Anisotropic Conditions Research Articles

Particle subgrid stress models for large Stokes numbers in particle-laden turbulence

For the Stokes number based on the Kolmogorov time scale ${St}_K$ up to $O(10^{2})$ , the particle subgrid stress (particle stress) in the volume-average framework is studied by comparing the fluid residual stress, the particle Smagorinsky model and the particle scale-similarity model. To obtain the numerical database of the particle-laden turbulence, two-way coupling direct numerical simulation is carried out with isotropic and anisotropic forcing conditions. As the particle stress is related to the local flow structure, which is not reflected by ${St}_K$ , a new Stokes number ${St}_R$ is introduced to extract the effect of the intensity of the fluid velocity fluctuation in the averaging volume. The degrees of agreement of the principal axes (eigenvectors) of the particle stress models to those of the fully resolved particle stress are regarded as functions of ${St}_R$ regardless of the averaging volume size. The fluid residual stress model shows the highest degree of agreement over a small ${St}_R$ range for both of the forcing cases, and similar predominance is also observed for the correlation coefficient reflecting the magnitude of the particle stress. The effects of ${St}_R$ , ${St}_K$ , the averaging volume size and the Reynolds number on the model coefficients are investigated based on the intensities of the deviatoric and isotropic parts of the fully resolved particle stress and its models. The Stokes number ${St}_R$ is found to be an essential factor to determine the model coefficients, as each effect is extracted reasonably by fixing ${St}_R$ .

An analytical prediction method for the bifurcation of an asymmetric rotor system partially filled with viscous incompressible fluid

Instability of a rotor partially filled with viscous incompressible fluid will cause the amplitudes of perturbations to increase exponentially. Many models of an isotropic rotor partially filled with fluid have been proposed to investigate its stability. However, the bifurcation of an anisotropic rotor partially filled with viscous incompressible fluid is complicated, which has rarely been studied. To investigate this problem, a continuous model is first established for the isotropic case and the hydrodynamic forces are calculated. The D-decomposition method is then used to determine the stable and unstable regions of the isotropic rotor. An analytical prediction method is then proposed in this paper, and the results for stable and unstable regions are the same as those obtained with the D-decomposition method. Then, this novel analytical prediction model is applied to an anisotropic rotor partially filled with viscous incompressible fluid, and the stable and unstable regions are analyzed. One isotropic and two anisotropic conditions are compared to verify the correctness of the proposed analytical method. The results show that the dimensionless damping and stiffness have significant effects on the stability of an anisotropic rotor partially filled with viscous incompressible fluid; in particular, it is found that there exists a single stable region for low values of the dimensionless damping coefficient and stiffness. Furthermore, the bifurcation law of different anisotropic parameters is first explored, which can provide theoretical guidance for the chosen external stiffness and damping coefficients.

Anisotropic slip boundary condition for three-dimensional lattice Boltzmann simulations of liquid microflows

To explore the anisotropic slip on hydrophobic surfaces, a new anisotropic slip boundary condition is proposed for three-dimensional simulations of liquid microflows using the lattice Boltzmann method with adjustable streamwise/spanwise slip length. The proposed boundary condition is derived based on the moment method, which is no longer limited to the assumption of the unidirectional steady flow. Numerical tests validated the effectiveness of the proposed method. Compared with the bounce-back and specular reflection scheme, the proposed method is more accurate and stable for capturing velocity profiles. The proposed method was applied to explore the effects of anisotropic slip on three-dimensional micro-lid-driven cavity flow. The numerical simulation results showed that the anisotropic slip has a greater influence on the flow than the pure streamwise/spanwise slip, and the streamwise slip plays a more important role in influencing the flow than the spanwise slip. The findings may hold significance for efficient development of microfluidic systems and micro-devices.

Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme.

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.

Unique superstructure of Pd–Ir aerogel as a robust three-dimensional electrocatalyst

Herein, a novel, facile, fast, and one-step strategy is introduced to synthesize a three-dimensional (3D) Pd–Ir aerogel. The Pd–Ir aerogel is synthesized by reducing metallic ions in the presence of sodium carbonate and formaldehyde, followed by CO2 supercritical drying. Controlling the type of generated nanostructures and the reaction kinetics is adjusted by the sodium carbonate concentration. The change of sodium carbonate concentration is employed for creating an efficient anisotropic condition to create a Pd–Ir aerogel. The aerogel depicts a 3D architecture with a large porosity and an ultra-low density (0.022 g cm−3). This unique architecture illustrates the exceptional electrocatalytic activity and durability owing to the following vital reasons. The 3D architecture with large open pores not only significantly facilitates the accessibility of ethanol molecules to inner active sites but also guarantees the interaction of ethanol molecules with the surface of aerogel. Furthermore, the downfall of durability observed in the Pd/C owing to corrosion can eliminate by the self-supported nature of assembled aerogel. Moreover, the presence of Ir in the structure of aerogel leads to an alteration in the electronic structure of palladium, which facilitates the electrooxidation of ethanol at a high pH environment.

Simulations of Fractures of Heterogeneous Orthotropic Fiber-Reinforced Concrete with Pre-Existing Flaws Using an Improved Peridynamic Model.

The propagation and coalescence of cracks in fiber-reinforced concretes (FRCs) is the direct cause of instability in many engineering structures. To predict the crack propagation path and failure mode of FRCs, an orthotropic-bond-based peridynamic (PD) model was established in this study. A kernel function reflecting long-range force was introduced, and the fiber bond was used to describe the macroanisotropy of the FRC. The crack propagation process of the FRC plate with flaws was simulated under uniaxial tensile loading. The results showed that under homogeneous conditions, the cracks formed along the centerline of the isotropic concrete propagate in a direction perpendicular to the load. Under anisotropic conditions, the cracks propagate strictly in the direction of the fiber bond. The failure degree of the FRC increases with the increase in heterogeneity. When the shape parameter is 10 and the fiber bond is 0°, the failure mode changes from tensile to shear failure. When the fiber bond is 45°, the FRC changes from a state where outer cracks penetrate the entire specimen to a state where cracks coalesce at the middle. It was found that the improved model can effectively simulate the crack propagation processes of orthotropic FRC materials.

An undrained expansion solution of cylindrical cavity in SANICLAY for K0-consolidated clays

This paper proposes a rigorous undrained solution for cylindrical cavity expansion problems in K0-consolidated clays, adopting a simple non-associated and anisotropic model, SANICLAY. The cavity expansion theory is well extended to consider non-associativity, K0-consolidation and stress-induced anisotropy with combined rotational and distortional hardening of yield surface and plastic potential in the multiaxial stress space. The developed solution can be recovered for validation against the modified Cam-clay (MCC) solution by simply setting model constants, avoiding non-associativity and anisotropy. The source code is provided to facilitate the use for extensions. After investigating the effects of overconsolidation ratio on the cavity pressure curves, stress distributions, evolutions of anisotropic parameters and stress paths, the variations with three-dimensional (3D) evolutions of yield surface and plastic potential during undrained cavity expansion are shown for various K0-consolidated clays. A parametric study on the model constants is presented to depict the influences on the stress distributions and paths, critical state surfaces and Lode's angles at failure. The proposed solution also provides a general framework for formulating equations for undrained expansion of cylindrical cavities under an initial cross anisotropic condition using sophisticated anisotropic soil models. It serves as a precise benchmark for extensions of analytical solutions, numerical simulations of cavity expansion, and back-calculations of geotechnical problems.

Cyclic resistance of fly ash influenced by anisotropic stress condition, sand contents, and gravel content

A series of cyclic triaxial tests were performed to study the effect of anisotropic stress, sand content (in a fly ash-sand mixture), and addition of gravel on the cyclic resistance of fly ash. The results indicated that the failure mode of pure fly ash in the presence of isotropic stress was cyclic mobility and that the cyclic resistance of pure fly ash was significantly lower than that of clean Nakdong River sand for given test conditions. The cyclic resistance of pure fly ash decreased when the effective confining stress increased from 100 to 200 kPa, as expected. The failure of pure fly ash conducted in the absence of stress reversal was due to the initial axial strain accumulation and subsequent sudden runaway deformation, and this failure mode differed dramatically from that of fly ash conducted under symmetrical stress reversal. An increase in the anisotropic ratio resulted in a decrease in the cyclic resistance of pure fly ash. Nakdong River sand and gravels were added to pure fly ash and it was examined whether the cyclic resistance of fly ash increased. Addition of sand was observed to decrease the cyclic resistance for 10% and 20% sand content by volume, regardless of the amount of increase in the dry density of the samples. Furthermore, the cyclic resistance of fly ash-gravel mixtures was greater than that of pure fly ash by approximately 17%.

Significance of magnetohydrodynamic Williamson Sutterby nanofluid due to a rotating cone with bioconvection and anisotropic slip

AbstractThe thermal transmission outcomes of Williamson Sutterby nanofluids owing to spinning cone with gyrotactic micro‐organisms such as self‐motivated microbes along with anisotropic slip conditions are probed in this article. The axi‐symmetric, unstable three‐dimensional stream of fluids is swayed by magnetic and buoyancy forces. Utilizing appropriate similarity variables, the leading partial differential formulation for velocity, temperature, concentration, and motile density of nanofluids are altered into nonlinear ordinary differential equations and these equations together with boundary constraints are resolved by computational code for Runga–Kutta method in MATLAB platform. A concise computational strategy is made by altering the inputs of influential factors. Nusselt number, Sherwood number, and motile density number are also computed and listed in tables. As the magnitudes of the slip parameters expand, the Nusselt number, and Sherwood number decline. The velocity along the x‐axis and the concentration variations amplify as the u‐velocity slip and solutal slip parameters are boosted. The temperature profile goes down for boosted values of A and . The fluids temperature distribution enhances directly with thermophoretic effect and Brownian motion of nano‐entities.

Grain growth behavior of ferroelectric ceramics under anisotropic grain boundary energy conditions simulated by the phase field method

The grain growth behavior of ferroelectric ceramics is different from that under the condition of an isotropic grain boundary energy, owing to the existence of many high-energy grain boundaries. A simple phase-field model based on the anisotropy of the grain boundary energy was developed to simulate the microstructure evolution of ferroelectric ceramics. The effects of the anisotropy of the grain boundary energy on the grain growth behavior and formation of characteristic regions were investigated using the phase-field method. The experimental data confirmed the simulation results. It was observed that the rapid migration of high-energy grain boundaries and slow migration of low-energy grain boundaries resulted in the appearance of both, small grains with edge numbers greater than six and numerous strip grains. The grain microstructures showed a specific orientation distribution in the 2-D cross section. The anisotropy of grain boundary energy can regulate the grain orientation distribution. This work provides a basis for microstructure control and the stable preparation of high-performance ferroelectric ceramics.

Generalized simple model for predicting the modulus degradation and strain accumulation of clay subject to long-term undrained cyclic loading

Modulus degradations and strain accumulations of clays under repeated environmental loads are important factors in the design of offshore foundations. In this study, a simple model is proposed for predicting the modulus degradation and strain accumulation of clays subject to long-term cyclic loading. The development of the proposed model is based on a comprehensive database, including a series of undrained cyclic triaxial tests on the reconstituted kaolin clays. The concept of fatigue failure under cyclic loading is adopted to develop the model. Several influence factors, such as the initial stress ratio, initial confining stress, and overconsolidation ratio, are considered in the prediction model. The main feature of the proposed model is to predict the modulus degradation and strain accumulation simultaneously. This process is typically achieved separately by different models. At the isotropic condition or the symmetric (two-way) loading condition, the model tends to predict the modulus degradation. At the anisotropic condition or the asymmetric (one-way) loading condition, the model tends to predict the strain accumulation. The model predicts the modulus degradation and strain accumulation at the intermedium conditions defined by the initial stress ratio. This physical-based model can be easily calibrated with new test results or extended with additional influence factors (e.g., loading frequency).

Aeroelastic modal dynamics of floating wind turbines in anisotropic conditions based on Floquet analysis

A reduced order model of a floating wind turbine with 22 degrees of freedom has been implemented and validated in comparison to the multibody, hydro-servo-aero-elastic code hGAST. The multi-blade Coleman transformation is applied and Floquet stability analysis is performed. This allows on one hand, to verify the actual Floquet implementation against the standard Coleman-based eigenvalue analysis in cases the transformed dynamic system has constant coefficients and on the other hand to analyze the effects of different anisotropies on stability. Mass imbalance of the rotor and yaw misalignment have been specifically addressed. In the mass imbalance scenario, the homogeneous results are not substantially altered while in the wind yaw scenario, there is slight change of the flapwise natural frequencies and of the tower lateral frequency as well as of the corresponding damping characteristics.

Data assimilation for the two-dimensional shallow water equations: Optimal initial conditions for tsunami modelling

Accurate modelling of tsunami waves requires complete boundary and initial data, coupled with the appropriate mathematical model. However, necessary data is often missing or inaccurate, and may not have sufficient resolution to capture the dynamics of such nonlinear waves accurately. We demonstrate that variational data assimilation for the continuous shallow water equations (SWE) is a feasible approach for recovering initial conditions. We showed that the necessary conditions for reconstructing one-dimensional initial conditions in Kevlahan et al. (2019) can be extended to the maximum Euclidean distance between pairwise observations to two-dimensions. We use Sadourny finite-difference finite volume simulations to verify convergence to the true initial conditions can be achieved for observations arranged in multiple configurations, for both isotropic and anisotropic initial conditions, and with realistic bathymetry data in two dimensions. We compare observations arranged in straight lines, in a grid, and along concentric circles, and assess the optimal number and configuration of observation points such that convergence to the true initial conditions is achieved. These idealised results with simplified two-dimensional geometry are a first step towards more physically realistic settings. Recent advances in altimetry observation data now permit much denser measurements of sea surface height than is possible with a fixed buoy network. This provides the opportunity to use the method developed here for more accurate tsunami forecasts in realistic settings.

Stability analysis of restricted non-static axial geometry in [formula omitted] gravity

The goal of this article is to investigate instability constraints under the influence of f(R,T) gravity in which the Lagrangian is taken as a varying function of Ricci scalar invariant (R) and trace of energy–momentum tensor (T). We examined the stable behavior of axial symmetrical compact fluid configuration with anisotropic conditions. We formulated modified field equations as well as conservation equations in the background of this particular gravity. We constitute the collapse equation, which follows from the perturbation method by applying it to the geometrical and material quantities. A particular f(R,T) gravity model, i.e, f(R,T)=R+αR2+σR+λT is used and perturbed along with conservation and field equations for the systematic analysis. Furthermore, to determine stability criteria of astral configuration, we impose substantial physical conditions in the expression of Γ (i.e., adiabatic index) at Newtonian (N) and post-Newtonian (pN) domains. Also, one can impose constraints on physical entities to establish and maintain its un/stable behavior with the influence of a certain f(R,T) model.

Effect of microwave radiation on mechanical behaviors of tight fine sandstone subjected to true triaxial stress

During the exploitation of deep resources, rock masses are under three-dimensional anisotropic stress conditions owing to tectonic conditions and engineering disturbances. Owing to the advantages of high heating efficiency and selective volume heating, microwaves have broad application prospects in fields such as unconventional low-permeability reservoir fracturing. Therefore, it is of great significance to study the mechanical behavior of rocks under true triaxial stress after microwave irradiation. In this study, true triaxial tests of sandstone under different microwave irradiation conditions were conducted. The results showed that the strength of the irradiated sandstone first increased and then decreased. The strength of the irradiated sandstone was significantly lower than that of the unirradiated sandstone. The pre-peak brittleness of the sandstone gradually increased with an increase in σ₂. The brittleness of the irradiated samples was lower than that of the unirradiated samples. For the post-peak brittleness index of the sandstone, with the increase of σ₂, the microwave irradiated and unirradiated sandstone both gradually decreased first and then slowly increased. The residual strength of the unirradiated sandstone showed a trend of first increasing and then stabilizing, while the residual strength of the irradiated sample showed a greater dispersion and fluctuation. And, the residual strength of sandstone first increased and then decreased with the increase of microwave duration. In addition, a new double logarithmic linear strength model was proposed, which is in good agreement with the experimental results. The true triaxial stress induced anisotropic damage and deformation of sandstone are critical to rock fracture. The stress difference induced by water vapor expansion and mineral thermal expansion is the main factor for microwave breaking water-bearing sandstone. This work is of great significance to the research and application of microwave assisted breaking hard rock and fracturing deep low-permeability reservoir rocks.

Using the coherence of the frequency-difference autoproduct to facilitate rough surface information identification

Acoustic waves, with wavenumber k and incidence angle θ, forward scattered from a randomly rough surface, with root-mean-square roughness height h, lose coherence with the incident field as khcosθ increases. Recovering reflected field-coherence is possible via the frequency-difference autoproduct, a quadratic product of complex field amplitudes at nearby frequencies within the signal bandwidth. By downshifting recorded frequencies, the apparent roughness of a surface is reduced and coherence can be regained. An additional consideration exists, however, as the nonlinearity of the frequency-difference autoproduct introduces a significant dependence on the surface autocorrelation function, and consequently, the surface power spectrum by Fourier transform. The relationship between coherence recovery, surface autocorrelation function, and surface power spectrum is discussed and results are shown. Furthermore, this presentation investigates the potential utility afforded by these relationships for environmental characterization in rough surface scattering. By employing coherence-based frequency-difference autoproduct methods, remote identification of the spectral content, lateral statistics, and vertical statistics of a rough surface are explored. The work uses acoustic data collected at sea during SW06 (off New Jersey, depth 80 m), where the geometry, signal bandwidth, and anisotropic ocean surface conditions put khcosθ > 2.5. [Work supported by ONR and by the US DoD through an NDSEG Fellowship.]

Hadron-quark phase transition at finite density in the presence of a magnetic field: Anisotropic approach

We investigate the hadron-quark phase transition at finite density in the presence of a magnetic field taking into account the anisotropy created by a uniform magnetic field in the system’s equations of state. We find a new anisotropic equilibrium condition that will drive the first-order phase transition along the boundary between the two phases. Fixing the magnetic field in the hadronic phase, the phase transition is realized by increasing the baryonic chemical potential at zero-temperature. It is shown that the magnetic field is mildly boosted after the system transitions from the hadronic to the quark phase. The magnetic-field discontinuity between the two phases is supported by a surface density of magnetic monopoles, which accumulate at the boundary separating the two phases. The mechanism responsible for the monopole charge density generation is discussed. Each phase is found to be paramagnetic with higher magnetic susceptibility in the quark phase. The connection with the physics of neutron stars is highlighted throughout the paper.

Tilt angle optimisation by Taylor’s series expansion for maximum solar radiation in humid subtropical regions of India

This paper presents a novel method for maximum utilisation of solar energy on solar collectors by optimising tilt angle (β). The optimisation has been done in two steps, in first, the partial differential equation of total radiation on tilted surface (H T) is differentiated with respect to β and in second, Taylor’s series expansion method is applied to find the optimised tilt angle (β Taylor). The results so obtained are applied to different locations of India and it is found that on anisotropic atmospheric conditions the total monthly radiation falling on collector surface βTaylor is increased significantly at each location. The maximum gain of 3.19% during winters, 2.46% during spring, no change during summers and 3.14% during autumn is observed in Kolkata. Only 1.42% radiation losses on seasonal and 8.14% radiation loss on annual basis as compared to radiation on monthly basis at New Delhi station are observed.

The final Kasner regime inside black holes with scalar or vector hair

The final (close to the singularity) dynamical behavior of the metric inside black holes with massive charged scalar or vector hair is analyzed for general anisotropic and inhomogeneous initial conditions. These solutions are relevant to a holographic realization of superconductivity. It is shown that the dynamics falls within the scope of the “cosmological billiard” description and that in both cases, the corresponding hyperbolic billiard region has infinite volume so that the system ultimately settles down to a final Kasner regime. For massive vector hair, the conclusion holds because the longitudinal mode plays the same role as a scalar field. There exists, however, a measure-zero subset of solutions characterized by vanishing longitudinal modes that exhibit a chaotic behavior with an infinite number of BKL oscillations as one goes to the singularity.

Mechanism of wetting–induced deformation and failure of unsaturated soils

AbstractThe mechanisms of hydraulic collapse (wetting‐induced deformation) are studied through a series of simulations using a model for unsaturated soils. The model is a critical state soil model extended for unsaturated soils using Bishop's effective stress tensor, the state boundary surface (SBS) moving with the change in the degree of saturation, and a rational soil‐water characteristic curve that takes account of density and hydraulic hysteresis. Comparisons with published experimental data validate the proposed model. The simulation results show that the model adequately captures the hydraulic collapse behavior under both isotropic and anisotropic stress conditions. The effects of density, mean net stress, and deviatoric stress on the hydraulic collapse behavior are further investigated through a parametric calculation, and the mechanics of the wetting–induced instability are discussed. The effects of suction history, namely repeated wetting and drying cycles, on the deformation and failure, are also presented. The proposed model provides a validated method for modeling hydromechanical collapse in unsaturated soil and provides a better understanding of the mechanisms involved.