Showing papers on "Fluid dynamics published in 1990"

Turbulence in fluids

Abstract: to Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards "Real World Turbulence".

Elementary Fluid Dynamics

Abstract: Introduction Elementary viscous flow Waves Classical aerofoil theory Vortex motion The Navier-Stokes equations Very viscous flow Boundary layers Instability Appendix hints and answers for exercises Bibliography Index.

The Physics of Fluid Turbulence

Abstract: Keywords: ecoulement : turbulent ; mecanique des : fluides ; statistique ; simulation ; structures ; turbulence ; fluides Reference Record created on 2005-11-18, modified on 2016-08-08

Fluid dynamics of viscoelastic liquids

Abstract: This text develops a mathematical and physical theory which takes a proper account of the elasticity of liquids. This leads to systems of partial differential equations of composite type in which some variables are hyperbolic and others elliptic. It turns out that the vorticity is usually the key hyperbolic variable. The relevance of this type of mathematical structure for observed dynamics of viscoelastic motions is evaluated in detail. Much attention has been paid to observations, most of which date from 1992 to 1997.

Dissolution of Trapped Nonaqueous Phase Liquids: Mass Transfer Characteristics

Abstract: Many groundwater contamination incidents begin with the release of an essentially immiscible fluid into the subsurface environment. Once in the subsurface, an immiscible fluid participates in a complex pattern of transport processes. For immiscible fluids that are commonly found in contaminated groundwater environments the interphase mass transfer between the nonaqueous phase liquids (NAPLs) phase and the aqueous phase is an important process. An experimental apparatus and procedure were used to isolate and measure mass transfer between toluene and water in glass bead media systems. The rate of interphase mass transfer was investigated in two-fluid systems as a function of aqueous phase velocity, aqueous- and nonaqueous-phase fluid saturations, and porous media characteristics. The rate of interphase mass transfer is found to be directly related to aqueous phase velocity and nonaqueous phase fluid saturation level, but no significant relation to mean particle size is found. Correlation expressions for the rate of interphase mass transfer are developed using relevant dimensionless parameters and are compared to literature values. Equilibrium between the two fluid phases investigated is shown to be achieved rapidly, over wide ranges of nonaqueous phase fluid saturations and aqueous phase velocities. The derived correlations provide a means for estimating the appropriateness ofmore » the local equilibrium assumption for a nonaqueous phase liquid-aqueous phase couple in multiphase groundwater systems.« less

Boundary Value Problems in Mechanics of Nonhomogeneous Fluids

Abstract: Models of the Dynamics of Heterogeneous Media and the Body of Mathematics Correctness ``In the Whole'' of the Boundary Problems for Equations of One-Dimensional Non-Stationary Motion of a Viscous Gas Initial-Boundary Value Problems for the Navier-Stokes Equations of Nonhomogeneous Viscous Incompressible Fluid Correctness of the Problem of Flow through an Ideal Incompressible Liquid Filtration of Immiscible Liquids References

Rapid, stable fluid dynamics for computer graphics

Abstract: We present a new method for animating water based on a simple, rapid and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations. The approximation gives rise to a version of the wave equation on a height-field where the wave velocity is proportional to the square root of the depth of the water. The resulting wave equation is then solved with an alternating-direction implicit method on a uniform finite-difference grid. The computational work required for an iteration consists mainly of solving a simple tridiagonal linear system for each row and column of the height field. A single iteration per frame suffices in most cases for convincing animation.Like previous computer-graphics models of wave motion, the new method can generate the effects of wave refraction with depth. Unlike previous models, it also handles wave reflections, net transport of water and boundary conditions with changing topology. As a consequence, the model is suitable for animating phenomena such as flowing rivers, raindrops hitting surfaces and waves in a fish tank as well as the classic phenomenon of waves lapping on a beach. The height-field representation prevents it from easily simulating phenomena such as breaking waves, except perhaps in combination with particle-based fluid models. The water is rendered using a form of caustic shading which simulates the refraction of illuminating rays at the water surface. A wetness map is also used to compute the wetting and drying of sand as the water passes over it.

Friction, overpressure and fault normal compression

Abstract: More than twenty-five years ago Miller and Low reported the existence of a threshold pore pressure gradient below which water would not flow through clay. Recent experimental observations of the shear strength of structured water on biotite surfaces have provided a physical basis for understanding this threshold gradient. The existence of this phenomenon has profound implications for the rheological properties of mature fault zones, such as the San Andreas, that contain large thickness of fault gouge. For example, a clay-filled fault zone about 1 km wide at the base of the surface could support core fluid pressure equal to the maximum principal stress over the entire seismogenic zone. As a result, the fault would have near-zero strength and the maximum principal stress measured on the flanks of the fault, would be oriented normal to the fault surface. Another consequence of the threshold gradient is that normal hydrostatic fluid pressures outside the fault zone could coexist with near-lithostatic fluid pressures in the interior of the fault zone without the need for continual replenishment of the overpressured fluid. In addition, the pore pressure at any point should never exceed the local minimum principal stress so that hydrofracture will not occur.

Liquid transport in micron and submicron channels

Abstract: An experimental investigation of fluid flow in extremely small channels is presented. Potential applications for such channels include cooling of electronic circuits, and reactors for modification and separation of biological cells. The immediate goal is to determine at what length scales the continuum assumptions break down and if the Navier-Stokes equations adequately predict fluid behavior. In order to accomplish this, experiments are being conducted in progressively thinner flow channels. We have constructed three channels of rectangular cross-section ranging in area from 7200 to 80 square microns, utilizing the recent advances in microfabrication. In this paper, preliminary results are reported pertaining to friction measurements. It is found that in the relatively large flow channels the experimental observations are in rough agreement with the predictions from the Navier-Stokes equations. However, in the smallest of the channels, there is a significant deviation from the Navier-Stokes predictions.

Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries

Abstract: In this paper a method is presented that can be used for both the Lagrangian and the Eulerian solution of the Navier–Stokes equations in a domain of arbitrary shape, bounded by boundaries which move in any prescribed time-varying fashion. The method uses the integral form of the governing equations for an arbitrary moving control volume, with pressure and Cartesian velocity components as dependent variables. Care is taken to also satisfy the space conservation law, which ensures a fully conservative computational procedure. Fully implicit temporal differencing makes the method stable for any time step. A detailed description is provided for the discretization in two dimensions, with a collocated arrangement of variables. Central differences are used to evaluate both the convection and diffusion fluxes. The well known SIMPLE algorithm is employed for pressure–velocity coupling. The resulting algebraic equation systems are solved iteratively in a sequential manner. Results are presented for a flow in a channel with a moving indentation; they show favourable agreement with experimental observations.

Computational Fluid Dynamics: An Introduction for Engineers

Abstract: 1. Introduction. 2. The simplest description of continuous fluid flow. 3. The finite difference method. 4. Diffusion problems. 5. Transport as a combination of addiction and diffusion. 6. Descriptions of unsteady flows. 7. Solution methods for unsteady free surface flows. 8. Equilibrium methods. 9. Computational fluid dynamics of turbulence. 10. An introduction to some other numerical methods. Index.

Symmetries, Conservation Laws, and Hamiltonian Structure in Geophysical Fluid Dynamics

Abstract: Publisher Summary This chapter discusses symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics Some basic definitions and results for finite-dimensional Hamiltonian dynamical systems, leading up to the introduction of the symplectic notation that proves crucial in the generalization to noncanonical, infinite-dimensional systems, such as the Eulerian representation of fluid flow are presented It is found that in addition to the invariants, such as energy and momentum that are associated with explicit symmetries, noncanonical Hamiltonian systems generally possess what are sometimes known as Casimir invariants or distinguished functions The equations of fluid dynamics are continuous in space and thus represent infinite-dimensional dynamical systems The existence of nonlinearly stable solutions whose stability relies on the full infinity of Casimir invariants strongly suggests a failure of ergodicity, because trajectories originating sufficiently close to those states cannot fill out the entire energy–enstrophy hypersurface It is found that the physical approximations made to derive the shallow-water equations from 3D incompressible flow consist of taking the fluid to be homogeneous and constrained to move in vertical columns

Analysis of Energy and Momentum Transport for Fluid Flow Through a Porous Bed

Abstract: This paper presents an analysis for the forced convective flow of a gas through a packed bed of spherical solid particles, and the associated heat transport processes. Ergun's correlation was used as the vapor phase momentum equation in order to account for the inertia effects as well as the viscous effects. No local thermal equilibrium was assumed between the solid and the vapor phases. A thorough discussion of the thermal interactions between the solid and vapor phases and their effect on the fluid flow as well as the pressure and density fields is presented. The analysis shows that the local thermal equilibrium condition was very sensitive to the particle Reynolds number (Re{sub p}) and the Darcy number (Da) while thermophysical properties did not have a very significant effect on this condition. On the other hand, two-dimensional behavior of certain variables was found to be very sensitive to thermophysical parameters but insensitive to Re{sub p} and Da.

Fluid Dynamics of Core Formation

Abstract: Past discussions of core formation are incorrect or incomplete because they assume that metallic iron-rich liquid is able to migrate through a mostly solid silicate matrix by percolation, prior to macrosegregation and diapiric descent. Experimental and theoretical considerations suggest that percolation is largely prevented because of the high surface tension of iron. Two alternative views of core formation are offered. One assumes that percolation is possible in the deep mantle (where perovskite is the major phase). Iron is then supplied to the deep mantle by Rayleigh-Taylor instabilities of a silicate-iron suspension in the shallow mantle, and drains efficiently from the deepest mantle into the core by Darcy flow. The other model assumes complete or nearly complete melting of all or part of the mantle. Despite vigorous convection, iron droplets approximately one centimeter in radius are predicted and settle rapidly by Stokes flow, either to the core or into a layer or ponds that provide iron-rich diapirs that can descend to the core. These stories generally suggest very efficient core formation in the sense that the typical residence time of metallic iron in the mantle is orders of magnitude shorter than the formation time of Earth (~10^8 years). Good chemical equilibrium between mantle and core phases is also predicted in many cases. Geochemical constraints and implications relevant to these scenarios are discussed but are largely inconclusive. The tentative inference of rapid core formation on Mars suggests a magma ocean and iron rainout.

Pressure drop in horizontal wells and its effect on production performance

Abstract: Fluid flow in horizontal pipes becomes turbulent at Reynolds numbers large than 2,000. In practical situations, turbulent flow in horizontal wells may occur at rates of thousands of cubic feet per day (for a 24.4-cm (9 5/8-in.) cased well). Wells flowing in a turbulent regime experience a flow resistance many orders of magnitude higher than that for laminar flow. Therefore, along-hole well-pressure gradients generally cannot be neglected, and a proper description of horizontal well flow needs to be included in the design of these wells (and in reservoir simulators). This is particularly imperative in situations of very low drawdowns (to avoid gas or water cresting). This paper presents a simple analytical method that links single-phase turbulent well flow to stabilized reservoir flow. The resulting second-order differential equation is solved numerically for the appropriate boundary conditions. Results are presented in dimensionless form for general applicability.

Conservation of mass and momentum for the flow of interdendritic liquid during solidification

Abstract: In this paper, mass and momentum conservation equations are derived for the flow of interdendritic liquid during solidification using the volume-averaging approach. In this approach, the mushy zone is conceived to be two interpenetrating phases; each phase is described with the usual field quantities, which are continuous in that phase but discontinuous over the entire space. On the microscopic scale, the usual conservation equations along with the appropriate interfacial boundary conditions describe the state of the system. However, the solution to these equations in the microscopic scale is not practical because of the complex interfacial geometry in the mushy zone. Instead, the scale at which the system is described is altered by averaging the microscopic equations over some representative elementary volume within the mushy zone, resulting in macroscopic equations that can be used to solve practical problems. For a fraction of liquid equal to unity, the equations reduce to the usual conservation equations for a single-phase liquid. It is also found that the resistance offered by the solid to the flow of interdendritic liquid in the mushy zone is best described by two coefficients, namely, the inverse of permeability and a second-order resistance coefficient. For the flow in columnar dendritic structures, the second-order coefficient along with the permeability should be evaluated experimentally. For the flow in equiaxial dendritic structures(i.e., isotropic media), the inverse of permeability alone is sufficient to quantify the resistance offered by the solid.

A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows

Abstract: Some draining or coating fluid-flow problems, in which surface tension forces are important, can be described by third-order ordinary differential equations. Accurate computations are provided here...

Sand ripples under sea waves Part 1. Ripple formation

Abstract: In the present paper we formulate a predictive theory of the formation of sand ripples under sea waves. The theory is based on a linear stability analysis of a flat sandy bottom subject to a viscous oscillatory flow. The conditions for decay or amplification of a bottom perturbation are determined along with the wavelength of the most unstable component as a function of the Reynolds number of the flow and of the Froude and Reynolds numbers of the sediments. A comparison between theoretical findings and experimental data supports the validity of the present theory. An analytical solution for viscous oscillatory flow over a small-amplitude wavy bottom is determined for arbitrary values of the ratio r between the amplitude of fluid displacement and the wavelength of bottom waviness. Previous works by Lyne (1971) and Sleath (1976), who considered small or large values of r, are thus extended.

Framework for constructing clastic reservoir simulation models

Abstract: This paper surveys practical methods for reservoir modeling. To eliminate unnecessary jargon and to promote synergy, a simple classification system of sand-body architecture is proposed that helps relate geology to fluid flow. Guidelines are given for treating reservoir heterogeneities and upscaling properties to gridblock-scale averages.

Quantification of jet flow by momentum analysis. An in vitro color Doppler flow study.

Abstract: Previous investigations have shown that the size of a regurgitant jet as assessed by color Doppler flow mapping is independently affected by the flow rate and velocity (or driving pressure) of the jet. Fluid dynamics theory predicts that jet momentum (given by the orifice flow rate multiplied by velocity) should best predict the appearance of the jet in the receiving chamber and also that this momentum should remain constant throughout the jet. To test this hypothesis, we measured jet area versus driving pressure, flow rate, velocity, orifice area, and momentum and showed that momentum is the optimal jet parameter: jet area = 1.25 (momentum).28, r = 0.989, p less than 0.0001. However, the very curvilinear nature of this function indicated that chamber constraint strongly affected jet area, which limited the ability to predict jet momentum from observed jet area. To circumvent this limitation, we analyzed the velocities per se within the Doppler flow map. For jets formed by 1-81-mm Hg driving pressure through 0.005-0.5-cm2 orifices, the velocity distribution confirmed the fluid dynamic prediction: Gaussian (bell-shaped) profiles across the jet at each level with the centerline velocity decaying inversely with distance from the orifice. Furthermore, momentum was calculated directly from the flow maps, which was relatively constant within the jet and in good agreement with the known jet momentum at the orifice (r = 0.99). Finally, the measured momentum was divided by orifice velocity to yield an accurate estimate of the orifice flow rate (r = 0.99). Momentum was also divided by the square of velocity to yield effective orifice area (r = 0.84). We conclude that momentum is the single jet parameter that best predicts the color area displayed by Doppler flow mapping. Momentum can be measured directly from the velocities within the flow map, and when combined with orifice velocity, momentum provides an accurate estimate of flow rate and orifice area.

Analysis of conductive and convective heat transfer in a sedimentary basin, demonstrated for the Rheingraben

Abstract: SUMMARY The identification and quantification of conductive and convective components in the heat transfer of a sedimentary basin is demonstrated for the Rheingraben. Three different methods of varying complexity as well as three independent data sets are employed: (1) energy budget considerations based on hydraulically perturbed thermal data from shallow boreholes ( lo00 m), and (3) 2-D finite difference modelling of the fully coupled fluid flow and heat transport equations on a vertical cross-section of the entire Rheingraben. Energy budget considerations yield a conductive basal heat flow density of 84 + 40/-10 mW mP2, and in good agreement with this Peclet number analysis, gives median values in the range 90 f 35 mW m-’. In the first case, the basement is formed by low permeable, tertiary sediments at about 500 m depth, and in the second by the transition from the sedimentary graben fill to the crystalline basement at depths of between 2000 and 4000m. It is shown how results from numerical modelling support the flow field assumptions made by methods (1) and (2), as well as the value of 80 f 10 mW m-’ for average basal heat flow density entering the graben from below. Conversely, the Peclet number range Pe I 1.2 inferred from method (2) can be applied for a (at least partial) calibration of the fully coupled hydrothermal model calculatioris. This technique is suggested as a potentially interesting thermal method for constraining regional-scale permeability. An interpretation of heat transport is presented that satisfies the experimentally established patterns of both temperature and heat flow density in the Rheingraben. Moreover, it is demonstrated that the thermal anomalies along the western rim of the graben (such as Pechelbronn, France or Landau, Germany) can be convincingly explained by a basin-wide, deep rooted E-W groundwater circulation that locally enhances a background basal heat flow density of about 80 mW m-’ on average by 50 per cent and at individual sites by as much as 120 per cent.

On the large‐eddy simulation of transitional wall‐bounded flows

Abstract: The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.

Boundary condition for fluid flow: Curved or rough surfaces.

Abstract: The curvature of the boundary is shown to alter the fluid's slip length, which may even become negative as a result. Due to the mesoscopic curvature of surface roughness, the microscopically calculated and the macroscopically measured slip lengths can be quite different.

Permeabilities, fluid pressures, and flow rates in the Barbados Ridge Complex

Abstract: Recent measurements from Ocean Drilling Program leg 110 and Deep Sea Drilling Project leg 78a indicate that pore pressures near the toe of the Barbados accretionary prism may be close to lithostatic and that the decollement is a zone with relatively high rates of fluid flow and methane transport. We used a numerical model of fluid flow to estimate intrinsic permeabilities, pore pressures, and flow velocities that are consistent with these observations. Model results suggest that the permeability of the decollement may be 3–5 orders of magnitude greater than that of adjacent prism sediments. If permeabilities in the prism vary with depth in a manner similar to those in sedimentary basins, the average intrinsic permeability of the decollement, kd, must be about 10−14 m2. When kd is 10−13 m2, high pore pressures do not develop near the deformation front in the model. If kd is 10−15 m2, simulated pressures are unrealistically high in both the prism and underthrust sediments arcward of the deformation front. Water originating from compaction in the decollement and underthrust sediments flows laterally seaward, while water expelled from prism sediments flows upward to the ocean floor. However, flow velocities are small, and the net motion of pore water in prism and underthrust sediments is arcward relative to the deformation front because of tectonic transport. Pore water migrates seaward in spite of tectonic transport only in discrete zones with higher permeability, in this case the decollement.

Fuel cell fluid flow field plate

Abstract: Novel fluid flow field plates for use in a solid polymer electrolyte fuel cell include in a major surface thereof, multiple continuous open-faced fluid flow channels each of which traverses the central area of the plate surface in a serpentine manner. Each of the channels has a fluid inlet at one end and a fluid outlet at the other end which are directly connected to common fluid supply and exhaust openings, respectively, defined in the plate.

Rapid, stable fluid dynamics for computer graphics

Abstract: We present a new method for animating water based on a simple, rapid and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations. T...