Equations Of Fluid Motion Research Articles

Computational Study on Melting Process Using Smoothed Particle Hydrodynamics

Recently, smoothed particle hydrodynamics (SPH) method has become popular in computational fluid dynamic and heat transfer simulation. The simplicity offered by this method made some complex system in physics such as moving interface in multiphase flow, heat conductivity jumping in multiple material boundaries and many geometrical difficulties become relative easy to calculate. We will treat a relative easy example of melting process to test the method in solving fluid motion equation coupled by heat transfer process. The main heat transfer processes are caused by solid-liquid (medium to medium) heat diffusion and convection. System interaction with ambient temperature can be modeled by gas surrounding fluid-solid system. For the ambient temperature, we proposed surface particle heat transfer governed by convectional heat flux. Using local particle number density value as surface detection method, we applied cooling and heating to surface particle on the melting ice cube and water system. The simulation result is also verified by experiment.

Some peculiarities of propagation pressure waves in the cochlea of the human inner ear

A simplified model of the cochlea as the cylindrical tube with variable sections, which consists of the perfect fluid, are presented. The models with elastic or rigid walls were analyzed by using differential equations of fluid motion in the tube.Influence of constriction in the tube is shown by the ratio of the amplitude values of the transmitted and incident pressure wave.Reference 5, figures 6.

Control Volume Based Finite Element Method Study of Nano-fluid Natural Convection Heat Transfer in an Enclosure Between a Circular and a Sinusoidal Cylinder

Abstract In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). The fluid in the enclosure is Cu-water nanofluid. Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results show that for all Rayleigh number, increasing number of undulations causes the average Nusselt number to augment except that the average Nusselt number for N = 4 is greater than N = 5.

Comparison between Cell-Centered Schemes Computer Code and Fluent Software for a Transonic Flow Pass through an Array of Turbine Stator Blades

The Finite Volume Method (FVM) is a discretization method which is well suited for the numerical simulation of various types (elliptic, parabolic or hyperbolic, for instance) of conservation laws; it has been extensively used in several engineering fields. The Finite volume method uses a volume integral formulation of the problem with a finite partitioning set of volumes to discretize the equations [. the developed computer code based Cell-centered scheme and Fluent software had been used to investigate the inviscid Transonic Flow Pass Through an array of Turbine Stator Blades. The governing equation of fluid motion of the flow problem in hand is assumed governed by the compressible Euler Equation. Basically this equation behave as a mixed type of partial differential equation elliptic and hyperbolic type of partial differential equation. If the local Mach number is less than one, the governing equation will behave as elliptic type of differential equation while if the Mach number is greater than one it will behave as hyperbolic type of differential equation. To eliminate the presence a mixed type behavior, the governing equation of fluid motion are treated as the governing equation of unsteady flow although the problem in hand is steady flow problems. Presenting the Euler equation in their unsteady form makes the equation becomes hyperbolic with respect to time. There are various Finite Volume Methods can used for solving hyperbolic type of equation, such as Cell-centered scheme [, Roe Upwind Scheme [ and TVD Scheme [. The present work use a cell centered scheme applied to the case of flow pass through an array of turbine stator blades. The comparison carried out with the result provided by Fluent Software for three different value of back pressure. The developed computer code shows the result close to the Fluent software although the Fluent software use a Time Averaged Navier stokes equation as its governing equation of fluid motion.

Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM

In this study magnetohydrodynamic effect on natural convection heat transfer of Cu–water nanofluid in an enclosure with hot elliptic cylinder is investigated. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the nanofluid flow and heat transfer. Control Volume based Finite Element Method (CVFEM) is applied to solve these equations. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations are performed for different governing parameters such as the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclined angle of inner cylinder. Also a correlation of average Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of nanoparticle volume fraction, Rayleigh numbers and inclination angle while it is a decreasing function of Hartmann number. Also it can be found that increasing Rayleigh number leads to decrease heat transfer enhancement while opposite trend is observed with augment of Hartmann number.

The Implementation of Cell-Centred Finite Volume Method over Five Nozzle Models

The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. The present work presents the developed computer code based on Finite Volume Methods (FVM) Cell-centred Finite Volume Method applied for the case of Quasi One dimensional Inviscid Compressible flow, namely the flow pass through a convergent divergent nozzle. In absence of the viscosity, the governing equation of fluid motion is well known as Euler equation. This equation can behave as Elliptic or as Hyperbolic partial differential equation depended on the local value of its flow Mach number. As result, along the flow domain, governed by two types of partial differential equation, in the region in which the local mach number is less than one, the governing equation is elliptic while the other part is hyperbolic due to the local Mach number is a higher than one. Such a mixed type of equation is difficult to be solved since the boundary between those two flow domains is not clear. However by treating as time dependent flow problems, in respect to time, the Euler equation becomes a hyperbolic partial differential equation over the whole flow domain. There are various Finite Volume Methods can be used for solving hyperbolic type of equation, such as Cell-centered scheme, Cusp Scheme Roe Upwind Scheme and TVD Scheme. The present work will concentrate on the case of one dimensional flow problem through five nozzle models. The results of implementation of Cell Centred Finite Volume method to these five flow nozzle problems are very encouraging. This approach able to capture the presence of shock wave with very good results.

Application of a new numerical solver to turbomachinery flow problems

The use of the physical linear characteristic of the modified equation of fluid motion allowed the authors to develop a novel numerical algorithm to solve advanced flow problems with reduced computational effort. The applied algorithm simplifies the velocity iteration procedure during the solver execution. The goal of the current paper is to describe an in-depth study of this numerical implementation of the modified equation of fluid motion for incompressible flow. The application of the developed solver is discussed for rotor–stator interaction in a radial pump. The results are evaluated by the numerical results from the Navier–Stokes solver and measurement data. The comparisons indicate that the developed solver, requires about 60% the computation time of the Navier–Stokes solver, and it produces physically reasonable results validated by measurement data.

Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method

In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner sinusoidal cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature and air filled the enclosure. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The calculations were performed for different governing parameters such as the Rayleigh number (Ra = 103, 104, 105 and 106), values of amplitude (A = 0.1, 0.3 and 0.5) and the number of undulations of the inner cylinder (N = 2, 3, 5 and 6). The results show that streamlines, isotherms, and the number, size and formation of the cells inside the enclosure strongly depend on the Rayleigh number, values of amplitude and the number of undulations of the enclosure.

Engineering fluid flow using sequenced microstructures

Controlling the shape of fluid streams is important across scales: from industrial processing to control of biomolecular interactions. Previous approaches to control fluid streams have focused mainly on creating chaotic flows to enhance mixing. Here we develop an approach to apply order using sequences of fluid transformations rather than enhancing chaos. We investigate the inertial flow deformations around a library of single cylindrical pillars within a microfluidic channel and assemble these net fluid transformations to engineer fluid streams. As these transformations provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and, therefore, create complex fluid structures without additional numerical simulation. To show the range of capabilities, we present sequences that sculpt the cross-sectional shape of a stream into complex geometries, move and split a fluid stream, perform solution exchange and achieve particle separation. A general strategy to engineer fluid streams into a broad class of defined configurations in which the complexity of the nonlinear equations of fluid motion are abstracted from the user is a first step to programming streams of any desired shape, which would be useful for biological, chemical and materials automation.

Hydrodynamic Simulation for Intake Valve of Reciprocating Compressor

The aim of the present paper is to simulate the work process of intake valve in reciprocating compressor.To understand the flow, temperature characters and valve plate movement, the Computational Fluid Dynamics (CFD) is used to simulate the process of expansion and suction. In each time step, the fluid motion equation is iteratively solved to obtain the pressure distribution on the valve plate, and the valve plate moving can been determined by solving the valve plate motion equation at the end of time step. The simulation result shows the pressure and temperature field is uniform in cylinder during compressor expansion, but very different in suction process. The valve plate opens from 53.2° to 219.5°, which is well consistent with the theoretical calculation results (56°, 220°). This study identifies that CFD is a valid tool for exactly investigating the flow and valve plate movement.

Numerical Analysis of Cold Crucible Induction Melting Employing FEM and MPS Method

This paper proposes a coupled method of 3-D finite element method (FEM) and moving particle semi-implicit (MPS) method for the analysis of cold crucible induction melting. In this method, the magnetic field is calculated by FEM and the fluid motion equation of the molten metal and the thermal distribution in the molten metal are calculated by the MPS method. In this paper, the phase transformation of the metal is not considered. The effectiveness of this method is verified through the analysis of the molten metal behavior in the crucible.

Numerical Analysis of Negative Ion by Electrostatic Atomization Employing FEM and MPS Method

This paper proposes a coupled method of 3-D finite element method (FEM) and Moving Particle Semi-implicit (MPS) method for the analysis of a negative ion that is produced by electrostatic atomization. In this method, the electric field is calculated by FEM and the fluid motion equation of a drop of water is calculated by the MPS method. The validity of this analysis method is verified by comparison with an experiment.

Decomposition and exact solutions of three-dimensional nonstationary linearized equations for a viscous fluid

A new exact method for solving three-dimensional linear systems of hydrodynamic equations is described based on decomposing these systems into three simpler equations. It is shown that the general solution to three-dimensional Stokes equations (when there are no mass forces) can be expressed by means of solutions to two independent equations: the heat conduction equation and the Laplace equation. A class of solutions with the linear dependence of velocity components on two space variables is studied, and their physical interpretation is given. Axial flows are considered, and certain hydrodynamic problems are solved. A general solution to three-dimensional Oseen equations is constructed. The linearized equations of motion for a viscoelastic Oldroyd fluid are studied

Selective decay by Casimir dissipation in inviscid fluids

The problem of parameterizing the interactions of larger scales and smaller scales in fluid flows is addressed by considering a property of two-dimensional (2D) incompressible turbulence. The property we consider is selective decay, in which a Casimir of the ideal formulation (enstrophy in 2D flows, helicity in three-dimensional flows) decays in time, while the energy stays essentially constant. This paper introduces a mechanism that produces selective decay by enforcing Casimir dissipation in fluid dynamics. This mechanism turns out to be related in certain cases to the numerical method of anticipated vorticity discussed in Sadourny and Basdevant (1981 C. R. Acad. Sci. Paris 292 1061–4, 1985 J. Atm. Sci. 42 1353–63). Several examples are given and a general theory of selective decay is developed that uses the Lie–Poisson structure of the ideal theory. A scale-selection operator allows the resulting modifications of the fluid motion equations to be interpreted in several examples as parametrizing the nonlinear, dynamical interactions between disparate scales. The type of modified fluid equation systems derived here may be useful in modelling turbulent geophysical flows where it is computationally prohibitive to rely on the slower, indirect effects of a realistic viscosity, such as in large-scale, coherent, oceanic flows interacting with much smaller eddies.

Modeling and experimental study of the mechanism of electrification from aero-engine jet

To investigate the mechanism of electrification from aero-engine jet and the electrification effect on the overall charging characteristics of vehicle, a simulation model of concentration of charged particles in aero-engine is build based on the equations of fluid motion. And concentration changes of various particles are simulated. To verify the simulation result, a special electrostatic induction sensor for detecting the electrification of engine jet is designed, according to the principle of the Faraday cup, to measure the dynamic potential when the turbofan engine starts, operates steadily, accelerates, decelerates and stops. The simulation and experimental results show that the aircraft is negatively charged by the electrification from aero-engine jet and the mechanism of electrification from aero-engine jet is described specifically. The research may provide a guidance to the further study on analyzing the overall charging characteristics of vehicle during the flight.

A variant of the classical von Karman flow for a Jeffrey fluid

An attempt is made to study the classical Von Karman flow problem for Jeffrey fluid by using a generalized non-similarity transformation. This approach is different from Von Karman's evolution of the flow. Here, physical quantities are allowed to develop non-axisymmetrically. The three-dimensional equations of motion for Jeffrey fluid are treated analytically yielding the derivation of a closed form solution for the velocity field. Exact expressions for the vorticity components, shear stresses and boundary layer thickness are also presented. Mathematics Subject Classification: 76A05

Physically-Based Feature Tracking for CFD Data

Numerical simulations of turbulent fluid flow in areas ranging from solar physics to aircraft design are dominated by the presence of repeating patterns known as coherent structures. These persistent features are not yet well understood, but are believed to play an important role in the dynamics of turbulent fluid motion, and are the subject of study across numerous scientific and engineering disciplines. To facilitate their investigation a variety of techniques have been devised to track the paths of these structures as they evolve through time. Heretofore, all such feature tracking methods have largely ignored the physics governing the motion of these objects at the expense of error prone and often computationally expensive solutions. In this paper, we present a feature path prediction method that is based on the physics of the underlying solutions to the equations of fluid motion. To the knowledge of the authors the accuracy of these predictions is superior to methods reported elsewhere. Moreover, the precision of these forecasts for many applications is sufficiently high to enable the use of only the most rudimentary and inexpensive forms of correspondence matching. We also provide insight on the relationship between the internal time stepping used in a CFD simulation, and the evolution of coherent structures, that we believe is of benefit to any feature tracking method applicable to CFD. Finally, our method is easy to implement, and computationally inexpensive to execute, making it well suited for very high-resolution simulations.

A Novel Numerical Scheme for a Scale-Invariant Form of Equation of Motion: Development of Solver and Application to Engineering Flow Problems

The goal of the current paper is to describe an in-depth study of a numerical implementation of the modified equation of fluid motion for incompressible flow. The applications of the developed solver are discussed for both laminar and turbulent flow problems. The results are evaluated by comparing them with those obtained by other methods, including the numerical results obtained by the Navier–Stokes solver measurement data. Then, the computational effort and accuracy of the solver are emphasized. The comparisons indicate that the developed solver, which is based on the modified equation of fluid motion, requires less computation time than the Navier–Stokes solver, and it produces physically reasonable results validated by measurement data

A numerical analysis of drop impact on solid surfaces by using smoothed particle hydrodynamics method

In this paper, we present a numerical simulation of a single liquid drop impacting onto solid surface with smoothed particle hydrodynamics (SPH). SPH is a Lagrangian, meshfree particle method, and it is attractive in dealing with free surfaces, moving interfaces and deformable boundaries. The SPH model includes an improved approximation scheme with corrections to kernel gradient and density to improve computational accuracy. Riemann solver is adopted to solve equations of fluid motion. An new inter-particle interaction force is used for modeling the surface tension effects, and the modified SPH method is used to investigate liquid drop impacting onto solid surfaces. It is demonstrated that the inter-particle interaction force can effectively simulate the effect of surface tension. It can well describe the dynamic process of morphology evolution and the pressure field evolution with accurate and stable results. The spread factor increases with the increase of the initial Weber number. The numerical results are in good agreement with the theoretical and experimental results in the literature.

Relativistic dissipative hydrodynamics with extended matching conditions for ultra-relativistic heavy-ion collisions

Recently we proposed a novel approach to the formulation of relativistic dissipative hydrodynamics by extending the so-called matching conditions in the Eckart frame (Phys. Rev. C 85, 14906 (2012)). We extend this formalism further to the arbitrary local rest frame. We discuss the stability and causality of solutions of fluid equations which are obtained by applying this formulation to the Landau-Lifshitz frame, which is more relevant to treat the fluid produced in ultra-relativistic heavy-ion collisions. We derive equations of motion for a relativistic dissipative fluid with zero baryon chemical potential and show that linearized equations obtained from them are stable against small perturbations. It is found that conditions for a fluid to be stable against infinitesimal perturbations are equivalent to imposing restrictions that the sound wave, $c_{s}$ , propagating in the fluid, must not exceed the speed of light c, i.e., $c_{s} < c$ . This conclusion is equivalent to that obtained in the previous paper using the Eckart frame (Phys. Rev. C 85, 14906 (2012)).