. Wind force is fully modeled by the Navier–Stokes fluid equation, and the blades react to this force as if they were being swept by the wind. We also propose the AGC interface (Arrow-Guided wind flow Control), which allows the direction and intensity of the wind to be manipulated using an arrow-shaped interface. Through this interface, users can have grass sway in response to user-defined wind forces in a real-time rate. We verified that the proposed algorithms can simulate 900% more grass blades than the compared paper's algorithms. [ABSTRACT FROM AUTHOR]