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The acceleration self-starting performance of hypersonic inlets is of critical importance for the stable operation of scramjet engines. The occurrence of soft unstart during the transition from hard unstart to start is an important flow state that has yet to be fully elucidated. The stability mechanism and corresponding self-starting characteristics of soft unstart remain poorly understood, and there is a pressing need for detailed modeling research in this area. This paper presents a rapid prediction model for the self-starting Mach number of two-dimensional hypersonic inlets with soft critical unstart mode, fully considering the influence of various geometric parameters and Reynolds number in the internal contraction section, and achieving a quantitative analysis of the two-dimensional soft unstart critical flow field. Given the incoming flow conditions and the inlet geometry, the prediction model is capable of accurately representing the actual viscous unstart flow field. It can fully map the unstart separation bubble and its surrounding critical wave structures, and calculate the minimum pressure rise required to maintain the current scale of the main separation bubble and the pressure rise exerted on the unstart separation bubble by the current actual flow field structure. Comparing the relative magnitude of these two pressures determines whether the inlet can transition from soft unstart to start. The proposed prediction model was validated using results from unsteady numerical simulations. The predicted results align well with the simulation results and are significantly better than previous prediction methods. [ABSTRACT FROM AUTHOR]

Particulate Taylor–Couette flow of a particle-laden viscous fluid between two coaxial rotating cylinders is studied using a novel hydrodynamic model. With the volume fraction of particles as the dimensionless small parameter, explicit leading-order solutions are derived for the general case of dispersed particles heavier or lighter than the carrier fluid. It is shown that, unlike the classical azimuthal velocity field of a clear fluid without particles, dispersed particles generally have a radial velocity toward the outer or inner cylinder depending on the angular velocities and radii of the two cylinders and whether the particles are heavier or lighter than the carrier fluid, in qualitative agreement with some known results reported in literature on heavier or lighter particles, respectively. In some cases, such as the flow driven by rotating inner cylinder with a wider gap between the two cylinders and a moderate value of Stokes number of particles, our results predict the existence of a circular ring between two cylinders, which attracts or repels heavier or lighter particles that could have relevant physical implications. Beyond existing literature on the Taylor–Couette flow with neutrally buoyant particles, these results could offer new insight and useful explicit solutions to the Taylor–Couette flow with particles heavier or lighter than the carrier fluid. [ABSTRACT FROM AUTHOR]

In this study, the hydrodynamic forces and power absorption performance of an autonomous underwater vehicle (AUV)-based two-body wave energy converter (2BWEC) are investigated. A theoretical model is developed within the framework of linear potential flow to solve for added mass, radiation damping, and wave excitation force using the matched eigenfunction expansion method (MEEM). A computational fluid dynamics (CFD) model is employed to account for vortex-shedding effects of the floater and inner cylinder with a damping plate under various excitation conditions. Empirical formulas for supplementary added mass and drag coefficients caused by flow separation are proposed based on curve-fitting the differences between CFD results and MEEM calculations. These formulas are integrated into motion equations to enhance accuracy in evaluating the power absorption of the 2BWEC. It has been found that in the context of viscous flow, both the added mass and damping coefficients are increased, particularly for the inner cylinder with a damping plate. In addition, the viscous hydrodynamic coefficients exhibit strong dependence on the Keulegan–Carpenter number, while showing insensitivity to changes in the frequency parameter β. The supplementary (viscous) added mass provides additional inertia for the AUV with a limited mass itself, which is advantageous for the power absorption of the AUV-based 2BWEC. Conversely, the presence of viscous damping from the damping plate impedes wave energy capture. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms by which fish sense vortical perturbations is crucial for both biological insights and technological advancements. We investigate the hydrodynamics of a solid plate moving vertically through the reverse Kármán vortex street generated by a horizontally moving flexible flapping plate in a viscous flow. The impacts of the horizontal distance between the two plates (D) and the moving speed of the solid plate ( v y ) are considered. The horizontal distance determines the vortical environments, i.e., whether the solid plate impinges through the vortex cores or the gaps. Different vortical environments exhibit varying vortex-induced velocities, resulting in distinct force and pressure patterns on the solid plate. The evolution of these sensed forces and pressures is mapped along the path of the solid plate, suggesting a potential mechanism by which fish detect the position and properties of surrounding vortices. Furthermore, it is found that increasing speed can amplify the sensed force and pressure signals by thinning boundary layers and strengthening friction force. Nevertheless, the established mapping relationships remain applicable across varying velocities, and a scaling relation has been derived to normalize this amplification effect on the vertical force. These findings enhance our understanding of fish sensory mechanisms and could inspire innovative designs and control strategies for underwater vehicles. [ABSTRACT FROM AUTHOR]

Coalbed methane (CBM) content is a crucial parameter for CBM exploitation and disaster prevention, with accurate gas loss calculation being essential for improving measurement precision. To investigate the physical response to gas loss and quantify the impact and interrelation of various factors, this study developed a comprehensive model incorporating the effects of gas diffusion, temperature, and pressure effects on porosity and coal deformation. By utilizing the OpenFOAM platform and C++ for numerical solution development and establishing an experimental system for gas loss measurement, the model's reliability was confirmed. The new model demonstrates an 8.56% average error, representing a significant improvement over traditional methods, with error reductions of 26.59% and 18.31% compared to the square root of time and power function methods, respectively. The hierarchy of gas loss is determined to be gas flow > gas-coal deformation coupling > gas-temperature coupling > gas-coal deformation-temperature coupling. Average diffusion contributions are identified as 41.43% from surface diffusion, 30.71% from Knudsen diffusion, and 27.86% from viscous flow. The factors affecting gas loss, in decreasing order of impact, are adsorption equilibrium pressure, temperature, porosity, moisture, and adsorption constants. These findings provide theoretical support for enhancing gas content measurement accuracy and techniques, significantly benefiting CBM extraction and mine safety. [ABSTRACT FROM AUTHOR]

We investigate the effectiveness and universality of the turbulence control strategy for wall-bounded shear flows proposed by Chagelishvili et al. The basis of this strategy is the continuous seeding of the flow viscous sub-layer with spanwise asymmetric and specially designed velocity perturbations. This seed velocity field, amplifying due to the shear flow non-normality, breaks the flow spanwise reflection symmetry, specifically leading to the generation of a secondary nonuniform spanwise mean flow, which significantly reduces the flow turbulence. For now, this strategy is realized by a weak near-wall volume forcing, which, though theoretical/hypothetical, initiates the needed seed velocity field in the flow. To confirm the practical significance of this control strategy, we evaluated its effectiveness in the plane Couette flow at various Reynolds numbers, and with the forcing locations at different distances from the wall. The universality of the discussed turbulence control strategy is shown through the direct numerical simulations. The simulations with the near-wall volume forcing having specially designed, fixed configuration and amplitude result in the reduction of turbulence kinetic energy production by 30%–40% across a wider range of Reynolds numbers, R e τ = 52 , 92 , 128 , and 270 , and the forcing various wall-normal localizations in plus units, y peak + = 0.16 , 0.28 , 0.38 , 0.81 , 2.56 , and 2.76. [ABSTRACT FROM AUTHOR]

We present a discrete filter for subgrid-scale model, coupled with the discretization corrected particle strength exchange method, for the simulation of three-dimensional viscous incompressible flow at high Reynolds flows. The majority of turbulence modeling techniques, particularly in complex geometries, face significant computational challenges due to the difficulties in implementing three-dimensional (3D) convolution operations for asymmetric boundary conditions or curved domain boundaries. In this contribution, Taylor expansion is used to define differential operators corresponding to the convolution filter, so that the transfer function remains very close to the unity of sizeable displacement in wave number, making the filter a good approximation to the convolution one. A discrete Gaussian filter, in both fourth and second-order forms, was evaluated with varying ratios of particle spacing to the cutoff length. The impact of the filter's order and the ratio's value is thoroughly examined and detailed in the study. Additionally, the Brinkman penalization technique is employed to impose boundary conditions implicitly, allowing for efficient and accurate flow simulations around complex geometries without the need for modifying the numerical method or computational domain. The incompressible flow is governed by the entropically damped artificial compressibility equations allowing explicit simulation of the incompressible Navier–Stokes equations. The effectiveness of the proposed methodology is validated through several benchmark problems, including isotropic turbulence decay, turbulent channel flow, and flow around four cylinders arranged in a square in-line configuration, which are representative but not exhaustive of the full range of engineering applications. These test cases demonstrate the method's accuracy in capturing the intricate flow structures characteristic of high Reynolds number flows (up to 15k), highlighting its applicability to turbulence modeling. [ABSTRACT FROM AUTHOR]

Steady solutocapillary convection and instability near the air–liquid interface are studied. First, under the assumption of the conically similar viscous flow, an exact axisymmetric solution of the steady solutocapillary convection near the air–liquid interface is determined due to a constant mass flux. It is shown that the constant mass flux and the radial surface tension cause the divergent motion at the interface and the Marangoni convection beneath the interface. Then, the linear stability of the steady solutocapillary convection in response to the azimuthal disturbance is analyzed. At a given Peclet number (or Schmidt number), the steady basic flow loses its stability when the Reynolds number is beyond its critical value. It is found that for the fixed Schmidt number, the critical Reynolds number increases monotonously as the harmonic wave number of the azimuthal disturbance increases. However, for the fixed Peclet number, a nonlinear relationship between the critical Reynolds number and the harmonic wave number of the azimuthal disturbance is found. The structures of iso-concentration lines and velocity fields in the three-dimensional flow system depend on the disturbance harmonic wave number, which is dominated by both the radial and the azimuthal surface tensions. This study provides a profound understanding of the soluble surfactant-driven instability of a divergent flow near the air–liquid interface, which is of great significance for practical applications in the micro-fluidics related to chemistry and biology. [ABSTRACT FROM AUTHOR]

The dynamics of a single flexible flag behind a semi-circular cylinder are investigated using vortex interaction study and dynamic mode decomposition (DMD). The problem is numerically solved using the immersed boundary method. For Reynolds number 300, by the variation of the streamwise gap between flag and bluff body ( D x ), five regions, each exhibiting its unique pattern of flapping, from symmetric and periodic to chaotic, are identified by vortex interaction study. DMD and kernel-DMD are utilized for modal analysis and reconstruction of a viscous flow behind a semi-circular cylinder with a flexible flag located at a streamwise distance of D x = 1.8 for moderate Reynolds number (Re = 30–500) with emphasis on representing the dynamics of the system using as few DMD modes as is practically possible. Sampling rate sensitivity study shows that low sampling rate data induce an additional frequency in the decomposition, which actually make up for the high frequency content in the vicinity of the flag and single frequency system is decomposed as the quasiperiodic system. According to the modal analysis, the fundamental frequency mode conjugate pair has the same frequency as the flag's vertical flapping and lift. It accounts for vortex production and advection from the bluff and flag and lift phenomenon. The first harmonic mode contains information regarding vortex shedding from the bluff body edges and flag tip and drag as they share same frequencies. DMD reconstruction demonstrates that 97.65% of the Re 100 post-transient system can be reconstructed using 28 DMD modes, whereas 86.71% of the Re 300 post-transient system requires 25 DMD modes. For fully transient cases, poor performance is achieved when using the DMD. The kernel-DMD application to full transient cases yields a non-oscillatory "mean mode," a "shift mode," and stable harmonic modes that are also present in post-transient analysis. The shift mode is famous in the modal analysis community, and it accounts for the correction to the mean mode for the transient region. In addition, these modes, there are additional modes that represent the transient dynamics of the system. 50 DMD modes reconstruct 86.98% and 77.65% of the Re 100 and Re 300 full-transient system, respectively. [ABSTRACT FROM AUTHOR]

We investigate the crack-healing mechanism of 4H silicon carbide (4H-SiC) and reveal the effect of dopants on the crack-healing behavior of 4H-SiC. Vickers indentation tests and thermal annealing are utilized to generate cracks and heal cracks in 4H-SiC, respectively. High-temperature thermal annealing in the air atmosphere is found to be capable of effectively healing indentation-induced cracks and releasing indentation-induced stress in undoped 4H-SiC by the formation and viscous flow of glass phase SiO2. Nitrogen (N) doping is found to assist the atomic diffusion of 4H-SiC. The crack healing of N-doped 4H-SiC is realized by the synergy of host solid diffusion and the padding of glassy SiO2. In contrast, vanadium (V) doping hinders the viscous flow of SiO2 and results in the incomplete healing of cracks in V-doped 4H-SiC. Although the generation of cracks lowers the bending strength of 4H-SiC, the healing of cracks by the padding of glassy SiO2 is found to effectively recover the bending strength of indented 4H-SiC samples. Our work opens a pathway to design thermal processing technologies to heal the cracks and enhance the mechanical properties of 4H-SiC wafers. [ABSTRACT FROM AUTHOR]

The goal of the work under consideration is to inspect the steady buoyancy driven flow for a viscous and density independent fluid along a cantilever shape, by considering the optically dense gray fluid. This study examines the characteristics of buoyancy driven convective heat and fluid flow adjacent to the cantilever shape. The governing equations constituting the aforementioned problem are converted into ordinary differential equations by utilizing the stream function formulation. The shooting technique BVP4C along with the MATLAB program is then used to obtain the numerical solutions. The impact of dimensionless cantilever shape parameter n, Prandtl number Pr, Richardson parameter λ, and thermal radiation parameter F on the velocity and temperature profile of the cantilever shape is demonstrated graphically. The tables provide the results for the skin friction and rate of heat transfer coefficient due to the impact of a number of evolving parameters. [ABSTRACT FROM AUTHOR]

The modified Knudsen equation was developed to calculate the gas flow rate through a cylindrical tube with arbitrary length-to-diameter ratio in any flow regime including molecular flow, viscous laminar flow, turbulent flow, critical flow, subcritical flow, and their intermediates in our laboratory. Here, it is upgraded for better agreement with literature data, and the upgraded version is compared with 83 literature sources including 31 gas flow equations to verify its reliability. For Kn > 10−5, the modified Knudsen equation mostly agrees with the literature data to within 20%, except for orifice flows with pd/pu ≈ 1. [ABSTRACT FROM AUTHOR]

In this work, a double distribution function-based lattice Boltzmann flux solver (LBFS) is proposed for simulating compressible viscous flows. This approach utilizes the double distribution function compressible lattice Boltzmann model and employs Chapman–Enskog expansion analysis to connect the lattice Boltzmann equation (LBE) with the Navier–Stokes (N–S) equations. Unlike conventional computational fluid dynamics methods that compute inviscid and viscous fluxes separately, the present method simultaneously evaluates both types of fluxes at the cell interface by locally reconstructing the solution of the LBE. Recognizing the significance of considering the non-equilibrium part of distribution functions for viscous flows, a straightforward method is introduced to calculate this component. This facilitates the derivation of computational expressions for macroscopic conservative variables and fluxes in the N–S equations. To validate the accuracy and stability of the present numerical scheme, various benchmark problems, including shock tube problem, Couette flow, lid-driven cavity flow, and flow around the NACA0012 airfoil, are tested. The obtained numerical results are compared with analytical solutions or existing reference data, confirming the capability of the proposed LBFS to deliver accurate and stable numerical results for compressible flows. Moreover, this method demonstrates effectiveness in handling viscous flow problems on non-uniform grids and with curved boundaries. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical model examining the interaction between a fibrous network and viscous fluid flow driven by an oscillating boundary. The aim is to understand how oscillating impacts are transmitted from the skull, through the arachnoid trabeculae network filled with cerebrospinal fluid, as observed in shaken baby syndrome. The model uses an effective medium approach to determine the fluid velocity field while each fiber is treated as a soft string undergoing deformation. Results indicate that the frequency of oscillation, fiber stiffness, and porous structure resistance significantly influence the oscillating shearing flow, as indicated by the Womersley (Wo), Brinkman (α), and Bingham (Bm) numbers. Application of the model to shaken baby syndrome suggests that oscillations in the cerebrospinal fluid and arachnoid trabeculae can significantly surpass those on the skull, leading to intense shear stress penetration to the brain. This model is the first study to integrate the dynamic response of string-like fibrous networks in fluid flows with oscillating boundaries and offers a quantitative framework for predicting the transmission of shearing forces from the skull to the brain matter. [ABSTRACT FROM AUTHOR]

Intestinal health heavily depends on establishing a mucus layer within the gut with physical properties that strike a balance between being sufficiently elastic to keep out harmful pathogens yet viscous enough to flow and turnover the contents being digested. Studies investigating dysfunction of the mucus layer in the intestines are largely confined to animal models, which require invasive procedures to collect the mucus fluid. In this work, we develop a nondestructive method to study intestinal mucus. We use an air–liquid interface culture of primary human intestinal epithelial cells that exposes their apical surface to allow in situ analysis of the mucus layer. Mucus collection is not only invasive but also disrupts the mucus microstructure, which plays a crucial role in the interaction between mucus and the gut microbiome. Therefore, we leverage a noninvasive rheology technique that probes the mechanical properties of the mucus without removal from the culture. Finally, to demonstrate biomedical uses for this cell culture system, we characterize the biochemical and biophysical properties of intestinal mucus due to addition of the cytokine IL-13 to recapitulate the gut environment of Nippostrongylus brasiliensis infection. [ABSTRACT FROM AUTHOR]

This study proposes a peridynamic differential operator (PDDO)-based Eulerian–Lagrangian hybrid particle method for weakly compressible viscous flows. The PDDO is utilized to transform the governing partial differential equations into their integral form; hence, the issue of local non-differentiability is eliminated. Both the Eulerian and Lagrangian formulations of particle methods for solving the governing integral equations are derived and then combined to propose the hybrid method. In the proposed method, the Eulerian and Lagrangian formulation is utilized to solve the governing equations in the inner computational domain and in areas with free surfaces, respectively. The results of these two domains are then merged to arrive at the solution. In such a way, the hybrid particle method effectively balances the computational demands and applicability. The numerical stability and interpolation consistency of the proposed method are shown by introducing the laminar viscosity model. A detailed numerical procedure is provided involving the boundary conditions and time-stepping strategy. The proposed method is validated by several benchmark problems. Furthermore, the method was applied to several benchmark problems including the hydrostatic test, Taylor–Green vortex, and numerical wave generation. The results of these numerical examples suggest that the proposed method is computationally less demanding while maintaining accuracy. [ABSTRACT FROM AUTHOR]

It is widely known that a low Mach number gas flow can be approximated as incompressible at the leading order in a small Mach number expansion of the full solution. However, it has been shown recently that such an incompressible approximation becomes invalid for a semi-sealed system with no inlets and no boundary movements. Studies based on linearized compressible Navier–Stokes equations for such a system made of small capillary tubes have revealed some counter-intuitive flow characteristics such as no-slip flow with a slip-like mass flow rate. Here, we extend these works to gas drainage from a semi-sealed porous system. It is shown that gas drainage is solely driven by its volumetric expansion, and it cannot be approximated as an incompressible flow modulated by a small compressible effect. At the pore-scale, gas motion is governed by a damped rarefaction wave, and multiple scattering of the wave leads to an effective diffusion of the gas at the macroscopic scale. A large number of pore-scale simulations are performed for various pore structures, and the results are used to extract the macroscopic wave-mediated effective diffusion coefficient. Experiments are carried out to validate the wave-mediated effective diffusion model. The flow rates predicted by the effective diffusion model agree well with the experiments while results based on Darcy's law severely underestimate the flow rate. It is established that Darcy's law cannot be applied to a semi-sealed system, and no-slip flow with a slip-like flow rate is inherently embedded in the compressible Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

Mixing performance in the combustion chamber is important in achieving the efficiency of scramjet for its compact structure and the short residence time caused by high velocity. This study focuses on predicting the mixing performance in a viscous supersonic flow past the cavity flame holder in the scramjet, using the discontinuous spectral element method with direct numerical simulation. The arrangement and distribution of a series of cavities are calculated at various inlet velocities. By comparing the contours of Mach number and static temperature, as well as analyzing the airflow residence time with a new calculating formula and the drag based on the numerical results, it is concluded that higher inlet velocities result in faster stabilization. It also leads to longer airflow residence time when the supersonic flow passes through the dual-cavity with a tandem connection rather than the parallel one or the single-cavity structures. As for the shortened rear wall of cavities, these structures can decrease the drag quickly, but they also decrease the airflow residence time seriously, which destroys the mixing performance. In addition, these conclusions are applied to a practical case of the cavity flame holder, verifying the effectiveness of tandem dual-cavity structures in enhancing the mixing performance by increasing the airflow residence time and maintaining or reducing the drag. This study can provide valuable suggestions in further design of cavity flame holders for different flow conditions. [ABSTRACT FROM AUTHOR]

The flow of viscous fluids is considered as the aggregation of the motion of fluid particles when the fluid is conceived to be made up by an infinite number of particles. As an alternative of this conventional model, fluid motion could be understood as the slip of fluid layers with a molecular scale over each other, where the slip structures of fluid and their associated small-scale motion are characterized by an axial-vector-valued differential 1-form, called the vortex field. In this paper, in the case of steady flows we define the swirling degree of the velocity field at a point, and further the swirl field of the steady flow, to study the slip topology of fluid or the local streamline pattern around the critical point. The linear velocity field in the right real Schur form is used to carry out detailed analyses around the isolated critical point. Theoretical deduction and numerical test unveil the connection between the swirling degree and the swirl field, greatly make clear the topological property of slip structures of fluid in steady flows, especially in three-dimensional space. [ABSTRACT FROM AUTHOR]

The sea surface can be described by means of the superposition of many sinusoidal functions. However, quite often the amplitude of each component turns out to be much smaller than its wavelength, and any component evolves independently of the others. Hence, it is common to investigate the dynamics of a simple monochromatic surface wave. Hereinafter, the flow generated by a monochromatic surface wave within the bottom boundary layer over a rippled sea bed is determined by means of the numerical integration of vorticity and continuity equations. The forcing term that drives the fluid motion within the boundary layer is evaluated assuming that the steepness of the monochromatic surface wave is much smaller than one and considering the first term of the Stokes expansion. Even though the irrotational flow that forces the viscous rotational flow near the sea bottom is symmetric with respect to the ripple crests, Blondeaux and Vittori ["A route to chaos in an oscillatory flow: Feigenbaum scenario," Phys. Fluids A 3(11), 2492–2495 (1991a)] showed that the symmetry of the flow field is broken when the Reynolds number becomes larger than a threshold value R δ , t 1 that depends on the geometrical characteristics of the ripples. The results of Blondeaux and Vittori ["A route to chaos in an oscillatory flow: Feigenbaum scenario," Phys. Fluids A 3(11), 2492–2495 (1991a)] suggest that, when the Reynolds number is larger than R δ , t 1 but not too far from it, a steady current is also generated. Hereinafter, the steady velocity component is determined as a function of the ripple characteristics. [ABSTRACT FROM AUTHOR]

The rapid advancement in aeronautics has led to the emergence of intricate dynamic processes and structures, such as vortices, shock waves, flow separation, and turbulence, resulting from the flow around airfoils. Acquiring a profound understanding of these local structures and unraveling the physical mechanisms underlying flow phenomena represents an essential and challenging issue in the field of flight science. In this research, the longitudinal–transverse force theory (L–T force theory), as proposed by previous researchers, is employed to quantitatively assess contributions of local flow structures to aerodynamic forces. Specifically, the research encompasses an analysis of steady and viscous compressible flow over the Royal Aircraft Establishment (RAE)-2822 airfoil, with free-stream Mach number ( M ∞ ) ranging from 0.1 to 2.0. We comprehensively estimate longitudinal forces (L-force) and transverse forces (T-force), along with effects of compressibility on aerodynamic forces. Furthermore, recognizing the necessity for high-precision algorithms in the computation of L–T force theory, this investigation utilizes a sixth-order accuracy algorithm for spatial discretization and differencing. Our analysis reveals that the influence of compressibility and the contributions of L-forces to aerodynamic forces become increasingly significant in high M ∞ regimes as shearing processes weaken. Additionally, a new similarity law is established to characterize aerodynamic forces acting on the RAE-2822 airfoil based on a novel moderating factor, ζmo, reduced from local Mach factors in the L–T force theory. This coefficient, ζmo, elucidates the degree to which transverse processes are modulated by longitudinal processes. Various angles of attack α and airfoils have also been analyzed, including National Advisory Committee for Aeronautics (NACA)0012 and NACA0006, by introducing a parameter denoted as κ to further validate the universality of the new similarity laws. The results demonstrate a high degree of accuracy in fitting the aerodynamic coefficients. [ABSTRACT FROM AUTHOR]

A metal/liquid-metal junction is a practical thermoelectric cell causing heat absorption or release according to the direction of electric current and temperature gradient. During thermoelectric processes, the possibility of activating the anomalous heat transfer is considered in this work based on adopting a fractional version of Jeffreys equation with three fractional parameters. Because of the connection between the mean-squared displacement of diffusive hot particles and the thermal conductivity, the fractional Jeffreys law is employed to simulate the low thermal conductivity with crossovers; accelerated or retarded transition, and the transition from high (superconductivity—above the Fourier heat conduction) to low (subconductivity—below the Fourier heat conduction) thermal conductivity. The Couette formulation describing a pressure-driven flow of a viscous thick liquid-metal layer bounded by two similar metallic plates, in the presence of a constant transverse magnetic field, is investigated. A triple-phase pressure gradient, consisting of the phases: (i) ramp-up, (ii) dwell, and (iii) exponential decay, is applied as a real-life flow cause and compared with the classical constant pressure gradient and the impulsive pressure gradient case. The velocity and temperature are obtained in the Laplace domain, and then a suitable numerical technique based on the Fourier series approximation is used to recover the solutions in the real domain. It is found that the retarded crossover of low thermal conduction shows "ultraslow" temperature propagation within the thick layer, which indicates to a case of ultralow heat conduction. As well as the strong correlation between the pressure gradient type (constant, impulsive, or three-phase) and direction (favorable or adverse) and its induced velocity, the temperature gradient between the two plates plays a key role in the determination of the velocity direction and magnitude. [ABSTRACT FROM AUTHOR]

Understanding the evolution of water droplets moving in a highly viscous bulk flow (e.g., bitumen) has attracted increasing attention in the context of numerous separation technologies due to various issues relating to the environment (re-use of water) and engineering failures (corrosion of pipelines). With this in mind, the main objectives of this work are to explore the dynamics of water droplets with a diameter of seven micrometers, moving in highly viscous bitumen flowing through a smoothly converging and diverging 11-micron channel using three-dimensional (3D) and two-dimensional (2D) droplet-resolved simulations and to adjust an existing population balance model (PBM) to predict geometry-driven coalescence for different flow rates. The Eulerian–Eulerian (EE) method coupled with a new PBM is used to predict the behavior of water droplets with a diameter of 7 μm. Numerical simulations were carried out for various capillary numbers (0.1 < C a < 3) and compared with the volume of fluid method combined with the level-set function (CLSVOF). Adaptive mesh refinement (up to six levels) was used in 3D and 2D CLSVOF simulations, producing interface cells measuring up to 30 nm. Good agreement was observed between EE-PBM and CLSVOF models. For comparison, we show the results of 2D CLSVOF simulations. This new PBM model can be used to predict water–oil separation in new cascade-formed geometries to enhance the coalescence of water droplets in highly viscous bulk flows. [ABSTRACT FROM AUTHOR]

In this study, a fluid flow with an incompressible axisymmetric steady couple stress translated through a porous media is analyzed between a hollow sphere and a concentric rigid sphere. In the permeable region, the flow field is regulated by Brinkman's equation. The slip and spin slip conditions are applied on both the rigid sphere and spherical cavity surfaces. Modified Bessel functions provide a systematic approach to the problem by utilizing the principle of a stream function. On the inner sphere, the wall correction factor that an incompressible couple stress fluid encounters is calculated. The effects of the slip, spin slip, coupling stress parameter, separation distance, and permeability parameter on the field functions and the normalized drag force are also graphically shown. The corresponding results are contrasted with the outcomes reported for particular cases of couple stress fluid and viscous fluid flow in two permeability-free concentric circles. Furthermore, graphs of the streamlines for various values of the relevant parameters have been included. [ABSTRACT FROM AUTHOR]

For the first time, the locally power-law preconditioning method (LPLPM) is used to formulate the preconditioned characteristic boundary conditions (CBCs). Then, it is implemented to solve the numerical modeling of unsteady and steady flows from viscous to turbulent regimes. The compatibility equations and Riemann invariants are mathematically derived and then utilized to the incompressible flow solvers as suitable boundary conditions. This method discretizes time derivative and governing equations' space terms by applying the four-stage, fourth-order Runge–Kutta method, and a finite volume, respectively. The preconditioning matrix in the LPLPM is automatically derived by local velocity sensors through a power-law formulation. The baseline k−ω is applied as an appropriate turbulence model. Several test cases are conducted around airfoils of Office National d'Etudes et de Recherches Aerospatiales, NACA0012 (National Advisory Committee for Aeronautics), and S809 at varied angles of attack of 0–20 and Reynolds numbers of 500 to 5.25 × 106 to examine the effectiveness and accuracy of the LPLPM employing preconditioned CBCs. A sensitivity analysis is also performed to examine how numerical parameters affect the simulation. The results show that using preconditioned CBCs in conjunction with LPLPM at the artificial boundary is precise, reliable, and computationally efficient in simulating viscous/turbulent flows. Furthermore, it is also concluded that the present approach considerably improves the convergence speed contrasted to the simplified boundary conditions. [ABSTRACT FROM AUTHOR]

In this study, we introduce a way to control the viscosity of the numerical approximation in the Godunov-like smoothed particle hydrodynamics (SPH) methods. This group of SPH methods includes momentum and energy fluxes in the right-hand sides of the equations, which are calculated by the solution of the Riemann problem between each pair of neighboring particles within the support radius of the smoothing kernel, which is similar to the procedure for the calculation of fluxes across cell boundaries in Godunov schemes. Such SPH methods do not require the use of artificial viscosity since the significant numerical viscosity is already introduced by a Riemann problem solution. We demonstrate that such a numerical viscosity may be measured and obtain the explicit expression for it depending on smoothed particle properties. In particular, we have found that Godunov-like SPH method with interparticle contact algorithms produces numerical viscosity several orders of magnitude higher than physical viscosity in materials. Modern approaches, such as SPH with monotonic upstream-centered scheme for conservation laws or weighted essentially non-oscillatory reconstruction techniques, have not only lower numerical viscosity but also too large for modeling real-world viscous flows. By constructing a correcting viscous stress tensor based on the analytical solution for discontinuous viscous flow, it is possible to reduce the viscous stresses of numerical origin. The use of such a correction makes it possible to improve the agreement with experiments in the simulation of viscous flows without using schemes of higher order reconstruction. [ABSTRACT FROM AUTHOR]

In this article, we present a boundary element method (or panel method) applied to a cavitating propeller to investigate its performance with/without cavitation. The present method models both sheet cavitation and developed tip vortex cavitation concurrently so they can coexist in the flow induced by a propeller. The sheet cavitation can be either partial cavitation or supercavitation depending on the imposed loading on the propeller, and the developed tip vortex cavitation considers loading from the blade tip to determine its sectional volume in space and time. Elaborate numerical schemes are introduced to model both cavities, and it is shown that the present method can predict cavity patterns closely following experimental observations at various loading conditions and cavitation numbers. With the predicted cavities considered, cavitating propeller performance is predicted in potential flow and compared with experimental data, results from a viscous flow solver, and fully wetted performance to verify the accuracy and feasibility of the present method. Steady flow is considered in this study, although the method can be readily extended to unsteady problems. [ABSTRACT FROM AUTHOR]

Recent experiments have revealed the interesting cleaning effects that take place due to the shape mode oscillation of bubbles over a rigid boundary. While a microbubble was undertaking shape oscillation moving over a bacterial biofilm, it removed the contaminants from the boundary and created a clean path through the biofilm. This demonstrated much higher cleaning efficiency than that associated with the volume oscillation of cavitation bubbles; however, the mechanism is unknown. Here, we study this phenomenon using the boundary integral method with the viscous effects modeled using the viscous potential flow theory and the compressible effects using the weakly compressible theory. The viscous stress at the rigid boundary is approximated using the boundary layer theory. We observed that the natural frequencies of shape mode oscillation decrease significantly due to the presence of the boundary. The shear stress at the boundary due to the shape oscillation of a nearby bubble is at least 20 times higher than that due to volume oscillation with the same energy and is significant only within the area directly beneath the bubble. This is explained by the notably faster decay for higher shape modes of the kinetic energy in the fluid as the distance to the center of the bubble r increases with the induced velocity of mode k decaying at a rate of O (r − (k + 2)) away from the bubble. These results achieve excellent agreement with the intriguing cleaning effects first observed in the experiment and explain the mechanism behind this new highly efficient method of cleaning. [ABSTRACT FROM AUTHOR]

Micro aerial vehicles are making a large impact in applications such as search-and-rescue, package delivery, and recreation. Unfortunately, these diminutive drones are currently constrained to carrying small payloads, in large part because they use propellers optimized for larger aircraft and inviscid flow regimes. Fully realizing the potential of emerging microflyers requires next-generation propellers that are specifically designed for low Reynolds number conditions and that include new features advantageous in highly viscous flows. One aspect that has received limited attention in the literature is the addition of roughness to propeller blades as a method of reducing drag and increasing thrust. To investigate this possibility, we used direct numerical simulation to conduct a numerical investigation of smooth and rough propellers. Our results indicate that roughness produces a 2% increase in thrust and a 5% decrease in power relative to a baseline smooth propeller operating at the same Reynolds number of Rec = 6500, held constant by rotational speed. We complement our numerical findings using thrust-stand-based experiments of 3D-printed propellers identical to those of the numerical simulations. Our study indicates that surface roughness is an additional parameter within the design space for micro-propellers, which may offer improved drone efficiencies and payloads. [ABSTRACT FROM AUTHOR]

Viscous oils, which are media commonly used for fluid power transmission, are characterized by high velocities, temperatures, and pressures when working in fluid components and mechanics. The transient nature of viscous oil makes it susceptible to complex operating conditions, which result in cavitation phenomena and can threaten the normal operation and safety of machinery and components. In this study, a three-dimensional computational fluid dynamics model that accounts for cavitation was developed to study the cavitation characteristics, formation conditions, and development of cavitating flow in viscous oil around a hydrofoil under various flow conditions. Moreover, a visual experimental system in which viscous oil flowed around the hydrofoil was proposed and developed to investigate the cavitation properties with regard to various flow conditions. Both numerical results and experimental data indicated that cavitation occurred on the suction surface of the hydrofoil head, and the cavitation characteristics in viscous oil are significantly influenced by the flow conditions. The maximum vapor volume change rate for the degree of effects on cavitation in viscous oil by flow conditions was calculated to be 1.78 cm3/(m/s), −130.66 cm3/MPa, 0.16 cm3/°C, and 4.52 cm3/°, respectively. Low velocities, high pressures, low temperatures, and small impact angles were proved to be able to suppress cavitation. This study provides a research method, an experimental mean, and data support for cavitation flow of viscous fluids, especially oil. It has significant engineering application significance for the development of fluid machinery. [ABSTRACT FROM AUTHOR]

We present a comprehensive study on the displacement flows of shear-thinning (power-law) fluids in a vertical eccentric annulus, employing both experimental and computational methods. This is a sequel to our previous studies [R. Zhang and I. Frigaard, J. Fluid Mech. 947, A32 (2022); R. Zhang and I. Frigaard, J. Fluid Mech. 972, A38 (2023)], which primarily discussed about the dispersive effects for the displacement flow of two Newtonian fluids. The same set of criteria has been applied to determine a steady/unsteady and dispersive/non-dispersive front. The overall classification map broadly aligns with findings from the Newtonian study, while also offering additional information due to the extreme viscosity ratio present. Our observations reveal that the flow behavior is significantly influenced by both the buoyancy force (b) and the viscosity ratio (M). Specifically, higher values of either b or M tend to induce a more steady and non-dispersive regime. Moreover, we have examined intriguing viscosity effects including viscosity dominant flows and viscous driven instabilities. Shear-thinning effects have also been observed and investigated in this study. [ABSTRACT FROM AUTHOR]