Showing papers on "Incompressible flow published in 1996"

Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid

Abstract: A moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. Deterministic particle interaction models representing gradient, Laplacian, and free surfaces are proposed. Fluid density is implicitly required to be constant as the incompressibility condition, while the other terms are explicitly calculated. The Poisson equation of pressure is solved by the incomplete Cholesky conjugate gradient method. Collapse of a water column is calculated using MPS. The effect of parameters in the models is investigated in test calculations. Good agreement with an experiment is obtained even if fragmentation and coalescence of the fluid take place.

High-resolution conservative algorithms for advection in incompressible flow

Abstract: A class of high-resolution algorithms is developed for advection of a scalar quantity in a given incompressible flow field in one, two, or three space dimensions. Multidimensional transport is modeled using a wave-propagation approach in which the flux at each cell interface is built up on the basis of information propagating in the direction of this interface from neighboring cells. A high-resolution second-order method using slope limiters is quite easy to implement. For constant flow, a minor modification gives a third-order accurate method. These methods are stable for Courant numbers up to 1. Fortran implementations are available by anonymous ftp.

Geometric constraints on potentially singular solutions for the 3-D Euler equations

Abstract: We discuss necessary and sufficient conditions for the formation of finite time singularities (blow up) in the incompressible three dimensional Euler equations. The well-known result of Beale, Kato and Majda states that these equations have smooth solutions on the time interval (0,t) if, and only if lim/t{r_arrow}T {integral}{sup t}{sub 0} {parallel}{Omega}({center_dot},s){parallel}{sub L}{sup {infinity}} (dx)dx < {infinity} where {Omega} = {triangledown} X u is the vorticity of the fluid and u is its divergence=free velocity. In this paper we prove criteria in which the direction of vorticity {xi} = {Omega}/{vert_bar}{Omega}{vert_bar} plays an important role.

An approximate projection scheme for incompressible flow using spectral elements

Abstract: SUMMARY An approximate projection scheme based on the pressure correction method is proposed to solve the NavierStokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is Mer validated by simulating the laminar flow over a backward-facing step. The solution of the Navier-Stokes equations for unsteady incompressible fluid flow is still a major challenge in the field of computational fluid dynamics. An overview of the most important aspects with respect to the solution of the incompressible Navier-Stokes equations can be found in References 1-5. The Navier-Stokes equations form a set of coupled equations for both velocity and pressure (or, better, the gradient of the pressure). One of the main problems related to the numerical solution of these equations is the imposition of the incompressibility constraint and consequently the calculation of the pressure. The pressure is not a thermodynamic variable, as there is no equation of state for an incompressible fluid. It is an implicit variable which instantaneously 'adjusts itself' in such a way that the velocity remains divergence-free. The gradient of the pressure, on the other hand, is a relevant physical quantity: a force per unit volume. The mathematical importance of the pressure in an incompressible flow lies in the theory of saddle-point problems (of which the steady Stokes equations are an example), where it acts as a Lagrangian multiplier that constrains the velocity to remain divergence-free. There are numerous approaches to solve the Navier-Stokes equations. For the solution of unsteady Navier-Stokes flow perhaps one of the most successful approaches to date is provided by the class of projection methods.&' Projection methods have been developed as a useful way of obtaining an efficient solution algorithm for unsteady incompressible flow. In this paper, projection methods are considered that are applied to the set of continuous equations, yielding very efficient and simple-toimplement algorithms. By decoupling the treatment of velocity and pressure terms, a set of easier-tosolve equations arises: a convectiondiffusion problem for the velocity, yielding an intermediate velocity which is not divergence-free; and a Poisson equation for the pressure (or a related quantity).

Self-similar solutions for navier-stokes equations in

Abstract: We construct self-similar solutions for three-dimensional incompressible Navier-Stokes equations, providing some examples of functional spaces where this can be done. We apply our results to a Part...

Reactive Transport and Immiscible Flow in Geological Media. I. General Theory

Abstract: Steady flow of incompressible fluids takes place in geological formations of spatially variable permeability The permeability is regarded as a stationary random space function (RSF) of given statistical moments The fluid carries reactive solutes and we consider, for illustration purposes, two types of reactions: nonlinear equilibrium sorption of a single species and mineral dissolution (linear kinetics) In addition, we analyse the nonlinear problem of horizontal flow of two immiscible fluids (the Buckley-Leverett flow) We consider injection at constant concentration in a semi-infinite domain at constant initial concentration and we neglect the effect of pore scale dispersion The field-scale transport problem consists of characterizing an erratic plume, or displacement front, emanating from a given source area along distinct random flow paths Reactive transport along three-dimensional flow paths is transformed to a one-dimensional Lagrangian-Eulerian domain ($\tau $, t), where $\tau $ is the fluid residence time and t is the real time Due to nonlinearity, discontinuities (shock waves) along a flow path may develop Close form solutions are obtained for the expected values of the spatial and temporal moments of a nonlinearly reacting solute plume, or of two immiscible fluids These results generalize the previous results for linearly reacting solute (Cvetkovic & Dagan 1994) The general results are illustrated and discussed in part II

Simulation of Coupled Viscous and Porous Flow Problems

Abstract: Theoretical and numerical formulations are presented for the conjugate problem involving incompressible flow and flow in a saturated porous medium. The major focus of the work is the development of...

On the stability of an axisymmetric rotating flow in a pipe

Abstract: The linear stability of an inviscid, axisymmetric and rotating columnar flow in a finite length pipe is studied. A well posed model of the unsteady motion of swirling flows with compatible boundary conditions that may reflect the physical situation is formulated. A linearized set of equations for the development of infinitesimal axially‐symmetric disturbances imposed on a base rotating columnar flow is derived. Then, a general mode of axisymmetric disturbances, that is not limited to the axial‐Fourier mode, is introduced and an eigenvalue problem is obtained. Benjamin’s critical state concept is extended to the case of a rotating flow in a finite length pipe. It is found that a neutral mode of disturbance exists at the critical state. In the case of a solid body rotating flow with a uniform axial velocity component, analytical solution of the eigenvalue problem is found. It is demonstrated that the flow changes its stability characteristics as the swirl changes around the critical level. When the flow is ...

Vorticity Dynamics on Boundaries

Abstract: Publisher Summary This chapter focuses on vorticity dynamics on boundaries. One of the central problems in vorticity and vortex dynamics is the interaction of vorticity field and boundaries. The boundary can be a rigid wall, a flexible solid wall, or an interface of two different fluids. Boundaries are the most basic source of vorticity (in particular, the unique source for incompressible flow of a homogeneous fluid in a conservative external body-force field), and the whole life of a vortex usually begins at a boundary. Due to the continuous creation of vorticity from boundaries, a bounded vortical flow is much more complicated than an unbounded flow, in particular in the regions near the boundary. This chapter presents a unified general theory of the vorticity dynamics on various boundaries for viscous compressible flows and then reviews its applications to specific problems mainly confined to incompressible flows. Two types of boundaries are considered in the chapter: a solid boundary, either rigid or flexible; and an interface of two immiscible fluids. Both are regarded as sharp material surfaces. Some other boundaries, such as a porous wall, regrettably are omitted, though they are also important in practice. The chapter also briefly reviews the development of boundary vorticity dynamics.

A remark on the inviscid limit for two-dimensional incompressible fluids

Abstract: In this article, we shall study the inviscid limit of two dimensional fluids with bounded voticity. We prove that the solution of incompressible Navier-Stokes system converges strongly in L2 to the...

Three-Dimensional Analysis of Partially Open Butterfly Valve Flows

Abstract: A numerical simulation of butterfly valve flows is a useful technique to investigate the physical phenomena of the flow field. A three-dimensional numerical analysis was carried out on incompressible fluid flows in a butterfly valve by using FLUENT, which solves difference equations. Characteristics of the butterfly valve flows at different valve disk angles with a uniform incoming velocity were investigated. Comparisons of FLUENT results with other results, i.e., experimental results, were made to determine the accuracy of the employed method. Results of the three-dimensional analysis may be useful in the valve design.

On the stability of non-columnar swirling flows

Abstract: The linear stability of an inviscid, axisymmetric and non‐columnar swirling flow in a finite length pipe is studied. A novel linearized set of equations for the development of infinitesimal axially‐symmetric disturbances imposed on a base non‐columnar rotating flow is derived. Then, a general mode of an axisymmetric disturbance, that is not limited to the axially‐periodic mode, is introduced and an eigenvalue problem is obtained. A neutral mode of disturbance exists at the critical state. The asymptotic behavior of the branches of non‐columnar solutions that bifurcate at the critical state is given. Using asymptotic techniques, it is shown that the critical state is a point of exchange of stability for these branches of solutions. This result, together with a previous result of Wang and Rusak [Phys. Fluids 8, 1007 (1996)] on the stability of columnar vortex flows, completes the investigation on the stability of all branches of solutions near the critical state. Results reveal the important relation between stability of vortex flows and the physical mechanism leading to the axisymmetric vortex breakdown phenomenon.

Kinetic theory for bubbly flow I: collisionless case

Abstract: A kinetic theory for incompressible dilute bubbly flow is presented. The Hamiltonian formulation for a collection of bubbles is outlined. A Vlasov equation is derived for the one-particle distribution function with a self-consistent field starting with the Liouville equation for the N-particle distribution function and using the point-bubble approximation. A stability condition which depends on the variance of the bubbles momenta and the void fraction is derived. If the variance is small then the linearized initial-value problem is ill posed. If it is sufficiently large, then the initial-value problem is well posed and a phenomenon similar to Landau damping is observed. The ill-posedness is found to be the result of an unstable eigenvalue, whereas the Landau damping arises from a resonance pole. Numerical simulations of the Vlasov equation in one dimension are performed using a particle method. Some evidence of clustering is observed for initial data with small variance in momentum.

Pair dispersion over an inertial range spanning many decades

Abstract: New numerical results on scalar pair dispersion through an inertial range spanning many decades are presented here. These results are achieved through a new Monte Carlo algorithm for synthetic turbulent velocity fields, which has been developed and validated recently by the authors [J. Comput. Phys. 117, 146 (1995)]; this algorithm is capable of accurate simulation of a Gaussian incompressible random field with the Kolmogoroff spectrum over 12–15 decades of scaling behavior with low variance. The numerical results for pair dispersion reported here are within the context of random velocity fields satisfying Taylor’s hypothesis for two‐dimensional incompressible flow fields. For the Kolmogoroff spectrum, Richardson’s t3 scaling law is confirmed over a range of pair separation distances spanning eight decades with a Richardson constant with the value 0.031±0.004 over nearly eight decades of pair separation, provided that the longitudinal component of the velocity structure tensor is normalized to unity. Rema...

Energy-Conserving Truncations for Convection with Shear Flow

Abstract: A method is presented for making finite Fourier mode truncations of the Rayleigh–Benard convection system that preserve invariants of the full partial differential equations in the dissipationless limit. These truncations are shown to have no unbounded solutions and provide a description of the thermal flux that has the correct limiting behavior in a steady‐state. A particular low‐order truncation (containing 7 modes) is selected and compared with the 6‐mode truncation of Howard and Krishnamurti [J. Fluid Mech. 170, 385 (1986)], which does not conserve the total energy in the dissipationless limit. A numerical example is presented to compare the two truncations and study the effect of shear flow on thermal transport.

Subharmonic transition to turbulence in a flat-plate boundary layer at Mach number 4.5

Abstract: The subharmonic transition process of a flat-plate boundary layer at a free-stream Mach number of M∞ = 4.5 and a Reynolds number of 10000 based on free-stream velocity and initial displacement thickness is investigated by direct numerical simulation up to the beginning of turbulence. A second-mode instability superimposed with random noise of low amplitude is forced initially. The secondary subharmonic instability evolves from the noise in accordance with theory and leads to a staggered Λ-vortex pattern. Finite-amplitude Λ-vortices initiate the build-up of detached high-shear layers below and above the critical layer. The detached shear-layer generation and break-up are confined to the relative-subsonic part of the boundary layer. The breakdown to turbulence can be separated into two phases, the first being the break-up of the lower shear layer and the second being the break-up of the upper shear layer. Four levels of subsequent roll-up of the lower, Y-shaped shear layer have been observed, leading to new vortical structures which are unknown from transition at low Mach numbers. The upper shear layer behaviour is similar to that of the well-known high-shear layer in incompressible boundary-layer transition. It is concluded that, as in incompressible flow, turbulence is generated via a cascade of vortices and detached shear layers with successively smaller scales. The different phases of shear-layer break-up are also reflected in the evolution of averaged quantities. A strong decrease of the shape factor, as well as an increase of the skin friction coefficient, and a gradual loss of spanwise symmetry indicate the final breakdown to turbulence, where the mean velocity and temperature profiles approach those measured in fully turbulent flow.

A pressure-correction method for the solution of incompressible viscous flows on unstructured grids

Abstract: SUMMARY An unstructured grid, finite volume method is presented for the solution of two-dimensional viscous, incompressible flow. The method is based on the pressure-correction concept implemented on a semi-staggered grid. The computational procedure can handle cells of arbitrary shape, although solutions presented herein have been obtained only with meshes of triangular and quadrilateral cells. The discretization of the momentum equations is effected on dual cells surrounding the vertices of primary cells, while the pressure-correction equation applies to the primary-cell centroids and represents the conservation of mass across the primary cells. A special interpolation scheme s used to suppress pressure and velocity oscillations in cases where the semi-staggered arrangement does not ensure a sufficiently strong coupling between pressure and velocity to avoid such oscillations. Computational results presented for several viscous flows are shown to be in good agreement with analytical and experimental data reported in the open literature.

Steady states and oscillatory instability of swirling flow in a cylinder with rotating top and bottom

Abstract: In this study we present a numerical investigation of steady states, onset of oscillatory instability, and slightly supercritical oscillatory states of an axisymmetric swirling flow of a Newtonian incompressible fluid in a cylinder, with independently rotating top and bottom. The first part of the study is devoted to the influence of co‐ and counter‐rotation of the bottom on the steady vortex breakdown, which takes place in the well‐known problem of flow in a cylinder with a rotating top. It is shown that weak counter‐rotation of the bottom may suppress the vortex breakdown. Stronger counter‐rotation may induce a stable steady vortex breakdown at relatively large Reynolds numbers for which a vortex breakdown does not appear in the case of the stationary bottom. Weak corotation may promote the vortex breakdown at lower Reynolds numbers than in the cylinder with the stationary bottom. Stronger corotation leads to the detachment of the recirculation zone from the axis and the formation of an additional vortex ring. The second part of the study is devoted to the investigation of the onset of oscillatory instability of steady flows. It is shown that the oscillatory instability sets in due to a Hopf bifurcation. The critical Reynolds number and the critical frequency of oscillations were calculated as a function of the rotation ratio (ξ=Ωbottom/Ωtop) for a fixed value of the aspect ratio γ (height/radius) of the cylinder γ=1.5. The stability analysis showed that there are several most unstable linear modes of the perturbation that become successively dominant with a continuous change of ξ. It is shown that the oscillatory instability may lead to an appearance and coexistence of more than one oscillating separation vortex bubble.

Study of the von Karman flow between coaxial corotating disks

Abstract: We report an experimental study of the swirling flow generated in the gap between two coaxial corotating disks. We use a free geometry, i.e., unshrouded disks in air, with moderate to high Reynolds numbers. When the relative rotation rate is varied, transitions in the flow can be observed by global power measurement and are related to the geometry of the external recirculating flow. The mean flow is studied in details with hot‐wire measurements using a boxcar‐type averaging technique. It involves a single turbulent vortex undergoing a slow precession motion. We show that statistical properties of the turbulent fluctuations are affected by the dynamics of the mean flow, which also displays a correlation with the global power fluctuations.