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This study assessed the boundary layer flow of micropolar fluid induced by the Riga plate. The significance of the flow is conducted from a rotating frame of perspective to produce consistency for enhanced thermodynamics across the Riga plate for fluid flow. The Riga plate is a familiar operator consisting of stably deployed magnetic and electrostatic elements that produce Lorentz force in an alternative way that substantially reduces with distance from the Riga plate. The unsteady, partially differentiated, three-dimensional expressions are reduced to two impartial dimensions (τ , η). For steady-state responses, (τ = 1) , Glerikin quantization is performed with MATLAB software for finite element simulation. For the resulting set of transformed equations, approximative series remedies are attained as convergent. The fluid temperature increased as a result of the rotational parameter, the Hartmann number, and the unstable parameter. The modifications to the Hartmann number (M h) and the material parameter (Λ) decelerate the primary flow velocity in the boundary layer region, while the secondary flow velocity accelerates. The greater modified Hartmann number (M h) and material parameters have a decreasing impact on the skin friction in the primary direction and an increasing impact on the magnitude of the coefficient in the secondary direction. An excellent agreement between the ongoing and previously existing results establishes the validity of the current findings. [ABSTRACT FROM AUTHOR]

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann–Bhatnagar–Gross–Krook equation introduced by the authors [Dzanic et al., J. Comput. Phys. 486, 112146 (2023)], consisting of a highly efficient high-order spatial discretization augmented with a discretely conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e., high spatial resolution) is significantly more important than particle collision (i.e., high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain. These findings suggest that highly accurate spatial schemes (e.g., high-order schemes) are a promising approach for solving molecular gas dynamics for complex flows and that the direct solution of the Boltzmann equation can be performed at a reasonable cost when compared to hydrodynamic simulations at the same level of resolution. [ABSTRACT FROM AUTHOR]

A volume penalization-based immersed boundary technique is developed and thoroughly validated for fluid flow problems, specifically flow over bluff bodies. The proposed algorithm has been implemented in an open source field operation and manipulation (OpenFOAM), a computational fluid dynamics solver. The immersed boundary method offers the advantage of inserting a complex solid object inside a Cartesian grid system, and therefore, the governing equations can be applied to such a simpler grid arrangement. For capturing the fluid–solid interface more accurately, the grid is refined near the solid surface using topoSetDict and refineMeshDict utilities in OpenFOAM. In order to avoid any numerical oscillation and to compute the gradients accurately near the interface, the present volume penalization method (VPM) is integrated with a signed distance function, which is also referred to as a level-set function. Benchmark problems, such as flows around a cylinder and a sphere, are considered and thoroughly validated with the results available in the literature. For the flow over a stationary cylinder, the Reynolds number is varied so that it covers from a steady two-dimensional flow to an unsteady three-dimensional flow. The capability of the present solver has been further verified by considering the flow past a vibrating cylinder in the cross-stream direction. In addition, a flow over a sphere, which is inherently three-dimensional due to its geometrical shape, is validated in both steady and unsteady regimes. The results obtained by the present VPM show good agreement with those obtained by a body-fitted grid using the same numerical scheme as that of the VPM, and also with those reported in the literature. The present results indicate that the VPM-based immersed boundary technique can be widely applicable to scientific and engineering problems involving flow past stationary and moving bluff bodies of arbitrary geometry. [ABSTRACT FROM AUTHOR]

An incompressible, steady-state, and three-dimensional rotatory micropolar fluid confined by the parallel co-axial disks is examined. The fluid motion is triggered by the two rotating stretchable disks. The heat transfer aspects in flow scenario are incorporated through Maxwell–Cattaneo law. The system of coupled momentum, angular momentum, and energy equations is first normalized in accordance with similarity variables and then is solved through numerical based built-in software using Runge–Kutta–Fehlberg (RKF-45) procedure. The nature of obtained physical constraints are reported on microrotation, temperature and velocity profiles. Three-dimensional flow configurations along with their respective contours are plotted against the engineering quantities for better flow visualization. Shear stresses, couple stresses, and heat transmission rate at the surfaces of higher and below disks are computed for the selected dimensionless quantities values. It is perceived that the influx flow along radial direction shifts toward faster moving disk for larger values of stretching parameters. The rotational effect of fluid elements along tangential direction is observed against the combined influence of micropolar parameters. The temperature field is reduced in the left half of the central plane while it is enhanced in the right half of the central region for increased values of the thermal relaxation time parameter. The results are also presented and compared well with published literature in limiting case of the Newtonian/viscous fluid flow. [ABSTRACT FROM AUTHOR]

We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli-function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions. [ABSTRACT FROM AUTHOR]

Due to costs and practical constraints, field campaigns in the atmospheric boundary layer typically only measure a fraction of the atmospheric volume of interest. Machine learning techniques have previously successfully reconstructed unobserved regions of flow in canonical fluid mechanics problems and two-dimensional geophysical flows, but these techniques have not yet been demonstrated in the three-dimensional atmospheric boundary layer. Here, we conduct a numerical analogue of a field campaign with spatially limited measurements using large-eddy simulation. We pose flow reconstruction as an inpainting problem, and reconstruct realistic samples of turbulent, three-dimensional flow with the use of a latent diffusion model. The diffusion model generates physically plausible turbulent structures on larger spatial scales, even when input observations cover less than 1% of the volume. Through a combination of qualitative visualization and quantitative assessment, we demonstrate that the diffusion model generates meaningfully diverse samples when conditioned on just one observation. These samples successfully serve as initial conditions for a large-eddy simulation code. We find that diffusion models show promise and potential for other applications for other turbulent flow reconstruction problems. [ABSTRACT FROM AUTHOR]

Discussed in this investigation is the three-dimensional gravity-driven flow of a thin fluid layer down an incline and over topography. A new three-dimensional integral-boundary-layer (IBL) model is proposed to describe the flow. Numerical simulations are presented and comparisons with lubrication and two-dimensional IBL models are discussed for both steady and unsteady flows. Subcritical and supercritical cases are considered, along with symmetrical and asymmetrical bottom topographies. Also, good agreement was found with experiments. [ABSTRACT FROM AUTHOR]

This research aims to study the 3D magnetohydrodynamics stagnation-point flow (SPF) over a horizontal plane surface (HPS) carrying water-based graphene oxide (GO) nanoparticles caused by an irregular heat source/sink used in heat transfer procedures. In addition, a Tiwari–Das model is used to inspect the dynamics of fluid flow behavior and heat transmission features of the nanoparticles with experiencing the impacts of thermal radiation. The acquired nonlinear set of partial differential equations (PDEs) is transfigured to a system of ordinary differential equations (ODEs) using similarity transformations. The accumulative dimensionless ODEs are then further tackled in MATLAB using the bvp4c solver. Tables and figures are prepared for the execution of several relevant constraints along with nodal/saddle indicative parameter, internal heat source/sink parameter, radiation parameter and nanoparticles volume fraction which divulges and clarify more accurately the posited quantitative data and graphical findings. Also, the velocity profile decelerated in the axial and transverse coordinate axes for a higher value of the nanoparticle volume fraction but the dimensionless temperature distribution is augmented. Additionally, thermal boundary layer thickness and profile of temperature enriches with higher impressions of radiation constraint. However, the internal heat sink factor declines the profiles of temperature while escalating with the superior value of the internal heat source parameter. [ABSTRACT FROM AUTHOR]

The LBM is used to investigate three-dimensional nanofluid (NFs) flow inside a square enclosure with a heat source in this research. The heat source is located in the enclosure's middle and operates at a high temperature. The sidewalls have a thickness, leading to heat transfer (HE-TR) from the sidewalls that are at low temperatures to the internal fluid due to their thermal conductivity. An inclined magnetic field (MF) uniformly affects the fluid flow. The effect of parameters such as Rayleigh number (Ra), thickness and thermal conductivity of the sidewall, dimensions of the heat source, Hartmann number (Ha), the volume fraction of nanoparticles (φ), and the angle of the MF on two- and three-dimensional field flow and HE-TR is investigated. Optimization is made on the parameters for maximum HE-TR. The lattice Boltzmann method has been used to simulate nanofluid flow. The results show that an enhancement in the Ha and the angle of the MF reduces the amount of HE-TR. HE-TR is improved by increasing the thermal conductivity of thick walls. The quantity of HE-TR is increased when nanoparticles are added to water. [ABSTRACT FROM AUTHOR]

We study the modal stability analysis for a three-dimensional fluid flowing over a saturated porous substrate where the porous medium is assumed to be anisotropic and inhomogeneous. A coupled system of time-dependent evolution equations is formulated in terms of normal velocity, normal vorticity, and fluid surface deformation, respectively, and solved numerically by using the Chebyshev spectral collocation method. Two distinct instabilities, the so-called surface mode instability and the shear mode instability, are identified. Modal stability analysis predicts that the Darcy number has a destabilizing influence on the surface mode instability but has a stabilizing influence on the shear mode instability. Similarly, the surface mode instability intensifies but the shear mode instability weakens with the increase in the value of the coefficient of inhomogeneity. Although the anisotropy parameter shows a stabilizing effect, increasing porosity exhibits a destabilizing effect on the shear mode instability. However, the anisotropy parameter and porosity have no significant impact on the surface mode instability. Spanwise wavenumber is found to have a stabilizing influence on both the surface mode and shear mode instabilities. [ABSTRACT FROM AUTHOR]

The present study investigates the steady three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet under the influence of Lorentz force. Heat transfer effects have been carried out for constant heat flux and Newtonian heating systems. The transformed governing equations of the flow model are solved by using the spectral relaxation method (SRM), taking into account similarity transformations. The effects of controlling parameters on flow and derived quantities have been presented in the form of graphs and tables. Numerical benchmarks are used to characterise the effects of skin friction and heat transfer rates. It is noticed that in the case of Newtonian heating, the rate of heat transfer is higher than that in the constant heat flux case. As the stretching parameter increases, the fluid temperature decreases in both Newtonian heating and constant heat flux. It was discovered that successive over (under) relaxation (SOR) approaches will considerably boost the convergence speed and stability of the SRM system. The current findings strongly agree with earlier studies in the case of Newtonian fluid when the magnetic field is absent. [ABSTRACT FROM AUTHOR]

We consider the evaporation/condensation process of diffusion type in two-layer fluid flows under the assumption that both viscous heat-conducting incompressible fluids, a liquid and a gas-vapor mixture, have a common interface and occupy an infinite threedimensional rectangular channel. Based on the exact solution to the convection equations, we study the fluid flows arising in the case of a linearly distributed thermal load on the substrate and thermal insulation of the upper and lateral walls of the channel. It is observed that some complex vortex structures are formed under the action of the longitudinal temperature gradient and transversely directed gravity field. For the ethanol–nitrogen system we present the characteristics of hydrodynamic, thermal, and concentration fields, in particular, the profiles of the evaporative mass flow rates and interface tangential stresses, the topology of flows, and the temperature and vapor concentration distributions. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive analytical modeling technology to model transient behaviors of multilayered reservoirs with inter-layer pure-planar crossflow induced by multi-stage hydraulically fractured horizontal well (MHFHW). The objective of this study is to develop an analytical model for multilayered reservoirs in conjunction with complex MHFHW and to achieve not only accurate and efficient computation, but also well-organized solutions expressed in a systematically integrated manner. The consideration of inter-layer crossflow across adjacent layers sets up the foundation for successful modeling of multilayered reservoirs. Source/sink function method (SSFM) is applied to describe fluid flow. Unsteady-state pressure or production rate solutions of MHFHW with the advantages of fast computation, accurate, and stable solutions are achieved. Comparative and consistent outcomes generated by this work and widely applied industry software have largely enhanced our technical confidence. More importantly, innovatively defined modified dimensionless terms that integrate systematic well-reservoir geometry information, as well as rock/fluid properties of each layer, have been newly applied to regulate the new modified dimensionless rate decline curve. This new technique sheds light on the reservoir characterization practice for complicated reservoir systems. Theoretical results in terms of transient pressure and rate were generated by the proposed multilayered model (SSFM-ML) for five scenarios of general concern, under various reservoir and well parameters, which were examined and discussed to demonstrate technical robustness. Not only does this study give solutions to the targeted multiple layered reservoirs, but it also provides insights into modeling three-dimensional fluid flow in heterogeneous reservoir with complex well configurations. It is recommended that future research should be conducted for more complicated two- and three-dimensional reservoirs, using the similar strategy of developing new type curves through adopting other new forms of modified dimensionless rate and time terms. [ABSTRACT FROM AUTHOR]

The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring–Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L × H . Starting from the initial velocity profiles (u 1 0 , u 2 0) in x y -planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u 1 0 , u 2 0) ∈ L 2 (Ω) , Ω = [ 0 , L ] × [ 0 , H ] × (0 , ∞) . Afterward, the results are extended for (u 1 0 , u 2 0) ∈ L p (Ω) ,  p > 2 . Lastly, the existence criteria are obtained when (u 1 0 , u 2 0) ∈ H 1 (Ω) . A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring–Powell fluids. [ABSTRACT FROM AUTHOR]

In this article, we numerically investigate a two-dimensional (2D) droplet deformation and breakup in simple shear flow using a phase-field model for two-phase fluid flows. The dominant driving force for a droplet breakup in simple shear flow is the three-dimensional (3D) phenomenon via surface tension force and Rayleigh instability, where a liquid cylinder of certain wavelengths is unstable against surface perturbation and breaks up into individual droplets to reduce the total surface energy. A 2D droplet breakup does not occur except in special cases because there is only one curvature direction of the droplet interface, which resists breakup. However, there have been many numerical simulation research works on the 2D droplet breakups in simple shear flow. This study demonstrates that the 2D droplet breakup phenomenon in simple shear flow is due to the lack of space resolution of the numerical grid. [ABSTRACT FROM AUTHOR]

Laminar flow control plays a vital role in reducing drag resulting enhancement in the vehicle power by a significant amount. Theoretical and experimental studies have proven that the transition from laminar to turbulent flow (causing the drag coefficient to enhance) may be delayed/prevented by the suction of the fluid from the boundary layer to the wall. The purpose of this work is to study the effects of periodic suction on the unsteady 3-dimensional fluctuating flow of a second grade incompressible fluid flowing laminarly over a horizontal porous infinite plate. The plate is subjected to a sinusoidal transverse suction velocity while the free stream velocity oscillates in time about a constant mean. The flow turns out to be 3-dimensional because of transverse direction of the periodic suction velocity. By the series expansion method, analytic expressions for transient velocity, skin friction components, and pressure are attained. Impact of nondimensional parameters evolving in the mathematical model of the problem on these physical quantities are visualized graphically and discussed analytically. The velocity component u is found to be rising with a growth in suction parameter α. The pressure is noted to be growing with a growth in Reynolds number R e. Further, due to suction at the plate and transient free stream velocity, the pressure increases near the plate and then reaches to a steady value far-off the plate. The skin friction along the main flow is noticed to be decreasing with the rise in α for 0.5 ≤ R e ≤ 1.4 , however, an exponential rise is observed for R e > 1.4. The skin friction along the cross flow is noted to be enhancing for the rising values of suction parameter and elastic parameter. The present results have excellent agreement with previous published results in the limiting sense. This study is beneficial in designing and manufacturing laminar flow control system to enhance the vehicle power requirement. [ABSTRACT FROM AUTHOR]

The heat transport analysis in the three-dimensional unsteady flow of non-Newtonian nanofluid is studied in this research communication. Comparison of water-based ternary hybrid nanofluid conveying three various shaped nanoparticles (titanium spherical-carbon nanotube (CNT) cylindrical-graphene platelet) and Zinc Oxide-Society of Automotive Engineers 50 nanolubricant (ZnO-SAE50Nanolubricant) is emphasized with two different models. Also, this paper is mainly focused on an electrically non-conducting and incompressible magnetic liquid with moderate saturation magnetization and low Curie temperature. An infinitely long, straight wire delivering an electric current generates a magnetic field that affects the fluid. To study heat transfer characteristics thermal radiation is taken into account. Pertinent flow expressions are reduced into ordinary differential equations (ODEs) through appropriate transformations. The obtained ODEs are solved by means of the numerical method Runge–Kutta–Fehlberg's fourth-fifth order method (RKF-45) with shooting technique. Results reveals that the ZnO-SAE50Nanolubricant flow shows maximum heat transport followed by titanium spherical-CNT cylindrical-graphene platelet-water hybrid nanofluid flow for increased values of radiation parameter. Further in this scenario, it is found that the heat transfer rate in ternary hybrid nanofluid increases about 2–5% whereas in Nanolubricant it is about 3–8% for the gradual increasing values of the ferromagnetic interaction parameter. [ABSTRACT FROM AUTHOR]

A perturbation analysis is presented to study the flow of a Newtonian fluid in a three-dimensional channel with impermeable walls of random tortuosity filled with a porous medium. The amplitude of the bumps is small compared to the mean distance between the two walls of the channel. Basset slip conditions are used on the channel walls. The effect of stochastic curvature of the channel walls on fluid flow is investigated. An expression is obtained for the mean flow rate, up to the second-order of the normalized amplitude, as a function of the permeability of the porous medium, slip parameter, and wavenumbers. A decrease in the flow rate as the permeability parameter increases is discovered. The phase difference and the longitudinal and transverse wavenumbers of corrugations play an important role in the flow rate. The limiting cases of Stokes and Darcy's flows are recovered. [ABSTRACT FROM AUTHOR]

We are concerned with the Cahn–Hilliard/Navier–Stokes equations for the stationary compressible flows in a three-dimensional bounded domain. The governing equations consist of the stationary Navier–Stokes equations describing the compressible fluid flows and the stationary Cahn–Hilliard-type diffuse equation for the mass concentration difference. We prove the existence of weak solutions when the adiabatic exponent γ satisfies γ > 4 3 . The proof is based on the weighted total energy estimates and the new techniques developed to overcome the difficulties from the capillary stress. [ABSTRACT FROM AUTHOR]

This numerical work is pertinent to exploring the effect of variation in momentum flux ratios, and geometrical parameters on discharge coefficient (Cd) of single and multiple row anti-screech hole arrangements which resembles as that of a conventional afterburner. The three-dimensional fluid flow domains of both single hole and multiple row hole configurations have been modelled in ANSYS ICEM CFD 20.0 tool and discretized with hexahedral elements to capture the velocity boundary layers more accurately. Flow physics between core and bypass flow through the anti-screech holes are obtained by solving the governing equations, namely the continuity, momentum in three directions and energy equations through the CFD code. Turbulence is captured by Reynolds averaged Navier–Stokes (RANS) two equation model, namely shear stress transport (SST) k-ω mode of closure. It is observed that Cd value increases in direct proportion to the diameter of the hole in case of single row hole configuration. An interesting fact of higher Cd values have been observed for trailing holes in case of multiple row hole configuration compared to the initial holes. The contours representing the static pressure and velocity along the midplane of the domains have been presented and analysed for exploring more insight into complex physics. The effect of hole diameter at lower and higher momentum flux values have been explored in this study with respect to the operating density, and it has been reported that Cd values for the initial holes are lesser than trailing holes in case of multiple row configuration. [ABSTRACT FROM AUTHOR]

• The influence bending stiffness of the support section on the flutter characteristics are investigated. • The elastic support with low bending stiffness drastically destabilizes the system. • The work done by the fluid force for various support conditions is determined. In the manufacturing processes of thin flexible plates (sheets) such as polarizing films, the flutter can be caused to the sheets due to the interaction between the motion of the sheets and fluid flow. Then, the flutter can cause serious damage to the sheets, leading to the wrinkles and scratches. Thus, it is crucial to investigate a detailed characteristics and excitation mechanism of the flutter. In the present study, a detailed flutter characteristics and excitation mechanism of a rectangular sheet with an elastic support is investigated. The elastic support is implemented using a fine flexible wire. The influence of bending stiffness of the support section on the flutter velocity and frequency is clarified through wind-tunnel experiments and numerical analysis. Moreover, the work done by the fluid force on the sheet surface was determined. The flutter velocity and frequency drastically decrease owing to decrease in bending stiffness of the support section regardless of the aspect and mass ratio. Then, the positive work region around the leading edge of the sheet expands owing to the large-amplitude oscillation around the leading edge. The expansion of positive work region owing to a large-amplitude oscillation around the leading edge of the sheet destabilizes the system. [ABSTRACT FROM AUTHOR]

Developing state-of-the-art bipolar plate structures, to optimize fluid distribution, is essential to achieve better cell performance. In this paper, a three-dimensional model of PEMFC is developed and two cathode-side flow field structures are designed: two-dimensional and three-dimensional types. The two-dimensional type is the traditional "bipolar plate + gas diffusion layer" flow field structure, easily resulting in uneven distribution of reactant gas and other problems. This study describes three novel three-dimensional type flow fields (metal foam, fine-mesh, and wire-mesh). Through comprehensive performance analysis using numerical simulations, it is found that the three-dimensional type flow fields significantly improve mass transfer and output performance compared to two-dimensional type flow fields. The proposed three-dimensional type flow fields create forced convective fluid flow. It further enhances the diffusion dispersion of reactant gas, thus making fuller use of the active region. Among them, the wire-mesh flow field shows the best performance in terms of oxygen distribution, water distribution and electrical properties. The net output power density produced is 0.75068 W cm−2, higher than parallel flow field by 32.78%. • The PEMFC model with different cathode-side flow fields is developed using CFD simulation. • The three-dimensional type of flow field structure enhances mass transport. • The optimal current density distribution uniformity index is 0.1199. • The net output power density of the developed wire-mesh flow field is 0.75068 W cm−2. [ABSTRACT FROM AUTHOR]

A hydrodynamic coupling has been one of the most important components for the driven machine using the flow of fluid. The internal flow field of the hydrodynamic coupling is characterized by an unsteady multi-scale eddy flow with multiple flow states and physical impacts. The overall flow inside depends mainly on the generation, development, and interaction of multi-scale vortices. It is necessary to finely characterize the unsteady multi-scale three-dimensional vortex structure inside the hydrodynamic coupling. In this study, a stress mixed eddy turbulence model was established to simulate the three-dimensional vortex flow field of the hydrodynamic coupling under the braking condition using computational fluid dynamics. A multi-scale analytical investigation was carried out to reveal the spatiotemporal evolution of the flow field and the mechanism of energy loss. Three types of vortex identification were used to extract the multi-scale vortex structure inside the turbine. The applicability of different vortex identification was analyzed from the perspective of spatial reconstruction, threshold selection range, and sensitivity. A Particle Image Velocimetry (PIV) flow field test was conducted to verify the accuracy and reliability of numerical simulation and vortex structure identification. Three-dimensional vortex structure characteristics and two-dimensional flow field maps were used to determine the temporal and spatial evolution of the turbulent flow inside the flow channel and the energy loss mechanism. The results show that there was a blind threshold selection in the Q criterion. Specifically, the structure extraction cannot concurrently capture both strong and weak vortex structures. There was also the incoherent structure of the vortex system, the insufficient reconstruction of the multi-scale vortex, and the missing vortex flow. As such, the Q criterion failed to accurately predict the continuous motion of the three-dimensional vortex space. By contrast, the Ω method captured the weak vortex structure within a large threshold range at the threshold of 0.51-0.59. Nevertheless, there were also no outstanding features of vortex structure extraction and the trend of vortex motion after the reconstruction of vortex system space. The ΩL method was not sensitive to the threshold selection, where the spatial vortex system refactoring performed the best when the threshold was 0.51-0.67. Correspondingly, the ΩL method can be expected to fully represent the structure characteristics of small-scale vortices and their movement trends. Strong and weak vortices can also be highly recognizable. Consequently, the overall flow inside the turbine can be defined as a large-scale counterclockwise circulation under braking conditions, accompanied by the local flow, such as the small-scale eddy currents. The mainstream vortex can be promoted by the vortex in the same direction, but hindered by that in the opposite. The fluid energy can be lost and dissipated in the form of heat energy, due to the tearing, crushing, separation, collision, friction, and extrusion of the vortex. [ABSTRACT FROM AUTHOR]

Experimental and numerical investigations are conducted in order to understand the flow around identical tandem circular cylinders confined in a duct (blockage ratio b = 0.1 and aspect ratio a = 5). In this work, the Reynolds number Re ranges from 40 to 200 and the spacing ratio (distance between two centers of tandem circular cylinders to diameter, L/d) from 0 to 8. When fluid flows around a single cylinder placed symmetrically in the duct (L / d = 0), it is found that the Strouhal numbers St and mean drag coefficients C d ¯ increase with the increase in Re, although the separation angle θs decreases. For the flows around two tandem circular cylinders, the research is focused on examining the coupling effect of Re and L/d on St, flow structures, θs, C d ¯ and reverse region length Lr. Based on numerical results, the mathematical descriptions are established, C d ¯ ∼ R e − 1 , θ s ∼ R e − 1 / 2 , and S t ∼ R e − 1 . The dependence of flow structures, drag forces, θs and Lr, on L/d is described in detail with the help of approaching velocity profiles, pressure coefficient Cp, and vorticity ω z * distribution on a cylinder's surface. Through numerical simulations, the detailed mechanisms about influences of these factors on the flow properties are revealed. The experimental results evidence the occurrence of three flow modes, i.e., no vortex shedding mode, single body mode, and reattachment mode, which are determined practically by the Reynolds number and space ratio. Both the measured St based on the dominate frequencies of vortex shedding and the visual flow field match well with numerical simulations. [ABSTRACT FROM AUTHOR]

Flow phenomena of three‐dimensional conducting Casson fluid through a stretching sheet are proposed in the present investigation with the impact of the magnetic parameter in a permeable medium. The adaptation of particular transformations is useful to modify the governing equations into their nondimensional as well as the ordinary form. However, these transformed equations are nonlinear and approximate analytical methods for the solution of the complex form of governing equations. In particular, the Adomian decomposition method is proposed for the solution. The behavior of several variables, such as the magnetic and porous matrix, on the flow profile as well as the rate of shear stress, are discussed via graphs and tables. The conformity of the current result with the earlier study shows a road map for further investigation. The major concluding remarks are; the retardation in the velocity distribution is rendered due to an increase in the Casson parameter moreover, the Casson parameter favors in reducing the rate of shear stress coefficient in magnitude. [ABSTRACT FROM AUTHOR]

Thermal-viscous fingering instability in porous media is a common phenomenon in nature as well as in many scientific problems and industrial applications. Despite the importance, however, thermal transport in flow of a non-Newtonian fluid in porous media and the resulting fingering has not been studied extensively, especially if the pore space is heterogeneous. In this paper, we propose a pore network model with full graphics processing unit-parallelized acceleration to simulate thermal transport in flow through three-dimensional unstructured pore networks at centimeter scale, containing millions of pores. A thermal Meter equation is proposed to model temperature- and shear stress-dependent rheology of the non-Newtonian fluids. After comparing the simulation results with an analytical solution for the location of the thermal front in a spatially uncorrelated pore network, thermal transport in flow of both Newtonian and non-Newtonian fluids is studied in the spatially uncorrelated and correlated pore networks over a range of injection flow rates. The simulations indicate that the injection flow rate, the shear-thinning rheology, and the morphological heterogeneity of the pore space all enhance thermal-viscous fingering instability in porous media, but with distinct patterns. In spatially correlated networks, the average temperature and apparent viscosity at the breakthrough point in flow of a shear-thinning fluid exhibit non-monotonic dependence on the injection flow rate. An analysis of the fractal dimension of thermal patterns at the breakthrough point supports the conclusion. The results highlight the importance of designing optimal flow conditions for application purposes. [ABSTRACT FROM AUTHOR]

Modal decomposition is a data-driven method widely used in fluid mechanics to extract energy and dynamically significant features of fluid flow. However, traditional modal decomposition methods have failed to capture physically interpretable multi-time-scale flow characteristics for complex flow phenomena, such as cavitation with multiple states. To address this issue, this paper combines the Proper Orthogonal Decomposition (POD) and Hidden Markov Models (HMM) methods, proposing a new approach termed state-based POD, applied to three-dimensional cavitating flow. This method comprises three steps: utilizing POD to extract cavitating flow features and visualizing them as spatiotemporal trajectories, employing HMM to probabilistically model these trajectories, obtaining flow field states, and probability models representing multi-time-scale flow information, and applying POD to perform modal decomposition on the multi-time-scale flow field information. This method provides a more detailed characterization of physical phenomena and offers a novel approach to analyzing cavitating flow. • A novel method combining POD and HMM to extract physically interpretable multi-time scale modal features. • Employing HMM to probabilistically model trajectory maps, achieving high accuracy in recognizing cavitation flow states. • State-based POD enables detailed modal decomposition of multi-time scale flow field information. [ABSTRACT FROM AUTHOR]

The backward substitution method is a newly developed meshless method that has been used for the simulation of many problems in science and engineering with high accuracy and efficiency. In this paper, we explore the feasibility of employing the backward substitution method for simulating two-dimensional incompressible flows. Two non-increment pressure correction projection methods are considered to decompose the original velocity and pressure coupling system into two boundary value problems of intermediate velocity and pressure. Then, two boundary value problems are solved by the backward substitution method in each time iteration step. Five numerical examples are provided to demonstrate the accuracy, computational efficiency and convergence of the method. Comparisons with some existing meshless methods verify the method's advantages and potential applications to engineering. • The backward substitution method is first raised for the simulation of incompressible flows. • Investigated effects of the time step and the number of collocation points on the accuracy. • Verification benchmark comprising several fluid flows problems. • Two projection methods are considered to verify the algorithm. • The algorithm is easily extended to three-dimensional incompressible flows. [ABSTRACT FROM AUTHOR]

The flow and heat transfer models of hot dry rock are mainly based on the assumption of two-dimensional model, which cannot fully reflect the physical process of three-dimensional flow and heat transfer in artificial fractures. The three-dimensional flow heat transfer numerical model of a single fracture was established by ANSYS Fluent, and the relevant numerical simulation calculation was carried out. The influence of different factors on the fluid temperature in the fracture of hot dry rock was analyzed, and the heat transfer rules of the fluid in the fracture under different conditions were obtained. Numerical simulation results show that the main factors affecting the heat transfer of hot dry rock fractures include: the injection rate of working fluid, fracture width, fracture length and initial fluid temperature. Under the conditions of a given fracture length and inflow velocity, the smaller the width of the artificial fracture, the higher the temperature of the fluid flowing out of the outlet, the longer the length of the fracture which the fluid flows through, and the greater the temperature increase. With the same fracture width and length, the smaller the flow rate, the higher the temperature at the fluid outlet, the slower the flow rate, the longer the heat exchange time, and the more heat is transferred. For different frac ture widths and different inflow speeds, after the fracture length reaches a certain level, the water temperature can be increased to be consistent with the bedrock. [ABSTRACT FROM AUTHOR]

This paper presents the findings from a research study using computational fluid dynamics (CFD) on the impact of different diameter Ball Tabulators Inserts (BTI) on the three-dimensional flow pattern and heat transfer characteristics within a circular tube. This analysis was carried under uniform heat flux conditions with different BTI diameters (1, 2, 3, 4, 5, 6, 7, and 8 mm). Fluid flow, pressure drop, dynamic pressure, velocity components, thermo-hydraulic, turbulent kinetic energy, and turbulent viscosity were analysed qualitatively and quantitatively. The performance evaluation results revealed that the characteristics of flow behaviour and the velocity field contours variations are closely associated with the BTI configurations. Also, the computational results indicated that the change in fluid flow velocity near the pipe wall and around the BTI is important parameters for the heat transfer enhancement as compared to that obtained without BTI under the same conditions. Moreover, using BTI presented a distinguished influence on the rate of heat transfer. Additionally, vortex flow through means of this kind of BTI is an important parameter in the enhancement of heat transfer. The use of BTI can enhance the rate of heat transfer performance by more than 46%. Furthermore, the maximum value for the PEF is found to be more than 1.03. [ABSTRACT FROM AUTHOR]

The flutter of a thin flexible plate in uniform flow is an interesting theoretical problem in fluid–structure interaction phenomena, as well as an important engineering problem. Therefore, understanding of the instability mechanism is crucial to preventing fatal defects caused by the flutter. In this study, the instability mechanism of a flexible plate in three-dimensional uniform flow is investigated in terms of the energy transfer between the plate motion and fluid flow. A theoretical aerodynamic model of the plate is developed using the unsteady lifting surface theory and linear beam theory. The aerodynamic stability of the plate is investigated by eigenvalue analysis. The developed model is validated by comparison with previous experimental results and other theoretical models. Furthermore, to understand the instability mechanism, the work done by the fluid force on the plate surface is determined, and its influence on the stability of the system is examined. [ABSTRACT FROM AUTHOR]

A radial turbine is one of the vital components of a helium liquefaction plant. The design of a turbine becomes critical due to its compact size and high‐speed configuration. In this study, numerical optimization has been performed for the three‐dimensional steady flow of helium gas in the radial inflow turbine of a helium liquefaction plant at a nominal condition. The mean line design is an appropriate method to obtain the approximate results. The computational fluid dynamics simulation algorithm is adopted in this study to reach the final results and Ansys CFX is used for the simulation. From the analysis, it has been reported that the number of rotor blades was overestimated in the mean line design. Performance parameters like total‐ to‐static efficiency and velocity ratio were also found to be optimum numerically under a preliminary design condition. Finally, power of 1.7 kW was achieved at total‐to‐static efficiency of 71.4%. The deviation in analytical and numerical results is within ±10% for performance as well as geometric parameters. [ABSTRACT FROM AUTHOR]

This study presents a probabilistic analysis of 3D Navier‐Stokes (NS) fluid flow through 30 randomly generated sheared fractures with equal roughness properties (Hurst exponent = 0.8). The results of numerous 3D NS realizations are compared with the highly simplified local cubic law (LCL) solutions regarding flow orientations and regimes. The transition between linear and nonlinear flow conditions cannot be described with a generally valid critical Reynolds number (Recrit), but rather depends on the individual fracture's void geometry. Over 10% reduction in flow is observed for increased global Re (>100) due to the increasing impact of nonlinear conditions. Furthermore, the fracture geometry promotes flow anisotropy and the formation of channels. Flow perpendicular to the shearing leads to increased channeling and fluid flow (∼40% higher) compared to flow parallel to the shearing. In the latter case, dispersed flow and irregular flow paths cause a reduction of LCL validity. Plain Language Summary: The movement of fluid and heat through fractured rocks is massively affected by the void space of the contributing fractures and the velocity of the fluid. The opposing offset of the two fracture surfaces creates complex and variable void geometries. A calculation of the expected flow rates is very difficult. In most studies, simplifications are adopted neglecting these complex features by using a plane surface and assuming that the flow is taking place smoothly. We therefore simulate the real flow using the three‐dimensional fracture void space and compare the results with simpler two‐dimensional models. It can be demonstrated that the difference between the two types of simulations depends not only on the local simplification but also on the flow direction within the fractures and that the difference increases with higher flow velocities. If the fractures are not considered as a whole continuum but on the local scale, preferential fluid pathways or channels are formed in which most of the flow takes place. Depending on the flow direction, channels are more or less pronounced. We can show that in well‐developed channels the differences between the calculation methods are much smaller than in the other parts of the domain. Key Points: Shearing of fractures generates a directional flow anisotropy, with an increased flow rate perpendicular to the shearingPreferential channels are formed which localize the largest part of the volumetric flow in small parts of the entire fracture domainSpatial differences between the complex Navier‐Stokes equations and the local cubic law can be explained by channeling processes [ABSTRACT FROM AUTHOR]

The impact of lateral walls and partial slip with different waveforms on peristaltic pumping of couple stress fluid in a rectangular duct with different waveforms has been discussed in the current article. By means of a wave frame of reference the flow is explored travelling away from a fixed frame with velocity c. Peristaltic waves generated on horizontal surface walls of rectangular duct are considered using lubrication technique. Mathematical modelling of couple fluid for three-dimensional flow are first discussed in detail. Lubrication approaches are used to simplify the proposed problem. Exact solutions of pressure gradient, pressure rise, velocity and stream function have been calculated. Numerical and graphical descriptions are displayed to look at the behaviour of diverse emerging parameters. [ABSTRACT FROM AUTHOR]

Water breaks through along fractures is a major concern in tight sandstone reservoirs with a bottom aquifer. Analytical models fail to handle the three-dimensional two-phase flow problem for partially penetrating inclined fractures, so time-consuming numerical simulation are often used for this problem. This paper presents an efficient semianalytical model for this problem considering three-dimensional fractures and two-phase flow. In the model, the hydraulic fracture is handled discretely with a numerical discrete method. The three-dimensional volumetric source function in real space and superposition principle are employed to solve the model analytically for fluid flow in the reservoir. The transient flow equations for flow in three-dimensional inclined fractures are solved by the finite difference method numerically, in which two-phase flow and stress-dependent properties are considered. The eventual solution of the model and transient responses are obtained by coupling the model for flow in the reservoir and discrete fracture dynamically. The validation of the semianalytical model is demonstrated in comparison to the solution of the commercial reservoir simulator Eclipse. Based on the proposed model, the effects of some critical parameters on the characteristics of water and oil flow performances are analyzed. The results show that the fracture conductivity, fracture permeability modulus, inclination angle of fractures, aquifer size, perforation location, and wellbore pressure drop significantly affect production rate and water breakthrough time. Lower fracture conductivity and larger inclination angle can delay the water breakthrough time and enhance the production rate, but the increment tends to decline gradually. Furthermore, water breakthrough will occur earlier if the wellbore pressure drop and aquifer size are larger. Besides, the stress sensitivity and perforation location can delay the water breakthrough time. [ABSTRACT FROM AUTHOR]

This article deals with three-dimensional non-Newtonian Jeffrey fluid in rotating frame in the presence of magnetic field. The flow is studied in the application of Hall current, where the flow is assumed in steady states. The upper plate is considered fixed, and the lower is kept stretched. The fundamental equations are transformed into a set of ordinary differential equations (ODEs). A homotopy technique is practiced for a solution. The variation in the skin friction and its effects on the velocity fields have been examined numerically. The effects of physical parameters are discussed in various plots. [ABSTRACT FROM AUTHOR]

This article deals with three-dimensional non-Newtonian Jeffrey fluid in rotating frame in the presence of magnetic field. The flow is studied in the application of Hall current, where the flow is assumed in steady states. The upper plate is considered fixed, and the lower is kept stretched. The fundamental equations are transformed into a set of ordinary differential equations (ODEs). A homotopy technique is practiced for a solution. The variation in the skin friction and its effects on the velocity fields have been examined numerically. The effects of physical parameters are discussed in various plots. [ABSTRACT FROM AUTHOR]

This study analyzes the thermocapillary flow of recalcitrant bubbles within thin channels using a hybrid finite difference lattice Boltzmann method (LBM). It extends a recently developed phase-field LBM to account for temperature effects by coupling the scheme with a fourth-order Runge–Kutta algorithm to solve the governing energy equation. The LBM makes use of a weighted-multiple relaxation-time collision scheme, which has been previously shown to capture high density and viscosity contrasts. This paper makes contributions in two fundamental areas relating to thermocapillary flow. First, it presents and verifies a novel, three-dimensional model to resolve thermocapillary dynamics for practical applications. The verification was undertaken via comparison with analytical solutions for the flow of immiscible fluids in a heated microchannel and for the migration of a droplet in a temperature field. Second, it provides new insight into the inherently three-dimensional nature of recalcitrant bubbles. It was found that the competing inertial and thermal effects allow these bubbles to propagate against the bulk motion of the liquid toward regions of low surface tension. [ABSTRACT FROM AUTHOR]

The fluid flow in a precessing cylinder is investigated numerically with focus on the Ekman boundary layers in the strongly forced regime. Not surprisingly, in that regime, we find deviations from the linear theory due to significant modifications of the base flow in terms of an axisymmetric geostrophic mode whose rotation is opposite to that of the container. The transition of the bulk flow from a three-dimensional non-axisymmetric base flow to a geostrophic axisymmetric pattern is reflected in the scaling of both the sidewall boundary layers and the Ekman boundary layers on top and bottom of the cylinder. In our simulations, the Ekman layers surpass the threshold of the first instability (class A) and show an increase in the thickness together with a marked vertical flow advection inside the boundary layer in a limited range of the forcing magnitude. However, due to numerical restrictions in our simulations, which limit the range of achievable Ekman numbers, no developed boundary layer turbulence is found. An estimation by extrapolation shows that, for this purpose, Ekman numbers smaller by a factor of two have to be achieved. [ABSTRACT FROM AUTHOR]

We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992) [1]. The domains we consider have a boundary consisting of three parts, one where fluid flows into the domain, one where the fluid flows out, and one which no fluid passes through. These three parts meet at right angles. An example of this would be a right cylinder with fluid flowing in at one end and out at the other, with no fluid going through the mantle. A large part of the proof is dedicated to studying the Poisson equation and the related compatibility conditions required for solvability in this kind of domain. [ABSTRACT FROM AUTHOR]

In the current work, pin-finned heat sink applications comprising crucial thermal engineering problems are taken into account. Nonetheless, design optimization is still required. The goal of the study was to fill a gap in the literature by using staggered pin fins using a variety of new combinations of perforation and fin shapes. For the pin-fin arrays under consideration, three-dimensional incompressible flow and heat transport are modeled using the ANSYS Fluent software. With the proper boundary conditions included, all of the governing equations of fluid flow are numerically solved. The turbulence is modeled by a realizable κ-ε model. The Nusselt number (Nu) improved by 47.85% and 50.93% for the elliptical perforated wavy pin fin and wavy perforated crinkle pin fin, respectively, at a Reynolds number of 44502. Approximately 13% pressure drop reduction was seen for an elliptical perforated hyperboloid shape that yields hydrothermal performance factor (HTPF) of roughly 45% compared to the cylindrical case. Also, at Re = 44502, the promising Copper-Diamond composite on a hyperboloid shaped pin fin with elliptical perforation case increased the HTPF by 95%. For a variety of industrial applications, this design can be incorporated. [ABSTRACT FROM AUTHOR]