A method for computing nonsteady, incompressible, viscous fluid flows /

"Contract W-7405-ENG. 36 with the U.S. Atomic Energy Commission."

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Investigation of a method for predicting AUV derivatives

The paper addresses the problem of autonomous underwater vehicle (AUV) modelling and parameter estimation as a means to predict the dynamic performance of underwater vehicles and thus provide solid guidelines during their design phase. The use of analytical and semi-empirical (ASE) methods to estimate the hydrodynamic derivatives of a popular class of AUVs is discussed. A comparison is done with the results obtained by using computational fluid dynamics to evaluate the bare hull lift force distribution around a fully submerged body. An application is made to the estimation of the hydrodynamic derivatives of the MAYA AUV, an autonomous underwater vehicle developed under a joint Indian-Portuguese project. The estimates obtained were used to predict the turning diameter of the vehicle during sea trials. (C) 2008 Elsevier Ltd. All rights reserved.

A method to correct the flow distortion of offshore wind data using CFD simulation and experimental wind tunnel tests

The assessment of wind energy resource for the development of deep offshore wind plants requires the use of every possible source of data and, in many cases, includes data gathered at meteorological stations installed at islands, islets or even oil platforms—all structures that interfere with, and change, the flow characteristics. This work aims to contribute to the evaluation of such changes in the flow by developing a correction methodology and applying it to the case of Berlenga island, Portugal. The study is performed using computational fluid dynamic simulations (CFD) validated by wind tunnel tests. In order to simulate the incoming offshore flow with CFD models a wind profile, unknown a priori, was established using observations from two coastal wind stations and a power law wind profile was fitted to the existing data (a=0.165). The results show that the resulting horizontal wind speed at 80 m above sea level is 16% lower than the wind speed at 80 m above the island for the dominant wind direction sector.

The potential field method and the nonlinear attractor dynamics approach: what are the differences?

One of the most popular approaches to path planning and control is the potential field method. This method is particularly attractive because it is suitable for on-line feedback control. In this approach the gradient of a potential field is used to generate the robot's trajectory. Thus, the path is generated by the transient solutions of a dynamical system. On the other hand, in the nonlinear attractor dynamic approach the path is generated by a sequence of attractor solutions. This way the transient solutions of the potential field method are replaced by a sequence of attractor solutions (i.e., asymptotically stable states) of a dynamical system. We discuss at a theoretical level some of the main differences of these two approaches.

An approximate solution method for boundary layer flow of a power law fluid over a flat plate

The work in this paper deals with the development of momentum and thermal boundary layers when a power law fluid flows over a flat plate. At the plate we impose either constant temperature, constant flux or a Newton cooling condition. The problem is analysed using similarity solutions, integral momentum and energy equations and an approximation technique which is a form of the Heat Balance Integral Method. The fluid properties are assumed to be independent of temperature, hence the momentum equation uncouples from the thermal problem. We first derive the similarity equations for the velocity and present exact solutions for the case where the power law index n = 2. The similarity solutions are used to validate the new approximation method. This new technique is then applied to the thermal boundary layer, where a similarity solution can only be obtained for the case n = 1.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Static structure and dynamics of the liquid Li-Na and Li-Mg alloys

We present calculations for the static structure and ordering properties of two lithium-based s-p bonded liquid alloys, Li-Na and Li-Mg. Our theoretical approach is based on the neutral pseudoatom method to derive the interatomic pair potentials, and on the modified-hypernetted-chain theory of liquids to obtain the liquid static structure, leading to a whole combination that is free of adjustable parameters. The study is complemented by performing molecular dynamics simulations which, besides checking the theoretical static structural results, also allow a calculation of some dynamical properties. The obtained results are compared with the available experimental data.

Flow structures at an idealized bifurcation : a numerical experiment

River bifurcations are key nodes within braided river systems controlling the flow and sediment partitioning and therefore the dynamics of the river braiding process. Recent research has shown that certain geometrical configurations induce instabilities that lead to downstream mid-channel bar formation and the formation of bifurcations. However, we currently have a poor understanding of the flow division process within bifurcations and the flow dynamics in the downstream bifurcates, both of which are needed to understand bifurcation stability. This paper presents results of a numerical sensitivity experiment undertaken using computational fluid dynamics (CFD) with the purpose of understanding the flow dynamics of a series of idealized bifurcations. A geometric sensitivity analysis is undertaken for a range of channel slopes (0.005 to 0.03), bifurcation angles (22 degrees to 42 degrees) and a restricted set of inflow conditions based upon simulating flow through meander bends with different curvature on the flow field dynamics through the bifurcation. The results demonstrate that the overall slope of the bifurcation affects the velocity of flow through the bifurcation and when slope asymmetry is introduced, the flow structures in the bifurcation are modified. In terms of bifurcation evolution the most important observation appears to be that once slope asymmetry is greater than 0.2 the flow within the steep bifurcate shows potential instability and the potential for alternate channel bar formation. Bifurcation angle also defines the flow structures within the bifurcation with an increase in bifurcation angle increasing the flow velocity down both bifurcates. However, redistributive effects of secondary circulation caused by upstream curvature can very easily counter the effects of local bifurcation characteristics. Copyright (C) 2011 John Wiley & Sons, Ltd.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Fluid dynamical prediction of changed v1-flow at energies available at the CERN Large Hadron Collider

Substantial collective flow is observed in collisions between lead nuclei at Large Hadron Collider (LHC) as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the global v1-flow, which at RHIC peaked at negative rapidities (named third flow component or antiflow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the quark-gluon plasma. Our calculations also take into account the initial state center-of-mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new"symmetrized" vS1(pt) function, and we also propose a new method to disentangle global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.

Fluid dynamical prediction of changed v1-flow at energies available at the CERN Large Hadron Collider

Substantial collective flow is observed in collisions between lead nuclei at Large Hadron Collider (LHC) as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the global v1-flow, which at RHIC peaked at negative rapidities (named third flow component or antiflow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the quark-gluon plasma. Our calculations also take into account the initial state center-of-mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new"symmetrized" vS1(pt) function, and we also propose a new method to disentangle global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.

Bernoulli correction to viscous losses: Radial flow between two parallel discs

For a massless fluid (density = 0), the steady flow along a duct is governed exclusively by viscous losses. In this paper, we show that the velocity profile obtained in this limit can be used to calculate the pressure drop up to the first order in density. This method has been applied to the particular case of a duct, defined by two plane-parallel discs. For this case, the first-order approximation results in a simple analytical solution which has been favorably checked against numerical simulations. Finally, an experiment has been carried out with water flowing between the discs. The experimental results show good agreement with the approximate solution