Showing papers on "Fluid dynamics published in 2012"

The Physics of Pulsatile Flow

Abstract: 1 Preliminary Concepts.- 1.1 Flow in a Tube.- 1.2 What Is a Fluid?.- 1.3 Microscopic and Macroscopic Scales.- 1.4 What Is Flow?.- 1.5 Eulerian and Lagrangian Velocities.- 1.6 Acceleration in a Flow Field.- 1.7 Is Blood a Newtonian Fluid?.- 1.8 No-Slip Boundary Condition.- 1.9 Laminar and Turbulent Flow.- 1.10 Problems.- 1.11 References and Further Reading.- 2 Equations of Fluid Flow.- 2.1 Introduction.- 2.2 Equations at a Point.- 2.3 Equations and Unknowns.- 2.4 Conservation of Mass: Equation of Continuity.- 2.5 Momentum Equations.- 2.6 Forces on a Fluid Element.- 2.7 Constitutive Equations.- 2.8 Navier-Stokes Equations.- 2.9 Problems.- 2.10 References and Further Reading.- 3 Steady Flow in Tubes.- 3.1 Introduction.- 3.2 Simplified Equations.- 3.3 Steady-State Solution: Poiseuille Flow.- 3.4 Properties of Poiseuille Flow.- 3.5 Balance of Energy Expenditure.- 3.6 Cube Law.- 3.7 Arterial Bifurcation.- 3.8 Arterial Tree.- 3.9 Entry Length.- 3.10 Noncircular Cross Section.- 3.11 Problems.- 3.12 References and Further Reading.- 4 Pulsatile Flow in a Rigid Tube.- 4.1 Introduction.- 4.2 Oscillatory Flow Equations.- 4.3 Fourier Analysis.- 4.4 Bessel Equation.- 4.5 Solution of Bessel Equation.- 4.6 Oscillatory Velocity Profiles.- 4.7 Oscillatory Flow Rate.- 4.8 Oscillatory Shear Stress.- 4.9 Pumping Power.- 4.10 Oscillatory Flow at Low Frequency.- 4.11 Oscillatory Flow at High Frequency.- 4.12 Tubes of Elliptic Cross Sections.- 4.13 Problems.- 4.14 References and Further Reading.- 5 Pulsatile Flow in an Elastic Tube.- 5.1 Introduction.- 5.2 Bessel Equations and Solutions.- 5.3 Balance of Forces.- 5.4 Equations of Wall Motion.- 5.5 Coupling with Fluid Motion.- 5.6 Matching at the Tube Wall.- 5.7 Wave Speed.- 5.8 Arbitrary Constants.- 5.9 Flow Properties.- 5.10 Problems.- 5.11 References and Further Reading.- 6 Wave Reflections.- 6.1 Introduction.- 6.2 One-Dimensional Wave Equations.- 6.3 Basic Solution of Wave Equation.- 6.4 Primary Wave Reflections in a Tube.- 6.5 Secondary Wave Reflections in a Tube.- 6.6 Pressure-Flow Relations.- 6.7 Effective Admittance.- 6.8 Vascular Tree Structure.- 6.9 Problems.- 6.10 References and Further Reading.- Appendix B. Solutions to Problems.

Control of interfacial instabilities using flow geometry

Abstract: When a low-viscosity fluid penetrates a fluid of higher viscosity confined by parallel plates, finger-like patterns propagate at the interface between the two fluids. Experiments now show that tapering the fluid cell can suppress this instability - providing interfacial control via a simple change in geometry.

High-Order Methods for Computational Physics

Abstract: R. Abgrall, T. Sonar, O. Friedrich, G. Billet: High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes * B. Cockburn: Discontinuous Galerkin Methods for Convection-Dominated Problems * R.D. Henderson: Adaptive Spectral Element Methods for Turbulence and Transition * C. Schwab: $hp$-FEM for Fluid Flow Simulation * C * W. Shu: High Order ENO and WENO Schemes for Computational Fluid Dynamics.

Rotation rate of rods in turbulent fluid flow.

Abstract: The rotational dynamics of anisotropic particles advected in a turbulent fluid flow are important in many industrial and natural settings. Particle rotations are controlled by small scale properties of turbulence that are nearly universal, and so provide a rich system where experiments can be directly compared with theory and simulations. Here we report the first three-dimensional experimental measurements of the orientation dynamics of rodlike particles as they are advected in a turbulent fluid flow. We also present numerical simulations that show good agreement with the experiments and allow extension to a wide range of particle shapes. Anisotropic tracer particles preferentially sample the flow since their orientations become correlated with the velocity gradient tensor. The rotation rate is heavily influenced by this preferential alignment, and the alignment depends strongly on particle shape.

Vapor delivery devices

Abstract: A vapor delivery device comprises a housing having a fluid inlet in fluid communication with a fluid outlet along a fluid flow path, and an energy storage unit, an atomizer, and a sensor within the housing. The energy storage unit is disposed in a chamber that fluidically isolates the energy storage unit from the fluid flow path.

Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions.

Abstract: The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid–structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibility of the coupled fluid–structure system in Eulerian form. Interaction between Lagrangian and Eulerian variables is mediated by integral equations with Dirac delta function kernels. The IB method provides a unified formulation for fluid–structure interaction models involving both thin elastic boundaries and also thick viscoelastic bodies. In this work, we describe the application of an adaptive, staggered-grid version of the IB method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve. Our model describes the thin leaflets of the aortic valve as immersed elastic boundaries, and describes the wall of the aortic root as a thick, semi-rigid elastic structure. A physiological left-ventricular pressure waveform is used to drive flow through the model valve, and dynamic pressure loading conditions are provided by a reduced (zero-dimensional) circulation model that has been fit to clinical data. We use this model and method to simulate aortic valve dynamics over multiple cardiac cycles. The model is shown to approach rapidly a periodic steady state in which physiological cardiac output is obtained at physiological pressures. These realistic flow rates are not specified in the model, however. Instead, they emerge from the fluid–structure interaction simulation.

Non-Newtonian Fluid Mechanics

Abstract: 1. Principles of Continuum Mechanics. Basic Concepts. Material Derivative. Deformation Rates. Rivlin-Ericksen Tensors. Strain Tensor. Kinematics of Steady Shear Flows. Continuity Equation. Stress and Volume Force. Equations of Motion. Energy Equation for Fluid Flow. 2. Material Properties Occurring in Steady Shear Flows. The Flow Function. The Normal Stress Functions. 3. Processes that are Controlled by the Flow Function. Rotational Viscometer. Pressure-Drag Flow in a Straight Channel. Radial Flow between Two Parallel Planes. Pipe Flow. Helical Flow. 4. Effect of Normal Stress Differences. Cone-and-Plate Flow. Weissenberg Effect. Die-Swell. Axial Shear Flow. 5. Simple Unsteady Flows. Linear Viscoelasticity. Non-Linear Effects in Unsteady Pipe Flow. 6. Nearly Viscometric Flows. Shear Flows with a Weak Unsteady Component. Plane Steady Boundary Layer Flows. Stability of Plane Shear Flows. 7. Extensional Flows. Theoretical Principles. Applications. 8. Special Rheological Laws. Fluids Without Memory. Integral Models. Differential Models. Approximation for Slow and Slowly Varying Processes. 9. Secondary Flows. General Theory. Rotational Symmetric Flows. Plane Flows. Steady Flow through Cylindrical Pipes. Periodic Pipe Flow. Appendix: Set of Formulas for Special Curvilinear Coordinates. References. Index.

Computational Fluid Dynamics: An Introduction

Abstract: Basic Philosophy of CFD.- Governing Equations of Fluid Dynamics.- Incompressible Inviscid Flows: Source andVortex Panel Methods.- Mathematical Properties of the Fluid Dynamic Equations.- Discretization of Partial Differential Equations.- Transformations and Grids.- Explicit Finite Difference Methods: Some Selected Applications to Inviscid and Viscous Flows.- Boundary Layer Equations and Methods of Solution.- Implicit Time-Dependent Methods for Inviscid and Viscous Compressible Flows, with a Discussion of the Concept of Numerical Dissipation.- to Finite Element Methods in Computational Fluid Dynamics.- to Finite Volume Methods in Computational Fluid Dynamics.- Aspects of CFD Computations with Commercial Packages.

The ℎ-principle and the equations of fluid dynamics

Abstract: In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov’s h-principle holds in several cases.

Self-affine elastic contacts: percolation and leakage.

Abstract: We study fluid flow at the interfaces between elastic solids with randomly rough, self-affine surfaces. We show by numerical simulation that elastic deformation lowers the relative contact area at which contact patches percolate in comparison to traditional approaches to seals. Elastic deformation also suppresses leakage through contacts even far away from the percolation threshold. Reliable estimates for leakage can be obtained by combining Persson's contact mechanics theory with a slightly modified version of Bruggeman's effective-medium solution of the Reynolds equation.

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

Abstract: The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.

Calculation of Temperature Rise in Air-cooled Induction Motors Through 3-D Coupled Electromagnetic Fluid-Dynamical and Thermal Finite-Element Analysis

Abstract: This paper investigates a 3-D coupled-field finite-element method (FEM) used in simulation of temperature distributions in air-cooled asynchronous induction motors. The temperature rise in motors is due to Joule's losses in stator windings and squirrel cages, and heat dissipation by air convection and solid conduction. The Joule's losses calculated by 3-D eddy-current field analysis are used as the input for the thermal field analysis, which is deeply dependent on accurate air fluid field analysis. Moreover, a novel multi-component fluid model is proposed to deal with the influence of rotor rotation upon the air convection. A test prototype is designed and manufactured. The good agreement of the temperature distributions between the simulated and measured results validates the proposed methodology.

Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

Abstract: Aquatic bacteria like Bacillus subtilis are heavier than water yet they are able to swim up an oxygen gradient and concentrate in a layer below the water surface, which will undergo Rayleigh–Taylor-type instabilities for sufficiently high concentrations. In the literature, a simplified chemotaxis–fluid system has been proposed as a model for bio-convection in modestly diluted cell suspensions. It couples a convective chemotaxis system for the oxygen-consuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force proportional to the relative surplus of the cell density compared to the water density. In this paper, we derive a high-resolution vorticity-based hybrid finite-volume finite-difference scheme, which allows us to investigate the nonlinear dynamics of a two-dimensional chemotaxis–fluid system with boundary conditions matching an experiment of Hillesdon et al. (Bull. Math. Biol., vol. 57, 1995, pp. 299–344). We present selected numerical examples, which illustrate (i) the formation of sinking plumes, (ii) the possible merging of neighbouring plumes and (iii) the convergence towards numerically stable stationary plumes. The examples with stable stationary plumes show how the surface-directed oxytaxis continuously feeds cells into a high-concentration layer near the surface, from where the fluid flow (recurring upwards in the space between the plumes) transports the cells into the plumes, where then gravity makes the cells sink and constitutes the driving force in maintaining the fluid convection and, thus, in shaping the plumes into (numerically) stable stationary states. Our numerical method is fully capable of solving the coupled chemotaxis–fluid system and enabling a full exploration of its dynamics, which cannot be done in a linearised framework.

2D longitudinal modeling of heat transfer and fluid flow during multilayered

Abstract: Derived from laser cladding, the Direct Laser Metal Deposition (DLMD) process is based upon a laser beam - powder - melt pool interaction, and enables the manufacturing of complex 3D shapes much faster than conventional processes. However, the surface finish remains critical, and DLMD parts usually necessitate post-machining steps. Within this context, the focus of our work is to improve the understanding of the phenomena responsible for deleterious surface finish by using numerical simulation. Mass, momentum, and energy conservation equations are solved using COMSOL Multiphysics® in a 2D transient model including filler material with surface tension and thermocapillary effects at the free surface. The dynamic shape of the molten zone is explicitly described by a moving mesh based on an Arbitrary Lagrangian Eulerian method (ALE). This model is used to analyze the influence of the process parameters, such as laser power, scanning speed, and powder feed rate, on the melt pool behavior. The simulations of a single layer and multilayer claddings are presented. The numerical results are compared with experimental data, in terms of layer height, melt pool length, and depth of penetration, obtained from high speed camera. The experiments are carried out on a widely-used aeronautical alloy (Ti-6Al-4V) using a Nd:YAG laser. The results show that the dilution ratio increases with increasing the laser power and the scanning velocity, or with decreasing the powder feed rate. The final surface finish is then improved.

Water transport through (7,7) carbon nanotubes of different lengths using molecular dynamics

Abstract: Non-equilibrium molecular dynamics simulations are used to investigate water transport through (7,7) CNTs, examining how changing the CNT length affects the internal flow dynamics. Pressure-driven water flow through CNT lengths ranging from 2.5 to 50 nm is simulated. We show that under the same applied pressure difference an increase in CNT length has a negligible effect on the resulting mass flow rate and fluid flow velocity. Flow enhancements over hydrodynamic expectations are directly proportional to the CNT length. Axial profiles of fluid properties demonstrate that entrance and exit effects are significant in the transport of water along CNTs. Large viscous losses in these entrance/exit regions lead into central “developed” regions in longer CNTs where the flow is effectively frictionless.

Map of fluid flow in fractal porous medium into fractal continuum flow.

Abstract: This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

A Detailed Heat and Fluid Flow Analysis of an Internal Permanent Magnet Synchronous Machine by Means of Computational Fluid Dynamics

Abstract: This paper presents a comprehensive computational fluid dynamics (CFD) model of a radial flux permanent magnet synchronous machine with interior magnets. In the CFD model, the water jacket cooling and a simplified model of the topology of the distributed stator winding are considered. The heat sources of the CFD model are determined from a finite-element analysis of the machine. The numerically determined temperature distributions of the machine are compared with measurement results from sensors located both in the stator and rotor. The particular focus of this paper is the analysis of the temperatures and the heat flow in the air gap and from the stator winding heads and the rotor to the inner air. Different operating conditions and two particular rotor designs with different inner air flow configurations are investigated. The potential of improving the thermal utilization of a rotor design with fan blades attached to the mounting plates of the rotor is shown.