Showing papers on "Fluid parcel published in 2007"

Acoustic concentration of particles in fluid flow

Abstract: An apparatus for acoustic concentration of particles in a fluid flow includes a substantially acoustically transparent membrane and a vibration generator that define a fluid flow path therebetween. The fluid flow path is in fluid communication with a fluid source and a fluid outlet and the vibration generator is disposed adjacent the fluid flow path and is capable of producing an acoustic field in the fluid flow path. The acoustic field produces at least one pressure minima in the fluid flow path at a predetermined location within the fluid flow path and forces predetermined particles in the fluid flow path to the at least one pressure minima.

An analysis of peristaltic transport for flow of a Jeffrey fluid

Abstract: The peristaltic mechanism of a Jeffrey fluid in a circular tube is investigated. The rheological effects and compressibility of the fluid are taken into account. The modeled equations are solved using perturbation technique when the ratio of the wave amplitude to the radius of the pore is small. In the second order approximation, a net flow due to a travelling wave is obtained and effects of Reynolds number, relaxation and retardation times, compressibility of the fluid and tube radius are studied. It is noticed that for the Jeffrey fluid the back flow only occurs for large values of the relaxation time and small values of the retardation time (less than 10 in the present analysis). Another interesting observation is that oscillatory behavior of the net flow rate in the Jeffrey fluid is less than that of a Maxwell fluid. Several results of other fluid models can be deduced as the limiting cases of our situation.

Chapter 7 - Mathematical Properties of the Solutions to the Equations Governing the Flow of Fluids with Pressure and Shear Rate Dependent Viscosities*

Abstract: A meaningful discussion of the mathematical properties of the equations governing the flow of fluids requires a proper understanding of what is meant by a fluid as well as a clear understanding of the nature of the specific fluid. It is impossible to provide a definition of fluid, without the definition's inadequacy being laid bare with an easy counterexample. Many of the definitions, including those in renowned dictionaries are circular; a fluid being defined as a material that flows and flow being defined as an innate property of the fluid. For the purposes of this chapter a body as a fluid is regarded, if in the time scale of observation of interest, it undergoes a flow that is discernible to the naked eye because of the application of a shear stress (that can be measured with the aid of reasonably unsophisticated instruments; i.e., the forces in question are robust, not mere picoNewtons). Based on how they are constituted, different fluids respond differently to the application of external stimuli. Many mathematical models have been developed to describe the diverse response exhibited by fluids, but Navier–Stokes fluid model enjoys a central place amongst them.

Rate of convergence of non-stationary flow to the steady flow of compressible viscous fluid

Abstract: We consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in R^3. In Shibata and Tanaka [Y. Shibata, K. Tanaka, On the steady flow of compressible viscous fluid and its stability with respect to initial disturbance, J. Math. Soc. Japan 55 (2003) 797-826], we proved the unique existence and some regularity of the steady flow and its globally in-time stability with respect to a small initial disturbance in the H^3-framework. In this paper, we investigate the rate of the convergence of the non-stationary flow to the corresponding steady flow when the initial data are small enough in the H^3 and also belong to L"6"/"5.

The Euler Equations of Compressible Fluid Flow

Abstract: This article is in celebration of the 300th anniversary of the birth of one of the greatest mathematicians and physicists in history, Leonhard Euler. The article is directly concerned with Euler’s work in fluid mechanics, although his work in the calculus of variations and in partial differential equations in general have been instrumental in the developments to be outlined here. Euler did have predecessors in the field of fluid mechanics, who had conceived some of the basic concepts. His immediate predecessor in this regard was his friend D. Bernoulli, whose 1738 work [Be] is likely to have had a great influence on him. However it was Euler who first formulated the general equations describing the motion of a perfect fluid. The general compressible Euler equations first appeared in published form in [Eu2], the second of three Euler articles on fluid mechanics which appeared in the same 1757 volume of the Mémoires de l’Academie des Sciences de Berlin. The third of these articles, [Eu3], is a continuation of the second, while the first, [Eu1], establishes the general validity of the basic concepts and formulates the equations in the static case. However, it seems that the article [Eu4], which formulates the equations of motion in the incompressible case and which was published only in 1761, was actually the first to be composed, as at least a preliminary version of it was presented to the Berlin Academy in 1752. Thus Euler’s fluid equations were among the first partial differential equations to be written down, preceded, it seems, only by D’Alembert’s 1749 formulation [DA] of the one-dimensional wave equation describing the motion of a vibrating string in the linear approximation. Euler was not content to confine himself to the formulation of the basic laws of fluid mechanics, but he proceeded to investigate and explain on the basis of these laws some of the basic observed phenomena. Thus in [Eu5] he made the first, albeit incomplete, study of convection, a phenomenon which depends on compressibility as well as on temperature variation in a gravitational potential. In [Eu7] he studied incompressible flows in pipes in the linear approximation, while in [Eu8] he studied compressible flows in the linear approximation, treating the generation and propagation of sound waves. The contrast to D’Alembert’s equation however could not be greater, for we are still, after the lapse of two and a half centuries, far from having achieved an adequate understanding of the observed phenomena which are supposed to lie within the domain of validity of Euler’s fluid equations. The phenomena displayed in the interior of a fluid fall into two broad classes: the phenomena of sound, the linear theory of which is acoustics, and the phenomena

The Eulerian description of dilute collisionless suspension

Abstract: We analyze the statistical properties of a Eulerian fluid model describing the evolution of a suspension of inertial particles in an incompressible flow. Regularity and compressibility of the velocity field for the inertial phase are investigated in the limit of heavy particles by means of numerical simulations in two- and three-dimensional flows. We show that in the small Stokes number regime the Eulerian fluid model is able to capture fine details of the clustering dynamics, and exhibits good agreement with fully Lagrangian simulations of inertial particle trajectories. The fluid description breaks down due to collisions at Stokes numbers 0.1, the actual value depending on the carrier flow characteristics.

Fluid flow through a helical pipe

Abstract: In this paper we study the flow of incompressible Newtonian fluid through a helical pipe with prescribed pressures at its ends. Pipe’s thickness and the helix step are considered as the small parameter ɛ. By rigorous asymptotic analysis, as ɛ→ 0 , the effective behaviour of the flow is found. The error estimate for the approximation is proved.

The calculation of stratospheric air parcel trajectories using satellite data

Abstract: Air parcel trajectories are calculated for the mid-stratosphere using data from the stratospheric sounding unit on board NOAA-6. In the analysis method all the orbital data for each 24 h period are combined into a single global analysis. Three trajectory methods are used-isobaric, isentropic and quasi-isentropic-and the results are compared and contrasted. For the quasi-isentropic method a radiation model is used, via the thermodynamic equation, to imply cross-isentrope flow at regular intervals along the trajectory. the positions of the parcels, computed using the three methods, are found in general to be in good agreement when projected on to a horizontal plane. However, the altitude varies according to the trajectory method used and changes by about 1 km along a quiescent trajectory and as much as 2 km along a disturbed trajectory, during a 10-day period. This has important implications in the study of chemistry along parcel trajectories during disturbed periods since the temperature- and pressure-dependent reactions will proceed at different rates under the different assumptions. Also, the high lapse rate in the vertical mixing ratio profile of ozone implies that the detailed photochemistry will depend critically on the height of the air parcel. Further, potential vorticity and potential temperature are used as quasi-conservative Lagrangian tracers, to try to determine which trajectory method is most realistic. For the quiescent period studied (June 1979 in the southern hemisphere) the isobaric and isentropic methods produced similar results throughout the ten days of the trajectory but the quasi-isentropic method was clearly superior. A disturbed period was also studied (the February 1979 stratospheric warming), but the results from the trajectories studied were consistent with the Lagrangian conservation laws for only 6 days, at most. These results illustrate the need for caution, particularly with regard to sensitivity to initial horizontal position, in using trajectories calculated for disturbed periods.

``Designing Lagrangian experiments to measure regional-scale trace gas fluxes''

Abstract: [1] Knowledge of trace gas fluxes at the land surface is essential for understanding the impact of human activities on the composition and radiative balance of the atmosphere An ability to derive fluxes at the regional scale (on the order of 102–104 km2), at the scale of ecosystems and political borders, is crucial for policy and management responses Lagrangian (“air mass-following”) aircraft experiments have potential for providing direct estimates of regional-scale fluxes by measuring concentration changes in air parcels as they travel over the landscape Successful Lagrangian experiments depend critically on forecasts of air parcel locations, rate of dispersion of air parcels, and proper assessment of forecast errors We describe an operational tool to forecast air parcel locations and dispersion and to guide planning of flights for air mass-following experiments using aircraft The tool consists of a particle dispersion model driven by mesoscale model forecasts from operational centers The particle model simulates time-reversed motions of air parcels from specified locations, predicting the source regions which influence these locations Forecast errors are incorporated into planning of Lagrangian experiments using statistics of wind errors derived by comparison with radiosonde data, as well as the model-to-model spread in forecast results We illustrate the tool’s application in a project designed to infer regional CO2 fluxes—the CO2 Budget and Rectification Airborne study, discuss errors in the forecasts, and outline future steps for further improvement of the tool

Chapter 3 - The Mathematical Theory of the Incompressible Limit in Fluid Dynamics

Abstract: The equations governing incompressible fluid flow differ from those for compressible flow in the evolution equation for the density, or the pressure is replaced by the constraint that the flow be divergence-free. The equations of incompressible flow can be derived by taking the limit of an appropriately rescaled version of the equations for compressible flow, as the scaling parameter tends to zero. In physical terms, the scaling parameter is the ratio of the fluid particle speed to the sound speed, and is called “Mach number.” The limit of the rescaled compressible equations as the Mach number tends to zero is known as “incompressible limit.” When the equations of compressible fluid flow tend to goes zero, one expects that solutions of the compressible fluid equations tend to solutions of the incompressible equations in that limit. This expectation has been justified in a wide variety of circumstances. Various extensions of these results and analogous results have been obtained for limits of other systems. This chapter also discusses the rescaling process and the formal limit of the resulting equations.

Solvability of the problem of the self-propelled motion of several rigid bodies in a viscous incompressible fluid

Abstract: In this paper, we investigate the problem of the motion of self-propelled rigid bodies in a viscous incompressible fluid filling a bounded container. The motion of the fluid is governed by the Navier-Stokes equations. The bodies move due both to the flow of the ambient fluid and to the engines which are modelled by fluxes of the fluid through the boundaries of the bodies. It is proved that the problem has at least one weak solution on an arbitrary time interval which does not include instants of collisions of the bodies.

Target-driven liquid animation with interfacial discontinuities

Abstract: We propose a novel method of controlling a multi-phase fluid so that it flows into a target shape in a natural way. To preserve the sharp detail of the target shape, we represent it as an implicit function and construct the level-set of that function. Previous approaches add the target-driven control force as an external term, which then becomes attenuated during the velocity projection step, making the convergence process unstable and causing sharp detail to be lost from the target shape. But we calculate the force on the fluid from the pressure discontinuity at the interface between phases, and integrate the control force into the projection step so as to preserve its effect. The control force is calculated using an enhanced version of the ghost fluid method (GFM), which guarantees that the fluid flows from the source shape and converges into the target shape, while achieving a more natural animation than other approaches. Our control force is merged during the projection step avoiding the need for a post-optimization process to eliminate divergence at the liquid interface. This makes our method easy to implement using existing fluid engines and it incurs little computational overhead. Experimental results show the accuracy and robustness of this technique. Copyright © 2007 John Wiley & Sons, Ltd.

Asymptotic analysis of the full Navier-Stokes-Fourier system: From compressible to incompressible fluid flows

Abstract: This is a survey of new results related to the study of the full Navier-Stokes-Fourier system for a general compressible, viscous, and heat conducting fluid, and its asymptotic behaviour as the Mach number approaches zero. The classical Navier-Stokes system for an incompressible fluid with lift, combined with the corresponding heat equation, is a limiting case.

Fluid flow on interacting deformable surfaces

Abstract: Fluid simulation on interacting deformable surfaces is a challenging problem that has many applications. In this paper, we present a framework in which artistic as well as physically realistic flows can be generated on surfaces during deformation and collision. Our simulation system provides comprehensive control over the motion and deformation of an object as well as the movement and density of the fluid on the surface. At the heart of our system is a numerical solver that allows viscous and incompressible flows to be directly generated on surfaces using concepts from differential geometry, such as geodesic polar maps and parallel transport. This solver is fast and stable even when the object undergoes deformation or collides with other surfaces. We also propose rules that allow deformation and collisions to impact fluid flows in a physically realistic manner. By combining these rules with a set of comprehensive design functionalities, we develop a system in which the user can specify shape deformation, collision, and fluid flow in a unified framework. We demonstrate the capability of our system with a number example scenarios. CR Categories: I.3.7 [COMPUTER GRAPHICS]: ThreeDimensional Graphics and Realism—Animation.

Fluid Flow and Coupled Hydro-Mechanical Behavior of Rock Fractures

Abstract: Publisher Summary This chapter presents the continuity equation (derived using the mass conservation law) and equations of motion (derived using the momentum conservation law). The most commonly applied conceptual model for flow through a single fracture is derived from a much simplified Navier–Stokes equation of viscous fluid flow through a pair of smooth parallel surfaces of narrow width often called the ‘parallel plate model’ or the Cubic Law in rock mechanics literature. The flow analysis of a fracture network is based on the elements of fracture segments, intersections, and cycles. The chapter describes the technique for modeling the fluid flow and deformation of rock fractures that assumes that rock blocks are impermeable, so that there is no fluid interaction between the fracture and its parent rock matrix. The fluid flow and block motion/fracture deformation are coupled through a two way interaction: (1) change of fluid pressures on the boundary surfaces of blocks affects the motion and deformation of blocks and, in turn, the deformation of fractures; and (2) the change of hydraulic apertures of fractures affects its transmissivity, flow rate, and fluid pressure distribution along the fracture surfaces. The effect of fluid pressure on the deformation and change of hydraulic aperture of fractures is represented by a similar ‘effective stress' concept and calculated through the constitutive laws of the fractures or point contacts in discrete element methods.

Mathematical Modeling of Flow Control Using Magnetic Fluid and Field

Abstract: In this paper some previous studies related to those for flow control aspects of the hydrodynamics of magnetic fluid and field are reviewed first and recent mathematical approaches for the corresponding systems of partial differential equations are discussed. Next, mathematical modeling of a two-fluid system, with one fluid being a non-conducting ferrofluid and another fluid being a regular non-ferrofluid is considered. A numerical method is used to solve the mathematical system for the problem, which, in particular, captures the flow structure in the two-fluid system. The convective flow velocities and the heat fluxes were determined for various values of the parameters of the problem. Certain aspects of the magnetic fluids and fields were found to be useful for convective flow control, which is important in many application areas including microgravity space applications. In particular, under some conditions, the surface force that can exist at the interface between the two fluid zones was found to reduce the magnitude of the flow velocity and instabilities that may occur in the two-fluid system.

An Overview of Atmospheric Convection

Abstract: The nature of atmospheric convection is briefly reviewed. We can assess the stability of a single air parcel with respect to vertical displacements by comparing the lapse rate of the parcel’s environment to the rate of temperature change within the displaced parcel owing to adiabatic expansion or compression and latent heating or chilling. We also can examine the tendency for convective overturning in a global sense, when buoyancy sources are distributed over a large area and the entire fluid is engaged in convective overturning. In this case, the onset of global dry convection due to thermal instability is determined by the Rayleigh number. Within the atmospheric boundary layer on a sunny day, the Rayleigh number is several orders of magnitude larger than the critical Rayleigh number; thus, convective overturning is a ubiquitous characteristic of the atmospheric boundary layer in sunny conditions. The structure of dry atmospheric convection depends to a large degree on the vertical wind shear within the atmospheric boundary layer, and quite possibly also is sensitive to surface characteristics and mean vertical motions.

Hybrid method for enforcing curvature related boundary conditions in solving one-phase fluid flow over a deformable domain

Abstract: An embodiment of the present invention may be a system or method for simulating the flow of a single-phase fluid flow. Markers represent a moving fluid boundary of the single-phase fluid at a first point in time. The moving fluid boundary separates a simulation space into a fluid space and a non-fluid space. The single-phase fluid inhabits the fluid space. A signed distance function is evaluated at points surrounding the moving fluid boundary based upon markers. The curvature of the moving fluid boundary based on the signed distance function is evaluated near the markers in the non-fluid space. The curvature is not evaluated at the moving fluid boundary. The velocity of the fluid is calculated based upon the curvature of the level set in the non-fluid space. Update the position of the moving fluid boundary at a second point in time based on the velocity of the fluid.

A note on the flow of a homogeneous intrusion into a two-layer fluid

Abstract: The intrusion of a constant density fluid at the interface of a two-layer fluid is considered. Numerical solutions are computed for a model of a steady intrusion resulting from flow down a bank and across a broad lake or reservoir. The incoming fluid is homogeneous and spreads across the lake at its level of neutral buoyancy. Solutions are obtained for a range of different inflow angles, flow rate and density differences. Except in extreme cases, the nature of the solution is predicted quite well by linear theory, with the wavelength at any Froude number given by a dispersion relation and wave steepness determined largely by entry angle. However, some extreme solutions with rounded meandering flows and non-unique solutions in the parameter space are also obtained.

The Influence of Actuator Parameters on Fluid Jetting Dispensing

Abstract: The actuator is an important component of the fluid jet-dispenser,and has an important influence on the fluid volume and velocity of the fluid jetted from the jet-dispenserThe calculation formula of cumulative fluid volume and its equivalent velocity based on fluid kinetic energy are deduced through central velocity at the nozzle outlet from the numerical simulation result,then cumulative fluid volume and equivalent velocity are computed under the condition of different actuator parameters by MATLAB programThis research supplies some foundation for the design and operation adjustment of the actuatorThe results show a good changeing characteristic of the cumulative fluid volume and equivalent velocity,the stroke of the ball-needle compared with its acceleration has less influence on the jetting fluid dispensing

Numerical Simulation of Viscous Flow: A Study of Molecular Dynamics and Computational Fluid Dynamics

Abstract: Molecular dynamics (MD) and computational fluid dynamics (CFD) allow researchers to study fluid dynamics from two very different standpoints. From a microscopic standpoint, molecular dynamics uses Newton's second law of motion to simulate the interatomic behavior of individual atoms, using statistical mechanics as a tool for analysis. In contrast, CFD describes the motion of a fluid from a macroscopic level using the transport of mass, momentum, and energy of a system as a model. This thesis investigates both MD and CFD as a viable means of studying viscous flow on a nanometer scale. Specifically, we investigate a pressure-driven Poiseuille flow. The results of the MD simulations are processed using software we created to measure velocity, density, and pressure. The CFD simulations are run on numerical software that implements the MacCormack method for the Navier-Stokes equations. Additionally, the CFD simulations incorporate a local definition of viscosity, which is usually uncharacteristic of this simulation method. Based on the results of the simulations, we point out similarities and differences in the obtained steady-state solutions. ACKNOWLEDGEMENTS First, I would like to thank my advisor, Dr. Pushkin Kachroo, for his guidance and insight during my research. At times, researching outside of my field was rough, but in the end it gave me a great sense of accomplishment. I would also like to thank my committee members, Dr. A. Lynn Abbott and Dr. Douglas K. Lindner, for serving on my committee and for their helpful remarks on my thesis. I also want to thank my parents, Mark and Mary Fried, for their help and encouragement throughout the past 7 years of college; my best friend and sister, Erin Fried, for helping me stay motivated through the hard times; and finally my cousins, Jen and Ryan Fried, and my aunt and uncle, Kevin and Sherry Fried, for their support over the years. Finally, I want to thank all of the friends that I've made in Blacksburg over the past 7 years. They have done everything from enduring my questions on fluid dynamics to providing much needed distractions to giving me a place to live for weeks at a time. Thanks guys.

Dynamic simulation of pressure driven flow of fluids with suspended ferrous particles in a micro channel under magnetic field

Abstract: This computational study focuses on the dynamics of individual ferrous particles and the flow of the incompressible Newtonian fluid under the effect of an externally applied magnetic field and pressure gradient in a two-dimensional micro channel with smooth walls. The particle dynamics is simulated as a discrete phase using MATLAB code and the fluid flow is solved as a continuous phase using Computational Fluid Dynamics Software FLUENT. Interaction between the particle and fluid phases are included as hydrodynamic forces predicated by the fluid phase simulation and updated particle locations determined by the particle phase solution under non-uniform magnetic field. Non-uniform magnetic field forces the particles to move to poles of the magnet, and results in their accumulation. This causes drastic change on the continuous phase flow and pressure distribution, which in turn influences the particle motion. Predicted dynamics of the suspended ferrous particles under magnetic field and flow of the carrier fluid with pressure gradient is in reasonably well agreement with previous work. The results show that non-uniform magnetic field generated by externally placed magnets can be used to control the locations of the particles and flow of the fluid in a micro channel.

Strong coupling for fluid structure interaction problems

Abstract: The computation of fluid forces acting on a rigid or deformable structure constitutes a major problem in fluid structure interaction. However, the majority of numerical tests consists in using two different codes to separately solve pressure of the fluid and structural displacements. In this paper, a monolithic with an ALE formulation approach is used to implicitly calculate the pressure of an incompressible fluid applied to the structure. The projection method proposed by Gresho is used to decouple the velocity and pressure.

Finite element analysis of elastic solid/Stokes flow interaction problem

Abstract: We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.