Equations Of Fluid Motion Research Articles

Numerical Simulation of the Sea Bottom Modifications Behind a T-head Groin

In this paper, we simulate the sea bottom modifications produced by the presence of a T-head groin. We present a simulation model of sea bottom modifications composed of two sub-models: a two-dimensional phase-resolving model that simulate the variation of the fluid dynamic variables inside the wave; a second sub-model to simulate the sea bottom modifications, in which the suspended sediment concentration is calculated by the wave-averaged advection-diffusion equation. The fluid motion equation and the concentration equation are expressed in a new contravariant formulation. The velocity fields from deep water up to just seaward of the surf-zone are simulated by a new integral contravariant form of the Fully Nonlinear Boussinesq Equations. The new integral form of the proposed continuity equation does not contain the dispersive term. The Nonlinear Shallow Water Equations, expressed in an integral contravariant form, are solved in order to simulate the breaking wave propagation. The momentum equation, integrated over the turbulent boundary layer, is solved to calculate the near-bed instantaneous flow velocity and the intra-wave hydrodynamic quantities. Starting from the contravariant formulation of the advection–diffusion equation for the suspended sediment concentration, it is possible to calculate the sea bottom modification. The advective sediment transport terms in the advection-diffusion equation are formulated according to a quasi-three-dimensional approach

Free and forced bending vibrations of a thin plate in a perfect compressible fluid with energy dissipation taken into account

AbstractA refined statement of stationary dynamic acoustoelasticity problems of thin isotropic plates surrounded from both sides by acoustic media assumed to be perfect compressible fluids has been studed. The problem statement takes into account the energy dissipation in the material of the plate and fluid on the basis of the Kelvin‐Voigt hysteresis model. The refinement of the fluid behavior is based on the assumption that the pressure increment is proportional not only to volumetric strain, but also to the rate of its volumetric strain. This assumption allows us to obtain the generalized Helmholtz wave equation by introducing Skudrzyk's complex sound velocity into consideration to take account of the energy dissipation. The motion equations of the plate are based on the classical Kirchhoff‐Love model and are obtained in two versions. In the first version unsimplified three‐dimensional wave equations are used to determine the aerohydrodynamic load acting on a plate. The second version is based on simplifying the equations of fluid motion by the introduction of the well‐known hypothesis of plane reflection and emission of sound waves. On the basis of the derived equations, exact analytical solutions of two types of problems are obtained. The first type is related to the problem of free vibrations of a rectangular plate hinged around the contour when complex eigenfrequencies were defined. The second type is related to the problem of forced vibrations of the plate under the action of a flat mono‐harmonic incident sound wave when sound transmission loss, the stress‐strain state parameters of the plate as well as the laws of change in sound pressure in a fluid were determined. It is shown that correct and more meaningful solutions of acoustoelasticity problems of the considered class are possible only in case of describing the behavior of a fluid with unsimplified three‐dimensional wave equations with consideration of the energy dissipation.

Simulation of fluid outflow from a channel with complex geometry

Topic of the paper is the simulation of fluid outflow from a channel with complex geometry. Subject of the study is the outflow of fluid from a channel with an arbitrary section, in particular, consisting of a parabolic inlet, cylindrical middle and hyperbolic outlet sections. The paper considers the integral form of determining the pressure and the average flow rate of the fluid in a channel with an arbitrary cross section. From the obtained expression for the pressure and from the equation of conservation of mass, given in integral form, it is necessary to determine the pressure and the average flow rate in successively located channels with a parabolic, cylindrical and hyperbolic section. Research methods are based on: Newton’s rheological law; the continuity equation and the Navier-Stokes equation, which are the basic equations of fluid motion; the method of mathematical modeling and the analytical method for their solution. The paper contains integral expressions for the hydrodynamic characteristics of a fluid flow in a channel with an arbitrary section. The pressure and average flow rate in the channel of successively located parabolic, cylindrical, hyperbolic segments are determined. Analytical expressions are obtained for the pressure and average flow rate of the liquid in a channel with an arbitrary cross section. As an example, the pressures and the average flow rate in the channel from the parabolic inlet, cylindrical middle and hyperbolic outlet sections are determined. In perspective, by substituting in them an arbitrary arithmetic expression of the channel cross-section, it is possible to determine the hydrodynamic characteristics of the flow with any geometry of the flow channel.

On Strong Solutions of a Fractional Nonlinear Viscoelastic Voigt-Type Model

Existence and uniqueness of a strong solution of the initial-boundary value problem for a system of the motion equations of a nonlinear viscoelastic fluid being a fractional analogue of the Voigt model are established in the plane case.

Analytical Solution of Sloshing in a Cylindrical Tank with an Elastic Cover

Coupled fluid-structure is significant in many aspects of engineering applications such as aerospace fuel tanks, the seismic safety of storage tanks and tuned liquid dampers. Numerical investigation of the effects of thin plate cover over a cylindrical rigid fuel tank filled by an inviscid, irrotational, and incompressible fluid is investigated. Governing equations of fluid motion coupled by plate vibration are solved analytically. A parameter study on the natural frequency of coupled fluid-structure interaction is performed. The results show the non-dimensional natural frequency of coupled fluid-structure is a function of mass ratio, plate elasticity number and aspect ratio. This function is derived numerically for high aspect ratios which in companion with a semi-analytical could be used in the engineering design of liquid tanks with a cover plate.

Numerical simulation for transient flow of Williamson fluid with multiple slip model in the presence of chemically reacting species

PurposeThe purpose of this paper is to analyze a mathematical model for the time-dependent flow of non-Newtonian Williamson liquid because of a stretching surface. The mathematical formulation of the current model is accomplished from the momentum, energy and concentration balances by assuming a laminar, two-dimensional and incompressible flow subjected to a variable magnetic field. The study further aimed at discovering the possible effects of temperature-dependent thermal conductivity on the heat transfer characteristics.Design/methodology/approachIn addition, a first-order chemical reaction is considered between the fluid and chemically reacting species. The governing transport model for Williamson fluid has been altered to ordinary differential equations via appropriate dimensionless parameters. These basic non-dimensional partially coupled differential equations of fluid motion are solved by an efficient Runge–Kutta–Fehlberg integration scheme along with the Nachtsheim–Swigert shooting technique.FindingsIt is found that the velocity slip parameter has a reducing impact on the skin friction coefficient. Moreover, we noticed that the Hartmann number and variable thermal conductivity parameters show prominent impacts on the velocity and temperature fields. It is also perceived that the fluid temperature shows an increasing trend with uplifting values of variable thermal conductivity.Originality/valueNo such work is yet published in the literature.

Numerical assessment of Bödewadt flow and heat transfer over a permeable disk with variable fluid properties

Impact of variable fluid properties on heat transfer in Bödewadt flow with wall suction is the main focus of present article. Recent studies have predicted that energy equation in Bödewadt flow can have physically compatible solution only when disk is porous. We utilize the usual von-Kármán variables to transform the governing equations of fluid motion and heat transfer (with variable properties) into self-similar differential equations. The final problem comprises of a parameter θe that measures the degree of dependence of fluid viscosity on temperature. A numerical approach is pursued to determine velocity components, wall stresses, temperature and heat transfer rate from the disk. Wall suction velocity is found to have a pivotal role on the solutions. The main outcome of the study is that fluid velocity and temperature around the disk are considerably altered by varying the parameter θe. The deviations of present results from those obtained with constant fluid properties are deliberated. Present results are in perfect agreement with the available literature in a limiting sense.

A Study on the Causes and the Treatment Measures of Slack Line Flow at the Crossing-over Points of the Oil Pipeline

This paper points out the definition of the oil pipeline crossing-over points, and thereby identifies the existence and the position of crossing-over points by applying the graphical method and the analytical method. Besides, this paper analyzes the phenomenon of slack line flow from the perspectives of thermodynamics, structural mechanics and fluid mechanics. In order to analyze the motion characteristics of slack line flow, this study divides the control volume in stratified flow into several sections, and then carries out a mechanical analysis of the accelerating and the uniform flow section. Based on the analysis, the equations of the gas-liquid two-phase volume and other parameters in the pipeline are worked out. What’s more, with the time-averaged continuum equation, momentum equation, energy equation for turbulent flow, and RNG k − ε two-equation turbulence modeling, this paper works out closed-form simultaneous equations for gas-liquid two-phase flow in order to establish the calculation model of slack line flow section. This paper also introduces the calculation methods of fluid motion equations and some common simulation software. Furthermore, taking into account the fast velocity and instability of slack line flow, and its buffering effect, this paper points out its hazards, and puts forward the application of its buffering effect and the energy dissipation measures to prevent and control slack line flow.

Numerical Computation of Brinkman Flow with Stable Mixed Element Method

Herein, we discuss a mixed finite element method applied to the Brinkman equation of fluid motion in porous medium, which covers a field of situation from the Darcy equation to the Stokes problem associated with various perturbation parameters. The finite element based on staggered meshes is shown to be stable and effective with each case as the corresponding error estimates for both velocity and pressure are established. Finally, we present numerical examples confirming the theoretical analysis and the stability of the finite spaces approximation.

A viscous damping model for piston mode resonance

A viscous damping model is proposed based on a simplified equation of fluid motion in a moonpool or the narrow gap formed by two fixed boxes. The model takes into account the damping induced by both flow separation and wall friction through two damping coefficients, namely, the local and friction loss coefficients. The local loss coefficient is determined through specifically designed physical model tests in this work, and the friction loss coefficient is estimated through an empirical formula found in the literature. The viscous damping model is implemented in the dynamic free-surface boundary condition in the gap of a modified potential flow model. The modified potential flow model is then applied to simulate the wave-induced fluid responses in a narrow gap formed by two fixed boxes and in a moonpool for which experimental data are available. The modified potential flow model with the proposed viscous damping model works well in capturing both the resonant amplitude and frequency under a wide range of damping conditions.

Theory and practice of micro water-oil displacement efficiency based on mathematical models

Theoretical study about quantitative influence of the micro parameters (interfacial tension, wetting angle, distance, unit length, bottom radius, boundary distance, etc.) on the macro parameters (oil displacement efficiency, pressure gradient, etc.) in water-oil displacement process is very important. This paper focuses on the micro oil displacement efficiency calculation method in oil reservoir, building a new bridge between these parameters. Combining fluid motion equation, continuity equation to pressure gradient equation, the occurrence radius equation of remaining oil in different capillary is established; Taking mercury intrusion porosimetry experiment and constructing the mathematical model, new normal probability distribution of pore radius is achieved, and then a new probability function for injected water entering pore throat is established based on the occurrence radius equation and pore radius distribution equation; By using the Darcy’s Law and definite integral theory, new micro oil displacement efficiency equation is obtained. The Nuclear Magnetic Resonance experiments show: new method gets high calculating accuracy, and can be used to guide oil reservoir development.

Assisting or opposing MHD flow of cross fluid along a non-isothermal surface with variable thermal conductivity

Locally similar solutions are developed for aiding or opposing MHD flow near stagnation-point on a vertical stretchable surface immersed in a generalized Newtonian fluid obeying Cross rheology equation. Heat transfer problem is resolved by assuming a linear surface temperature distribution. Furthermore, fluid having variable thermal conductivity is treated. By choosing the usual transformations, the governing equations of fluid motion and energy transfer are changed into similar forms. The structure of boundary layer is controlled by a parameter measuring the ratio of free stream velocity to the wall velocity. Numerical computations are performed to address the influences of Cross fluid parameters on mean physical quantities. In particular, shear thinning character of Cross fluid is visible from the obtained simulations. Computations are found in perfect line with those of the existing literature. The physical outcomes concerning the effects of embedded parameters on wall drag coefficient and heat transfer rates are also explained in detail.

Some exact solutions of two-dimensional Navier–Stokes equations by generalizing the local vorticity

This article is proposed to discuss the solutions of two-dimensional equations of motion for viscous fluid. Different situations for the solution have been investigated while employing inverse solution methods. On assuming the stream functions in a certain form without prescribing boundary conditions, the expressions for streamlines and velocity components are explicitly presented. Moreover, a series of graphical results for streamlines and velocity components are plotted.

Crack Opening Models Based on the Exact Solutions of the Navier-Stokes Equations

Different approximate crack opening models in a porous stratum are derived, based on a priori representations of the crack size, accurate solutions of motion equations of viscous fluid, approximate expressions of the filtering model in the stratum, and approximate expressions of the theory of elasticity of the stratum. The law of conservation of mass of the fluid in the crack is used to obtain quasilinear parabolic equations, describing the crack opening.

Development of a computational fluid dynamics model for mucociliary clearance in the nasal cavity

Intranasal drug delivery has attracted significant attention because of the opportunity to deliver systemic drugs directly to the blood stream. However, the mucociliary clearance poses a challenge in gaining high efficacy of intranasal drug delivery because cilia continuously carry the mucus blanket towards the laryngeal region. To better understand mucus flow behaviour on the human nasal cavity wall, we present computational model development, and evaluation of mucus motion on a realistic nasal cavity model reconstructed from CT-scans. The model development involved two approaches based on the actual nasal cavity geometry namely: (i) unwrapped-surface model in 2D domain and (ii) 3D-shell model. Conservation equations of fluid motion were applied to the domains, where a mucus production source term was used to initiate the mucus motion. The analysis included mucus flow patterns, virtual saccharin tests and quantitative velocity magnitude analysis, which demonstrated that the 3D-shell model results provided better agreement with experimental data. The unwrapped-surface model also suffered from mesh-deformations during the unwrapping stage and this led to higher mucus velocity compared to experimental data. Therefore, the 3D-shell model was recommended for future mucus flow simulations. As a first step towards mucus motion modelling this study provides important information that accurately simulates a mucus velocity field on a human nasal cavity wall, for assessment of toxicology and efficacy of intranasal drug delivery.

РЕКОНСТРУКЦИЯ ВХОДЯЩЕГО ПОТОКА ВЯЗКОЙ ЖИДКОСТИ ПО ИЗМЕРЕНИЯМ СКОРОСТИ НА ДОСТУПНОМ УЧАСТКЕ СВОБОДНОЙ ПОВЕРХНОСТИ ТЕЧЕНИЯ

A method has been developed and an algorithm has been elaborated in order to determine an unknown distribution of inflow velocity of viscous heterogeneous incompressible fluid into its common flow. The main data for solution of this problem are changes in the fluid velocity at some observable section of free surface of this flow. Also, movement of the fluid is considered isothermal and stationary. In order to simplify the model of fluid movement, let us believe that the Reynolds number for the fluid flow under consideration is very small. The number indeed is very small at a high viscosity and (or) slow motion of the fluid. Smallness of the Reynolds number allows discarding the total derivative from the time velocity vector in the Navier–Stokes equation of fluid motion. Thus, in a number of cases, the Stokes equation may be considered as the main one when simulating the motion of viscous fluid. The formulated problem gets formalized as an inverse boundary value problem for the model of motion of viscous fluid. The model includes the Stokes equation, the incompressibility equation, and the corresponding boundary conditions. The problem is ill-posed in regard to perturbation of the velocity under measurement. Therefore, numerical solution of the problem requires development of special sustainable methods. We offer using the variational method. For that, we introduce some assessment function which is a disparity between the observed velocity and the virtual velocity calculated out of a specially-set auxiliary boundary control problem, which is usually called the direct problem. Control is the inflow velocity. Desired solution of the problem is the minimum point of the residual functional which is obtained through the gradient descent method. Implementation of the method leads to a sequential solution of the corresponding correctly-posed boundary control problem. Model example has been calculated.

Diagnostics of the location of damage to tubing oil well pipes

The study is devoted to the mathematical description of the process of oil outflow in places of leakage of the tubing string, which allows a computer to locate a leakage in the tubing. The authors propose methodology for identifying defects in the tubing and determining the location of the leak. The uniqueness of this methodology lies in quick determination of the place of leakage without the use of specialists, sophisticated and specialized equipment. Mathematical modeling of oil flow in the tubing requires the apparatus of continuum mechanics. It is a general belief that the movement of oil in the pipe flows at low speeds due to its outflow from the hole. Using the general equations of mass and energy balance, the authors have obtained differential equations of fluid motion in a vertical pipe in the process of its outflow from the tubing and in the process of injection. Analytical expressions are the solution to these equations, as they can help in estimating the degree of damage and its location, as well as the feasibility of its eliminating. The results show that an increase in the leakage and injection times leads to improving accuracy of locating damage. Thus, when conducting various geological and technical measures (GTM) at the well, it is possible to assess the presence of leakage and its intensity when deciding on the repair of tubing.

Numerical simulation of the flow into a circular pipe section

Computational Fluid dynamics (CFD) is the science that evolves rapidly in numerical solving of fluid motion equations to produce quantitative results and analyses of phenomena encountered in the fluid flow. When properly used, CFD is often ideal for parameterization studies or physical significance investigations of flow that would otherwise be impossible to replicate through theoretical or experimental tests. The aim of this paper is the study of the turbulent airflow and how the vortices formed in turbulent airflow are influenced by the evolution of the hydraulic characteristics of the fluid flow. Unsteady numerical simulation were performed using Reynolds Average Navier-Stokes (RANS) turbulence model adapted to conventional flow into a pipe with variable section which was implemented in the ANSYS FLUENT expert software.

The examples of hydraulic calculations of pressure collecting and distributing perfo-rated pipelines

The examples of detailed engineering calculation of pressure collecting and distributing perforated pipelines with a constant diameter and with a constant intensity of perforation of the side walls along the length are presented in the article. The proposed calculation dependencies were obtained by the authors on the basis of solving a system of initial differential equations that describe the motion of a fluid with a variable flow rate in pressure channels and the conditions for the fluid passing through their side walls. The differential equation of fluid motion with a variable mass is used as the first equation. As the second, the equation of continuity in the form of the equation for the fluid outflow through holes or perforation slots. In the first example, the calculation of collecting pipelines that operate with fluid attachment along the path is considered. In the second – distributing pipelines, which distribute the liquid through its side surface. The proposed methods can be used to calculate short, long pipes and pipes of intermediate length. As the result of calculations, discharges and pressures are found in arbitrary sections of pipes. In addition, these methods allow to determine the geometric characteristics of the pipes elements under consideration (diameter and length of the channel, diameter and number of perforation holes) that can provide the optimal technologically specified mode of fluid collection or distribution. In the proposed methods, the results of experimental studies of such pipes operation, conducted personally by the authors, are widely used. Namely, the empirical dependencies, auxiliary graphs and tables for determining the magnitude of the hydraulic coefficient of friction and the perforation holes discharge coefficient for the case of fluid movement with variable flow along the path are quite simple and convenient to use. The calculation results are in good agreement with the existing experimental data.

Modelling of Heat and Mass Transfer for Wire-Based Additive Manufacturing Using Electric Arc and Concentrated Sources of Energy

The paper presents a model developed by the authors and aimed to describe heat and mass transfer during wire-based additive manufacturing, when electron beam, plasma or arc are used as energy sources in case of non-consumable electrode welding. The model describes non-stationary and non-equilibrium conjugated processes of heat and mass transfer in free-surface liquid metal. The solution of differential equations of viscous fluid motion (Navier-Stokes), with convective terms and at laminar flow, has become the model base. Melting and crystallization of the metal is recognized by heat release in a two-phase region. The material density variation during phase transitions of the first and the second order can be described by introducing a certain dependence on temperature. The model is able to consider the use of preliminary and additional induction heating by changing the initial temperature and establishing an additional distributed bulk heat source. Variables for the simulation of heat and mass transfer during additive formation are the intensity and type of the heat source, the plate initial temperature, the power density distribution, the intensity of the additional bulk heating, the dependence of material thermal and physical characteristics on temperature, the characteristics of the phase transitions, the motion velocity of the heat source, the rate of wire feeding.