Showing papers on "Fluid dynamics published in 1985"

Foundations of Radiation Hydrodynamics

Abstract: Exposes the great foundation-stones of research on radiating flows in astrophysics. Upon them are built the walls of methodology (some understandably incomplete). Concentration is on fundamentals but with only few applications. Coverage broadly involves non-radiating fluids, physics of radiation, radiation transport, and dynamics of radiating fluids, and finally the elements of sensor calculus as used in this volume. Contents, abridged: Microphysics of gases. Dynamics of ideal fluids. Relativistic fluid flow. Radiation and radiative transfer. Radiating flows. Glossary of physical symbols. Index.

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

A practical method for modeling fluid and heat flow in fractured porous media

Abstract: A Multiple Interacting Continua method (MINC) is presented which is applicable for numerical simulation of heat and multi-phase fluid flow in multidimensional, fractured porous media. This method is a generalization of the double-porosity concept. The partitioning of the flow domain into computational volume elements is based on the criterion of approximate thermodynamic equilibrium at all times within each element. The thermodynamic conditions in the rock matrix are assumed to be primarily controlled by the distance from the fractures, which leads to the use of nested grid blocks. The MINC concept is implemented through the Integral Finite Difference (IFD) method. No analytical approximations are made for the coupling between the fracture and matrix continua. Instead, the transient flow of fluid and heat between matrix and fractures is treated by a numerical method. The geometric parameters needed in a simulation are preprocessed from a specification of fracture spacings and apertures, and the geometry of the matrix blocks. The MINC method is verified by comparison with the analytical solution of Warren and Root. Illustrative applications are given for several geothermal reservoir engineering problems.

Open Channel Hydraulics

Abstract: Concepts of fluid flow energy principle the momentum principle development of uniform flow concepts computation of uniform flow theory and analysis of gradually and spatially varied flow design of channels flow measurement rapidly varied flow in nonprismatic channels turbulent diffusion and dispersion in steady open-channel flow turbulent, buoyant, surface jets and associated phenomena gradually varied, unsteady flow rapidly varied, unsteady flow hydraulic models.

A theoretical model for saltating grains in water

Abstract: The equations of motion for a sediment grain near a noncohesive bed and those for the local fluid flow are combined to produce a set of differential equations that can be solved numerically to describe the trajectory of a saltating grain as a function of time. The lift coefficient is set based on a reanalysis of data produced by Chepil, and the other parameters of the problem are set using standard fluid mechanical relationships; the initial velocity and position are specified with a separate model. The heights of the resulting trajectories are found to be significantly lower than available measurements would indicate; therefore two extensions of the model are examined: the effect that spin lift and form lift have on a series of trajectories, and the effect of partially elastic collisions between a moving grain and the bed over which it is traveling. A model that includes the second process is less complicated than one that includes the first, and it yields trajectories that agree very well with available experimental measurements when a rebound coefficient that varies around 0.5 and depends on the impact momentum is used. We conclude that the model provides a reasonable representation of saltation in water and that both fluid-solid and solid-solid interactions are required to reproduce the parameters of measured trajectories.

Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity

Abstract: An ultrasonic levitation device operable in both ordinary ground-based as well as in potential space-borne laboratories is described together with its various applications in the fields of fluid dynamics, material science, and light scattering. Some of the phenomena which can be studied by this instrument include surface waves on freely suspended liquids, the variations of the surface tension with temperature and contamination, the deep undercooling of materials with the temperature variations of their density and viscosity, and finally some of the optical diffraction properties of transparent substances.

A Model for Steady Fluid Flow in Random Three‐Dimensional Networks of Disc‐Shaped Fractures

Abstract: A model for steady fluid flow in three-dimensional, random networks of fractures has been developed. In this model the fractures are disc shaped discontinuities in an impermeable matrix. The fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture, radius orientation, and density. Thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature. After the boundary conditions and the desired fractures are specified, the intersections (nodes) between these discs (elements) are identified. Then steady flow through the network is calculated using a mixed analytical-numerical technique. In each fracture, analytic equations for flow into or out of each node as a function of the average head at each node are developed. The equations are based on image theory and the assumption that each node is a source (or sink) of uniform strength. A set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture. These equations are solved for the average head at each node, and flux between fractures can then be calculated by substituting the average head values back into the analytical equations. The model has been successfully checked against analytical results for several cases of two and three intersecting fractures. We plan to use these techniques to measure the permeability of fracture networks.

Fluid flow and weld penetration in stationary arc welds

Abstract: Weld pool fluid flow can affect the penetration of the resultant weld significantly. In this work, the computer simulation of weld pool fluid flow and its effect on weld penetration was carried out. Steady-state, 2-dimensional heat and fluid flow in stationary arc welds were computed, with three driving forces for fluid flow being considered: the buoyancy force, the electromagnetic force, and the surface tension gradient at the weld pool surface. The computer model developed agreed well with available analytical solutions and was consistent with weld convection phenomena experimentally observed by previous investigators and the authors. The relative importance of the influence of the three driving forces on fluid flow and weld penetration was evaluated, and the role of surface active agents was discussed. The effects of the thermal expansion coefficient of the liquid metal, the current density distribution in the workpiece, and the surface tension temperature coefficient of the liquid metal on weld pool fluid flow were demonstrated. Meanwhile, a new approach to free boundary problems involving simultaneous heat and fluid flow was developed, and the effort of computation was reduced significantly.

Hydrologic Mechanisms Governing Fluid Flow in a Partially Saturated, Fractured, Porous Medium

Abstract: In contrast to the saturated zone within which fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during the drainage process, and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force, in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix-fracture flow areas as functions of pressure. The effects of distortion of flow paths by the air pockets are taken into account by a phase-separation constriction factor in a generalized cubic law for fracture flow under a partially saturated condition. The reduction of matrix-fracture flow area is taken into account by summing the aperture distribution function to a saturation cutoff aperture, which is inversely proportional to the suction head. Drainage from a column of fractured tuff is simulated using available parameters for the densely welded tuff of the Topopah Spring Member at Yucca Mountain, southern Nevada. The column is bounded by discrete vertical fractures and dissected by horizontal fractures with the fracture spacings determined by the frequencies and orientations of fractured cores. The fraction of fracture surfaces with coatings is assumed to correspond to the fraction of in situ fracture contact area. The characteristic curves for the matrix are based on laboratory measurements of tuff samples. From the cases simulated for the fractured, porous columns with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi-steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into account.

The Formation of Freckles in Binary Alloys

Abstract: This paper presents a synopsis of some recent work, still in progress, aimed at elucidating a quantitative explanation of the processes by which flow chimneys form when certain types of alloys are directionally solidified. If (for example) light fluid is released at the liquid-solid "mushy" (dendrite) zone, and cooling is from below, then the intermediate fluid flow undergoes convection through the porous dendrite mass. This can lead to an "instability" of the form of the mushy zone, such that upwelling light fluid flows preferentially in channels within the dendrite mass. What we seek to develop here, is a mathematical basis by which this phenomenon may be properly understood. Accordingly, a mathematical model is developed, simplified, and partially analysed, and as a result we are able to make one specific prediction concerning a criterion for the onset of convection and freckling. This prediction is equivalent to the classical Rayleigh number condition for convective instability.

Transport of Immiscible Fluids Within and Below the Unsaturated Zone: A Numerical Model

Abstract: A numerical model is developed that describes the simultaneous flow of water and a second immiscible fluid under saturated and unsaturated conditions in porous media. The governing equations are a simplified subset of the three-phase flow equations commonly used in petroleum reservoir simulation. The simplification is analogous to that used to derive the Richard's equation for the flow of water in the unsaturated zone. The assumption that pressure gradients in the air phase are negligible leads to two partial differential equations. The proposed formulation is posed in terms of volumetric water saturation and fluid pressure in the immiscible fluid. The two-dimensional equations for flow in a vertical plane are approximated by finite differences. The fully implicit equations are solved by a direct matrix technique and Newton-Raphson iteration on nonlinear terms. The resulting numerical model is potentially applicable to many problems associated with immiscible contaminants in groundwater. Unfortunately, data such as relative permeabilities and capillary pressures for the types of fluids and porous materials present in hazardous waste sites are not readily available. As this type of data becomes available and field investigation techniques improve, applications of this type of model will become more practical. Examples are used to demonstrate themore » potential application of the model and sensitivity of results to fluid properties.« less

Determining modes and fractal dimension of turbulent flows

Abstract: Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier–Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier–Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated.

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.

Hyperbolicity and change of type in the flow of viscoelastic fluids

Abstract: The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.

Power steering system

Abstract: A power steering system which includes an engine-driven pump, a fluid motor for supplementing manual steering torque, a fluid control valve for distributing fluid to the fluid motor, and a reaction device for applying hydraulic reaction or feeling to a steering wheel. A first flow control valve is utilized to deliver first fluid flow to a fluid control valve from the pump and to lead excess flow to a bypass passage. A second flow control valve is connected between the bypass passage and the reaction device to deliver second fluid flow to the reaction device and to lead excess flow to a reservoir. A magnetic pressure control valve is connected to the reaction device to control fluid pressure applied thereto in accordance with a predetermined vehicle operating condition, such as vehicle speed.

Effect of Capillary Number and Its Constituents on Two-Phase Relative Permeability Curves

Abstract: One primary goal of any enhanced recovery project is to maximize the ability of the fluids to flow through a porous medium (i.e., the reservoir). This paper discusses the effect of capillary number, a dimensionless group describing the ratio of viscous to capillary forces, on twophase (oil-water) relative permeability curves. Specifically, a series of steady-state relative permeability measurements were carried out to determine whether the capillary number causes changes in the two-phase permeabilities or whether one of its constituents, such as flow velocity, fluid viscosity, or interfacial tension (IFT), is the controlling variable.

Fluid Mechanics and Transfer Processes

Abstract: This textbook deals with the fundamental principles of fluid dynamics, heat and mass transfer. The basic equations governing the convective transfer by fluid motion of matter, energy and momentum, and the transfer of the same properties by diffusion of molecular motion, are presented at the outset. These concepts are then applied systematically to the study of fluid dynamics in an engineering context and to the parallel investigation of heat and mass transfer processes. The influence of viscosity and the dominant role of turbulence in fluid motion are emphasised. Individual chapters are concerned with the important subjects of boundary layers, flow in pipes and ducts, gas dynamics, and flow in turbo-machinery and of a liquid with a free surface. Later chapters cover some of the special types of flow and transfer process encountered in chemical engineering applications, including two-phase flow, condensation, evaporation, flow in packed beds and fluidized solids.

Fluid flow sensing apparatus for in vivo and industrial applications employing novel differential optical fiber pressure sensors

Abstract: An optical fiber fluid flow device is provided for in vivo determination of blood flow in arteries. The device includes a fiber optical fluid pressure measuring device having at least first and second optical fiber sensors which optical fiber sensors are positioned in the blood passage and in a restricted flow area in the blood passage and the two fiber optical pressure fluid sensors are connected to an interferometer associated with an opto-electronic demodulator which has an output signal representing the differential pressure between the two sensed area. The device also has utility in industrial applications.

Vlsi chemical reactor

Abstract: A VLSI chemical reactor includes a fluid flow guide (12) spaced fror- the corresponding substrate (14) in the form of a wafer for significantly reducing contamination in the processing of semiconductor wafers. Processing chemicals are introduced in a continuous process through a central tube and through the fluid flow guide (12) which is substantially planar and which is parallel to the surface (32) of the wafer. A predetermined gap (30) is maintained between the guide (12) and the wafer (14) such that fluid is maintained in the gap (30) at all times critical in the processing of the wafer. In one embodiment, the guide (12) is optically transparent at predetermined portions (110) to permit monitoring of the chemical reaction taking place on the surface (32) of the wafer (14) to permit control of fluid flow to the wafer. Because of the uniform gap (30),the fluid guide (12) insures a constant thickness and composition of the optical path, and thus more accurate measurements. All drying steps are done directly and include the steps of replacing the working fluid with an inert gas and increasing the speed of rotation of either the wafer (14) or the guide (12) to remove any liquid or particulate matter by centrifugal force. Bubble reduction and fluid mixing apparatus, including different fluid guide configurations, gas relief orifices and offset rotational axes, are also described. Moreover, in one embodiment orthogonal and orbital vibrating arrangements are used in lieu of rotating motion.

Pore-fluid pressures and frictional heating on a fault surface

Abstract: This study considers the effects of heat transfer and fluid flow on the thernal, hydrologic, and mechanical response of a fault surface during seismic failure. Numerical modeling techniques are used to account for the coupling of the thermal, fluid-pressure, and stress fields. Results indicate that during an earthquake the failure surface is heated to a tempeature required for the thermal expansion of pore fluids to balance the rate of fluid loss due to flow and the fluid-volume changes due to pore dilatation. Once this condition is established, the pore fluids pressurize and the shear strength decreases rapidly to a value sufficient to maintain the thermal pressurization of pore fluids at near-lithostatic values. If the initial fluid pressure is hydrostatic, the final temperature attained on the failure surface will increase with depth, because a greater pressure increase can occur before a near-lithostatic pressure is reached. The rate at which thermal pressurization proceeds depends primarily on the hydraulic characteristics of the surrounding porous medium, the coefficient of friction on the fault surface, and the slip velocity. If either the permeability exceeds 10−15 m2 or the porous medium compressibility exceeds 10−8 Pa−1, then frictional melting may occur on the fault surface before thermal pressurization becomes significant. If the coefficient of friction is less than 10−1 and if the slip velocity is less than 10−2 msec−1, then it is doubtful that either thermal pressurization or frictional melting on the fault surface could cause a reduction in the dynamic shear strength of a fault during an earthquake event.

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

Isotropic homogeneous universe with viscous fluid

Abstract: Exact solutions are obtained for the isotropic homogeneous cosmological model with viscous fluid. The fluid has only bulk viscosity and the viscosity coefficient is taken to be a power function of the mass density. The equation of state assumed obeys a linear relation between mass density and pressure. The models satisfying Hawking’s energy conditions are discussed. Murphy’s model is only a special case of this general set of solutions and it is shown that Murphy’s conclusion that the introduciton of bulk viscosity can avoid the occurrence of space‐time singularity at finite past is not, in general, valid.

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.

Type curves for finite radial and linear gas-flow systems: constant-terminal-pressure case

Abstract: This paper presents gas production rate results in type curve form for finite radial and linear flow systems produced at a constant terminal (bottomhole) pressure. These results can be utilized in the analysis of actual gas and oil rate-time data to estimate reservoir size and make some inference about reservoir shape. The type curves are based upon dimensionless variables that are a generalized form of those presented previously. In addition, a previously presented drawdown parameter is used. Example applications are given which demonstrate the applicability of the type curves to a variety of reservoir configurations. The Appendix contains derivations of the dimensionless variables and the drawdown parameter.