Infinite Fluid Research Articles

Characteristics of Bubble Oscillations During Laser-Activated Irrigation of Root Canals and Method of Improvement.

Background and ObjectivesLaser‐activated irrigation of dental root canals is being increasingly used as its efficacy has been shown to be superior compared with conventional techniques. The method is based on laser‐initiated localized fluid evaporation and subsequent rapid bubble expansions and collapses, inducing microfluid flow throughout the entire volume of the cavity. The irrigation efficacy can be further improved if optimally delayed “SWEEPS” double laser pulses are delivered into the canal. This study aims to show that the irrigation efficacy, as measured by the induced pressure within the canal, is related to the double pulse delay, with the maximal pressure generated at an optimal delay. The second aim is to find a method of determining the optimal delay for different cavity dimensions and/or laser parameters.Study Design/Materials and MethodsExperiments were made in transparent models of root canals where Er:YAG laser (λ = 2.94 μm, pulse duration t p = 25 or 50 microseconds, and pulse energies up to E L = 40 mJ) was used with a combination of cylindrical and conical fiber‐tip geometries (diameters 400 and 600 µm). High‐speed photography (60,000 fps) and average pressure measurements inside the canal were used for process characterization.ResultsThe results show that a pressure amplification of more than 1.5 times occurs if the laser pulse delay approximately coincides with the bubble oscillation time. Correlations between normalized oscillation time and canal diameter for a wide range of laser pulse energies (R 2 = 0.96) and between the average pressure within the canal and the bubble oscillation periods (R 2 = 0.90) were found. A relationship between the bubble oscillation time and the diameter of the treated cavity was found depending on the bubble oscillation time in an infinite fluid reservoir.ConclusionsThe bubble oscillation time within a constrained volume can be determined based on the known oscillation time in infinite space, which offers a fast and simple solution for optimization of the laser parameters. These findings enable determination of optimal conditions for shock wave generation, and improvement of root canal irrigation at the same dose of laser energy input, leading to improved treatment efficacy and safety. Lasers Surg. Med. © 2020 The Authors. Lasers in Surgery and Medicine published by Wiley Periodicals, Inc.

Effect of impeller diameter on Nusselt number in mechanically agitated vessel

PurposeThe purpose of the study is to developed the effect of Nusselt number on impeller diameter in agitated vessel, which is beneficial to find out the heat transfer coefficient in the process industry. A comparison has been done between the experimental and calculated Nusselt numbers with standard deviation found to be 8.03 per cent.Design/methodology/approachFor studying the effect of impeller diameter on Nusselt Number, the heat transfer measurements were made with three different impellers of diameter. Although the diameter of impeller, Da shows its effect in Reynolds number, an attempt has been made to find the relationship between the impeller diameter and Nusselt number. A correlation between (NNuj/N″Pra1/3 N″Rea2/3) vs Da/DT and (NNuoc/N″Pra1/3 N″Rea2/3) vs Da/Dc in which data of three fluids [1, 2 and 4 per cent carboxy methyl cellulose solution of A type (CMC-A) solutions] have been plotted.FindingsThe heat transfer data for agitated Newtonian and non-Newtonian fluids have been successfully correlated by using the viscosity of the fluid evaluated at the impeller tip assuming a cylinder of diameter equal to that of impeller rotating in an infinite fluid. Data of 1, 2 and 4 per cent CMC-A, for three impeller diameters, have been correlated by equations. Using the above concepts of Reynolds and Prandtl numbers, Nusselt Numbers and Da/DT, it is also possible to correlate the available published data for other non-Newtonian fluids obtained with different impeller geometries.Originality/valueA set up was made for studying the effect of impeller diameter, the heat transfer measurements were made with three impellers of diameter 7.5, 12.7 and 18.35 cm respectively. Although the diameter of impeller, Da shows its effect is Reynolds number, an attempt has been made to find the effect of Da/DT ratio on Nusselt number.

Thermodynamic analysis and prediction of reservoir temperature distribution for steam stimulation

During steam stimulation of horizontal wells in heavy oil reservoir, it is necessary to estimate the reservoir temperature distribution, which has a huge impact on oil production and ultimate oil recovery. Most of previous models were derived based on infinite boundary condition and constant fluid velocity, which were not consistent with real situation of reservoir. In this paper, new energy balance equations combined with mobile boundary conditions were developed for increasing the accuracy of predicted results. Based on dimensionless conversion and numerical analysis, the optimum solution of equation system could be easily obtained, and its good performance in predicting temperature distribution was also validated. Moreover, thermodynamic mechanism of hot fluid, latent heat and sensible heat of steam, and their contributions to heating reservoir were also discussed to investigate the heat transfer pattern in reservoir. Finally, factors that could influence the reservoir temperature distribution were analyzed. It is found that: (a) both the heat conduction and the heat convection contribute to the heat transfer in hot liquid zone, and the heat convection predominates; (b) both the condensation front and heat front move outward with the injection of steam, but their expanding rates gradually drop with time; (c) as the radius increases, the radial fluid velocity will go down, leading the heat convection effect to be weakened and the heat conduction effect to become obvious; (d) there are some factors that can influence the reservoir temperature distribution including steam injection duration, fluid velocity, volumetric heat capacity of fluid, steam quality and thermal conductivity of reservoir.

Interaction dam-reservoir: study of conservative and dissipative effects

Abstract In this paper, the Laplace’s equation is solved analytically in the complex plane for the field of hydrodynamic pressures generated by the rigid body movement of a dam against a reservoir with infinite domain and incompressible fluid. The force the reservoir fluid exerts on the face of the dam is determined through the integration of the hydrodynamic pressure in the complex plane. The conservative effects (real part) and dissipative effects (imaginary part) of the force are analyzed as a function of the Froude number. The asymptotic solution of the aforementioned effects are also presented in this paper.

Acoustic Analysis of a Finite Cylindrical Shell in an Acoustic Half-Space Based on Fourier Transform Technique

In marine and ocean engineering area, some underwater cylindrical shell structures or vehicles may approach a free surface (water surface) or a rigid wall (seabed). The existence of the free surface or rigid wall makes the surrounding fluid around the structure an acoustic half-space, causing that the vibroacoustic characteristics of the shell may have much difference from those in an infinite fluid field. In this study, the far-field acoustic radiation of a finite cylindrical shell with an arbitrary, time-harmonic surface velocity distribution positioned within an acoustic semi-space is studied. The Fourier transform method is utilized to express acoustical pressure in the wavenumber domain, and the acoustic boundary effect is considered through the use of the Graf’s addition theorem and the image approach. Then, the relationship between acoustical pressure and the normal velocity on the structure surface is established in the wavenumber domain. Finally, the far-field acoustical pressure could be expressed by the stationary phase method approximately. The accuracy of the present approach is verified by contrast with the boundary element method. It could be observed that there are many similarities between the directivity of the far-field acoustical pressure of the cylindrical shell and the acoustical dipole due to the interference of sound waves. For the case of a rigid wall boundary, a similar interference phenomenon also exists. The present method has the advantages of simpleness and fewer calculations; it can be utilized to rapidly predict the far-field acoustical pressure in an acoustic half-space. Besides, after discussing the multiple scattering effects between the acoustic boundary and the shell, a simpler physical model is successfully put forward to resolve the far-field acoustical pressure of an inclined shell within an acoustic semi-space, assuming that the distance between the shell and the acoustical boundary is larger than a certain value (five-time radiuses in the present study).

A thermoelastic microelongated layer immersed in an infinite fluid and subjected to laser pulse heating

Abstract The present investigation deals with the twodimensional deformation because of laser pulse heating in a thermoelastic microelongated layer with a thickness of 2d, which is immersed in an infinite nonviscous fluid. Normal mode analysis technique is applied to obtain the analytic expressions for displacement component, force stress, temperature distribution, and microelongation. The effect of elongation and laser pulse rise time on the derived components have been depicted graphically.

Nonlinear dynamic and acoustic analysis of orthogonally stiffened composite laminated cylindrical shells containing piecewise isolators

This paper presents a numerical method for analyzing the nonlinear structural and acoustic responses of a coupled stiffened composite laminated cylindrical shell and piecewise isolation system immersed in an infinite acoustic fluid. The cylindrical shell is reinforced by a series of circumferential rings and longitudinal stringers, which may be few or many in number, non-uniform or uniform in size, and arbitrarily distributed in space. The isolation system in the shell contains motion-limiting stops, and the restoring forces of the isolators are assumed as bi-linear functions of the isolator deformations. A modified variational approach for the shell combined with a discrete element method for the rings and the stringers is employed to establish the nonlinear dynamics model of the structural system. The exterior acoustic fluid is computed by a time-domain Kirchhoff boundary integral formulation. The structural and acoustic models are coupled together by considering the compatibility conditions on their interface. The validity of the present method for predicting the structural and acoustic responses of the coupled shell and isolator system is confirmed. The contribution of the grouped circumferential wave modes of the shell to the vibration and radiated sound of the coupled structural system is examined. The effects of the excitation frequency of the external load, as well as the stiffness ratio and the gap of the suspension springs in each isolator on the structural and acoustic responses of the coupled system are discussed.

Force on a spherical particle oscillating in a viscous fluid perpendicular to an impermeable planar wall

The slow motion of a hard spherical particle embedded in a semi-infinite viscous fluid bounded by an impermeable plane wall is considered. The particle oscillates with small amplitude along a diameter perpendicular to the wall. At both surfaces of the particle and plane wall, the no-slip kinematic condition is used. An analytical procedure with a numerical solution based on collocation technique is considered. The solution is found to be accurate for the low and high frequency of oscillations. The drag force coefficients acting on the particle are plotted and tabulated against the frequency and the separation distance. The drag coefficients are found in good agreement with the corresponding problem of a steady case and with the oscillation of a particle embedded in an infinite viscous fluid.

Added Masses of generic shape bodies interacting with external walls

The aim of this paper is to propose an efficient method to evaluate the Added Masses of generic shape bodies in infinite fluid or in the proximity of external walls. The Added Masses (AM) are the result of the inertial reaction of the fluid in response to an accelerated movement of a body immersed in it. The AM effects are more evident when the body density is similar to that of the surrounding fluid, as in the case of airships. In the take-off or landing phases, the proximity to the ground causes an increase in the Added Masses that must be correctly estimated to properly size the airship controls. In our method, the calculation of the Added Masses matrix is carried out by the Boundary Element Method (BEM). To verify the accuracy of the results, the study cases are based on simple shapes, whose Added Masses are well known. The analyses in infinite fluid and in the presence of a flat wall are carried out. Numerical results are compared to the theoretical values found in literature. The calculated Added Masses are intrinsically dependent on the mesh definition and the relative error, referred to the theoretical values, depends on the surface and volume discretization. In the case of interaction between geometries with complex shapes, the influence on the Added Masses is very difficult to predict without a numerical approach. The method proposed gives a good compromise in terms of quality of results and computational cost.

Seismic response analysis of the reef-seawater system under incident SV wave

The seismic response analysis of a reef engineering site is the foundation for the seismic design of artificial islands and other upper constructions. This study proposes a two-dimensional seismic analysis model for the reef-seawater system, where the fluid-solid coupling effect is considered and the wave radiation effects of infinite fluid and solid domains are simulated by corresponding artificial boundary conditions. Meanwhile, the seismic wave input method based on the substructure of artificial boundaries is modified to accomplish the process of inputting the seismic waves with arbitrary incident angles into the calculation region. The accuracy of the proposed model is verified by numerical examples. Afterwards, we conduct the parametric studies and the seismic analysis of a series of practical layered reef models. The results indicate that the least favorable slope gradient for the seismic response is generally at approximately 30°, and the feature of wave velocity reduction along the vertical direction significantly magnifies the seismic response on the reef flat. The peak acceleration ratio near the edges of the reef flat distributes between 3 and 4. While in the middle area, it is usually between 1.5 and 2.5, and can reach up to 4 when the width of reef flat decreases.

Guided circumferential wave propagation characteristics for porous cylinder immersed in infinite fluid

Underground water, gas and oil all exist in the fractured or porous strata. Waves that propagate through porous cylinder immersed in infinite fluid are of considerable interest in the estimation of porous parameter, such as an underwater concrete column may present pore characteristics after a long time water immersion. Compared with longitudinal guided wave, circumferential guided wave has its advantages in the ultrasonic nondestructive inspection of porous cylinder. In order to investigate the propagation characteristics of guided waves in a porous cylinder immersed in infinite fluid and analyze the effects of the porous medium parameters on the dispersion characteristic, a model of porous cylinder surrounded by fluid is built. Based on the elastic-dynamic theory and modified liquid-saturated porous theory, the characteristic equation of guided wave is established, and the dispersion curves are obtained numerically. The effects of cylindrical radius and pore parameters on the propagation characteristics of guided waves are discussed; the attenuation characteristics of guided waves are also analyzed; the time domain waveforms of the guided circumferential waves are obtained by numerical inversion, and the influence of porous parameters on waveforms is simulated. It is found that the dispersion curves are similar to that of elastic cylinder in the fluid, there exist multiple mode guided waves and approximate shear velocity of medium for higher modes, and higher order modes are more affected by the radius, but it does not change the tendency of curve. The phase velocity decreases with porosity increasing at the same frequency and the effect of porosity on higher order modes is greater than that on mode 1; due to the dissipation in the medium, the attenuation increases porosity increasing. It can be seen from the transient responses that the wave packets move backward and the displacement amplitude decreases with the porosity increasing. The characteristics of the inversed transient response are in good agreement with theoretical dispersion and attenuation. The results show that the propagation of guided circumferential wave is affected by the pore parameters, especially for porosity, which can provide a theoretical reference for the non-destructive evaluation of the porous cylinder surrounded by infinite fluid.

Global Exponential Nonlinear Stability for Double Diffusive Convection in Porous Medium

Nonlinear stability of the motionless double-diffusive solution of the problem of an infinite horizontal fluid layer saturated porous medium is studied. The layer is heated and salted from below. By introducing two balance fields and through defining new energy functionals it is proved that for CLe ≥ R, Le ≤ 1 the motionless double-diffusive solution is always stable and for CLe < R, Le < 1 the solution is globally exponentially and nonlinearly stable whenever R < 4π2+LeC, where Le, C and R are the Lewis number, Rayleigh number for solute and heat, respectively. Moreover, the nonlinear stability proved here is global and exponential, and the stabilizing effect of the concentration is also proved.

Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation

Обсуждается разрешимость переопределенной системы уравнений тепловой конвекции в приближении Буссинеска. Система уравнений Обербека-Буссинеска, дополненная уравнением несжимаемости, является переопределенной. Количество уравнений превосходит количество неизвестных функций, поскольку изучаются неоднородные слоистые потоки вязкой несжимаемой жидкости (одна из компонент вектора скорости тождественно равна нулю). Проведено исследование разрешимости нелинейной системы уравнений Обербека-Буссинеска. Исследование разрешимости переопределенной системы нелинейных уравнений в частных производных Обербека-Буссинеска осуществлялось при помощи построения нескольких частных точных решений. Приведен новый класс точных решений для описания трехмерных нелинейных слоистых течений вертикальной завихренной вязкой несжимаемой жидкости. Вертикальная компонента завихренности в невращающейся жидкости генерируется неоднородным полем скоростей на нижней границе бесконечного горизонтального слоя жидкости. Конвекция в вязкой несжимаемой жидкости индуцируется линейными источниками тепла. Основное внимание уделено исследованию свойств поля скоростей течения. Исследована зависимость структуры этого поля от величины вертикальной закрутки. Показано, что одна из компонент вектора скорости при ненулевой вертикальной закрутке допускает расслоение на пять зон по толщине рассматриваемого слоя (четыре застойные точки). Анализ поля скоростей показал, что кинетическая энергия жидкости может дважды принимать нулевой значение по толщине слоя.

The Comparison of Newtonian and Non-Newtonian Rheology Cases of the Solution of 2D Hydrodynamic Equations in the Boussinesq Approximation: A Mechanism of Upwelling Convective Flow Transporting Hydrocarbons

Thermo-mechanical model of the mantle wedge between the base of the overlying Scythian lithospheric plate and the upper surface of the Black Sea micro-plate subducting under the Scythian one with a velocity V at an angle β is obtained for the infinite Prandtl number fluid as a solution of non-dimensional 2D hydrodynamic equations in the Boussinesq approximation. For both Newtonian and non-Newtonian rheology cases 2D thermal viscous dissipationdriven convection mechanism in the mantle wedge above the Black Sea micro-plate subducting under the Crimea peninsula is modelled numerically. The effects of 410 km and 660 km phase transitions are taken into account. In the case of Newtonian rheology, the upwelling convective flow transporting heat to the Earth’s surface locates at far greater distance from the trench than they observed 2D heat flux anomaly. In the case of non-Newtonian rheology, the upwelling convective flow transporting heat to the Earth’s surface locates at twice greater distance from the trench than they observed 2D heat flux anomaly, the velocity in the convective vortices being over ∼10 m per year.

The effects of a horizontal magnetic field on the Rayleigh–Taylor instability

The stability of a thin conductive liquid film flowing along a solid wall is an important problem that occurs in many proposed fusion device designs. In this paper we investigate the linear stability of an electrically conductive liquid film of finite thickness in the presence of a strong magnetic field. Inviscid flows of finite and infinite electric conductivity are considered. The magnetic field is found to decrease the unstable growth rate for both finite and infinite conductivity fluids but only narrows the unstable modes for infinite conductivity fluids. Our theory serves as an extension to the classical theory by Chandrasekhar (1961) [1] by considering the finite-thickness and finite-conductivity effects.

Study of Weakly nonlinear Mass transport in Newtonian Fluid with Applied Magnetic Field under Concentration/Gravity modulation

AbstractIn the present paper, a weakly nonlinear stability analysis is used to analyze the effect of time-periodic concentration/gravity modulation on mass transport. We have considered an infinite horizontal fluid layer with constant appliedmagnetic flux salted from above, subjected to an imposed time-periodic boundary concentration (ITBC) or gravity modulation (ITGM). In the case of ITBC, the concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated. In the case of ITGM, the gravity fleld consists of two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. We have expanded the infinitesimal disturbances in terms of power series of an amplitude of modulation, which is assumed to be small. Ginzburg-Landau equation is derived for dinding the rate of mass transfer. Effect of various parameters on the mass transport is also discussed. It is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation.

Dispersion Waves in a Submerged Thermo-Piezoelectric Membrane

Abstract Wave propagation in a thermo piezoelectric membrane immersed in an infinite fluid medium is discussed using three-dimensional linear theory of elasticity and thermos piezoelectricity. Three displacement potential functions are introduced to uncouple the equations of motion, heat and electric conduction equations. The frequency equations are obtained for longitudinal and flexural modes at the solid fluid interfacial boundary conditions. The numerical results are analyzed for PZT-4 material and the computed stress, strain, electric displacement and temperature distribution are presented in the form of dispersion curves and its characteristics are studied.

Analytical Model of Wave Loads and Motion Responses for a Floating Breakwater System with Attached Dual Porous Side Walls

A set of two-dimensional analytical solutions considering the effects of diffraction and radiation are presented in this study to investigate the hydrodynamic interaction between an incident linear wave and a proposed floating breakwater system consisting of a rectangular-shaped body and two attached vertical side porous walls in an infinite fluid domain with finite water depth. The Matched Eigenfunction Expansion Method (MEEM) for multiple fluid domains is applied to derive theoretically the velocity potentials and associated unknown coefficients for wave diffraction and body motion induced radiation in each subdomain. Also, the exciting forces, as well as the added mass and damping coefficients for the floating breakwater system under the surge, heave, and pitching motions, are formulated. The displacements of breakwater motions are determined by solving the equation of motion. As a verification of the analytical model, the present solutions of the limiting cases in terms of exciting forces, moments, added masses, and damping coefficients are found to be well matched with other published numerical results. Additionally, the hydrodynamic performances and the dynamic responses in terms of Response Amplitude Operators (RAOs) of the proposed floating breakwater system are evaluated versus various dimensionless variables, such as wavelength and porous-effect parameter. The results show that the attached porous walls with selected porous properties are observed to have the advantages of reducing wave impacts on the floating breakwater system and at the same time its dynamic responses are also noticeably improved.

Natural Frequencies of Submerged Structures Using an Efficient Calculation of the Added Mass Matrix in the Boundary Element Method

This work presents an efficient way to calculate the added mass matrix, which allows solving for natural frequencies and modes of solids vibrating in an inviscid and infinite fluid. The finite element method (FEM) is used to compute the vibration spectrum of a dry structure, then the boundary element method (BEM) is applied to compute the pressure modes needed to determine the added mass matrix that represents the fluid. The BEM requires numerical integration which results in a large computational cost. In this work, a reduction of the computational cost was achieved by computing the values of the pressure modes with the required numerical integration using a coarse BEM mesh, and then, interpolation was used to compute the pressure modes at the nodes of a fine FEM mesh. The added mass matrix was then computed and added to the original mass matrix of the generalized eigenvalue problem to determine the wetted natural frequencies. Computational cost was minimized using a reduced eigenvalue problem of size equal to the requested number of natural frequencies. The results show that the error of the natural frequencies using the procedure in this work is between 2% and 5% with 87% reduction of the computational time. The motivation of this work is to study the vibration of marine mammals' ear bones.

Water wave scattering by an array of rectangular breakwaters on a step bottom topography

Water wave scattering by an array of identical rectangular breakwaters is investigated in the presence of a heterogenous bottom boundary in the cases of both infinite and semi-infinite fluid domains. Boundary value problem is formulated by employing small amplitude water wave theory and is reduced to a system of linear algebraic equations using matching eigenfunction expansion method. These equations are solved numerically to perceive the complete solution of the problems under present interest. The reflection and transmission coefficients are computed in different modes, and the energy relation is used to check the accuracy of computed results. Effects of different parameters on the total reflected and transmitted wave energy are computed and analyzed. Further, the surface motion is computed to see the wave phenomena in the vicinity of the breakwaters. The unknown coefficients appearing in velocity potentials are estimated, the frequency of resonance mode is resolved, and resonance surface modes are plotted in the case of the semi infinite fluid domain. This study is useful for the breakwater designer to install breakwaters near an uneven bottom topography.