Cylindrical Fluid Research Articles

Numerical Modelling of Cylindrical Fluid Filled Tank

The demand for drinking and service water storage is rising with changing climate conditions and increasing life expectancy. The tanks are commonly used to store large volumes of liquids and materials in various fields of the economy. This paper presents the model of the numerical simulation for the steel tank filled with fluid, using the finite element method. The results of the tank filled with water are presented, by the results: the pressure of the fluid the effective stress, and the maximum deformation of the tank solid domain. The correctness of the pressure values was verified by the simple calculation of the fluid pressure. Finally, the paper documents the results for various fluid fillings with a considered range of fluid densities. The influence of the fluid filling height on the behavior of the solid domain of the fluid filling container loaded by the static loading as well as the effect of the width of the tank on the behavior of the solid domain of the fluid filling container.

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids: anisotropic pressure

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids: anisotropic pressure

Nonlinear electro-rheological instability of two moving cylindrical fluids: An innovative approach

The present article examines the nonlinear stability of two viscoelastic electrified cylindrical fluids immersed in permeable media. The current structure consists of two endless vertical cylinders containing two electrified fluids. An axial unchanged electric field (EF) is applied to the entire construction; additionally, the impact of the surface tension is reflected. The main driving force for understanding this challenge has increasing significance in atmospheric and oceanic dynamics. The viscous potential theory is employed to ease the mathematical processes. The fundamental hydrodynamic equations are combined with Maxwell's equations in the quasi-static approximation to set the boundary-value problem. The appropriate boundary conditions (BCs) are expressed in a nonlinear form; this nonlinearity is achieved by addressing the linearized controlling equations of the motion. The viscoelastic impacts are considered to illustrate how the BCs produce their contributions. Consequently, the equations of motion are tackled without the effects of viscoelasticity parameters. The interface displacement consequently interacts vertically along with the cylindrical axis. The Rayleigh Helmholtz–Duffing oscillator describes the propagation of the interface between the two fluids. The non-perturbative approach (NPA), based on the He's frequency formula, transforms the typical nonlinear differential equation (NDE) into a linear one. The non-dimensional analysis reveals a lot of dimensionless physical numerals. These non-dimensional physical characteristics can be utilized to study the fundamental character of the liquid movement. They are also used to reduce the quantity of variables that are needed to comprehend the framework. A quick explanation of NPA is also presented. The stability study reveals the real/complex coefficients of the NDE. The numerical simulations show that there is a consistent solution and that the increases in the axial EF, as well as axial wavenumber, stabilize the system. The obtained findings help to understand and explain diverse nonlinear progressions that have taken place in fluid mechanics. To show the impact of the different factors and the efficiency of the stability approach, diverse PolarPlot diagrams are graphed for both actual and hypothetical portions.

Prospects for mathematical modeling in mining system development: accounting for global oscillations and seismic waves

The article discusses the potential of mathematical modeling in understanding the impact of vibrations and seismic waves, aiming at enhancing the sustainability of systems within the mining industry. It explores the dynamic response of a tall, elastic structure with a uniform cross-section and a fixed cylindrical fluid reservoir, subject to various complex boundary conditions. The study delves into the vibrational behavior of the structure when exposed to seismic and harmonic forces, calculating frequency, vibration periods, and deriving formulas for stress, tension, deformation, bending moments, and shear forces in different parts of the structure through both theoretical and experimental approaches. Additionally, the article derives the differential equation for the free oscillation of a tall hydraulic structure in pure bending with an incorporated mass load under appropriate boundary conditions, identifying specific vibration frequencies and periods. The forced vibration scenario is also examined, focusing on the structure's foundation movement due to external harmonic forces. Numerical computation technology is utilized to analyze the change laws of principal quantities that describe both free and forced vibrational movements of the hydraulic structure, showcasing the applicability of these models in predicting and mitigating the effects of seismic activities on mining infrastructure.

Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.

High sensitivity composite F-P cavity fiber optic sensor based on MEMS for temperature and salinity measurement of seawater.

We proposed an optical fiber salinity sensor with a composite Fabry-Perot (F-P) cavity structure for simultaneous measurement of temperature and salinity based on microelectromechanical system (MEMS) technology. The sensor contains two sensing cavities. The silicon cavity is used for temperature sensing, and the seawater cavity processed by the glass microstructure is sensitive to the refractive index of seawater for salinity sensing. At the same time, the influence of the salinity-temperature cross-sensitivity error of the seawater cavity is effectively compensated by using the temperature single parameter sensitivity characteristics of the silicon cavity. The structural design of the sensor seawater cavity includes a cross-shaped groove and a cylindrical fluid cavity. The surface hydrophilicity treatment was performed on the interior of the cavity to solve the effect of no water injection in the cavity caused by the miniaturization of the sensor. The optical path difference (OPD) demodulation method is used to demodulate the two F-P cavities with large dynamic range and high resolution. In the range of 5∼40°C and 5∼ 40 ‰, the temperature and salinity sensitivity of the sensor can reach 110.25 nm/°C and 178.75 nm/‰, respectively, and the resolution can reach 5.02 × 10-3°C and 0.0138‰. It has the advantages of mass production, high stability, and small size, which give it great potential for marine applications.

Interior spacetimes sourced by stationary differentially rotating irrotational cylindrical fluids. Perfect fluids

In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D 104, 064040 (2021); J. Math. Phys. 64, 022501 (2023); J. Math. Phys. 64, 032501 (2023); J. Math. Phys. 64, 042501 (2023); and J. Math. Phys. 64, 052502 (2023)]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed.

Boundary layers for a fluid–particle interaction system with density-dependent viscosity and cylindrical symmetry

In this paper, we study the initial boundary value problem for a cylindrical symmetry fluid–particle interaction system in three dimensions. The boundary layer phenomena is investigated when the shear viscosity μ=κρβ goes to zero. Furthermore, we establish the boundary layer thickness of the order O(κα) for more general initial data when 0<α<12 and give the optimal boundary-layer thickness for the system with more general initial data. As a byproduct, this work improves the corresponding results in Yao et al. (2011) for isentropic compressible Navier–Stokes equations where 0<α<14.

Instability evolution of a shock-accelerated thin heavy fluid layer in cylindrical geometry

Instability evolutions of shock-accelerated thin cylindrical SF $_6$ layers surrounded by air with initial perturbations imposed only at the outer interface (i.e. the ‘Outer’ case) or at the inner interface (i.e. the ‘Inner’ case) are numerically and theoretically investigated. It is found that the instability evolution of a thin cylindrical heavy fluid layer not only involves the effects of Richtmyer–Meshkov instability, Rayleigh–Taylor stability/instability and compressibility coupled with the Bell–Plesset effect, which determine the instability evolution of the single cylindrical interface, but also strongly depends on the waves reverberated inside the layer, thin-shell correction and interface coupling effect. Specifically, the rarefaction wave inside the thin fluid layer accelerates the outer interface inward and induces the decompression effect for both the Outer and Inner cases, and the compression wave inside the fluid layer accelerates the inner interface inward and causes the decompression effect for the Outer case and compression effect for the Inner case. It is noted that the compressible Bell model excluding the compression/decompression effect of waves, thin-shell correction and interface coupling effect deviates significantly from the perturbation growth. To this end, an improved compressible Bell model is proposed, including three new terms to quantify the compression/decompression effect of waves, thin-shell correction and interface coupling effect, respectively. This improved model is verified by numerical results and successfully characterizes various effects that contribute to the perturbation growth of a shock-accelerated thin heavy fluid layer.

Chemo-hydro-mechanics in a reactive rock under cylindrical fluid pressurization

Cylindrical cavity expansion in a geomaterial due to internal fluid pressurization occurs in many geo-energy and geo-environmental engineering problems involving fluid injection into the subsurface. Often, acidic substances are incorporated in the fluid injection posing a chemically aggressive environment at the cavity wall which diffuses into the matrix affecting the rock’s mechanical as well as hydraulic properties via mineral mass removal. Here we propose a coupled chemo-hydro-mechanical model for such scenarios to study the complex interplay between the process of chemical mass removal, damage evolution, rock strength degradation and an alteration of the hydraulic field due to chemical erosion. A homogeneous fully saturated carbonate rock is chosen for qualitative and quantitative assessments as a representative of chemically reactive geomaterials. Plane strain conditions are assumed and all the fields involved in the reaction-transport-deformation process zone are axisymmetric. The rock behaviour is chemically controlled in both the elastic and plastic domain adopting a chemo-elasticity concept and a yield limit depending on the accumulated mass removal, i.e. the total amount of mineral dissolution under high Damköhler number conditions. The rate of chemical dissolution at a continuum scale is described as a function of a variable specific surface area of the solid–fluid interface per unit volume affected by the irreversible micro-cracking process, as well as the local acidity. The irreversible damage evolution is coupled to the hydraulic field via the porosity generation by chemical mass removal, affecting the acid delivery. The presented framework is the first rock cavity expansion model to our knowledge that underpins a spontaneous transition from the diffusion-dominant to a diffusion–advection regime enabled by damage-enhanced chemical mass removal.

Force dipole interactions in tubular fluid membranes

We construct viscous fluid flow sourced by a force dipole embedded in a cylindrical fluid membrane, coupled to external embedding fluids. We find analytic expressions for the flow in the limit of infinitely long and thin tubular membranes. We utilize this solution to formulate the in-plane dynamics of a pair of pusher-type dipoles along the cylinder surface. We find that a mutually perpendicular dipole pair generically moves together along helical geodesics. Since the cylindrical geometry breaks the in-plane rotational symmetry of the membrane, there is a difference in flows along the axial (ẑ) and transverse (θ̂) directions of the cylinder. This in turn leads to anisotropic hydrodynamic interaction between the dipoles and is remarkably different from flat and spherical fluid membranes. In particular, the flow along the compact θ̂ direction of the cylinder has a local rigid rotation term (independent of the angular coordinate but decays along the axis of the cylinder). Due to this feature of the flow, we observe that the interacting dipole pair initially situated along the axial direction ẑ exhibits an overall “drift” along the compact angular direction θ̂ of the tubular fluid membrane. We find that the drift for the dipole pair increases linearly with time. Our results are relevant for non-equilibrium dynamics of motor proteins in tubular membranes arising in nature, as well as in vitro experiments.

A shallow layer laboratory model of large-scale atmospheric circulation

A new shallow layer laboratory model of global atmospheric circulation is realised and studied by experiments and numerical simulations. A shallow rotating cylindrical fluid layer of 30 mm thickness and 690 mm diameter, with a localised heater at the bottom periphery and localised cooler in the central part of the upper boundary is considered. The rim heater imitates the equator heating and disc cooler – the North pole cooling. The flow transforms from the Hadley-like regime to the baroclinic wave regime through transitional states. The decrease in the thermal Rossby number for the fixed value of Taylor number results in the regularisation of the baroclinic waves. All wave regimes, even with regular wave structures, are characterised by strong non-periodic fluctuations. The observed baroclinic wave structures are a combination of temporarily evolving different baroclinic modes. The important outcome of the shallow layer model is a realisation of the Earth-like meridional three-cell structure. It is shown that the three-cell structure with analogs of polar, Ferrel and Hadley cells exist only in a limited range of parameters. A comparison of the results for the water and silicon oil demonstrated that the physical properties of the fluid can have a strong impact on the baroclinic wave structure.

Three-Dimensional Numerical Modeling of Lava Dynamics Using the Smoothed Particle Hydrodynamics Method

Lava domes and lava flows are major manifestations of effusive volcanic eruptions. Less viscous lava tends to flow long distances, depending on the volcanic slope topography, the eruption rate, and the viscosity of the erupted magma. When magma is highly viscous, its eruption to the surface leads to the formation of lava domes and their growth. The meshless smoothed particle hydrodynamics (SPH) method is used in this paper to simulate lava dynamics. We describe the SPH method and present a numerical algorithm to compute lava dynamics models. The numerical method is verified by solving a model of cylindrical dam-break fluid flow, and the modelled results are compared to the analytical solution of the axisymmetric thin-layer viscous current problem. The SPH method is applied to study three models of lava advancement along the volcanic slope, when the lava viscosity is constant, depends on time and on the volume fraction of crystals in the lava. Simulation results show characteristic features of lava flows, such as lava channel and tube formation, and lava domes, such as the formation of a highly viscous carapace versus a less viscous dome core. Finally, the simulation results and their dependence on a particle size in the SPH method are discussed.

Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. IV. Radial pressure

This article belongs to a series where the influence of anisotropic pressure on gravitational properties of rigidly rotating fluids is studied using new exact solutions of GR constructed for the purpose. For mathematical simplification, stationarity and cylindrical symmetry implying three Killing vectors are considered. Moreover, two pressure components are set to vanish in turn. In Papers I and II, the pressure is axially directed, while it is azimuthal in Paper III. In present paper (Paper IV), a radially directed pressure is considered. Since a generic differential equation, split into three parts, emerges from field equations, three different classes of solutions can be considered. Two could only be partially integrated. The other one, which is fully integrated, yields a set of solutions with a negative pressure. Physical processes where a negative pressure is encountered are depicted and give a rather solid foundation to this class of solutions. Moreover, these fully integrated solutions satisfy the axisymmetry condition, while they do not verify the so-called “regularity condition.” However, since their Kretschmann scalar does not diverge on the axis, this feature must be considered as reporting a mere coordinate singularity. Finally, the matching of these solutions to an exterior appropriate vacuum enforces other constraints on the two constant parameters defining each solution in the class. The results displayed here deserve to be interpreted in light of those depicted in the other four papers in the series.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces.

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Stability characteristics of the cylindrical power-law viscoelastic fluid interface with heat transfer

The analytical study of heat and mass transport at the viscous fluid-viscoelastic fluid is carried out using the irrotational flow theory of viscous-viscoelastic fluids. The interface of viscous-viscoelastic fluid experiences capillary instability. The viscoelastic fluid is taken as power-law fluid and both asymmetric and axisymmetric disturbances are analyzed. The fluids are enclosed in an annular region bounded by two rigid concentric cylinders. The non-dimensional dispersion relation depends on the capillary number, Weber number, power-law index, heat transfer coefficient, viscosity ratio of fluids, etc. The transfer of heat and mass has a significant impact on the stability of the interface. It is also found that the viscosity of viscous fluid delays instability.

Five-dimensional cylindrical anisotropic fluid in Einstein–Gauss–Bonnet gravity

In this paper, we present a static solution for the five-dimensional Einstein–Gauss–Bonnet (EGB) gravitational field equations with a cylindrical symmetry and an anisotropic fluid as a source. We consider whole set of equations in the interior space which sourced by static cylindrical anisotropic fluid and junction conditions required for smoothly matching with exterior space which is a cylindrical vacuum solution of five dimensional EGB equation. We achieve density and pressures as functions of cylindrical radial coordinate and give some graphically analysis under numerical solution.

Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. III. Azimuthal pressure

The investigation of interior spacetimes sourced by stationary cylindrical anisotropic fluids is pursued and specialized here to rigidly rotating fluids with an azimuthally directed pressure. Based on the occurrence of an extra degree of freedom in the equations, two general methods for constructing different classes of exact solutions to the field equations are proposed. Exemplifying such recipes, a bunch of solutions are constructed. Axisymmetry and regularity conditions on the axis are examined, and the spacetimes are properly matched to a vacuum exterior. A number of classes and subclasses are thus studied, and an analysis of their features leads to sorting out three classes whose appropriate mathematical and physical properties are discussed. This work is part of a larger study of the influence of anisotropic pressure in general relativity, using cylindrical symmetry as a simplifying assumption, and considering, in turn, each principal stress direction. It has been initiated in companion Papers I and II, where the pressure was assumed to be axially directed, and is followed by Paper IV considering radial pressure and Paper V contrasting the previous results with the corresponding dust and perfect fluid solutions.

Analytic characterization of sub-Alfvénic turbulence energetics

Magnetohydrodynamic (MHD) turbulence is a cross-field process relevant to many systems. A prerequisite for understanding these systems is to constrain the role of MHD turbulence, and in particular, the energy exchange between kinetic and magnetic forms. The energetics of strongly magnetized and compressible turbulence has so far resisted attempts to understand them. Numerical simulations reveal that kinetic energy can be orders of magnitude higher than fluctuating magnetic energy. We solved this lack-of-balance puzzle by calculating the energetics of compressible and sub-Alfvénic turbulence based on the dynamics of coherent cylindrical fluid parcels. Using the MHD Lagrangian, we proved analytically that the bulk of the magnetic energy transferred to kinetic energy is the energy that is stored in the coupling between the ordered and fluctuating magnetic field. The analytical relations are in strikingly good agreement with numerical data, up to second-order terms.

Study of stationary rigidly rotating anisotropic cylindrical fluids with new exact interior solutions of GR. II. More about axial pressure

This paper is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of general relativity. The configurations have been specialized to three different cases where the pressure is, in turn, directed alongside each principal stress. The two first articles in the series display the analysis of the axial pressure case. Indeed, the first axial class published in Paper I is merely a special case. It is recalled here and its properties are revised and supplemented. Moreover, a fully general method aiming at constructing different classes of such solutions is displayed. This method described in Paper II represents a key result of this work. It is exemplified and applied to two new classes of solutions depending on a single constant parameter. One of them, denoted Class A, is shown to verify every condition needing to be satisfied by a fully achieved set of exact solutions: axisymmetry and, when appropriate, regularity conditions; matching to an exterior vacuum; proper metric signature; and weak and strong energy conditions. Other properties and general rules are exhibited, some shedding light on rather longstanding issues. Astrophysical and physical applications are suggested.