Showing papers on "Incompressible flow published in 2004"

Arbitrary Lagrangian–Eulerian Methods

Abstract: The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior. Keywords: ALE description; convective transport; finite elements; stabilization techniques; mesh regularization and adaptation; fluid dynamics; nonlinear solid mechanics; stress-update procedures; fluid–structure interaction

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

Abstract: [1] We provide a numerical procedure for the simulation of two-phase immiscible and incompressible flow in two- and three-dimensional discrete-fractured media. The concept of cross-flow equilibrium is used to reduce the fracture dimension from n to (n-1) in the calculation of flow in the fractures. This concept, which is often referred to as the discrete-fracture model, has a significant effect on the reduction of computational time. The spatial discretization is performed with the control-volume method. This method is locally conservative and allows the use of unstructured grids to represent complex geometries, such as discrete-fracture configurations. The relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes, which is consistent with the physics of fluid flow. The system of partial differential equations is decoupled and solved using the implicit-pressure, explicit-saturation (IMPES) approach. The algorithm has been successfully tested in two- and three-dimensional numerical simulations of wetting phase fluid injection (such as water) in discrete-fractured media saturated by a nonwetting phase (such as nonaqueous phase liquid or oil) with mild to high nonlinearity in relative permeability and capillary pressure. To the best of our knowledge, results for simulations of two-phase immiscible and incompressible flow in three-dimensional discrete-fractured media, including capillary and gravity effects, are the first to appear in the literature.

Lattice-Boltzmann, Finite Element and Finite Volume Methods for laminar Flows

Abstract: The goal of this article is to contribute to a more precise discussion of the question whether Lattice-Boltzmann (LB) methods can be regarded as ecient CFD solvers. After a short review of the basic model and recommendable extensions, we compare the accuracy and computational eciency of two research simulation codes based on the LB and the Finite-Element method (FEM) for incompressible laminar two-dimensional flow problems in complex geometries. As LB methods are weakly compressible by nature, we also study the influence of the Mach number on the solution by comparing compressible and incompressible results obtained by the LB code and the commercial code CFX. Our results indicate, that for the quantities studied (lift, drag, pressure drop) our LB prototype is at least competitive for incompressible transient problems, but asymptotically slower for steady-state Stokes flow as the asymptotic algorithmic complexity of the classical LB-method is not optimal compared to the multigrid solvers incorporated in the FEM and CFX code. For the weakly compressible case, the LB approach has a significant wall clock time advantage as compared to CFX. In addition, we demonstrate that the influence of the finite Mach number in LB simulations of incompressible flow is easily underestimated.

Wall effects in flow past a circular cylinder in a plane channel: a numerical study

Abstract: This paper describes a numerical study on the steady flow of an incompressible Newtonian fluid past a circular cylinder confined in a plane rectangular channel. Using FLUENT (version 6), two-dimensional steady state computations were carried out for an uniform inlet velocity and for different values of the Reynolds numbers in the range between 0.1 and 200 and blockage ratios (ratio of the channel width to the cylinder diameter) in the range between 1.54 and 20. The flow parameters such as drag coefficient, length of the recirculation zone, and the angle of separation are presented as functions of the Reynolds number and blockage ratio. The total drag coefficient (CD) was found to decrease with an increase in the blockage ratio (λ) for a fixed value of the Reynolds number (Re) and to decrease with increasing Reynolds number for a fixed value of λ. Similarly, for a fixed value of λ, both the angle of separation and the length of the recirculation zone increase with the increasing Reynolds number.

Turbulent Inflow Conditions for Large-Eddy-Simulation of Compressible Wall-Bounded Flows

Abstract: The issue of turbulent inflow conditions for large-eddy simulation (LES) is addressed through three representative examples recently treated at ONERA. First, the performance of an extension to compressible flows of the rescaling method of Lund et al. is assessed. The second example, the flow above a deep cavity shows that the imposition of turbulent fluctuations has nearly no influence on the accuracy of the simulation on this acoustically driven flow. The third case demonstrates that particular attention must he paid to the response of the inflow condition to acoustic perturbations when local hybrid Reynolds-averaged Navier-Stokes/LES approaches are considered

Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids

Abstract: The linearized Navier–Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate n obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface p∞ increases (less compressible flow), n increases towards the uniform density result, while as the ratio of specific heats γ increases (less compressible fluid), n decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in γ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of p∞ and γ. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.

A model for restart of a pipeline with compressible gelled waxy crude oil

Abstract: The restart of a pipeline containing gelled waxy crude oil after shutdown is simulated using a two-fluid displacement model. The model assumes that the gelled oil is to be displaced by pumping in another fluid under constant pressure and that the incoming fluid displays Bingham plastic behaviour. The rheological behaviour of the gelled oil is characterised by a time-dependent constitutive equation with a yield stress, based on modelling of a North Sea waxy crude oil. The start-up flow model takes into account the compressibility and longitudinal variations in physical and rheological properties of both fluids as they flow along the pipeline. The effects of yield stress and the compressible nature of the gelled oil are effectively handled by introducing the concept of a propagating yield front and initial compression flow, that precede viscous flow of the gelled oil for a successful start-up. The model predicts that start-up flow is subjected to two delay times, one due to the transient yield stress behaviour of the gelled oil and the other due to the compressibility effects. Oil compressibility has a positive effect on flow rate, movement of the fluid–oil interface and the time taken to clear the gelled oil from the pipe. The effects of other factors such as start-up pressure, initial compression time and liquid hold-up on flow after restart are also examined. The model produces a more realistic prediction of the start-up situation than a previous model developed for incompressible fluids.

Three dimensional simulation of fluid flow in X-ray CT images of porous media

Abstract: A numerical scheme is developed in order to simulate fluid flow in three dimensional (3-D) microstructures. The governing equations for steady incompressible flow are solved using the semi-implicit method for pressure-linked equations (SIMPLE) finite difference scheme within a non-staggered grid system that represents the 3-D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3-D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2-D X-ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.

Steady non-Newtonian flow past a circular cylinder: a numerical study

Abstract: The steady and incompressible flow of non-Newtonian fluids past a circular cylinder is investigated for power law indices n between 0.2 and 1.4, blockage ratios of 0.037, 0.082 and 0.164, and the Reynolds numbers Re of 1, 20 and 40, using a stream function/vorticity formulation. The governing field equations have been solved by using a second-order accurate finite difference method to determine the drag coefficient, wake length, separation angle and flow patterns, and to investigate their dependence on power law index, blockage ratio and Reynolds number. The results reported here provide fundamental knowledge on the dependence of engineering flow parameters on blockage ratio and power law index, and further show that the effects on stream line and iso-vorticity patterns which result from an increase in the blockage ratio are similar to those which result from a decrease in the power law index.

Heating effect on steady and unsteady horizontal laminar flow of air past a circular cylinder

Abstract: Extensive numerical experiments were carried out to study the effect of cylinder heating on the characteristics of the flow and heat transfer in a two-dimensional horizontal laminar flow of air past a heated circular cylinder for the range of Reynolds numbers 0.001⩽Re⩽170. The fluid was treated as incompressible (density is independent of the pressure) while the variation of the fluid properties with temperature was taken into account. By including the transient density term of the continuity equation, which was neglected in a previous study by Lange, Durst, and Breuer [Int. J. Heat Mass Transfer 41, 3409 (1998)], we were able to predict correctly the vortex shedding frequency at various overheat ratios using an incompressible flow solver. The effect of dynamic viscosity and density variations on the flow dynamics occurring with the cylinder heating was analyzed separately. Another emphasis of the work was to investigate the physical mechanism behind the “effective Reynolds number” concept widely applied ...

Three‐dimensional incompressible flow calculations using the characteristic based split (CBS) scheme

Abstract: SUMMARY In this paper, the characteristic based split scheme is employed for the solution of three-dimensional incompressible viscousow problems on unstructured meshes Many algorithm related issues are dis- cussed Fully explicit and semi-implicit forms of the scheme are explained and employed in the cal- culation of both isothermal and non-isothermal incompressibleows simulation The extension of the scheme to porous mediumows is also demonstrated with relevant examples Copyright ? 2004 John Wiley & Sons, Ltd

Solutions of 2D and 3D Stokes laws using multiquadrics method

Abstract: In this paper, velocity–vorticity formulation and the multiquadrics method (MQ) with iterative scheme are used to solve two (2D) and three-dimensional (3D) steady-state incompressible Stokes cavity flows. The method involves solving of Laplace type vorticity equations and Poisson type velocity equations. The solenoidal velocity and vorticity components are obtained by iterative procedures through coupling of velocity and vorticity fields. Both the Poisson type velocity equations and the Laplace type vorticity equations are solved using the MQ, which renders a meshless (or meshfree) solution. Here, the results of 2D Stokes flow problems in a typical square cavity and a circular cavity are presented and compared with other model results. Besides utilizing the MQ to solve the 3D Stokes cubic cavity flow problem, we are also obtaining promising results for the accuracy of the velocity and vorticity. The MQ model has been found to be very simple and powerful for analyzing the 2D and 3D internal Stokes flow problems.

An adjoint‐based design methodology for CFD problems

Abstract: A complete CFD design methodology is presented. The main components of this methodology are a general edge‐based compressible/incompressible flow solver; a continuous adjoint formulation for the gradient computations; a steepest descent technique for the change of design variables; evaluation of the gradient of the discretized flow equations with respect to mesh by finite differences; a CAD‐free pseudo‐shell surface parametrization, allowing every point on the surface to be optimized to be used as a design parameter; and a level type scheme for the movement of the interior points. Several examples are included to demonstrate the methodology developed.

Meshfree weak–strong (MWS) form method and its application to incompressible flow problems

Abstract: A meshfree weak–strong (MWS) form method has been proposed by the authors' group for linear solid mechanics problems based on a combined weak and strong form of governing equations. This paper formulates the MWS method for the incompressible Navier–Stokes equations that is non-linear in nature. In this method, the meshfree collocation method based on strong form equations is applied to the interior nodes and the nodes on the essential boundaries; the local Petrov–Galerkin weak form is applied only to the nodes on the natural boundaries of the problem domain. The MWS method is then applied to simulate the steady problem of natural convection in an enclosed domain and the unsteady problem of viscous flow around a circular cylinder using both regular and irregular nodal distributions. The simulation results are validated by comparing with those of other numerical methods as well as experimental data. It is demonstrated that the MWS method has very good efficiency and accuracy for fluid flow problems. It works perfectly well for irregular nodes using only local quadrature cells for nodes on the natural boundary, which can be generated without any difficulty. Copyright © 2004 John Wiley & Sons, Ltd.

Vessel Segmentation and Blood Flow Simulation Using Level-Sets and Embedded Boundary Methods

Abstract: In this article we address the problem of blood flow simulation in realistic vascular objects. The anatomical surfaces are extracted by means of Level-Sets methods that accurately model the complex and varying surfaces of pathological objects such as aneurysms and stenoses. The surfaces obtained are defined at the sub-pixel level where they intersect the Cartesian grid of the image domain. It is therefore straightforward to construct embedded boundary representations of these objects on the same grid, for which recent work has enabled discretization of the Navier- Stokes equations for incompressible fluids. While most classical techniques require construction of a structured mesh that approximates the surface in order to extrapolate a 3D finite-element gridding of the whole volume, our method directly simulates the blood flow inside the extracted surface without losing any complicated details and without building additional grids. D 2004 CARS and Elsevier B.V. All rights reserved.