Showing papers on "Incompressible flow published in 1985"

Computational methods for fluid flow

Abstract: Keywords: methodes : numeriques ; programmation ; differences : finies ; methode : integrale ; ecoulement : incompressible ; ecoulement : compressible ; ecoulement : visqueux ; mecanique des : fluides ; viscosite Reference Record created on 2005-11-18, modified on 2016-08-08

Computing Three-Dimensional Incompressible Flows with Vortex Elements

Abstract: The techniques, capabilities and applicability of numerical models of three-dimensional, unsteady vortical flows with high Re are assessed. Vorticity is calculated only in appropriate regions and the velocity field is derived from the boundary conditions. Vorticity is assumed to take the shape of tubes with uniform core structures in the case of turbulence. The efforts being made to simplify equations for dense collections of vortex filaments in order to make them tractable to computer simulations are described. The effectiveness of vorticity arrow representations for accurately describing vorticity fields near surfaces is discussed, along with Lagrangian vortex elements, which may be of use in modelling the rotational part of flows around bluff bodies, nonuniform density flows and chemically reacting flows.

Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals

Abstract: The well-known analogy between the Euler equations for steady flow of an inviscid incompressible fluid and the equations of magnetostatic equilibrium in a perfectly conducting fluid is exploited in a discussion of the existence and structure of solutions to both problems that have arbitrarily prescribed topology. A method of magnetic relaxation which conserves the magnetic-field topology is used to demonstrate the existence of magnetostatic equilibria in a domain [Dscr ] that are topologically accessible from a given field B0(x) and hence the existence of analogous steady Euler flows. The magnetostatic equilibria generally contain tangential discontinuities (i.e. current sheets) distributed in some way in the domain, even although the initial field B0(x) may be infinitely differentiable, and particular attention is paid to the manner in which these current sheets can arise. The corresponding Euler flow contains vortex sheets which must be located on streamsurfaces in regions where such surfaces exist. The magnetostatic equilibria are in general stable, and the analogous Euler flows are (probably) in general unstable.The structure of these unstable Euler flows (regarded as fixed points in the function space in which solutions of the unsteady Euler equations evolve) may have some bearing on the problem of the spatial structure of turbulent flow. It is shown that the Euler flow contains blobs of maximal helicity (positive or negative) which may be interpreted as ‘coherent structures’, separated by regular surfaces on which vortex sheets, the site of strong viscous dissipation, may be located.

Local instant formulation of two-phase flow

Abstract: The local instant formulation of mass, momentum and energy conservations of two-phase flow has been developed. Distribution, an extended notion of a function, has been introduced for this purpose because physical parameters of two-phase flow media change discontinuously at the interface and the Lebesgue measure of an interface is zero. Using a characteristic function of each phase, the physical parameters of two-phase flow have been defined as field quantities. In addition to this, the source terms at the interface are defined in terms of the local instant interfacial area concentration. Based on these field quantities, the local instant field equations of mass, momentum and total energy conservations of two-phase flow have been derived. Modification of these field equations gives the single field representation of the local instant field equations of two-phase flow. Neglecting the interfacial force and energy, this formulation coincides with the field equations of single-phase flow, except in the definition of differentiation. The local instant two-fluid formulation of two-phase flow has also been derived. This formulation consists of six local instant field equations of mass, momentum and total energy conservations of both phases. Interfacial mass, momentum and energy transfer terms appear in these equations, which are expressed in terms of the local instant interfacial area concentration.

Application of time-iterative schemes to incompressible flow

Abstract: The computation of steady incompressible flows by an Euler implicit algorithm is studied using both the incompressible equations and the low Mach number compressible equations. The incompressible equations are handled by adding an artificial time derivative to the continuity equation. This allows both the pressure and velocity to be obtained implicitly. In one-dimensional problems, both systems converge rapidly, even at low Mach numbers where the eigenvalues are very stiff. In two dimensions where approximate factorization is required, the presence of stiff eigenvalues is highly detrimental. Stiffness can be avoided in the incompressible equations by selecting an appropriate "pseudo"-Mach number. This insures reliable convergence and results in an efficient incompressible flow algorithm. In the case of compressible equations, the Mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed. A matrix preconditioning factor that accomplishes this is developed and demonstrated. With this modification, the convergence rate is the same as in the incompressible case and is independent of Mach number. Rapid convergence is observed at Mach numbers as low as 6.05.

Numerical simulation of three‐dimensional flow in a cavity

Abstract: SUMMARY Previous three-dimensional simulations of the lid-driven cavity flow have reproduced only the most general features of the flow. Improvements to a finite difference code, REBUFFS, have made possible the first completely successful simulation of the three-dimensional lid-driven cavity flow. The principal improvement to the code was the incorporation of a modified QUICK scheme, a higher-order upwind finite difference formulation. Results for a cavity flow at a Reynolds number of 3200 have reproduced experimentally observed Taylor-Gortler-like vortices and other three-dimensional effects heretofore not simulated. Experimental results obtained from a unique experimental cavity facility validate the calculated results.

Computation of inviscid incompressible flow with rotation

Abstract: The standard hyperbolic methods used to solve the compressible Euler equations are not effective in the limit of incompressible flow. The sound waves dominate the system and it becomes poorly conditioned for numerical solution. For steady flow governed by the incompressible Euler equations, artificial compressibility is a technique that removes the troublesome sound waves. It leads to a hyperbolic system of equations that we solve by finite-volume differences centred in space, and explicit multistage time-stepping. The stability of this novel system is analysed, its allowable discontinuities are described, and appropriate far-field and solid-wall boundary conditions are introduced. Results are presented for both two- and three-dimensional flows, including vorticity shed from a delta wing. Whether vorticity is produced or not depends very strongly on the body geometry, the accuracy of the solution method, and the transient discontinuities that evolve in the flow field. The results are analysed for the total-pressure losses in the flow fields, and for the diffusion of the vortex sheets.

Two-phase flow in random network models of porous media

Abstract: To explore how the microscopic geometry of a pore space affects the macroscopic characteristics of fluid flow in porous media, the authors have used approximate solutions of the Navier-Stokes equations to calculate the flow of two fluids in random networks. The model pore space consists of an array of pores of variable radius connected by throats of variable length and radius to a random number of nearest neighbors. The various size and connectedness distributions may be arbitrarily assigned, as are the wetting characteristics of the two fluids in the pore space. The fluids are assumed to be incompressible, immiscible, Newtonian, and of equal viscosity. In the calculation, the authors use Stokes flow results for the motion of the individual fluids and incorporate microscopic capillary force via the Washburn approximation. At any time, the problem is mathematically identical to a random electrical network of resistors, batteries and diodes. From the numerical solution of the latter, the authors compute the fluid velocities and saturation rates of change, and use a discrete time-stepping procedure to follow the subsequent motion. The scale of the computation has so far restricted the authors to networks of modest size (100-400 pores) in two dimensions. Within these limitations,more » the authors discuss the dependence of residual oil saturations and interface shapes on network geometry and flow conditions.« less

Nonlinear stability of circular vortex patches

Abstract: This paper proves that circular vortex patches in the plane are stable for the nonlinear dynamical system generated by the Euler equations of incompressible fluids. This is achieved by establishing a relative variational principle in terms of either energy or angular momentum. Thus, we exploit and extend Arnold's idea in (1965, 1969) to a nonsmooth setting as well.

An algorithm for the use of the Lagrangian specification in Newtonian fluid mechanics and applications to free-surface flow

Abstract: An algorithm is constructed for the use of the Lagrangian kinematic specification in Newtonian fluid mechanics. The algorithm is implemented with a finite-element method, and it is demonstrated that the method accurately describes free-surface flow, including the effects of surface tension, with the use of just bilinear isoparametric elements. Moving contact lines are modelled with a small amount of slip near the contact lines. The contact angle boundary condition is included in the form of a net interfacial force specified at the contact line. Simulations of measurements in a parallel-plate geometry show that the measured apparent contact angle is not the true angle, and that the true angle is always very close to the equilibrium value.

Three-dimensional periodic flows with high-symmetry

Abstract: A class of three-dimensional periodic flows of an incompressible viscous fluid with high symmetry in space is proposed to be used for numerical simulation of large Reynolds number flows in order to increase the effective resolution. Information for a single component of the velocity in a domain of 1/64 in volume of a periodicity box is sufficient to describe the whole velocity field. Necessary memory therefore may be reduced to 1/192 of that required for a general non-symmetric periodic flow.

Instability at the interface between two shearing fluids in a channel

Abstract: The linear stability of plane Couette flow composed of two immiscible fluids in layers is considered. The fluids have different viscosities and densities. For the case of equal densities, there is a critical Reynolds number above which the interfacial mode of the bounded problem is approximated by that of the unbounded problem for wavelengths that are not short enough to be in the asymptotic short‐wavelength range, as well as for short waves. The full linear analysis reveals unstable situations missed out by the long‐ and short‐wavelength asymptotic analyses, but which have comparable orders of magnitudes for the growth rates. For the case of unequal densities, it is found that the arrangement with the heavier fluid on top can be linearly stable if the viscosity stratification, volume ratio, surface tension, Reynolds number, and Froude number are favorable.

A structure for laminar flow past a bluff body at high Reynolds number

Abstract: The steady planar symmetric motion of an incompressible fluid, past a symmetric bluff body fixed in an otherwise uniform stream, is considered for large Reynolds numbers Re. A laminar-flow structure is proposed which consists primarily of (a) the large-scale flow and (b) the smaller, body-scale, flow. Here (a) involves a pair of massive, effectively inviscid, recirculating eddies set up behind the body and bounded by viscous shear layers. Each eddy has small constant vorticity and its length and width both increase linearly with Re, so that the large-scale potential flow outside the eddies is significantly disturbed from the oncoming stream. This reduces the effective free stream acting on (b), The latter has the Kirchhoflf property of a parabolic growth in the eddy width downstream; but its eddy vorticity is non-uniform and substantial, contrary to the Kirchhoflf and Prandtl-Batchelor models, and secondary separation is possible. The non-uniform vorticity is provoked by the thick return jet, which is forced back along the centreline in (a) from downstream. Buffer zones, e.g. of length ocRe 1/2 , are required to join (b) fully to (a). The resulting drag coefficient c D is believed to be 0(1) generally, and is controlled, along with the eddy length and vorticity, by a combination of the viscous-inviscid flow problems posed in both (a) and (b). A special case of small c D is also covered. The structure seems self-consistent so far, and tends to compare reasonably well with recent numerical solutions of the Navier-Stokes equations at increased Re. An Appendix describes the inviscid parts of (a) for relatively thin eddies. © 1985, Cambridge University Press. All rights reserved.

Experiments with several elements for viscous incompressible flows

Abstract: SUMMARY We present a numerical procedure to eliminate internal nodes from elements designed to approximate incompressible flow problems. We compare six elements in academic and industrial like flow problem and we discuss their relative qualities. A surprising conclusion is that richer elements may behave less well than simple ones if a good enforcement of incompressibility is not maintained.

Velocity Field Characteristics of a Swirling Flow Combustor

Abstract: Data for reacting and nonreacting flows obtained by laser anemometry in a swirl combustor are reported and discussed. The combustor consists of two confined, concentric swirling jets. The central jet flow is premixed methane/air; the annular jet flow is air. The two flow conditions investigated are flow rotation in the same direction (coswirl) and in opposite directions (counterswirl). A closed, central recirculation zone is observed in both swirl conditions for reacting flow, but only in counterswirl for nonreacting flow. Large, anisotropic velocity fluctuations are observed in high shear regions and in the vicinity of the recirculation zone. Mechanisms for swirl-generated recirculation zone formation are discussed.

Unsteady lifting-line theory as a singular-perturbation problem

Abstract: Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).

Solution of the incompressible mass and momentum equations by application of a coupled equation line solver

Abstract: This paper describes an iterative technique for solving the coupled algebraic equations for mass and momentum conservation for an incompressible fluid flow. The technique is based on the simultaneous solution for pressure and velocity along lines. In a manner similar to ADI methods for a single variable, the solution domain is entirely swept line-by-line in each co-ordinate direction successively until a converged solution is obtained. The tight coupling between the equations that is guaranteed by the method results in an economical solution of the equation set.

Viscous flow through a rotating square channel

Abstract: Fully developed flow of an incompressible Newtonian fluid driven by a pressure gradient through a square channel that rotates about an axis perpendicular to the channel roof is analyzed here with the aid of the penalty/Galerkin/finite element method Coriolis force throws fast‐moving fluid in the channel core in the direction of the cross product of the mean fluid velocity with the channel’s angular velocity Two vortex cells form when convective inertial force is weak Asymptotic limits of rectilinear flow and geostrophic plug flow are approached when viscous force or Coriolis force dominates, respectively A flow structure with an ageostrophic, virtually inviscid core is uncovered when Coriolis and convective inertial forces are both strong This ageostrophic two‐vortex structure becomes unstable when the strength of convective inertial force increases past a critical value The two‐vortex family of solutions metamorphoses into a family of four‐vortex solutions at an imperfect bifurcation composed of a pair of turning points

New higher-order upwind scheme for incompressible Navier-Stokes equations

Abstract: A new upwind scheme for computation of incompressible flow has been developed. It was found that this scheme works well at high Reynolds number even using limited number of mesh points.

Numerical investigation of the steady viscous flow past a stationary deformable bubble

Abstract: A method for solving the Navier–Stokes equations in domains with moving boundaries is proposed. By means of a coordinate transformation, the region under consideration is converted to a region with known boundaries which are coordinate surfaces. An appropriate difference scheme with an algorithm for its implementation is constructed. The method is applied to the case of steady incompressible viscous flow past a resting deformable bubble. Results are obtained for wide ranges for Reynolds and Weber numbers and compared with other theoretical or experimental works in the common regions for the governing parameters. A separation of the flow and the occurrence of a toroidal vortex in the rear of the bubble is observed and verified through a number of computations. Typical flow patterns as well as a variety of practically important relations between the parameters of the flow are shown graphically.

Numerical experiments on subcritical transition mechanisms

Abstract: A spectral algorithm for simulating three-dimensional, incompressible, parallel shear flows is described. It applies to the channel, to the parallel boundary layer, and to other shear flows with one wall-bounded and two periodic directions. Simulations performed for the channel identify the one nonlinear interaction which is crucial to the secondary instability. Moreover, it is shown that subharmonic instability ensues for Reynolds numbers as low as 1500. Simulations performed for the heated water boundary layer reveal the operation of the secondary instability in this controlled flow.

Theoretical fluid dynamics

Abstract: This introduction to a wide range of theoretical studies in fluid dynamics, covers a great deal of material and offers updated information on topics such as stability and turbulence. It surveys nearly the entire field of classical fluid dynamics and discusses the various conceptual and analytical models of fluid flow.

Swirling flow in a research combustor

Abstract: Measurements of turbulent, confined, swirling flows have been obtained by means of a two-color laser Doppler velocimeter in a research combustor and compared with other experimental data and numerical results obtained by means of two two-equation models of turbulence. The combustor consists of two confined, con- centric, swirling jets whose mass flow rates and swirl numbers can be controlled independently, and which can be used to study cold flow, premixed and non-premixed reactive flows, and two-phase flows. Results are reported for cold flow conditions under co- and counterswirl. It is shown that under both conditions a closed recirculation zone is created at the combustor centerline. This zone is characterized by the presence of a one-celled toroidal vortex, low tangential velocities, high turbulent intensities, and large dissipation rates of turbulence kinetic energy. The experimental data agree satisfactorily with the numerical results, but do not agree with other ex- perimental data under coswirl flow conditions. The reasons for the discrepancies are discussed. N important application of swirling flows lies in its use to provide flame stabilization and improved mixing in many combustion chambers.1 In order to achieve enhanced flame stabilization and better control of the mixing process, multiple coaxial swirling streams can be introduced in swirl combustors. Yetter and Gouldin2 carried out a series of experiments on a model combustor which uses two coaxial swirling jets. They found that the fluid mechanical aspects play an important role in determining the operation of the combustor; combustion under coswirl conditions (jets rotating in the same direction) was found to be significantly different from combustion under counterswirl conditions. Vu and Gouldin3 performed experiments in a model combustor composed of two confined coaxial swirling jets under nonreacting conditions. They found that a recirculation zone occurs only with counterswirl near the exit of the inner jet. The recirculation zone was in the form of a one-celled toroidal vortex having very low swirl velocities. Habib and Whitelaw4 performed similar experiments in confined coaxial jets although under weak swirl conditions, i.e., no recir- culation zone at the combustor centerline appeared in their experimental work. Gouldin et al. 5 performed experiments similar to those reported here and in Ref. 3 by means of a laser Doppler velocimeter (LDV) and found that a recir- culation zone is created at the combustor centerline only under counterswirl flow conditions. The results of Gouldin et al.5 and Vu and Gouldin3 indicate that, in the geometrical arrangement employed by these investigators, coswirl does not result in a recirculation zone under incompressible flow conditions. The results presented in this paper show that a recirculation does exist under both co- and counterswirl flow conditions. Experimental work on turbulent, confined, swirling flows has also been performed by Rhode,6 Rhode et al.,7 Gupta et al.,8 and Yoon and Lilley.9 Rhode6 and Rhode et al.7 studied swirling flows in a combustor provided with a sudden ex- pansion by means of a visualization technique in which neutrally buoyant helium filled soap bubbles were employed. The results of the visualization technique were compared with a two-equation model of turbulence and showed that the model predicts the gross features of the flowfield. Gupta et

The Unsteady Potential Flow in an Axially Variable Annulus and Its Effect on the Dynamics of the Oscillating Rigid Center-Body

Abstract: This paper presents an analytical investigation of the unsteady potential flow in a narrow annular passage formed by a motionless rigid duct and an oscillating rigid center-body, both of axially variable cross section, in order to determine the fluid-dynamic forces exerted on the center-body. Based on this theory, a first-approximation solution as well as a more accurate solution are derived for the unsteady incompressible fluid flow. The stability of the center-body is investigated, in terms of the aerodynamic (or hydrodynamic) coefficients of damping, stiffness and inertia (virtual mass), as determined by this theory. The influence of various system parameters on stability is discussed.